10-K

UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 10-K

☒	ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934
	OR
☐	TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934

For the Fiscal Year Ended December 31, 2022 Commission File No. 001-16209

ARCH CAPITAL GROUP LTD.

(Exact name of registrant as specified in its charter)

Bermuda	98-0374481
(State or other jurisdiction of incorporation or organization)	(I.R.S. Employer Identification No.)

Waterloo House, Ground Floor
100 Pitts Bay Road,	Pembroke	HM 08,	Bermuda	(441)	278-9250
(Address of principal executive offices)				(Registrant’s telephone number, including area code)

Securities registered pursuant to Section 12(b) of the Exchange Act:

Title of each class	Trading Symbol (s)	Name of each exchange on which registered
Common Shares, $0.0011 par value per share	ACGL	NASDAQ	Stock Market
Depositary shares, each representing a 1/1,000th interest in a 5.45% Series F preferred share	ACGLO	NASDAQ	Stock Market
Depositary shares, each representing a 1/1,000th interest in a 4.55% Series G preferred share	ACGLN	NASDAQ	Stock Market

Securities registered pursuant to Section 12(g) of the Exchange Act: None

Indicate by check mark if the registrant is a well-known seasoned issuer, as defined in Rule 405 of the Securities Act. Yes ☑ No ☐

Indicate by check mark if the registrant is not required to file reports pursuant to Section 13 or Section 15(d) of the Exchange Act.

Yes ☐     No ☑

Indicate by check mark whether the registrant (1) has filed all reports required to be filed by Section 13 or 15(d) of the Exchange Act during the preceding 12 months (or for such shorter period that the registrant was required to file such reports), and (2) has been subject to such filing requirements for the past 90 days. Yes ☑ No ☐

Indicate by check mark whether the registrant has submitted electronically every Interactive Data File required to be submitted pursuant to Rule 405 of Regulation S-T (§232.405 of this chapter) during the preceding 12 months (or for such shorter period that the registrant was required to submit such files). Yes ☑    No ☐

Indicate by check mark whether the registrant is a large accelerated filer, an accelerated filer, a non-accelerated filer, a smaller reporting company, or an emerging growth company. See the definitions of “large accelerated filer,” “accelerated filer,” “smaller reporting company,” and “emerging growth company” in Rule 12b-2 of the Exchange Act.

Large accelerated Filer ☑ Accelerated Filer ☐ Non-accelerated Filer ☐ Smaller reporting company ☐ Emerging Growth Company ☐

If an emerging growth company, indicate by check mark if the Registrant has elected not to use the extended transition period for complying with any new or revised financial accounting standards provided pursuant to Section 13(a) of the Exchange Act. ☐

Indicate by check mark whether the registrant has filed a report on and attestation to its management's assessment of the effectiveness

of its internal control over financial reporting under Section 404(b) of the Sarbanes-Oxley Act (15 U.S.C. 7262(b)) by the registered

public accounting firm that prepared or issued its audit report. ☑

Indicate by check mark whether the registrant is a shell company (as defined in Rule 12b-2 of the Exchange Act). Yes ☐  No ☑

The aggregate market value of the voting and non-voting common equity held by non-affiliates, computed by reference to the closing price as reported by the NASDAQ Stock Market as of the last business day of the Registrant’s most recently completed second fiscal quarter, was approximately $16.3 billion.

As of February 17, 2023, there were 371,196,508 of the registrant’s common shares outstanding.

DOCUMENTS INCORPORATED BY REFERENCE

Portions of Part III and Part IV incorporate by reference our definitive proxy statement for the 2023 annual meeting of shareholders to be filed with the Securities and Exchange Commission pursuant to Regulation 14A within 120 days after December 31, 2022.

ARCH CAPITAL GROUP LTD.
TABLE OF CONTENTS
Item		Page
PART I
ITEM 1.	BUSINESS	3
ITEM 1A.	RISK FACTORS	37
ITEM 1B.	UNRESOLVED STAFF COMMENTS	58
ITEM 2.	PROPERTIES	58
ITEM 3.	LEGAL PROCEEDINGS	58
ITEM 4.	MINE SAFETY DISCLOSURES	58
PART II
ITEM 5.	MARKET FOR REGISTRANT'S COMMON EQUITY, RELATED STOCKHOLDER MATTERS AND ISSUER PURCHASES OF EQUITY SECURITIES	59
ITEM 6.	[RESERVED]	60
ITEM 7.	MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS OF OPERATIONS	61
ITEM 7A.	QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK	93
ITEM 8.	FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA	94
ITEM 9.	CHANGES IN AND DISAGREEMENTS WITH ACCOUNTANTS ON ACCOUNTING AND FINANCIAL DISCLOSURE	169
ITEM 9A.	CONTROLS AND PROCEDURES	169
ITEM 9B.	OTHER INFORMATION	170
ITEM 9C.	DISCLOSURE REGARDING FOREIGN JURISDICTIONS THAT PREVENT INSPECTIONS	170
PART III
ITEM 10.	DIRECTORS, EXECUTIVE OFFICERS AND CORPORATE GOVERNANCE	170
ITEM 11.	EXECUTIVE COMPENSATION	170
ITEM 12.	SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND MANAGEMENT AND RELATED STOCKHOLDER MATTERS	171
ITEM 13.	CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS, AND DIRECTOR INDEPENDENCE	171
ITEM 14.	PRINCIPAL ACCOUNTANT FEES AND SERVICES	171
PART IV
ITEM 15.	EXHIBITS AND FINANCIAL STATEMENT SCHEDULES	172
ITEM 16.	FORM 10-K SUMMARY	183

Cautionary Note Regarding Forward-Looking Statements 

The Private Securities Litigation Reform Act of 1995 (“PSLRA”) provides a “safe harbor” for forward-looking statements. This report or any other written or oral statements made by or on behalf of us may include forward-looking statements, which reflect our current views with respect to future events and financial performance. All statements other than statements of historical fact included in or incorporated by reference in this report are forward-looking statements. Forward-looking statements, for purposes of the PSLRA or otherwise, can generally be identified by the use of forward-looking terminology such as “may,” “will,” “expect,” “intend,” “estimate,” “anticipate,” “believe” or “continue” and similar statements of a future or forward-looking nature or their negative or variations or similar terminology.

Forward-looking statements involve our current assessment of risks and uncertainties. Actual events and results may differ materially from those expressed or implied in these statements. Important factors that could cause actual events or results to differ materially from those indicated in such statements are discussed below and elsewhere in this report and in our periodic reports filed with the Securities and Exchange Commission (“SEC”), and include:

•our ability to successfully implement our business strategy during “soft” as well as “hard” markets;

•acceptance of our business strategy, security and financial condition by rating agencies and regulators, as well as by brokers and our insureds and reinsureds;

•our ability to consummate acquisitions and integrate the business we have acquired or may acquire into our existing operations;

•our ability to maintain or improve our ratings, which may be affected by our ability to raise additional equity or debt financings, by ratings agencies’ existing or new policies and practices, as well as other factors described herein;

•general economic and market conditions (including inflation, interest rates, unemployment, housing prices, foreign currency exchange rates, prevailing credit terms and the depth and duration of a recession, including those resulting from COVID-19) and conditions specific to the reinsurance and insurance markets in which we operate;

•competition, including increased competition, on the basis of pricing, capacity (including alternative sources of capital), coverage terms, or other factors;

•developments in the world’s financial and capital markets and our access to such markets;

•our ability to successfully enhance, integrate and maintain operating procedures (including information technology) to effectively support our current and new business;

•the loss and addition of key personnel;

•material differences between actual and expected assessments for guaranty funds and mandatory pooling arrangements;

•accuracy of those estimates and judgments utilized in the preparation of our financial statements, including those related to revenue recognition, insurance and other reserves, reinsurance recoverables, investment valuations, intangible assets, bad debts, income taxes, contingencies and litigation, and any determination to use the deposit method of accounting;

•greater than expected loss ratios on business written by us and adverse development on claim and/or claim expense liabilities related to business written by our insurance and reinsurance subsidiaries;

•the adequacy of the Company’s loss reserves;

•severity and/or frequency of losses;

•greater frequency or severity of unpredictable natural and man-made catastrophic events;

•claims for natural or man-made catastrophic events or severe economic events in our insurance, reinsurance and mortgage businesses could cause large losses and substantial volatility in our results of operations;

•the effect of climate change on our business;

•the effect of contagious diseases (including COVID-19) on our business;

•acts of terrorism, political unrest and other hostilities or other unforecasted and unpredictable events;

•availability to us of reinsurance to manage our gross and net exposures and the cost of such reinsurance;

ARCH CAPITAL 1 2022 FORM 10-K

•the failure of reinsurers, managing general agents, third party administrators or others to meet their obligations to us;

•the timing of loss payments being faster or the receipt of reinsurance recoverables being slower than anticipated by us;

•our investment performance, including legislative or regulatory developments that may adversely affect the fair value of our investments;

•changes in general economic conditions, including sovereign debt concerns or downgrades of U.S. securities by credit rating agencies, which could affect our business, financial condition and results of operations;

•the volatility of our shareholders’ equity from foreign currency fluctuations, which could increase due to us not matching portions of our projected liabilities in foreign currencies with investments in the same currencies;

•changes in accounting principles or policies or in our application of such accounting principles or policies;

•changes in the political environment of certain countries in which we operate or underwrite business;

•a disruption caused by cyber attacks or other technology breaches or failures on us or our business partners and service providers, which could negatively impact our business and/or expose us to litigation;

•statutory or regulatory developments, including as to tax matters and insurance and other regulatory matters such as the adoption of proposed legislation that would affect Bermuda-headquartered companies and/or Bermuda-based insurers or reinsurers and/or changes in regulations or tax laws applicable to us, our subsidiaries, brokers or customers, including the possible implementation of the Organization for Economic Cooperation and Development (“OECD”) Pillar I and Pillar II initiatives; and

•the other matters set forth under Item 1A “Risk Factors,” Item 7 “Management’s Discussion and Analysis of Financial Condition and Results of Operations” and other sections of this Annual Report on Form 10-K, as well as the other factors set forth in Arch Capital Group Ltd.’s other documents on file with the SEC, and management’s response to any of the aforementioned factors.

All subsequent written and oral forward-looking statements attributable to us or persons acting on our behalf are expressly qualified in their entirety by these cautionary statements. The foregoing review of important factors should not be construed as exhaustive and should be read in conjunction with other cautionary statements that are included herein or elsewhere. We undertake no obligation to publicly update or revise any forward-looking statement, whether as a result of new information, future events or otherwise.

ARCH CAPITAL 2 2022 FORM 10-K

PART I

ITEM 1. BUSINESS

As used in this report, references to “we,” “us,” “our,” “Arch” or the “Company” refer to the consolidated operations of Arch Capital Group Ltd. (“Arch Capital”) and its subsidiaries. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted. We refer you to Item 1A “Risk Factors” for a discussion of risk factors relating to our business.

OUR COMPANY

General

Arch Capital is a publicly listed Bermuda exempted company with approximately $15.6 billion in capital at December 31, 2022 and is part of the S&P 500 index. Arch provides insurance, reinsurance and mortgage insurance on a worldwide basis through its wholly owned subsidiaries. While we are positioned to provide a full range of property, casualty and mortgage insurance and reinsurance lines, we focus on writing specialty lines of insurance and reinsurance. For 2022, we wrote $11.1 billion of net premiums and reported net income available to Arch common shareholders of $1.4 billion. Book value per share was $32.62 at December 31, 2022, compared to $33.56 per share at December 31, 2021.

Arch Capital’s registered office is located at Clarendon House, 2 Church Street, Hamilton HM 11, Bermuda (telephone number: (441) 295-1422), and its principal executive offices are located at Waterloo House, Ground Floor, 100 Pitts Bay Road, Pembroke HM 08, Bermuda (telephone number: (441) 278-9250). Arch Capital makes available free of charge through its website, located at www.archgroup.com, its annual reports on Form 10-K, quarterly reports on Form 10-Q, current reports on Form 8-K, and all amendments to those reports as soon as reasonably practicable after such material is electronically filed with, or furnished to, the U.S. Securities and Exchange Commission (“SEC”). The SEC maintains an Internet site that contains reports, proxy and information statements, and other information regarding issuers that file electronically with the SEC (such as Arch Capital) and the address of that site is www.sec.gov.

Our History

Arch Capital was formed in September 2000 and became the sole shareholder of Arch Capital Group (U.S.) Inc. (“Arch-U.S.”) pursuant to an internal reorganization transaction completed in November 2000. In October 2001, Arch Capital launched an underwriting initiative to meet current and future demand in the global insurance and reinsurance markets that included the recruitment of new management teams and an equity capital infusion of $763.2 million, which created a strong capital base that was unencumbered by significant pre-2002 risks. Since then, we have attracted a proven management team with extensive industry experience and continued to build our global underwriting platform for our insurance, reinsurance and mortgage insurance businesses.

Our insurance underwriting platform initially consisted of our Bermuda and U.S. operations, followed by the establishment of our United Kingdom-based carrier, Arch Insurance (U.K.) Limited (“Arch Insurance (U.K.)”) in 2004 and Canadian operations in 2005. In 2009, we established a managing agency and syndicate at Lloyd’s of London (“Lloyd’s”) and significantly expanded our U.K. presence in 2019 through the acquisition of Barbican Group Holdings Limited (“Barbican Holdings”) and its subsidiaries (collectively, “Barbican”). Our U.S. platform grew with the 2018 acquisition of McNeil & Company, Inc. (“McNeil”), a U.S. nationwide leader in specialized risk management and program administration. See “Operations—Insurance Operations” for further details on our insurance operations.

Our reinsurance underwriting platform initially consisted of Arch Reinsurance Ltd. in Bermuda (“Arch Re Bermuda”) and Arch Reinsurance Company (“Arch Re U.S.”), our U.S.-licensed reinsurer. Our reinsurance operations in Europe began in 2006 in Zurich, Switzerland and with the formation of a Danish underwriting agency in 2007. In addition to the U.S. reinsurance treaty activities of Arch Re U.S., we launched our property facultative reinsurance underwriting operations in 2007, which underwrite in the U.S., Canada and Europe. In 2008, we formed Arch Reinsurance Europe Designated Activity Company (“Arch Re Europe”), our Ireland-based reinsurance company headquartered in Ireland with offices in Switzerland and the U.K. The acquisition of Barbican in 2019 also contributed to our reinsurance operations. In 2021, Arch Re Bermuda completed the acquisition of Somerset Bridge Group Limited, Southern Rock Holdings Limited and affiliates (“Somerset Group”). The acquisition included Somerset’s motor insurance managing general agent, distribution capabilities through

ARCH CAPITAL 3 2022 FORM 10-K

direct and aggregator channels, affiliated insurer and fully integrated claims operation. See “Operations—Reinsurance Operations” for further details on our reinsurance operations.

Our mortgage operations include U.S. and international mortgage insurance and reinsurance operations, as well as participation in government sponsored enterprise (“GSE”) credit risk-sharing transactions. The U.S. mortgage platform was established in 2014 and expanded greatly in 2016 through the acquisition of United Guaranty Corporation (“UGC”). Our U.S. primary mortgage operations provide mortgage insurance products and services to the U.S. market. These operations include providers which are also approved as eligible mortgage insurers by Federal National Mortgage Association (“Fannie Mae”) and Federal Home Loan Mortgage Corporation (“Freddie Mac”), each a GSE. The mortgage operations also include participation in GSE credit risk-sharing transactions and direct mortgage insurance to U.S. mortgage lenders with respect to mortgages that lenders intend to retain in portfolio or include in non-agency securitizations along with mortgage insurance and reinsurance on a global basis. Our European business is written through our Ireland-based carrier, Arch Insurance (EU) Designated Activity Company (“Arch Insurance (EU)”), which was authorized in 2011 to provide mortgage insurance products and services to the European and U.K. markets. In 2019, Arch LMI Pty Ltd. (“Arch LMI”) was authorized by the Australian Prudential Regulation Authority (“APRA”) to write lenders’ mortgage insurance on a direct basis in Australia. We expanded our presence in Australia in August 2021 by acquiring Westpac Lenders Mortgage Insurance Limited, another APRA approved writer of lenders’ mortgage insurance, which has since been renamed Arch Lenders Mortgage Indemnity Ltd. (“Arch Indemnity”). In December 2022, we converted Arch LMI into a services company for our Australian LMI operations and the company relinquished its APRA authorization. See “Operations—Mortgage Operations” for further details on our mortgage operations.

It is our belief that our underwriting platform, our experienced management team and our strong capital base have enabled us to establish a strong presence in the markets in which we participate.

In 2014, we acquired approximately 11% of Somers Holdings Ltd. (formerly Watford Holdings Ltd.). Somers Holdings Ltd. is the parent of Somers Re Ltd. (formerly Watford Re Ltd.), a multi-line Bermuda reinsurance company (together with Somers Holdings Ltd., “Somers”). In the 2020 fourth quarter, Arch Capital, Somers, and Greysbridge Ltd., a wholly-owned subsidiary of Arch Capital, entered into an Agreement and Plan of Merger (as amended, the “Merger Agreement”). Arch Capital assigned its rights under the Merger Agreement to Greysbridge Holdings Ltd. (“Greysbridge”). The merger and the related Greysbridge

equity financing closed on July 1, 2021. Somers is wholly owned by Greysbridge, and Greysbridge is owned 40% by Arch, 30% by certain funds managed by Kelso & Company (“Kelso”) and 30% by certain funds managed by Warburg Pincus LLC (“Warburg”). In 2017, we acquired approximately 25% of Premia Holdings Ltd. Premia Holdings Ltd. is the parent of Premia Reinsurance Ltd., a multi-line Bermuda reinsurance company (together with Premia Holdings Ltd., “Premia”). In 2021, the Company completed the share purchase agreement with Natixis, a French financial services firm, to purchase 29.5% of the common equity of Coface SA (“Coface”), a France-based leader in the global trade credit insurance market. See “Operations—Other Operations” for further details on Somers, Premia and Coface.

The Board of Directors of Arch Capital (the “Board”) has authorized the investment in Arch Capital’s common shares through a share repurchase program. Repurchases under the share repurchase program may be effected from time to time in open market or privately negotiated transactions through December 31, 2024. Since the inception of the share repurchase program in February 2007 through December 31, 2022, Arch Capital has repurchased 433.6 million common shares for an aggregate purchase price of $5.9 billion. At December 31, 2022, the total remaining authorization under the share repurchase program was $1.0 billion. The timing and amount of the repurchase transactions under this program will depend on a variety of factors, including results of operations, market conditions and the development of the economy, as well as other factors. We will consider share repurchases on an opportunistic basis. During the 2022 fiscal year, we repurchased 12,891,405 shares for an aggregate amount of $585.8 million under our share repurchase program.

OPERATIONS

We classify our businesses into three underwriting segments– insurance, reinsurance and mortgage and two operating segments– corporate and ‘other.’ For an analysis of our underwriting results by segment, see note 4, “Segment Information,” to our consolidated financial statements in Item 8 and “Management’s Discussion and Analysis of Financial Condition and Results of Operations—Results of Operations.”

COVID-19 Pandemic

The global pandemic resulting from the coronavirus (including variants of the coronavirus “COVID-19”) disrupted the global economy, causing a significant slowdown in economic activity around the world. Businesses around the world, including ours, were impacted by the restrictions on travel, some business activities and non-essential services and the severe curtailment of normal

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activities. During 2022, the restrictions relating to the pandemic were largely lifted in the regions where we do business, shifting us to an endemic stage in 2023. Our employees and businesses have adapted to the changing needs of our clients, customers and business partners with our 5,800 employees returning to the office under a hybrid work model.

Insurance Operations

Our insurance operations are conducted in Bermuda, the United States, the United Kingdom, Europe, Canada, and Australia. Our insurance operations in Bermuda are conducted through Arch Insurance (Bermuda), a division of Arch Re Bermuda, and Alternative Re Limited.

In the U.S., our insurance group’s principal insurance subsidiaries are Arch Insurance Company (“Arch Insurance”), Arch Specialty Insurance Company (“Arch Specialty”), Arch Indemnity Insurance Company (“Arch Indemnity Insurance”) and Arch Property Casualty Insurance Company (“Arch P&C”). Arch Insurance is an admitted insurer in 50 states, the District of Columbia, Puerto Rico, the U.S. Virgin Islands and Guam. Arch Specialty is an approved excess and surplus lines insurer in 50 states, the District of Columbia, Puerto Rico and the U.S. Virgin Islands and an authorized insurer in one state. Arch Indemnity Insurance is an admitted insurer in 50 states and the District of Columbia. Arch P&C, which is not currently writing business, is an admitted insurer in 40 states and the District of Columbia and is filing applications for admission in all remaining states where it is not yet admitted. Our insurance group also operates McNeil, a specialized risk manager and a program administrator based in Cortland, New York. The headquarters for our insurance group’s U.S. support operations (excluding underwriting units) are in Jersey City, New Jersey. The insurance group has offices throughout the U.S., including five regional offices located in Alpharetta, Georgia, Chicago, Illinois, New York, New York, San Francisco, California, Dallas, Texas and additional branch offices.

Our insurance operations in Canada are conducted through Arch Insurance Canada Ltd. (“Arch Insurance Canada”), a Canada domestic company which is authorized in all Canadian provinces and territories. Arch Insurance Canada is headquartered in Toronto, Ontario.

In 2019, Arch Insurance (EU), based in Dublin, Ireland, received authorization from the Central Bank of Ireland (“CBI”) to expand its authorized classes of business as part of our plan to address the U.K.’s departure from the European Union (“Brexit”). At the end of 2020, Arch Insurance (U.K.) received court approval in the U.K. to transfer its legacy book of business written in the European Economic Area (“EEA”) to Arch Insurance (EU) under Part VII of the U.K. Financial Services and Markets Act 2000. As

of January 2020, all of the insurance business in the European Union (“EU”) previously written by Arch Insurance (U.K.) is now written through Arch Insurance (EU). Arch Insurance (EU) has branches in Italy and the U.K.

We conduct insurance operations on several platforms in the U.K., including Arch Insurance (U.K.) and our Lloyd’s syndicates: Arch Syndicate 2012 (“Arch Syndicate 2012”) and Arch Syndicate 1955 (“Arch Syndicate 1955” and, together with Arch Syndicate 2012, our “Lloyd’s Syndicates”). Arch Managing Agency Limited (“AMAL”) is the managing agent of our Lloyd’s Syndicates. These operations provide us access to Lloyd’s extensive distribution network and worldwide licenses. AMAL also acts as managing agent for third party members of Arch Syndicate 1955. Arch Underwriting at Lloyd’s (Australia) Pty Ltd, based in Sydney, Australia, is a Lloyd’s services company which underwrites exclusively for our Lloyd’s Syndicates. As part of the Barbican acquisition, we also acquired Castel Underwriting Agencies Limited (“Castel”) in the U.K. and Castel Underwriting Europe BV in the Netherlands, giving us additional underwriting intermediary capabilities for our underwriting platforms. Collectively, the U.K. insurance operations are referred to as “Arch U.K.” Arch U.K. conducts its operations from London and other locations in the U.K.

Strategy. Our insurance group’s strategy is to operate in lines of business in which underwriting expertise can make a meaningful difference in operating results. The insurance group focuses on talent-intensive rather than labor-intensive business and seeks to operate profitably (on both a gross and net basis) across all of its product lines. To achieve these objectives, our insurance group’s operating principles are to:

•Capitalize on profitable underwriting opportunities. Our insurance group believes that its experienced management and underwriting teams are positioned to locate and identify business with attractive risk/reward characteristics. As profitable underwriting opportunities are identified, our insurance group will continue to grow its product portfolio in order to take advantage of market trends. This includes adding underwriting and other professionals with specific expertise in specialty lines of insurance.

•    Centralize responsibility for underwriting. Our insurance group consists of a range of product lines. The underwriting executive in charge of each product line oversees all aspects of the underwriting product development process within such product line. Our insurance group believes that centralizing the control of such product line with the respective underwriting executive allows for close management of underwriting and creates clear accountability for results. Our U.S. insurance group has five regional offices, and the

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executive in charge of each region is primarily responsible for all aspects of the marketing and distribution of our insurance group’s products, including the management of broker and other producer relationships in such executive’s respective region. In our non-U.S. offices, a similar philosophy is observed, with responsibility for the management of each product line residing with the senior underwriting executive in charge of such product line.

•    Maintain a disciplined underwriting philosophy. Our insurance group’s underwriting philosophy is to generate an underwriting profit through prudent risk selection and proper pricing. Our insurance group believes that the key to this approach is adherence to uniform underwriting standards across all types of business. Our insurance group’s senior management closely monitors the underwriting process.

•    Focus on providing superior claims management. Our insurance group believes that claims handling is an integral component of credibility in the market for insurance products. We believe our ability to handle claims expeditiously and satisfactorily is a key to our success. Our insurance group employs experienced claims professionals and also utilizes experienced external claims managers (third party administrators) where appropriate.

•    Promote and utilize an efficient distribution system. Our insurance group believes that promoting and utilizing a multi-channel distribution system provides efficient access to its broad customer base. We work with select international, national and regional retail and wholesale brokers and leading managing general agencies and program administrators, including McNeil, to distribute our insurance products. The Arch U.K. Regional Division has a retail distribution network in the U.K.

•Grow strategic partnerships in stable and niche areas. Our insurance group aims to build more integrated long-term alignment with strategic partners offering superior access to niche opportunities, quality scalable businesses, or lines with reliable defensive qualities.

Our insurance group writes business in the U.S. on both a U.S. admitted and U.S. non-admitted basis. Our insurance group focuses on various specialty lines, as described in note 4, “Segment Information,” to our consolidated financial statements in Item 8.

Underwriting Philosophy. Our insurance group’s underwriting philosophy is to generate an underwriting profit (on both a gross and net basis) through prudent risk selection and proper pricing across all types of business. One key to this philosophy is the adherence to uniform underwriting

standards across each product line that focuses on the following:

•    risk selection;

•    desired attachment point;

•    limits and retention management;

•    due diligence, including financial condition, claims history, management, and product, class and territorial exposure;

•    underwriting authority and appropriate approvals; and

•    collaborative decision making.

Marketing. Our insurance group’s products are marketed principally through a group of licensed independent retail and wholesale brokers. Clients (insureds) are referred to our insurance group through a large number of international, national and regional brokers and captive managers who receive from the insured or insurer a set fee or brokerage commission usually equal to a percentage of gross premiums. Our insurance group may enter into contingent commission arrangements with some brokers that provided for the payment of additional commissions based on volume or profitability of business. Currently, some of our contracts with brokers provide for additional commissions based on volume. It is the practice for the brokers and producers to make the client aware of any contingent commissions arrangements that may be in place with us. We have also entered into service agreements with select international brokers that provide access to their proprietary industry analytics. In general, our insurance group has no implied or explicit commitments to accept business from any particular broker and neither brokers nor any other third parties have the authority to bind our insurance group, except in the case where underwriting authority may be delegated contractually to select program administrators. Such administrators are subject to a financial and operational due diligence review prior to any such delegation of authority and ongoing reviews and audits are carried out as deemed necessary by our insurance group to assure the continuing integrity of underwriting and related business operations. See “Risk Factors—Risks Relating to Our Industry, Business and Operations—We could be materially adversely affected to the extent that important third parties with whom we do business do not adequately or appropriately manage their risks, commit fraud or otherwise breach obligations owed to us.” For information on major brokers, see note 18, “Commitments and Contingencies—Concentrations of Credit Risk,” to our consolidated financial statements in Item 8.

Risk Management and Reinsurance. In the normal course of business, our insurance group may cede a portion of its premium on a quota share or excess of loss basis through treaty or facultative reinsurance agreements. Reinsurance arrangements do not relieve our insurance group from its

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primary obligations to insureds. Reinsurance recoverables are recorded as assets, predicated on the reinsurers’ ability to meet their obligations under the reinsurance agreements. If the reinsurers are unable to satisfy their obligations under the agreements, our insurance subsidiaries would be liable for such defaulted amounts. Our principal insurance subsidiaries, with oversight by a group-wide reinsurance steering committee (“RSC”), are selective with regard to reinsurers, seeking to place reinsurance with only those reinsurers which meet and maintain specific standards of established criteria for financial strength. The RSC evaluates the financial viability of its reinsurers through financial analysis, research and review of rating agencies’ reports and also monitors reinsurance recoverables and collateral with unauthorized reinsurers. The financial analysis includes ongoing qualitative and quantitative assessments of reinsurers, including a review of the financial stability, appropriate licensing, reputation, claims paying ability and underwriting philosophy of each reinsurer. See note 8, “Reinsurance,” to our consolidated financial statements in Item 8.

For catastrophe-exposed insurance business, our insurance group seeks to limit the amount of exposure to catastrophic losses it assumes through a combination of managing aggregate limits, underwriting guidelines and reinsurance. For a discussion of our risk management policies, see “Management’s Discussion and Analysis of Financial Condition and Results of Operations—Summary of Critical Accounting Estimates—Ceded Reinsurance” and “Risk Factors—Risks Relating to Our Industry, Business and Operations—The failure of any of the loss limitation methods we employ could have a material adverse effect on our financial condition or results of operations.”

Claims Management. Our insurance group’s claims management function is performed by claims professionals, as well as experienced external claims managers (third party administrators), where appropriate. In addition to investigating, evaluating and resolving claims, members of our insurance group’s claims departments work with underwriting professionals as functional teams in order to develop products and services desired by the group’s clients.

Reinsurance Operations

Our reinsurance operations are conducted on a worldwide basis through our reinsurance subsidiaries, Arch Re Bermuda, Arch Re U.S., Arch Syndicate 2012, Arch Syndicate 1955 and Arch Re Europe. Arch Re Bermuda is dual-licensed as a Class 4 general business insurer and Class C long-term insurer and is headquartered in Hamilton, Bermuda. Arch Re Bermuda has been approved as a “certified reinsurer” in certain U.S. states that allow reduced collateral for reinsurance ceded to such reinsurers. Arch Re Bermuda has also been approved in certain U.S. states as a “reciprocal jurisdiction reinsurer,” which allows ceding

companies to eliminate collateral requirements for reinsurance ceded to such reinsurers and still take credit for that reinsurance. Arch Re U.S. is licensed or is an accredited or otherwise approved reinsurer in 50 states, the District of Columbia and Puerto Rico, the provinces of Ontario and Quebec in Canada with its principal U.S. offices in Morristown, New Jersey. Treaty operations in Canada are conducted through the Canadian branch of Arch Re U.S. (“Arch Re Canada”). Arch Re U.S. is also an admitted insurer in Guam. Our property facultative reinsurance operations are conducted primarily through Arch Re U.S. The property facultative reinsurance operations have offices throughout the U.S., Canada, Europe and the U.K. Arch Re Europe, licensed and authorized as a non-life reinsurer and a life reinsurer, is headquartered in Dublin, Ireland with branch offices outside the EEA in Zurich and London. AMAL is the managing agent for the reinsurance operations of Arch Syndicate 2012 and Arch Syndicate 1955.

In December 2022, Arch Group Reinsurance Ltd. (“AGRL”) was registered as a Class 3A general business insurer carrying on affiliated reinsurance business pursuant to the Insurance Act of 1978 of Bermuda. AGRL, a wholly-owned subsidiary of Arch-U.S., was established to provide internal quota share reinsurance covering certain U.S. lines of business. AGRL will be a U.S. taxpayer through a section 953(d) voluntary election under the Internal Revenue Code of 1986, as amended.

Strategy. Our reinsurance group’s strategy is to capitalize on our financial capacity, experienced management and operational flexibility to offer multiple products through our operations. The reinsurance group’s operating principles are to:

•Actively select and manage risks. Our reinsurance group only underwrites business that meets certain profitability criteria, and it emphasizes disciplined underwriting over premium growth. To this end, our reinsurance group maintains centralized control over reinsurance underwriting guidelines and authorities.

•Maintain flexibility and respond to changing market conditions. Our reinsurance group’s organizational structure and philosophy allows it to take advantage of increases or changes in demand or favorable pricing trends. Our reinsurance group believes that its existing platforms in Bermuda, the U.S., U.K., Europe and Canada, broad underwriting expertise and substantial capital facilitate adjustments to its mix of business geographically and by line and type of coverage. Our reinsurance group believes that this flexibility allows it to participate in those market opportunities that provide the greatest potential for underwriting profitability.

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•Maintain a low cost structure. Our reinsurance group believes that maintaining tight control over its staffing level and operating primarily as a broker market reinsurer permits it to maintain low operating costs relative to its capital and premiums.

Our reinsurance group writes business on both a proportional and non-proportional basis and writes both treaty and facultative business. In a proportional reinsurance arrangement (also known as pro rata reinsurance, quota share reinsurance or participating reinsurance), the reinsurer shares a proportional part of the original premiums and losses of the reinsured. The reinsurer pays the cedent a commission which is generally based on the cedent’s cost of acquiring the business being reinsured (including commissions, premium taxes, assessments and miscellaneous administrative expenses) and may also include a profit factor. Non-proportional (or excess of loss) reinsurance indemnifies the reinsured against all or a specified portion of losses on underlying insurance policies in excess of a specified amount, which is called a “retention.” Non-proportional business is written in layers and a reinsurer or group of reinsurers accepts a band of coverage up to a specified amount. The total coverage purchased by the cedent is referred to as a “program.” Any liability exceeding the upper limit of the program reverts to the cedent.

The reinsurance group’s treaty operations generally seek to write significant lines on less commoditized classes of coverage, such as specialty property and casualty reinsurance treaties. However, with respect to other classes of coverage, such as property catastrophe and casualty clash, the reinsurance group’s treaty operations participate in a relatively large number of treaties where they believe that they can underwrite and process the business efficiently. The reinsurance group’s property facultative operations write reinsurance on a facultative basis whereby they assume part of the risk under primarily single insurance contracts. Facultative reinsurance is typically purchased by ceding companies for individual risks not covered by their reinsurance treaties, for unusual risks or for amounts in excess of the limits on their reinsurance treaties.

For additional information regarding the business written by the reinsurance group, please refer to note 4, “Segment Information,” to our consolidated financial statements in Item 8.

Underwriting Philosophy. Our reinsurance group employs a disciplined, analytical approach to underwriting reinsurance risks that is designed to specify an adequate premium for a given exposure commensurate with the amount of capital it anticipates placing at risk. A number of our reinsurance group’s underwriters are also actuaries. It is our reinsurance group’s belief that employing actuaries on the front-end of

the underwriting process gives it an advantage in evaluating risks and constructing a high quality book of business.

As part of the underwriting process, our reinsurance group typically assesses a variety of factors, including:

•adequacy of underlying rates for a specific class of business and territory;

•the reputation of the proposed cedent and the likelihood of establishing a long-term relationship with the cedent, the geographic area in which the cedent does business, together with its catastrophe exposures, and our aggregate exposures in that area;

•historical loss data for the cedent and, where available, for the industry as a whole in the relevant regions, in order to compare the cedent’s historical loss experience to industry averages;

•projections of future loss frequency and severity; and

•the perceived financial strength of the cedent.

Marketing. Our reinsurance group generally markets its reinsurance products through brokers, except our property facultative reinsurance group, which generally deals directly with the ceding companies. Brokers do not have the authority to bind our reinsurance group with respect to reinsurance agreements, nor does our reinsurance group commit in advance to accept any portion of the business that brokers submit to them. Our reinsurance group generally pays brokerage fees to brokers based on negotiated percentages of the premiums written through such brokers. For information on major brokers, see note 18, “Commitments and Contingencies—Concentrations of Credit Risk,” to our consolidated financial statements in Item 8.

Risk Management and Retrocession. Our reinsurance group currently purchases a combination of per event excess of loss, per risk excess of loss, proportional retrocessional agreements and other structures that are available in the market. Such arrangements reduce the effect of individual or aggregate losses on, and in certain cases may also increase the underwriting capacity of, our reinsurance group. Our reinsurance group will continue to evaluate its retrocessional requirements based on its net appetite for risk. See note 8, “Reinsurance,” to our consolidated financial statements in Item 8.

For catastrophe exposed reinsurance business, our reinsurance group seeks to limit the amount of exposure it assumes from any one reinsured and the amount of the aggregate exposure to catastrophe losses from a single event in any one geographic zone. For a discussion of our risk management policies, see “Management’s Discussion and Analysis of Financial Condition and Results of Operations—Summary of Critical Accounting Estimates—Ceded

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Reinsurance” and “Risk Factors—Risks Relating to Our Industry, Business and Operations—The failure of any of the loss limitation methods we employ could have a material adverse effect on our financial condition or results of operations.”

Claims Management. Claims management includes the receipt of initial loss reports, creation of claim files, determination of whether further investigation is required, establishment and adjustment of case reserves and payment of claims. Additionally, audits are conducted for both specific claims and overall claims procedures at the offices of selected ceding companies. Our reinsurance group makes use of outside consultants for claims work from time to time.

Mortgage Operations

Our mortgage operations include mortgage insurance and reinsurance in the U.S. and internationally, as well as participation in GSE credit risk-sharing transactions. Our mortgage group includes direct mortgage insurance in the U.S. primarily through Arch Mortgage Insurance Company, United Guaranty Residential Insurance Company, and Arch Mortgage Guaranty Company (together, “Arch MI U.S.”); mortgage reinsurance primarily through Arch Re Bermuda to mortgage insurers on both a proportional and non-proportional basis globally; mortgage insurance and reinsurance in the EEA and U.K. through Arch Insurance (EU), and in Australia through Arch Indemnity; and participation in various GSE credit risk-sharing products primarily through Arch Re Bermuda.

In 2014, we entered the U.S. mortgage insurance marketplace, underwriting on the Arch Mortgage Insurance Company platform. Arch Mortgage Insurance Company is licensed and operates in all 50 states, the District of Columbia and Puerto Rico. In December 2016, we completed the acquisition of UGC and its primary operating subsidiary, United Guaranty Residential Insurance Company, which is licensed and operates in all 50 states and the District of Columbia.

Arch Mortgage Insurance Company and United Guaranty Residential Insurance Company have each been approved as an eligible mortgage insurer by Fannie Mae and Freddie Mac, subject to maintaining certain ongoing requirements (“eligible mortgage insurer”). Arch Mortgage Guaranty Company offers direct mortgage insurance to U.S. mortgage lenders with respect to mortgages that lenders intend to retain in portfolio or include in non-agency securitizations. Arch Mortgage Guaranty Company, which is licensed in all 50 states and the District of Columbia, insures mortgages that are not intended to be sold to the GSEs, and it is therefore not approved by either GSE as an eligible mortgage insurer.

In 2019, Arch LMI was authorized by APRA to write lenders’ mortgage insurance. In August 2021, we acquired Arch Indemnity, which is also authorized by APRA to write lenders’ mortgage insurance. In December 2022, we converted Arch LMI to a services company for our Australian lenders mortgage insurance operations and the company relinquished its APRA authorization. Arch LMI and Arch Indemnity are headquartered in Sydney, Australia. Following the conversion of Arch LMI, Arch Indemnity is the primary provider of direct lenders’ mortgage insurance and reinsurance to the Australian market.

Strategy. The mortgage insurance market operates on a distinct underwriting cycle, with demand driven mainly by the housing market and general economic conditions. As a result, the creation of the mortgage group provides us with a more diverse revenue stream. Our mortgage group’s strategy is to capitalize on its financial capacity, mortgage insurance technology platform, operational flexibility and experienced management to offer mortgage insurance, reinsurance and other risk-sharing products in the U.S. and around the world.

Our mortgage group’s operating principles and goals are to:

•Capitalize on profitable underwriting opportunities. Our mortgage group believes that its experienced management, analytics and underwriting teams are positioned to identify and evaluate business with attractive risk/reward characteristics.

•Maintain a disciplined credit risk philosophy. Our mortgage group’s credit risk philosophy is to generate underwriting profit through disciplined credit risk analysis and proper pricing. Our mortgage group believes that the key to this approach is maintaining discipline across all phases of the applicable housing and mortgage lending cycles.

•Provide superior and innovative mortgage products and services. Our mortgage group believes that it can leverage its financial capacity, experience across insurance product lines and the mortgage finance industry, and its analytics and technology to provide innovative products and superior service. The mortgage group believes that its delivery of tailored products that meet the specific, evolving needs of its customers will be a key to the group’s success.

•Maintain our position as a leading provider of U.S. mortgage insurance business. With the acquisition of UGC in 2016, a leading provider of mortgage insurance products and services to national and regional banks and mortgage originators, we became a leading provider of U.S. mortgage insurance.

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Our mortgage group focuses on the following areas:

•Direct mortgage insurance in the United States. Under their monoline insurance licenses, each of Arch’s eligible mortgage insurers may only offer private mortgage insurance covering first lien, one-to-four family residential mortgages. Nearly all of our mortgage insurance written provides first loss protection on loans originated by mortgage lenders and sold to the GSEs. Each GSE’s Congressional charter generally prohibits it from purchasing a mortgage where the principal balance of the mortgage is in excess of 80% of the value of the property securing the mortgage unless the excess portion of the mortgage is protected against default by lender recourse, participation or by a qualified insurer. As a result, such “high loan-to-value mortgages” purchased by Fannie Mae or Freddie Mac generally are insured with private mortgage insurance.

Mortgage insurance protects the insured lender, investor or GSE against loss in the event of a borrower’s default. If a borrower defaults on mortgage payments, private mortgage insurance reduces, and may eliminate, losses to the insured. Private mortgage insurance may also facilitate the sale of mortgage loans in the secondary mortgage market because of the credit enhancement it provides. Our primary U.S. mortgage insurance policies predominantly cover individual loans and are effective at the time the loan is originated. We also may enter into insurance transactions with lenders and investors, under which we insure a portfolio of loans at or after origination. Although not currently a significant product, we may offer mortgage insurance on a “pool” basis in the future. Under pool insurance, the mortgage insurer provides coverage on a group of specified loans, typically for 100% of all contractual or policy-defined losses on every loan in the portfolio, subject to an agreed aggregate loss limit. Pool insurance may be in a first loss position with respect to loans that do not have primary mortgage insurance policies, or it may be in a second loss position, covering losses in excess of those covered by the primary mortgage insurance policy.

•Mortgage insurance and reinsurance in Europe and other countries where we identify profitable underwriting opportunities. Since 2011, Arch Insurance (EU) has offered mortgage insurance to European mortgage lenders in order to reduce lenders’ credit risk and regulatory capital requirements associated with the insured mortgages. In certain European countries, lenders purchase mortgage insurance to facilitate regulatory compliance with respect to high loan-to-value residential lending. Arch Insurance (EU) offers mortgage insurance on both a “flow” basis to cover new originations and through structured transactions to cover one or more portfolios of previously originated

residential loans. Increasingly, Arch Insurance (EU) and Arch Re Bermuda are providing protection to European banks on structured capital relief transactions. In Australia, Arch Indemnity provides lenders’ mortgage insurance on a flow basis to cover new originations and offers coverage through structured transactions to cover one or more portfolios of previously originated residential loans.

•Reinsurance. Arch Re Bermuda provides quota share reinsurance covering U.S. and international mortgages.

•Other credit risk-sharing products. In addition to providing traditional mortgage insurance and reinsurance, we offer various credit risk-sharing products to government agencies and mortgage lenders. The GSEs have reduced their exposure to mortgage risk by shifting a portion of it to the private sector, creating opportunities for insurers to assume additional mortgage risk. In 2013, Arch Re Bermuda became the first (re)insurance company to participate in Freddie Mac’s program to transfer certain credit risk in its single-family portfolio to the private sector. Since that time, Arch Re Bermuda and its affiliates have regularly participated in both Fannie Mae and Freddie Mac single family and multifamily risk sharing programs.

In 2019 we established Arch Credit Risk Services (Bermuda) (“Arch CRS”) Ltd. Arch CRS is licensed by the Bermuda Monetary Authority (“BMA”) as an insurance agent in Bermuda. Arch CRS offers mortgage credit assessment and underwriting advisory services with respect to participation in GSE credit risk transfer transactions.

Underwriting Philosophy. Our mortgage group believes in a disciplined, analytical approach to underwriting mortgage risks by utilizing proprietary and third party models, including forecasting delinquency and future home price movements with the goal of ensuring that premiums are adequate for the risk being insured. Experienced actuaries and statistical modelers are engaged in analytics to inform the underwriting process. As part of the underwriting process, our mortgage group typically assesses a variety of factors, including the:

•ability and willingness of the mortgage borrower to pay its obligations under the mortgage loan being insured;

•characteristics of the mortgage loan being insured and the value of the collateral securing the mortgage loan;

•financial strength, quality of operations and reputation of the lender originating the mortgage loan;

•expected future home price movements which vary by geography;

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•projections of future loss frequency and severity; and

•adequacy of premium rates.

Sales and Distribution. In the U.S., we employ a sales force to directly sell mortgage insurance products and services to our customers, which include mortgage originators such as mortgage bankers, mortgage brokers, commercial banks, savings institutions, credit unions and community banks. Our largest single mortgage insurance customer in the U.S. (including branches and affiliates) accounted for 7.1% and 6.3% of our gross premiums written for the years ending December 31, 2022 and 2021, respectively. No other customer accounted for greater than 2.8% of the gross premiums written for the years ending December 31, 2022 and 2021, respectively. The percentage of gross premiums written on our top 10 customers was 23.6% and 22.7% as of December 31, 2022 and 2021, respectively. In Europe, Bermuda and Australia, our products and services are/or will be distributed on a direct basis and through brokers. Each country represents a unique set of opportunities and challenges that require knowledge of market conditions and client needs to develop effective solutions.

Risk Management. Exposure to mortgage risk is monitored globally and managed through underwriting guidelines, pricing, reinsurance, utilization of proprietary risk models, concentration limits and limits on net probable loss resulting from a severe economic downturn in the housing market. Exposure to climate risk has also been incorporated into the risk management framework of our mortgage group to monitor and manage our exposure to potential (i) losses related to the direct physical impact of extreme weather conditions or events in certain transactions; and/or (ii) adverse economic or housing market conditions caused by the physical impact of extreme weather conditions or events on a region or the financial impact of transitioning to a zero or low carbon economy on a region. Generally, mortgage insurance policies exclude direct physical losses resulting from physical damages, such as damaged caused by extreme weather events, though we do have some exposure to physical damage in certain GSE credit risk transfer (“CRT”) transactions. Additionally, we actively monitor developments in the housing market, financial regulation and public policy in the geographies where our mortgage group operates to facilitate implementation of laws, regulations and policies which support sustainable environmental behavior and mitigate the effects of climate change. For a discussion of our risk management policies, see “Management’s Discussion and Analysis of Financial Condition and Results of Operations—Summary of Critical Accounting Estimates—Ceded Reinsurance” and “Risk Factors—Risks Relating to Our Industry, Business and Operations—The failure of any of the loss limitation methods we employ could have a material adverse effect on our financial condition or results of operations.”

Our mortgage group has ceded a portion of its premium on a quota share basis through certain reinsurance agreements and through aggregate excess of loss reinsurance agreements which provide reinsurance coverage for delinquencies on portfolios of in-force policies issued between certain periods. See note 8, “Reinsurance,” to our consolidated financial statements in Item 8 for further details.

Reinsurance arrangements do not relieve our mortgage group from its primary obligations to insured parties. Reinsurance recoverables are recorded as assets, predicated on the reinsurers’ ability to meet their obligations under the reinsurance agreements. If the reinsurers are unable to satisfy their obligations under the agreements, our mortgage subsidiaries would be liable for such defaulted amounts. For our U.S. mortgage insurance business, in addition to utilizing reinsurance, we have developed a proprietary risk model that simulates the maximum loss resulting from severe economic events impacting the housing market. See “Management’s Discussion and Analysis of Financial Condition and Results of Operations—Catastrophic Events and Severe Economic Events.”

Claims Management. With respect to our direct mortgage insurance business, the claims process generally begins with notification by the insured or servicer to us of a default on an insured loan. The insured is generally required to notify us of a default after the borrower misses two consecutive monthly payments. Borrowers default for a variety of reasons, including a reduction of income, unemployment, divorce, illness, inability to manage credit, rising interest rate levels and declining home prices. Upon notice of a default, in certain cases we may coordinate with loan servicers to facilitate and enhance retention workouts on insured loans. Retention workouts include payment forbearance, loan modifications and other loan repayment options, which may enable borrowers to cure mortgage defaults and retain ownership of their homes. If a retention workout is not viable for a borrower, our loss on a loan may be mitigated through a liquidation workout option, including a pre-foreclosure sale or a deed-in-lieu of foreclosure.

In the U.S., our master policies generally provide that within 60 days of the perfection of a primary insurance claim, we have the option of:

•paying the insurance coverage percentage specified in the certificate of insurance multiplied by the loss amount;

•in the event the property is sold pursuant to an approved prearranged sale, paying the lesser of (i) 100% of the loss amount less the proceeds of sale of the property, or (ii) the specified coverage percentage multiplied by the loss amount; or

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•paying 100% of the loss amount in exchange for the insured’s conveyance to us of good and marketable title to the property, with us then selling the property for our own account.

While we select the claim settlement option that best mitigates the amount of our claim payment, in the U.S. we generally pay the coverage percentage multiplied by the loss amount.

Other Operations

In 2014, we and HPS Investment Partners, LLC (formerly Highbridge Principal Strategies, LLC) (“HPS”), sponsored the formation of Somers. Arch Re Bermuda invested $100.0 million in Somers common equity. Somers’ strategy is to combine a diversified reinsurance and insurance business with a disciplined investment strategy. Somers’ own management and board of directors are responsible for its results and profitability. Arch Re Bermuda has appointed three directors to serve on the seven person board of directors of Somers. In the 2020 fourth quarter, Arch Capital, Somers and Greysbridge, a wholly-owned subsidiary of Arch Capital, entered into a Merger Agreement pursuant to which, among other things, Arch Capital agreed to acquire all of the common shares of Somers not owned by Arch for a cash purchase price of $35.00 per common share. Arch Capital has assigned its rights under the Merger Agreement to Greysbridge. The merger and the related Greysbridge equity financing closed on July 1, 2021. Effective July 1, 2021, Somers is wholly owned by Greysbridge, and Greysbridge is owned 40% by Arch, 30% by certain investment funds managed by Kelso and 30% by certain investment funds managed by Warburg. See note 12, “Variable Interest Entity and Noncontrolling Interests,” to our consolidated financial statements in Item 8 for further details.

In 2017 we and Kelso sponsored the formation of Premia. Premia’s strategy is to reinsure or acquire companies or reserve portfolios in the non-life property and casualty insurance and reinsurance run-off market. Arch Re Bermuda and certain Arch co-investors invested $100.0 million and acquired approximately 25% of Premia as well as warrants to purchase additional common equity. Arch Re Bermuda is providing a 25% quota share reinsurance treaty on certain business written by Premia, and subsidiaries of Arch Capital are providing certain administrative and support services to Premia, in each case pursuant to separate multi-year agreements. Arch Re Bermuda has appointed two directors to serve on the seven person board of directors of Premia. In the 2019 fourth quarter, Barbican entered into certain reinsurance and related transactions with Premia pursuant to which Premia assumed a transfer of liability for the 2018 and prior years of account of Barbican as of July 1, 2019. See note 16, “Transactions with Related Parties,” to our consolidated financial statements in Item 8 for further details.

In 2021, the Company completed the share purchase agreement with Natixis to purchase 29.5% of the common equity of Coface. This is a long-term, strategic investment in Coface, and fits with Arch’s efforts to develop uncorrelated sources of underwriting income. Our companies share a focus on specialty underwriting where knowledge and expertise create value for our clients, and trade credit contributes to Arch’s specialty-driven business model. Arch has appointed four directors to serve on the ten person board of directors of Coface.

Climate Change Considerations

We are taking steps to address the effects of climate change and facilitate the transition toward decarbonization in all our underwriting segments. We seek to identify business opportunities associated with environmentally friendly trends and incentivize responsible environmental behaviors. We have adopted a thermal coal policy and provide environmentally sustainable insurance solutions in certain product lines.

HUMAN CAPITAL

We are driven by our common purpose of “Enabling Possibility” for our customers, our communities and our employees. This purpose is supported by our collaborative, results-driven culture which relies on our dedicated, engaged and talented people. By offering a meaningful and inclusive employee experience, we not only help people perform at their best among colleagues who care, but also support our strategy of delivering specialty products and innovative solutions to our customers in each of our business segments. As of February 1, 2023, we had just over 5,800 employees globally, compared to around 5,200 last year, which directly speaks to our ability to grow and retain our talent despite the challenges we all faced with the global pandemic. We have approximately 3,300 employees in North America (U.S., Canada and Bermuda), 1,500 employees in Europe and the U.K. and 1,000 employees in the Philippines, Australia and the rest of the world.

Our People and Culture. In 2022, Arch employees began to return to offices globally as the pandemic eased. We recognize the incredible resiliency of the team to work remotely for over two years while balancing that with the opportunity to maximize in-person collaboration across departments. Arch is providing flexibility in our return to office model utilizing specific “office days” for teams as part of a hybrid working model.

Through the global pandemic, the spirit of agility that is part of our entrepreneurial roots allowed us to transition virtually overnight to a home-based employee population. Since the start of the pandemic we recognized and supported the

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wellness needs of our employees. We provided additional resources including webinars with a psychologist who specializes in building resilience and continued our Arch Cares program to provide financial support to employees affected by COVID-19.

An important part of our culture is building an inclusive, diverse workforce. By better reflecting the demographics in the markets in which we operate while also actively instilling norms for inclusive behavior, we leverage all the best contributions and thinking across our Company. To that end, we are committed to further integrating diversity and inclusion principles in our operations. In addition to “embedding” inclusion into our talent processes, e.g., promotion reviews, over 500 employees (mostly managers) have attended our intensive, six-week Fostering Inclusive Leadership program. Importantly, this program requires participants to complete a business-related project as well as attend group discussions, where participants focus on how to apply inclusive techniques into the work experience. Finally, in 2022 our six employee networks provided a forum for over 1,000 employees to share ideas, build community and belonging, provide leadership opportunities for members, and contribute meaningfully to business outcomes. Importantly, our networks include significant ally representation, which underscores the inclusive behavior of our people.

Talent Acquisition, Development, Rewards and Retention. Our employees are our greatest asset, and we maintain a sharp focus on improving the ways we attract, develop and retain our high-performing talent. Our goal is to cultivate a workplace culture where all our employees can thrive by building awareness of inclusive practices and incorporating them into our regular course of business. We continue to enhance our talent acquisition process through a new model which will modernize our approach to talent acquisition for candidates and hiring managers, while providing an enhanced ability to proactively source and build pipelines for the best diverse talent. The model will help streamline this process across our Company by using a common platform and approach, which we can easily scale as we grow.

We provide unique career growth opportunities through a combination of on-the-job training, exposure to top-notch colleagues who coach and mentor, and education and training programs designed to accelerate learning and applying new skills and behaviors. We offer competitive compensation and comprehensive benefits packages, including an employee share purchase plan, parental leave, generous contributions to retirement savings plans and programs to support employee mental and physical well-being. We recognize the financial burden of educational loans in the United States and have supported our employees with a student debt assistance program. Since the inception of the program in 2018, Arch has contributed $4.1 million to this program, including $0.9 million in 2022. We also match eligible contributions to

qualified charitable organizations and employees are eligible to receive time-off to volunteer with an eligible non-profit organization. Our Arch Achieve program has recognized over 400 employees for excellence since its inception in 2009, and each recipient is awarded shares of our common stock (or a cash bonus in certain cases), to recognize their accomplishments.

In 2022, our senior leadership team was able to meet in person to dive deep into our business strategy and recruitment and employee retention strategy and enhance opportunities for employee development and networking opportunities globally.

In the U.S., we lowered the cost of benefits for many employees based on a tiered salary approach for the fall 2022 enrollment period. This is meant to address some of the impacts of inflation in 2023 for many employees who are hit the hardest by rising prices.

We also encourage employees to continue their educational and professional development through tuition reimbursement plans. To attract the best talent to our industry, we offer internship programs and an Early Career Program with an Underwriting Track which provides participants with a robust introduction and real technical skills to build a successful career at Arch. As part of our talent attraction, we have targeted programs aimed at diversifying our workforce. Experienced professionals at Arch may participate in manager and leadership development programs and, for our mortgage insurance segment employees, we offer the opportunity to seek a Mortgage Bankers Association Certified Banker designation.

RESERVES

Reserves for losses and loss adjustment expenses (“Loss Reserves”) represent estimates of what the insurer or reinsurer ultimately expects to pay on claims at a given time, based on facts and circumstances then known, and it is probable that the ultimate liability may exceed or be less than such estimates. Even actuarially sound methods can lead to subsequent adjustments to reserves that are both significant and irregular due to the nature of the risks written. Loss Reserves are inherently subject to uncertainty.

For detail on our Loss Reserves by segment and potential variability in the reserving process, see the Loss Reserves section of “Summary of Critical Accounting Estimates” in Item 7. For an analysis of losses and loss adjustment expenses and a reconciliation of the beginning and ending Loss Reserves and information about prior year reserve development, see note 5, “Reserve for Losses and Loss Adjustment Expenses,” to our consolidated financial statements in Item 8. For information on our reserving

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process, see note 6, “Short Duration Contracts,” to our consolidated financial statements in Item 8.

Unpaid and paid losses and loss adjustment expenses recoverable were approximately $6.6 billion at December 31, 2022. For detail on our unpaid and paid losses and loss adjustment expenses, see the Reinsurance Recoverables section of “Financial Condition, Reinsurance Recoverables” in Item 7.

INVESTMENTS

At December 31, 2022, total investable assets held by Arch were $28.1 billion. Our current investment guidelines and approach stress preservation of capital, market liquidity and diversification of risk. Our investments are subject to market-wide risks and fluctuations, as well as to risks inherent in particular securities. While maintaining our emphasis on preservation of capital and liquidity, we expect our portfolio to become more diversified and, as a result, we may in the future expand into areas which are not part of our current investment strategy. For detail on our investments, see the Investable Assets Held by Arch section of “Financial Condition” in Item 7 and note 9, “Investment Information,” to our consolidated financial statements in Item 8.

RATINGS

Our ability to underwrite business is affected by the quality of our claims paying ability and financial strength ratings as evaluated by independent agencies. Such ratings from third party internationally recognized statistical rating organizations or agencies are instrumental in establishing the financial security of companies in our industry. We believe that the primary users of such ratings include commercial and investment banks, policyholders, brokers, ceding companies and investors. Insurance ratings are also used by insurance and reinsurance intermediaries as an important means of assessing the financial strength and quality of insurers and reinsurers, and are often an important factor in the decision by an insured or intermediary of whether to place business with a particular insurance or reinsurance provider.

The financial strength ratings of our operating insurance and reinsurance subsidiaries are subject to periodic review as rating agencies evaluate us to confirm that we continue to meet their criteria for ratings they have assigned to us. Such ratings may be revised or revoked at the discretion of such ratings agencies in response to a variety of factors, including capital adequacy, management, earnings, forms of capitalization and risk profile. A.M. Best Company (“A.M. Best”), Fitch Ratings (“Fitch”), Moody’s Investors Service (“Moody’s”) and Standard & Poor’s (“S&P”) are ratings

agencies which have assigned financial strength and/or issuer ratings to Arch Capital and/or one or more of its subsidiaries.

The ratings issued on our companies by these agencies are announced publicly and are available directly from the agencies. Our website www.archgroup.com (Investor Relations-Credit Ratings) contains information about our ratings, but such information on our website is not incorporated by reference into this report.

COMPETITION

The worldwide insurance markets are highly competitive. We compete, with major U.S. and non-U.S. insurers and reinsurers, some of which have greater financial, marketing and management resources and longer-term relationships with insureds and brokers than us. We compete primarily on the basis of overall financial strength, ratings assigned by independent rating agencies, geographic scope of business, strength of client relationships, premiums charged, contract terms and conditions, products and services offered, speed of claims payment, reputation, employee experience, and qualifications and local presence. See “Risk Factors—Risks Relating to Our Industry, Business and Operations—“We operate in a highly competitive environment, and we may not be able to compete successfully in our industry.”

In our property casualty insurance and reinsurance businesses, we compete with insurers and reinsurers that provide specialty property and casualty lines of insurance, including, but not limited to Allianz, American Financial Group, Inc., American International Group, Inc., Aviva, AXA XL, AXIS Capital Holdings Limited, Berkshire Hathaway, Inc., Chubb Limited, CNA Financial Corp., Convex Group Limited, Everest Re Group Ltd., Fairfax Financial Holdings Limited, Hannover Rück SE, The Hartford Financial Services Group, Inc., Liberty Mutual Group, Lloyd’s, Markel Corporation, Munich Re Group, PartnerRe Ltd., RenaissanceRe Holdings Ltd., RLI Corp., SCOR, Sompo International, Swiss Reinsurance Company, Tokio Marine, The Travelers Companies, Inc., W.R. Berkley Corp. and Zurich Insurance Group.

In our mortgage business, we compete with insurers and reinsurers that provide mortgage insurance, including the U.S mortgage insurance subsidiaries of Essent Group Ltd., Enact Holdings Inc., MGIC Investment Corporation, NMI Holdings Inc. and Radian Group Inc. The private mortgage insurance industry is highly competitive. Private mortgage insurers generally compete on the basis of underwriting guidelines, pricing, terms and conditions, financial strength, product and service offerings, customer relationships, reputation, the strength of management, technology, and innovation in the delivery and servicing of insurance products. Arch MI U.S. and other private mortgage insurers compete with federal and

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state government agencies that sponsor their own mortgage insurance programs. The private mortgage insurers’ principal government competitor is the Federal Housing Administration (“FHA”) and, to a lesser degree, the U.S. Department of Veterans Affairs (“VA”). Future changes to the FHA program, including any reduction to premiums charged may impact the demand for private mortgage insurance.

In addition, Arch MI U.S. and other private mortgage insurers increasingly compete with multi-line reinsurers and capital markets alternatives to private mortgage insurance. The GSEs continued their respective mortgage CRT programs including the use of front and back-end transactions with multi-line reinsurers, with approximately 25 unique insurers that regularly participate in transactions in addition to funded credit investors. These transactions continue to create opportunities for multi-line property casualty reinsurance groups and capital markets participants.

In our non-U.S. mortgage insurance businesses, we compete with insurance subsidiaries of Helia Group Ltd. (formerly a Genworth Financial Inc. subsidiary) and QBE Insurance Group, Ltd. in Australia; in Europe, our competitors on structured capital relief transactions include approximately 5-10 highly rated multi-line (re)insurers in addition to over 30 funded credit investors.

ENTERPRISE RISK MANAGEMENT

General. Enterprise Risk Management (“ERM”) is a key element in our philosophy, strategy and culture. We employ an ERM framework that includes underwriting, reserving, investment, credit and operational risks. Risk appetite and exposure limits are set by our executive management team, reviewed with the Board and its committees and routinely discussed with business unit management. These limits are articulated in our risk appetite statement, which details risk appetite, tolerances and limits for each major risk category, and are integrated into our operating guidelines. Exposures are aggregated and monitored periodically by our corporate risk management team. The reporting, review and approval of risk management information is integrated into our annual planning process, capital modeling and allocation, reinsurance purchasing strategy and reviewed at insurance business reviews, reinsurance underwriting meetings and board level committees.

Risk Management Process and Procedures. The following narrative provides an overview of our risk management framework and our methodology for identifying, measuring, managing and reporting on the key risks affecting us. It outlines our approach to risk identification and assessment and provides an overview of our risk appetite and tolerance for each of the following major risks: underwriting

(insurance) risk including pricing, reserving and catastrophe; investment including market and liquidity risks; group risk including strategic, governance, rating agency and capital market risk; credit risk; and operational risk, including regulatory, investor relations (reputational risk) and outsourcing risks. We view environmental, social and governance (“ESG”) – related risks not as standalone risks but as an integral part of our enterprise-wide risk management strategy. Consequently, evaluations of these risks are embedded throughout our risk management framework.

The framework includes details of our risk philosophy and policies to address the material risks confronting us and the approach and procedures to control and or mitigate these risks. The actions and policies implemented to meet our business management and regulatory obligations form the core of this framework. We have adopted a holistic approach to risk management by analyzing risk from both a top-down and bottom-up perspective.

Risk Identification and Assessment. The Finance, Investment and Risk Committee (“FIR Committee”), Audit Committee and Underwriting Oversight Committee of the Board oversee the top-down and bottom-up review of our risks. Given the nature and scale of our operations, these committees consider all aforementioned risks within the scope of the assessment. Arch Capital’s Chief Risk Officer (“CRO”) assists these committees in the identification and assessment of all key risks. The CRO is responsible for maintaining Arch Capital’s risk register and continually reviewing and challenging risk assessments, including the impact of emerging risks and significant business developments. Any new high-level risks or change in inherent or residual designations are brought to the Board’s or the relevant committee’s attention.

Risk Monitoring and Control. Arch Capital’s risk management framework requires risk owners to monitor key risks on a continuous basis. The highest residual risks are actively managed by the Board and relevant committees. The remaining risks are managed and monitored at a process level by the risk owners and/or the CRO. Risk owners have ultimate responsibility for the day-to-day management of each designated risk, reporting to the CRO on the satisfactory management and control of the risk and timely escalation of significant issues that may arise in relation to that risk. The CRO is responsible for overseeing the monitoring of all risks across the business and for communicating to the relevant risk owners if she becomes aware of issues, or potential and actual breaches of risk appetite, relevant to the assigned risks. A key element of these monitoring activities is the periodic evaluation of our position relative to risk tolerances and limits approved by the Board.

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Risk Reporting. Quarterly, the CRO compiles the results of the key risk review process into a report to the Board and relevant committees for review and discussion at their next meeting. The report includes an overview of selected key risks; a risk dashboard that depicts the status of risk limit and tolerance metrics; changes in the rating of high-level risks in the Arch Capital risk register; and summaries of our largest exposures and reinsurance recoverables. If necessary, risk management matters reviewed at the committee meetings are presented for discussion by the Board. The CRO is responsible for immediately escalating any significant risk matters to executive management, the respective Board Committee and/or the Board for approval of the required remediation. As part of our corporate governance, the Board and certain of its committees hold regular executive sessions with members of our management team. These sessions are intended to ensure an open and frank dialogue exists about various forms of risk across the organization.

Implementation and Integration. We believe that an integrated approach to developing, measuring and reporting our Own Risk and Solvency Assessment (“ORSA”) is an important part of the risk management framework. The ORSA process provides the link between Arch Capital’s risk profile, its board-approved risk appetite including approved risk tolerances and limits, its business strategy and its overall solvency requirements. The ORSA is the entirety of the processes and procedures employed to identify, assess, monitor, manage, and report the short and long-term risks we face or may face and to determine the capital necessary to ensure that our overall solvency needs are met at all times. The ORSA also makes the link between actual reported results and the capital assessment.

The ORSA is the basis for risk reporting to the Board and its committees and acts as a mechanism to embed the risk management framework within our decision making processes and operations. The Board has delegated responsibility for supervision and oversight of the ORSA to the FIR Committee. This oversight includes regular reviews of the ORSA process and output. An ORSA report is produced at least annually and the results of each assessment are reported to the Board. The Board actively participates in the ORSA process by steering how the assessment is performed and challenging its results. This assessment is also taken into account when formulating strategic decisions.

The ORSA process and reporting are also important parts of our business strategy, tailored specifically to fit into our organizational structure and risk management system with the appropriate techniques in place to assess our overall solvency needs, taking into consideration the nature, scale and complexity of the risks inherent in the business.

We also take the results of the ORSA into account within our system of governance, including long-term capital

management, business planning and new product development. The results of the ORSA also contribute to various elements of our strategic decision-making including how best to optimize capital management, establishing the most appropriate premium levels and deciding whether to retain or transfer risks.

For further discussion of our risk management policies, see the Ceded Reinsurance section of “Summary of Critical Accounting Estimates” in Item 7.

REGULATION

General

Our insurance and reinsurance subsidiaries are subject to varying degrees of regulation and supervision in the various jurisdictions in which they operate. We are subject to extensive regulation under applicable statutes in these countries and any other jurisdictions in which we operate. The current material regulations under which we operate are described below. We may become subject in the future to regulation in new jurisdictions or to additional regulations in existing jurisdictions.

Bermuda

General. Our main Bermuda insurance operating subsidiary, Arch Re Bermuda, is a Class 4 general business insurer and a Class C long-term insurer and is subject to the Insurance Act 1978 of Bermuda and related regulations, as amended (“Insurance Act”). Among other matters, the Insurance Act imposes certain solvency and liquidity standards, auditing and reporting requirements, the submission of certain period examinations of its financial conditions and grants the BMA powers to supervise, investigate, require information and demand the production of documents and intervene in the affairs of insurance companies. Significant requirements include the appointment of an independent auditor, the appointment of a loss reserve specialist, the appointment of a principal representative in Bermuda, the filing of annual Statutory Financial Returns, the filing of annual financial statements in accordance with U.S. generally accepted accounting principles (“GAAP”), the filing of an annual capital and solvency return, compliance with minimum and enhanced capital requirements, compliance with certain restrictions on reductions of capital and the payment of dividends and distributions, compliance with group solvency and supervision rules, if applicable, and compliance with the Insurance Code of Conduct (relating to corporate governance, risk management and internal controls).

Arch Re Bermuda must also comply with a minimum liquidity ratio and minimum solvency margin in respect of its general business. The minimum liquidity ratio requires that the value of relevant assets must not be less than 75% of the

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amount of relevant liabilities. The minimum solvency margin, which varies depending on the class of the insurer, is determined as a percentage of either net reserves for losses and loss adjustment expenses (“LAE”) or premiums or pursuant to a risk-based capital measure. Arch Re Bermuda is also subject to an enhanced capital requirement (“ECR”) which is established by reference to either the Bermuda Solvency Capital Requirement model (“BSCR”) or an approved internal capital model. The BSCR model is a risk-based capital model which provides a method for determining an insurer’s capital requirements (statutory capital and surplus) by taking into account the risk characteristics of different aspects of the insurer’s business. The BMA has established a target capital level for each Class 4 insurer equal to 120% of its ECR. While a Class 4 insurer is not currently required to maintain its available statutory economic capital and surplus at this level, the target capital level serves as an early warning tool for the BMA, and failure to maintain statutory capital at least equal to the target capital level will likely result in increased regulatory oversight. As a Class C insurer, Arch Re Bermuda is also required to maintain available statutory economic capital and surplus in respect of its long-term business at a level equal to or in excess of its long-term enhanced capital requirement that is established by reference to either the Class C BSCR model or an approved internal capital model.

Arch Re Bermuda is prohibited from declaring or paying any dividends during any financial year if it is in breach of its general business or long-term business enhanced capital requirements, minimum solvency margins or its general business minimum liquidity ratio or if the declaration or payment of such dividends would cause such a breach. If it has failed to meet its minimum solvency margins or minimum liquidity ratio on the last day of any financial year, Arch Re Bermuda will be prohibited, without the approval of the BMA, from declaring or paying any dividends during the next financial year. In addition, Arch Re Bermuda is prohibited from declaring or paying in any financial year dividends of more than 25% of its total statutory capital and surplus (as shown on its previous financial year’s statutory balance sheet) unless it files (at least seven days before payment of such dividends) with the BMA an affidavit stating that it will continue to meet the required margins. Without the approval of the BMA, Arch Re Bermuda is prohibited from reducing by 15% or more its total statutory capital as set out in its previous year’s financial statements and any application for such approval must include an affidavit stating that it will continue to meet the required margins. Where such an affidavit is filed, it shall be available for public inspection at the offices of the BMA. Under the Bermuda Companies Act of 1981, as amended (the “Companies Act”), Arch Re Bermuda may declare or pay a dividend out of distributable reserves only if it has reasonable grounds for believing that it is, or would after the payment

be, able to pay its liabilities as they become due and if the realizable value of its assets would thereby not be less than its liabilities.

Policyholder Priority. The Insurance Amendment (No. 2) Act 2018 amended the Insurance Act to provide for the prior payment of policyholders’ liabilities ahead of general unsecured creditors in the event of the liquidation or winding up of an insurer. The amendments provide inter alia that, subject to certain statutorily preferred debts, the insurance debts of an insurer must be paid in priority to all other unsecured debts of the insurer. Insurance debt is defined as a debt to which an insurer is or may become liable pursuant to an insurance contract excluding debts owed to an insurer under an insurance contract where the insurer is the person insured.

Group Supervision. The BMA acts as group supervisor of our group of insurance and reinsurance companies (“Group”) and has designated Arch Re Bermuda as the designated insurer (“Designated Insurer”). As our Group supervisor, the BMA performs a number of functions including: (i) coordinating the gathering and dissemination of relevant or essential information for going concerns and emergency situations, including the dissemination of information which is of importance for the supervisory task of other competent authorities; (ii) carrying out supervisory reviews and assessments of our Group; (iii) carrying out assessments of our Group's compliance with the rules on solvency, risk concentration, intra-group transactions and good governance procedures; (iv) planning and coordinating through regular meetings held at least annually (or by other appropriate means) with other competent authorities, supervisory activities in respect of our Group; both as a going concern and in emergency situations (v) coordinating any enforcement action that may need to be taken against our Group or any Group members; and (vi) planning and coordinating meetings of colleges of supervisors in order to facilitate the carrying out of these functions. As Designated Insurer, Arch Re Bermuda is required to facilitate compliance by our Group with the group insurance solvency and supervision rules.

On an annual basis, the Group is required to file Group statutory financial statements, a Group statutory financial return, a Group capital and solvency return, audited Group financial statements, a Group Solvency Self-Assessment (“GSSA”), and a financial condition report with the BMA. The GSSA is designed to document our perspective on the capital resources necessary to achieve our business strategies and remain solvent, and to provide the BMA with insights on our risk management, governance procedures and documentation related to this process. In addition, the Designated Insurer is required to file quarterly group financial returns with the BMA. The Group is also required to maintain available Group statutory economic capital and

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surplus in an amount that is at least equal to the group enhanced capital requirement (“Group ECR”) and the BMA has established a group target capital level equal to 120% of the Group ECR.

Fit and Proper Controllers. The BMA maintains supervision over the controllers of all Bermuda registered insurers, brokers, agents and insurance marketplace providers. For so long as the shares of Arch Capital are listed on the NASDAQ or another recognized stock exchange, any person who, directly or indirectly, becomes a holder of at least 10%, 20%, 33% or 50% of our common shares must notify the BMA in writing within 45 days of becoming such a holder (or ceasing to be such a holder). The BMA may object to such a person and require the holder to reduce its holding of common shares and direct, among other things, that voting rights attaching to the common shares shall not be exercisable.

Economic Substance Act. In December 2018, Bermuda enacted the Economic Substance Act 2018 (as amended) of Bermuda and its related regulations (together, the “ES Act”). The ES Act came into force on January 1, 2019, and provides that a registered entity other than an entity which is resident for tax purposes in certain jurisdictions outside Bermuda (“non-resident entity”) that carries on as a business any one or more of the “relevant activities” referred to in the ES Act must comply with economic substance requirements. The list of “relevant activities” includes carrying on any one or more of the following activities: banking, insurance, fund management, financing, leasing, headquarters, shipping, distribution and service center, intellectual property and holding entities. Under the ES Act, if a company is engaged in one or more “relevant activities”, it is required to maintain a substantial economic presence in Bermuda and to comply with the economic substance requirements set forth in the ES Act. A company will comply with those economic substance requirements if it: (a) is managed and directed in Bermuda; (b) undertakes “core income generating activities” (as may be prescribed under the ES Act) in Bermuda in respect of the relevant activity; (c) maintains adequate physical presence in Bermuda; (d) has adequate full time employees in Bermuda with suitable qualifications; and (e) incurs adequate operating expenditure in Bermuda in relation to the relevant activity undertaken by it.

Companies that are licensed under the Insurance Act and thereby carry on insurance as a relevant activity are generally considered to operate in Bermuda with adequate substance if they comply with the existing provisions of (a) the Companies Act relating to corporate governance; and (b) the Insurance Act, that are applicable to the economic substance requirements, and the Registrar will have regard to such companies’ compliance in his assessment of compliance with the economic substance requirements. That being said, such companies are still required to complete and file a Declaration Form, with the Bermuda Registrar of Companies

and the Registrar will also have regard to the information provided in that Declaration Form in making his assessment of compliance with the ES Act.

Insurance Sector Operational Cyber Risk Management Code of Conduct (“Cyber Risk Management Code of Conduct”). The BMA recognized that cyber incidents can cause significant financial losses and/or reputational impacts across the insurance industry and implemented the Cyber Risk Management Code of Conduct in October 2020. All Bermuda insurers, insurance managers and intermediaries registered under the Insurance Act are required to company with the BMA’s Cyber Risk Management Code of Conduct, which established duties, requirements and standards to be complied by each registrant in relation to operational cyber risk management. This requires Arch Re Bermuda to develop a cyber risk policy, which is to be delivered pursuant to an operational cyber risk management program and appoint an appropriately qualified member of staff or outsourced resource to the role of Chief Information Security Officer. The role of the Chief Information Security Officer is to deliver the operational cyber risk management program.

It is expected that the cyber risk policy will be approved by the Arch Re Bermuda board of directors at least annually. The BMA will assess Arch Re Bermuda’s compliance with the Cyber Risk Management Code of Conduct in a proportionate manner relative to the nature, scale and complexity of its business. Failure to comply with the requirements of the Cyber Risk Management Code of Conduct will be taken into account by the BMA in determining whether Arch Re Bermuda is conducting its business in a sound and prudent manner as prescribed by the Insurance Act and may result in the BMA exercising its powers of intervention and investigation.

Notification of Cyber Reporting Events. Every Bermuda insurer is required to notify the BMA forthwith on it coming to the knowledge of the insurer, or where the insurer has reason to believe that a Cyber Reporting Event has occurred. Within fourteen (14) days of such notification, the insurer must also furnish the BMA with a written report setting out all of the particulars of the Cyber Reporting Event that are available to it. A Cyber Reporting Event includes any act that results in the unauthorized access to, disruption, or misuse of electronic systems or information stored on such systems of an insurer, including breach of security leading to the loss or unlawful destruction or unauthorized disclosure of or access to such systems or information where there is a likelihood of an adverse impact to policyholders, clients or the insurer’s insurance business, or an event that has occurred for which notice is required to be provided to a regulatory body or government agency.

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United States

General. Our U.S. based insurance operating subsidiaries are subject to extensive governmental regulation and supervision by the states and jurisdictions in which they are domiciled, licensed and/or approved to conduct business. The insurance laws and regulations of the state of domicile have the most significant impact on operations. We currently have U.S. insurance and/or reinsurance subsidiaries domiciled in Delaware, North Carolina, Missouri, Wisconsin, Kansas and the District of Columbia and we may acquire insurers domiciled in other states in the future. State insurance regulation and supervision is designed to protect policyholders rather than investors. Generally, state regulatory authorities have broad regulatory powers over such matters as licenses, standards of solvency, premium rates, policy forms, marketing practices, claims practices, investments, methods of accounting, form and content of financial statements, certain aspects of governance, ERM, amounts we are required to hold as reserves for future payments, minimum capital and surplus requirements, annual and other report filings and transactions among affiliates. Our U.S. based subsidiaries are required to file detailed quarterly and audited annual statutory financial statements with state insurance regulators. In addition, regulatory authorities conduct periodic financial, claims and market conduct examinations. Certain insurance regulatory requirements are highlighted below. In addition to regulation applicable generally to U.S. insurance and reinsurance companies, our U.S. mortgage insurance operations are affected by federal and state regulation relating to mortgage insurers, mortgage lenders, and the origination, purchase and sale of residential mortgages. Arch Insurance (U.K.) is also subject to certain governmental regulation and supervision in the states where it writes excess and surplus lines insurance.

Holding Company Regulation. All states have enacted legislation that regulates insurance holding company systems. These regulations generally provide that each insurance company in the system is required to register with the insurance department of its state of domicile and furnish information concerning the operations of companies within the holding company system which may materially affect the operations, management or financial condition of the insurers within the system. Notice to the state insurance departments is required prior to the consummation of certain material transactions between an insurer and any entity in its holding company system and certain transactions may not be consummated without the applicable insurance department’s prior approval or non-disapproval after receiving notice. The holding company acts also prohibit any person from directly or indirectly acquiring control of a U.S. insurance or reinsurance company unless that person has filed an application with specified information with such company’s domiciliary commissioner and has obtained the commissioner’s prior approval. Under most states’ statutes

acquiring 10% or more of the voting securities of an insurance company or its parent company is presumptively considered an acquisition of control of the insurance company, although such presumption may be rebutted.

State holding company acts and regulations also impose extensive informational requirements on parents and other affiliates of licensed insurers or reinsurers with the purpose of protecting them from enterprise risk, including requiring an annual enterprise risk report by the ultimate controlling person identifying the material risks within the insurance holding company system that could pose enterprise risk to the licensed companies and requiring a person divesting its controlling interest to make a confidential advance notice filing.

The National Association of Insurance Commissioners (“NAIC”) Insurance Holding Company System Model Act and Model Regulation includes provisions that, when adopted by states, will require the ultimate controlling person of an insurance holding company system to file an annual group capital calculation, unless the ultimate controlling person or its insurance holding company system is exempt from the filing requirement. The group capital calculation is designed to assist state insurance regulators in understanding the financial condition of non-insurance entities that are part of an insurance holding company system and the degree to which insurance companies are supporting those non-insurance entities.

Regulation of Dividends and Other Payments from Insurance Subsidiaries. The ability of an insurer to pay dividends or make other distributions is subject to insurance regulatory limitations of the insurer’s state of domicile. Such laws generally limit the payment of dividends or other distributions above a specified level. Dividends or other distributions in excess of such thresholds are “extraordinary” and are subject to prior notice and approval, or non-disapproval after receiving notice.

Credit for Reinsurance. Arch Re U.S. is subject to insurance regulation and supervision that is similar to the regulation of licensed primary insurers. However, except for certain mandated provisions that must be included in order for a ceding company to obtain credit for reinsurance ceded, the terms and conditions of reinsurance agreements generally are not subject to regulation by any governmental authority.

A U.S. primary insurer ordinarily will enter into a reinsurance agreement only if it is able to obtain credit for the reinsurance ceded on its U.S. statutory-basis financial statements. As a result of the requirements relating to the provision of credit for reinsurance, Arch Re U.S. and Arch Re Bermuda are indirectly subject to certain regulatory requirements imposed by U.S. jurisdictions in which ceding companies are domiciled. In general, credit for reinsurance is

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allowed if the reinsurer is licensed or “accredited” in the state in which the primary insurer is domiciled; or if none of the above applies, to the extent that the reinsurance obligations of the reinsurer are collateralized appropriately, typically through the posting of a letter of credit for the benefit of the primary insurer or the deposit of assets into a trust fund established for the benefit of the primary insurer.

U.S. primary insurers also may receive credit for reinsurance ceded to unauthorized reinsurers without collateral or with less than 100% collateral under revisions to the NAIC Credit for Reinsurance Model Law (#785) and the Credit for Reinsurance Model Regulation (#786) (collectively, the “NAIC Model Law and Regulation”). All U.S. states, the District of Columbia and Puerto Rico have adopted revisions to the NAIC Model Law and Regulation that allow full credit to U.S. ceding insurers for reinsurance ceded to reinsurers that have been approved as “certified reinsurers” based upon less than 100% collateralization. As of February 23, 2023, Arch Re Bermuda is approved as a “certified reinsurer” in 44 states with applications pending in 8 additional states and territories. In addition, 2019 amendments to the NAIC Model Law and Regulation eliminate reinsurance collateral requirements for reinsurers that (1) have their head office or are domiciled in member states of the EU, the U.K. and other jurisdictions deemed “reciprocal jurisdictions” by the NAIC (although individual states may reject the designation of such other jurisdictions as a “reciprocal jurisdiction”), and (2) have been approved as a “reciprocal jurisdiction reinsurer.” The NAIC list of reciprocal jurisdictions includes Bermuda, Japan and Switzerland. All U.S. states, the District of Columbia and Puerto Rico have adopted the 2019 amendments to the NAIC Model Law and Regulation. As of February 23, 2023, Arch Re Bermuda is approved as a “reciprocal jurisdiction reinsurer” in 45 states with applications pending in 7 additional states and territories.

Risk Management and ORSA. The NAIC Risk Management and Own Risk Solvency Assessment Model Act (“ORSA Model Act”) provides that domestic insurers, or their insurance group, must regularly conduct an ORSA consistent with a process comparable to the ORSA Guidance Manual process. The ORSA Model Act also provides that, no more than once a year, an insurer’s domiciliary regulator may request that an insurer submit an ORSA summary report, or any combination of reports that together contain the information described in the ORSA Guidance Manual, with respect to the insurer and/or the insurance group of which it is a member. States may impose additional internal review and regulatory filing requirements on licensed insurers and their parent companies. All states have enacted the ORSA Model Act or substantially similar legislation.

Cybersecurity and Privacy. The NAIC has adopted an Insurance Data Security Model Law, requires insurers, insurance producers and other entities required to be licensed

under state insurance laws to comply with certain requirements under state insurance laws, such as developing and maintaining a written information security program, conducting risk assessments and overseeing the data security practices of third-party vendors and meeting expanded breach notification requirements. This model law has been adopted in states in which our U.S. subsidiaries are licensed and operate. In addition, certain state insurance regulators are developing or have developed regulations that may impose regulatory requirements relating to cybersecurity on insurance and reinsurance companies (potentially including insurance and reinsurance companies that are not domiciled, but are licensed, in the relevant state). Many regulators, including the Federal Trade Commission (“FTC”), the New York Department of Financial Services (“NYDFS”), and the U.S. Department of the Treasury’s Office of Foreign Assets Control (“OFAC”), have issued new guidance on managing cybersecurity risks which expand existing regulatory requirements. Additional guidance and rules relating cybersecurity that are applicable to us are expected, especially from NYDFS.

In March 2022, the U.S. government passed the Cyber Incident Reporting for Critical Infrastructure Act of 2022, which will require companies deemed to be part of U.S. critical infrastructure to report any substantial cybersecurity incidents or ransom payments to the federal government within 72 and 24 hours, respectively. The implementing regulations are not expected for another two-to-three years. In addition, on March 9, 2022, the SEC proposed amendments to certain rules regarding cybersecurity disclosure in order to standardize and enhance disclosures made by public companies. Such rulemaking undertakes to expand security incident reporting requirements and may subject public companies to additional and uncertain requirements in the event of an actual or perceived security incident.

Privacy legislation and regulation has also become an issue of increasing focus in many states. The California Consumer Privacy Act of 2018 (“CCPA”), came into effect on January 1, 2020, and grants California consumers certain rights to, among other things, access and delete data about them subject to certain exceptions, as well as a private right of action related to cybersecurity breaches with statutory penalties. Additionally, the California Privacy Rights Act of 2020 (“CPRA”) passed as part of the November 2020 ballot and became fully effective on January 1, 2023. The CPRA applies to some of our data collecting and processing activities, and it provides for additional consumer privacy rights, and additional regulatory obligations over certain data. It also created a new privacy focused California regulatory agency with enforcement authority, the California Privacy Protection Agency (“CPPA”). The CPPA is also currently finalizing proposed regulations implementing the CPRA, and

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is mandated by the CPRA to adopt additional regulations that have yet to be proposed.

A range of new cybersecurity and privacy laws are also under consideration in other states, as well as by the federal government. The American Data Privacy and Protection Act introduced in the U.S. Congress, if enacted, would also apply to our U.S. operations. Several states, including Virginia, Colorado, Connecticut and Utah, have adopted new comprehensive data privacy legislation that is coming into effect in 2023. While these state laws provide consumer privacy rights and protections like those in the CCPA and CPRA, they exempt entities subject to the Gramm-Leach-Bliley Act from their requirements.

Risk-Based Capital Requirements. Licensed U.S. property and casualty insurance and reinsurance companies are subject to risk-based capital requirements that are designed to assess capital adequacy and to raise the level of protection that statutory surplus provides for policyholder obligations. The risk-based capital model for property and casualty insurance companies measures three major areas of risk facing property and casualty insurers: underwriting, which encompasses the risk of adverse loss developments and inadequate pricing; declines in asset values arising from credit risk; and declines in asset values arising from investment risks. An insurer will be subject to varying degrees of regulatory action depending on how its statutory surplus compares to its risk-based capital calculation. Under the approved formula, an insurer’s total adjusted capital is compared to its authorized control level risk-based capital. If this ratio is above a minimum threshold, no company or regulatory action is necessary. Below this threshold are four distinct action levels at which an insurer’s domiciliary state regulator can intervene with increasing degrees of authority over an insurer as the ratio of surplus to risk-based capital requirement decreases. The mildest regulatory action requires an insurer to submit a plan for corrective action; the most severe requires an insurer to be rehabilitated or liquidated.

Our mortgage insurance operations are not currently subject to state risk-based capital requirements, but rather are subject to state risk to capital or minimum policyholder position requirements. The NAIC has established a Mortgage Guaranty Insurance Working Group which is engaged in developing changes to the Mortgage Guaranty Insurers Model Act, including the development of supplemental disclosures schedules unique to mortgage guaranty insurers.

Guaranty Funds. Most states require all admitted insurance companies to participate in their respective guaranty funds which cover certain claims against insolvent insurers. Solvent insurers licensed in these states are required to cover the losses paid on behalf of insolvent insurers by the guaranty funds and are generally subject to annual assessments in the states by the guaranty funds to cover these losses. Mortgage

guaranty insurance, among other lines of business, is typically exempt from participation in guaranty funds.

Climate Change and Financial Risks. U.S. state insurance regulators have increased their oversight of insurance company governance, reporting and disclosure relating to the potential risks presented by climate change and one or more states may adopt climate-change-related requirements that impact our insurance and reinsurance companies. In 2020, NYDFS issued a circular letter stating that NYDFS expects insurers authorized in New York to integrate the consideration of climate risks into their governance frameworks, risk management processes and business strategies, including the designation of a board committee or member and senior management function to be accountable for the company’s assessment and management of the financial risks from climate change. In 2021, NYDFS issued additional Guidance for New York Domestic Insurers on Managing the Financial Risks from Climate Change that reiterates many of the principles outlined in the 2020 circular letter. New York and other states also require licensed insurers with countrywide premium written of at least $100 million to annually provide disclosure of their assessment and management of climate related risks.

Federal Regulation. Although state regulation is the dominant form of regulation for insurance and reinsurance business, a number of federal laws affect and apply to the insurance industry. The Dodd-Frank Wall Street Reform and Consumer Protection Act of 2010 (“Dodd-Frank”) created the Federal Insurance Office (“FIO”) within the Department of Treasury (“U.S. Treasury”), which is not a federal regulator or supervisor of insurance, but monitors the insurance industry for systemic risk, administers the Terrorism Risk Insurance Program (“TRIP”), consults with the states regarding insurance matters, develops federal policy on aspects of international insurance matters, and is authorized to assist the U.S. Secretary of the Treasury in negotiating “covered agreements” between the U.S. and foreign governments that address insurance prudential measures. In 2022 and 2021, the FIO requested public comment on insurance responses to climate-related financial risks and catastrophic cyber incidents affecting critical infrastructure. This information gathering could culminate in recommendations for new legislation to the U.S. Congress. On October 18, 2022, the FIO issued a proposed data collection from insurers to assess climate related financial risk across the United States. See “Risk Factors—Risks Relating to Our Industry, Business and Operations—We could face unanticipated losses from war, terrorism, cyber attacks, pandemics and political instability, and these or other unanticipated losses could have a material adverse effect on our financial condition and results of operations” for more information on TRIP.

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Certain other federal laws also directly or indirectly impact mortgage insurers, including the Real Estate Settlement Procedures Act of 1974, the Homeowners Protection Act of 1998, the Equal Credit Opportunity Act, the Fair Housing Act, the Truth In Lending Act, the Fair Credit Reporting Act of 1970, and the Fair Debt Collection Practices Act. Among other things, these laws and their implementing regulations prohibit payments for referrals of settlement service business, require fairness and non-discrimination in granting or facilitating the granting of credit, govern the circumstances under which companies may obtain and use consumer credit information, define the manner in which companies may pursue collection activities, and require disclosures of the cost of credit and provide for other consumer protections.

GSE Eligible Mortgage Insurer Requirements. GSEs impose requirements on private mortgage insurers so that they may be eligible to insure loans sold to the GSEs, known as the Private Mortgage Insurer Eligibility Requirements (“PMIERs”). The PMIERs apply to our eligible mortgage insurers, but do not apply to Arch Mortgage Guaranty Company, which is not GSE-approved. The PMIERs impose limitations on the type of risk insured, the forms and insurance policies issued, standards for the geographic and customer diversification of risk, procedures for claims handling, acceptable underwriting practices, standards for certain reinsurance cessions and financial requirements, among other things. The financial requirements require an eligible mortgage insurer’s available assets, which generally include only the most liquid assets of an insurer, to meet or exceed “minimum required assets” as of each quarter end. Minimum required assets are calculated from PMIERs tables with several risk dimensions (including origination year, original loan-to-value, original credit score of performing loans, and the delinquency status of non-performing loans).

Russian Sanctions. The U.S. first imposed sanctions on the Russian Federation following its annexation of Crimea in 2014. Since February 2022, the U.S. has imposed additional sanctions on Russia in response to the Russian invasion of Ukraine and the ongoing hostilities. Given the evolving situation, we are closely monitoring developments and the sanctions imposed, to ensure our business remains in compliance with any applicable sanctions measures imposed.

Canada

Arch Insurance Canada and Arch Re Canada are subject to federal, as well as provincial and territorial, regulation in Canada in the provinces and territories in which they underwrite insurance/reinsurance. The Office of the Superintendent of Financial Institutions (“OSFI”) is the federal regulatory body that, under the Insurance Companies Act (Canada), prudentially regulates federal Canadian and non-Canadian insurance and reinsurance companies operating in Canada. Arch Insurance Canada is licensed to

carry on insurance business by OSFI and in each province and territory. Arch Re Canada is licensed to carry on reinsurance business by OSFI and in the provinces of Ontario and Quebec.

Under the Insurance Companies Act (Canada), Arch Insurance Canada is required to maintain an adequate amount of capital in Canada, calculated in accordance with a test promulgated by OSFI called the Minimum Capital Test, and Arch Re Canada is required to maintain an adequate margin of assets over liabilities in Canada, calculated in accordance with a test promulgated by OSFI called the Branch Adequacy of Assets Test. OSFI has implemented a risk-based methodology for assessing insurance/reinsurance companies operating in Canada known as its “Supervisory Framework.” In applying the Supervisory Framework, OSFI considers the inherent risks of the business and the quality of risk management for each significant activity of each operating entity. Under the Insurance Companies Act (Canada), approval of the Minister of Finance (Canada) is required in connection with certain acquisitions of shares of, or control of, Canadian insurance companies such as Arch Insurance Canada, and notice to and/or approval of OSFI is required in connection with the payment of dividends by or redemption of shares by Canadian insurance companies such as Arch Insurance Canada.

United Kingdom

General. The Prudential Regulation Authority (“PRA”) and the Financial Conduct Authority (“FCA”) regulate insurance and reinsurance companies and the FCA regulates firms carrying on insurance distribution activities operating in the U.K. under the Financial Services and Markets Act 2000 (the “FSMA”). In May 2004, Arch Insurance (U.K.) was granted the relevant permissions for the classes of insurance business which it underwrites in the U.K. AMAL currently manages Arch Syndicate 2012 and Arch Syndicate 1955 pursuant to its authorizations by the U.K. regulators and Lloyd’s. All U.K. companies are also subject to a range of statutory provisions, including the laws and regulations of the Companies Act 2006 (as amended) (the “U.K. Companies Act”).

The objectives of the PRA are to promote the safety and soundness of all firms it supervises and to secure an appropriate degree of protection for policyholders. The objectives of the FCA are to ensure customers receive financial services and products that meet their needs, to promote sound financial systems and markets and to ensure that firms are stable and resilient with transparent pricing information and which compete effectively and have the interests of their customers and the integrity of the market at the heart of how they run their business. The PRA has responsibility for the prudential regulation of banks and insurers, while the FCA has responsibility for the conduct of business regulation in the wholesale and retail markets. The

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PRA and the FCA adopt separate methods of assessing regulated firms on a periodic basis. Arch Insurance (U.K.) and AMAL are subject to periodic assessment by the PRA along with all regulated firms. Arch Insurance (U.K.) and AMAL are subject to regulation by both the PRA and FCA. Castel is authorized and regulated by the FCA and is subject to periodic assessment and review by the FCA.

Lloyd’s Supervision. The operations of AMAL (as managing agent of Arch Syndicate 2012 and Arch Syndicate 1955) and each syndicate’s respective corporate members, are subject to the byelaws and regulations made by (or on behalf of) the Council of Lloyd’s, and requirements made under those byelaws. The Council of Lloyd’s, established in 1982 by Lloyd’s Act 1982, has overall responsibility and control of Lloyd’s. Those byelaws, regulations and requirements provide a framework for the regulation of the Lloyd’s market, including specifying conditions in relation to underwriting and claims operations of Lloyd’s participants. The Council of Lloyd’s has discretionary powers to regulate corporate members’ underwriting at Lloyd’s. Lloyd’s is also subject to the provisions of the FSMA. Lloyd's is authorized by the PRA and regulated by the PRA and FCA. Those entities acting within the Lloyd’s market are required to comply with the requirements of the FSMA and provisions of the PRA’s or FCA's rules, although the PRA has delegated certain of its powers, including some of those relating to prudential requirements, to Lloyd’s. Each corporate member of Lloyd’s is required to contribute a percentage of the member’s premium income for each year of account to the Lloyd’s central fund. The Lloyd’s central fund is available if members of Lloyd’s assets are not sufficient to meet claims for which the member is liable. Each corporate member of Lloyd’s may also be required to contribute to the central fund by way of a supplement to a callable layer of up to 5% of the corresponding member’s premium income limit for the relevant year of account.

Principles for doing business at Lloyd’s (the “Principles”) replaced the Lloyd’s Minimum Standards (the previous regime which set out the Lloyd’s regulatory requirements for Lloyd’s managing agents) and became effective from the third quarter of 2022. The Principles set out the fundamental responsibilities expected of all managing agents, including AMAL, and is the basis against which Lloyd’s will review and categorize all syndicates and managing agents in terms of their capacity and performance. While offering greater flexibility, the principles-based oversight requires greater reliance on AMAL to interpret and apply the rules.

Financial Resources. The European solvency framework and prudential regime for insurers and reinsurers, the Solvency II Directive 2009/138/EC (“Solvency II”), took effect in full on January 1, 2016. See “European Union—Insurance and Reinsurance Regulatory Regime” below for additional details.

Arch Insurance (U.K.), and the corporate members of Arch Syndicate 2012 and Arch Syndicate 1955 are currently required to meet economic risk-based solvency requirements imposed under Solvency II. Solvency II, together with European Commission “delegated acts” and guidance issued by the European Insurance and Occupational Pensions Authority (“EIOPA”) sets out classification and eligibility requirements, including the features which capital must display in order to qualify as regulatory capital.

On January 31, 2020, the U.K. withdrew from the EU with the terms of Brexit set forth in the Withdrawal Agreement agreed by the U.K. Parliament and the EU Parliament. At the expiration of the transition period from January 31, 2020 until December 31, 2020 (the “Transition Period”), during which time the U.K. remained in the EU customs union and single market, the European Union (Withdrawal) Act 2018, as amended, has transposed all applicable direct EU legislation into domestic U.K. law, thus ensuring the continuing application of Solvency II under the U.K.’s financial services regulatory regime.

The U.K. government commenced a post-Brexit review of Solvency II in June 2020. The response to the review, published in early July 2021, suggested that there will likely be changes in the U.K. Solvency II framework, including the removal of certain prescriptive requirements. In parallel, the PRA also undertook a review of Solvency II and, launched a quantitative study which contained both quantitative studies and qualitative questions intended to guide future reforms of Solvency II in the U.K. Additionally, the U.K. government had undertaken a Future Regulatory Framework Review to determine how the financial services regulatory framework should adapt to the U.K.’s new position outside of the EU. On April 28, 2022, HM Treasury announced a third consultation period for Solvency II, which will inform the design of the final reform package. In HM Treasury’s consultation response, published on November 17, 2022, the government stated it will introduce a simpler, clearer and more tailored regime. Significant changes to be introduced by these reforms include the proposal to reduce the risk margin component of the solvency capital calculation by 30% for general insurers and remove branch capital requirements.

In January 2022, the U.K. Parliament, via its Industry and Regulators Committee (the “Committee”), launched an inquiry into the U.K. insurance and reinsurance industry and, specifically, into the regulation of the London market, the U.K.’s market for commercial and wholesale specialty risks. The inquiry reviewed the extent to which regulatory policy is well-designed and proportionately applied, the possibilities for optimizing policy following Brexit, the roles of the current U.K. regulators, such as the FCA and the Bank of England, as well as the appropriateness of regulation. Following its enquiry, the Committee outlined industry

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concerns regarding a perceived lack of proportionality in the regulation of the London Market by the PRA and FCA, which was described as overly burdensome and demanding. The Committee explained industry concerns that an overly inflexible culture within the regulators may inhibit new forms of business within the U.K.’s commercial (re)insurance industry. The result of these reviews by the U.K. government may have an impact on whether the U.K. is granted Solvency II equivalence status by the EU in any of the three areas to which equivalence applies.

Financial Services Compensation Scheme. The Financial Services Compensation Scheme (“FSCS”) is a scheme established under FSMA to compensate eligible policyholders of insurance companies who may become insolvent. The FSCS is funded by the levies that it has the power to impose on all insurers. Arch Insurance (U.K.) could be required to pay levies to the FSCS.

Restrictions on Acquisition of Control. Under FSMA, the prior consent of the PRA or FCA, as applicable, is required, before any person can become a controller or increase its control over any regulated company, including Arch Insurance (U.K.), or over the parent undertaking of any regulated company. Therefore, the PRA's or FCA's prior consent, as applicable, is required before any person can become a controller of Arch Capital. Prior consent is also required from Lloyd’s before any person can become a controller or increase its control over a corporate member or a managing agent or a parent undertaking of a corporate member or managing agent. A controller is defined for these purposes as a person who holds (either alone or in concert with others) 10% or more of the shares or voting power in the relevant company or its parent undertaking.

Restrictions on Payment of Dividends. Under English law, all companies are restricted from declaring a dividend to their shareholders unless they have “profits available for distribution.” The calculation as to whether a company has sufficient profits is based on its accumulated realized profits minus its accumulated realized losses. U.K. insurance regulatory laws do not prohibit the payment of dividends, but the PRA or FCA, as applicable, requires that insurance companies, insurance intermediaries and other regulated entities maintain certain solvency margins and may restrict the payment of a dividend by Arch Insurance (U.K.), AMAL or Castel, for example.

European Union Considerations. During the Transition Period, there was no change in passporting rights for financial institutions in the U.K. Under our Brexit plan, since January 2020 nearly all of the EEA insurance business of Arch Insurance (U.K.) has been conducted by Arch Insurance (EU). As part of our Brexit planning, and in advance of the Transition Period expiring, a transfer of the EEA legacy business (excluding inwards reinsurance) from Arch

Insurance (U.K.) to Arch Insurance (EU) was completed under Part VII of the U.K. Financial Services and Market Act 2000 at the end of December 2020 (“Part VII Transfer”).

Despite the loss of passporting rights, AMAL, Syndicate 2012 and Syndicate 1955 are still able to write business in the EEA via the Lloyd’s Insurance Company, S.A. (“Lloyd’s Brussels”). Lloyd’s has been in discussions with the Belgium Financial Services Markets Authority (“Belgium FSMA”) and the National Bank of Belgium regarding the Lloyd’s Brussels operating model. In January 2021, Lloyd’s released a communication stating that its discussions with supervisors had focused on certain risk placement services for open market business which was being performed by managing agents on behalf of Lloyd’s Brussels. Lloyd’s Brussels is in an ongoing dialogue with the Belgium FSMA in its effort to overhaul its initial underwriting structures and is deploying significant efforts and investment to adjust its operating model to satisfy the Belgian authority in the post-Brexit environment. This may have an impact on the way managing agents and syndicates access and operate on the Lloyd’s platform. Lloyd’s Brussels is seeking to ensure that the claims it pays and complaints it processes preserve the objectives of policyholder protection and market discipline under the Insurance Distribution Directive.

The U.K. government established a Temporary Permissions Regime (“TPR”) which came into force with effect from January 1, 2021, which allows EEA firms such as Arch Re Europe and Arch Insurance (EU), covered by a passport prior to that date, who wish to continue carrying out business in the U.K. in the longer term, to operate in the U.K. for a limited period while they seek authorization or recognition from the U.K. regulators. However, no TPR-equivalent regime is in place for U.K. firms who wish to continue carrying out business in the EEA. In the absence of a TPR-equivalent regime for U.K. firms, the ability of U.K. firms (including, Arch Insurance (U.K.), AMAL and Castel) to continue doing business in the EEA depends on applicable EEA state local law and regulation. Similarly, there has been no decision yet made by the European Commission on whether or not the U.K.’s financial services regulatory regime will be granted third-country equivalence for the purposes of reinsurance, solvency calculation and/or group supervision under Solvency II. In the absence of such declarations, U.K. firms are subject to more stringent requirements in carrying out reinsurance business with EEA firms.

The long-term implications of Brexit on the Solvency II framework in the U.K. continues to remain uncertain in relation to the arrangements that will allow U.K. and EU-established firms to continue to effectively transact business with each other and how the future relationship between the two parties will adversely affected regulated entities. See

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“Risk Factors—Risks Relating to Our Industry, Business and Operations—New legislation or regulations relating to the U.K.’s withdrawal from the EU could adversely affect us.”

On December 24, 2020, the EU and the U.K. agreed the EU-U.K. Trade Cooperation Agreement (the “TCA”) which details the terms of the future cooperation between the U.K. and the EU. The TCA was signed by both the EU and U.K. on December 30, 2020 and entered into force on May 1, 2021. The TCA did not preserve the status of financial services and as a result, under the provisions of the TCA, EEA financial institutions (including our Irish operating subsidiaries) lost their passporting rights into the U.K. Absent any future agreement between the U.K. and the EU on the provision of financial services by U.K. financial institutions into the EU, the post-Brexit status and rules applicable to U.K. branches of EEA financial institutions will be primarily driven by U.K. law and regulation. See “Risk Factors—Risks Relating to Our Industry, Business and Operations—New legislation or regulations relating to the U.K.’s withdrawal from the EU could adversely affect us.”

In February 2022, a U.K.-EU Financial Services inquiry was launched by the U.K. Parliament. The European Affairs Committee (“EA Committee”) published the report in June 2022, finding that the TCA contains only limited provisions relating to insurance and financial services and raising concerns about the lack of a functioning framework for U.K.-EU co-operation. The report also found an absence of EU equivalence decisions over financial services, which will determine how London will fit into the EU market post-Brexit. Overall, the EA Committee called on the U.K. government to step up its political and diplomatic engagement with the EU regarding financial services. In June 2022, the Treasury Select Committee announced the formation of a subcommittee to scrutinize proposed post-Brexit financial regulations in the U.K., replacing the role previously held by the EU. See “Risk Factors—Risks Relating to Our Industry, Business and Operations—New legislation or regulations relating to the U.K.’s withdrawal from the EU could adversely affect us.”

ESG Considerations. The U.K. government has a long-term ambition to “green” the financial system and align it with the U.K.’s 2050 “Net Zero” target (i.e.,100% greenhouse gas emissions reduction) under the Climate Change Act 2008. As part of those efforts, on January 17, 2022, the U.K. passed mandatory climate related financial disclosure requirements under the Companies (Strategic Report) (Climate-related Financial Disclosure) Regulations 2022. The regulations apply to large companies (including some of our U.K. entities) for financial years starting on or after April 6, 2022. The regulations generally align risk disclosures (aligned with the recommendations of the Taskforce on Climate-related Financial Disclosures (“TCFD”)).

In 2021, the U.K. government published its Greening Finance Roadmap to Sustainable Investing (the “Roadmap”), which announced proposals to extend the scope of the U.K.’s sustainable finance framework beyond climate change. Further to the Roadmap, the FCA issued a consultation paper in November 2022 on its proposed regime of Sustainability Disclosure Requirements (“SDR”), which would require corporate disclosures, asset manager and asset owner disclosures, and investment product disclosures covering a broader range of sustainability topics. The SDR rules are expected to be finalized in the first half of 2023, with disclosures applying from 2024 and reporting commencing in 2025.

In October 2022, the Green Technical Advisory Group ("GTAG") published its advice to the U.K. government on the development of the U.K. Green Taxonomy. Whilst not binding, the GTAG advice gives a likely indication as to what the U.K. Green Taxonomy may look like and how it might differ from the EU Sustainable Finance Taxonomy Regulation (“EU Taxonomy”). The GTAG report notes that the primary focus of the U.K. Green Taxonomy should be on investors and financial market participants and, as many U.K. financial market participants will also be subject to the EU Taxonomy, the U.K. should ensure close alignment with the EU Taxonomy so as to limit divergence and market fragmentation. If the GTAG advice is adopted, the U.K. Green Taxonomy should align with the EU Taxonomy except where doing so impact the simplicity or usability of the activity classification system or increases the risk of greenwashing.

On December 14, 2022, the U.K. Government said it would delay secondary legislation under the taxonomy regulations (originally anticipated by the end of 2022). Instead, the U.K. will restate EU law around the taxonomy and take another year to decide the U.K.’s approach. In addition, Lloyd’s has mandated that managing agents must create an ESG framework and strategy, for sign-off in the 2023 business planning cycle. Lloyd’s has also imposed ESG focused outcomes by way of the Principles with a particular focus on culture, investment and underwriting profitability. See “Lloyd’s Supervision” above for additional details.

Russian Sanctions. Since the Russian invasion of Ukraine in February 2022, the U.K. government has instituted a new sanctions regime targeting Russia. The sanctions imposed include prohibitions on providing financial services (including insurance and reinsurance) to persons connected with Russia in relation to certain restricted goods and services, and the freezing of assets owned or controlled by designated persons. The U.K., U.S. and EU often consult with each other with respect to their respective sanctions programs.

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Ireland

General. The CBI regulates insurance and reinsurance companies and intermediaries authorized in Ireland. Our three Irish operating subsidiaries are Arch Re Europe, Arch Insurance (EU) and Arch Underwriters Europe Limited (“Arch Underwriters Europe”). Arch Re Europe was licensed and authorized by the CBI as a non-life reinsurer in October 2008 and as a life reinsurer in November 2009. Arch Insurance (EU) was licensed and authorized by the CBI as a non-life insurer in December 2011. As part of our Brexit plan, Arch Insurance (EU) received approval from the CBI to expand the nature of its business in 2019 and commenced writing expanded insurance lines in the EEA in 2020 with the Part VII Transfer completed at the end of December 2020. Arch Underwriters Europe was registered by the CBI as an insurance and reinsurance intermediary in July 2014. Arch Re Europe, Arch Insurance (EU) and Arch Underwriters Europe are subject to the supervision of the CBI and must comply with Irish insurance acts and regulations as well as with directions and guidance issued by the CBI.

Arch Re Europe and Arch Insurance (EU) are required to comply with Solvency II requirements. See “European Union —Insurance and Reinsurance Regulatory Regime” below for additional details. As an intermediary, Arch Underwriters Europe is subject to a different regulatory regime and is not subject to solvency capital rules but must comply with requirements such as to maintain professional indemnity insurance and to have directors that are fit and proper. Our Irish subsidiaries are also subject to the general body of Irish company laws and regulations including the provisions of the Companies Act 2014.

Financial Resources. Arch Re Europe and Arch Insurance (EU) are required to meet economic risk-based solvency requirements imposed under Solvency II. Solvency II, together with European Commission “delegated acts” and guidance issued by EIOPA sets out classification and eligibility requirements, including the features which capital must display in order to qualify as regulatory capital.

Restrictions on Acquisitions. Under Irish law, the prior consent of the CBI is required before any person can acquire or increase a qualifying holding in an Irish insurer or reinsurer, including Arch Insurance (EU) and Arch Re Europe, or their parent undertakings. A qualifying holding is defined for these purposes as a direct or indirect holding that represents 10% or more of the capital of, or voting rights, in the undertaking or makes it possible to exercise a significant influence over the management of the undertaking.

Restrictions on Payment of Dividends. Under Irish company law, Arch Re Europe, Arch Insurance (EU) and Arch Underwriters Europe are permitted to make distributions only out of profits available for distribution. A company’s profits

available for distribution are its accumulated, realized profits, so far as not previously utilized by distribution or capitalization, less its accumulated, realized losses, so far as not previously written off in a reduction or reorganization of capital duly made. Further, the CBI has powers to intervene if a dividend payment were to lead to a breach of regulatory capital requirements.

In response to the COVID-19 pandemic, the CBI issued guidance in April 2020, based on guidance issued by EIOPA, that insurance firms postpone any payment of dividend distributions or similar transactions until they can forecast their costs and future revenues with a greater degree of certainty. However, the CBI modified its guidance, with effect from October, 1 2021, so that the general restrictions on the payment of dividend distributions or variable remuneration are no longer in place. The CBI still requires (re)insurance firms to notify it in advance of any proposed distribution.

European Union Considerations. As Arch Re Europe, Arch Insurance (EU) and Arch Underwriters Europe are authorized by the CBI in Ireland, a Member State of the EU, those authorizations are recognized throughout the EEA. Subject only to certain notification and application requirements, Arch Re Europe, Arch Insurance (EU) and Arch Underwriters Europe can provide services, or establish a branch, in any other Member State of the EEA. Although, in doing so, they may be subject to the laws of such Member States with respect to the conduct of business in such Member State, company law registrations and other matters, they will remain subject to financial and operational supervision by the CBI only. Arch Insurance (EU) has branches in Italy and the U.K. Arch Re Underwriting ApS in Denmark (“Arch Re Denmark”) is an underwriting agency underwriting accident and health and other reinsurance business for Arch Re Europe. Arch Re Europe also has branches in the U.K. and Switzerland (“Arch Re Europe Swiss Branch”).

From January 1, 2021, under the provisions of the TCA our Irish regulated entities have lost their passporting rights into the U.K. See “Risk Factors—Risks Relating to Our Industry, Business and Operations—New legislation or regulations relating to the U.K.’s withdrawal from the EU could adversely affect us.”

ESG Considerations. ESG matters have been on the CBI's agenda for a number of years. In November 2021, the CBI issued its expectations in respect of climate and broader ESG issues for all regulated firms in Ireland (including (re)insurers). The CBI's expectations focus on five key areas: governance, risk management, scenario analysis (including, but not limited to, stress testing for the purposes of the ORSA), disclosures and strategy and business model risk. The CBI has indicated that its expectations will be applied in

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a proportionate manner. In August 2022, the CBI published a Consultation Paper setting out its proposed guidance on climate change risk for the (re)insurance sector. The proposed guidance clarifies the CBI’s expectations on how (re)insurers should address climate change risks in their business and to assist (re)insurers develop their governance and risk management frameworks to do this. It is expected that over time, disclosures in respect to ESG matters may be captured in the Solvency and Financial Condition Reports of Arch's Irish entities. While this guidance is currently in draft format, Arch is closely monitoring its development given the potential impact it may have on Arch's Irish entities. See also “European Union – ESG Considerations.”

Irish Individual Accountability Framework Bill. The Central Bank (Individual Accountability Framework) Bill 2022 (the “Bill”) was published in July 2022 and legislative scrutiny of the Bill is ongoing in the Irish parliament. This Bill proposes substantive changes to the fitness and probity regime maintained by the CBI in Ireland and imposes certain additional obligations and liability for senior executives in Irish regulated financial service entities, including (re)insurance companies. The Bill is expected to come into effect in late 2023 or early 2024. See also “European Union – ESG Considerations.”

European Union

Insurance and Reinsurance Regulatory Regime. Solvency II took effect in full on January 1, 2016. Solvency II imposes economic risk-based solvency requirements across all EU Member States and consists of three pillars: Pillar I-quantitative capital requirements, based on a valuation of the entire balance sheet; Pillar II-qualitative regulatory review, which includes governance, internal controls, enterprise risk management and supervisory review process; and Pillar III-market discipline, which is accomplished through reporting of the insurer’s financial condition to regulators and the public. Solvency II is supplemented by European Commission Delegated Regulation (EU) 2015/35 (the “Delegated Regulation”), other European Commission “delegated acts” and binding technical standards, and guidelines issued by EIOPA. The Delegated Regulation sets out more detailed requirements for individual insurance and reinsurance undertakings, as well as for groups, based on the overarching provisions of Solvency II, which together make up the core of the single prudential rulebook for insurance and reinsurance undertakings in the EU.

In December 2020, EIOPA provided an opinion to the European Commission in relation to the review of the Solvency II regime. This review was initiated by the European Commission to determine if the Solvency II regime remains fit for purpose. In its opinion, EIOPA confirms that the overall Solvency II framework is working well from a prudential perspective, suggesting that there are no

fundamental changes needed but that a number of amendments are required to ensure the regime continues as a well-functioning risk-based regime. In September 2021, the European Commission published legislative proposals for amendments to the Solvency II Directive arising out of EIOPA's review of the Solvency II regime. The proposed amendments cover a number of areas including proportionality, quality of supervision, sustainability risks and group and cross-border supervision. The European Parliament and the Council will consider the proposed amendments and it is anticipated that the amendments will be approved and in force by 2023 or 2024.

In addition to the above Solvency II reform proposals, the European Commission continues to promote the development of the Insurance Recovery and Resolution Directive (“IRRD”). The proposal aims to harmonize national laws on recovery and resolution of (re)insurance undertakings. Political agreement on the IRRD should be reached by the EU Council and Parliament in 2023 and the Directive is likely to enter into force in late 2023 or in 2024.

Following entry into the TCA by the U.K. and the EU, and the U.K.’s withdrawal from the EU under the provisions of the TCA, U.K. financial institutions have lost their passporting rights into the EU. It was originally envisaged that there would be a level of cooperation in relation to financial services, to be reflected in a Memorandum of Understanding between the U.K. and the EU. However, while the text of the Memorandum of Undertaking has been agreed in principle, a formal version has not yet been published. Additionally, in early February 2023, EIOPA issued its finalized Supervisory Statement on the use by EU-authorized (re)insurers of governance arrangements (such as branches) in third countries to perform functions or activities in respect of EU policyholders and risks. Arch is assessing the impact of the Supervisory Statement on its EU operations. See “Risk Factors—Risks Relating to Our Industry, Business and Operations—New legislation or regulations relating to the U.K.’s withdrawal from the EU could adversely affect us.”

Arch Re Europe and Arch Insurance (EU), being established in Ireland and authorized by the CBI, are able to establish branches and provide reinsurance services, subject to similar regulatory notifications and there being no objection from the CBI and the Member States concerned and, in respect of Arch Insurance (EU), insurance services in all EEA states.

Solvency II does not prohibit EEA insurers from obtaining reinsurance from reinsurers licensed outside the EEA, such as Arch Re Bermuda. As such, and subject to the specific rules in each Member State, Arch Re Bermuda may do business from Bermuda with insurers in EEA Member States, but it may not directly operate its reinsurance business within the EEA. Article 172 of Solvency II provides that reinsurance

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contracts concluded by insurance undertakings in the EEA with reinsurers having their head office in a country whose solvency regime has been determined to be equivalent to Solvency II shall be treated in the same manner as reinsurance contracts with undertakings in the EEA authorized under Solvency II. From January 1, 2016, Bermuda was deemed by the European Commission to be equivalent for Solvency II purposes. Solvency II also includes specific measures providing for the supervision of insurance and reinsurance groups. However, as a consequence of the above determination of equivalence, pursuant to Article 260 of Solvency II, regulators within the EEA are required to rely on the worldwide group supervision exercised by the BMA. EIOPA has also indicated that, on a case by case basis, groups subject to this worldwide supervision may be exempted from any EEA sub-group supervision, where this results in more efficient supervision of the group and does not impair EEA supervisors in respect of their individual responsibilities.

The Insurance Distribution Directive (“IDD”) was published in February 2016. EEA Member States were required to transpose the IDD by October 1, 2018. It replaces the existing Insurance Mediation Directive. The IDD applies to all distributors of insurance and reinsurance products (including insurers and reinsurers selling directly to customers) and strengthens the regulatory regime applicable to distribution activities through increased transparency, information and conduct requirements. The principal impact of the IDD is on the insurance market, however, requirements that apply across insurance and reinsurance include more specific conditions regarding knowledge and continuing professional development requirements for those involved in distribution of (re)insurance products. The IDD continues the existing ability for intermediaries established in a Member State of the EU to establish branches and provide services to all EEA states. Arch Underwriters Europe, being established in Ireland and authorized by the CBI, is able, subject to regulatory notifications and there being no objection from the CBI, to establish branches and provide services in all EEA states.

Privacy. The European General Data Protection Regulation (the “EU GDPR”) came into effect on May 25, 2018. The EU GDPR governs the collection, use, disclosure, transfer or other processing of personal data, and its scope extends to certain entities not established in the EEA if they process personal data or offer goods or services to, or monitor the behavior of, EEA data subjects. The EU GDPR contains a number of requirements regarding the processing of personal data about individuals, including mandatory security breach reporting, new and strengthened individual rights, evidenced data controller accountability for compliance with the GDPR principles (including fairness and transparency), maintenance of data processing activity records and the implementation of “privacy by design,” including through the completion of

mandatory Data Protection Impact Assessments in connection with higher risk data processing activities.

In addition, the EU GDPR increases scrutiny of transfers of personal data to jurisdictions which the European Commission does not recognize as having “adequate” data protection laws. In particular, on July 16, 2020, the Court of Justice of the EU (Court of Justice) in Schrems II invalidated the European Union-United States (EU-U.S.) Privacy Shield on the grounds that the EU-U.S. Privacy Shield failed to offer adequate protections to EU personal information transferred to the U.S. While the Court of Justice upheld the use of other data transfer mechanisms, such as the Standard Contractual Clauses (“SCCs”), the decision has led to some uncertainty regarding the use of such mechanisms for data transfers to the U.S. and the Court of Justice made clear that reliance on SCCs alone may not necessarily be sufficient in all circumstances. The European Data Protection Board issued additional guidance regarding international transfers which may require us to implement additional safeguards to further enhance the security of data transferred out of the EEA and the European Commission published new versions of the SCCs in June 2021, which place onerous obligations on the parties. On October 7, 2022, the U.S. President introduced an Executive Order to facilitate a new Trans-Atlantic Data Privacy Framework which will act as a successor to the invalidated EU-U.S. Privacy Shield. If approved by the European Commission and implemented, the agreement will facilitate the transatlantic flow of personal data and provide additional safeguards to any existing data transfer mechanisms (including SCCs) for companies transferring personal data from the EU to the U.S. However, before entities rely on the new EU-U.S. Privacy Shield, there are still legislative and regulatory steps that must be undertaken both in the U.S. and in the EU. Therefore, at present SCCs are still the primary safeguard available for personal data transfers from the EU to the U.S.

The EU GDPR imposes substantial fines for breaches and violations (up to the greater of €20 million or 4% of global turnover). The EU GDPR allows data subjects and consumer associations to lodge complaints with supervisory authorities, seek judicial remedies and obtain compensation for damages resulting from violations of the EU GDPR.

Following the end of the Transition Period on December 31, 2020, GDPR was implemented in the U.K. (the “U.K. GDPR”) with similar fines for non-compliance. The requirements of the U.K. GDPR are virtually identical to those of the EU GDPR, including the prohibition on the transfer of personal data from the U.K. to other countries that are not recognized as having “adequate” data protection laws, including the U.S., in a similar manner to the EU. Transfers of personal data from the U.K. to the EEA are unrestricted and do not require additional safeguards. In June, 2021 the European Commission formally adopted an adequacy

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decision for the U.K., meaning data can flow freely from the EU to the U.K. This adequacy decision will remain in place for four years (until June 27, 2025) after which the adequacy decision may be renewed if the U.K. continues to ensure an adequate level of data protection. However, the European Commission retains the power to suspend, repeal or amend the adequacy decision if the U.K. deviates from the level of protection currently in place. In addition, the U.K. government has published its own form of SCCs, known as the International Data Transfer Agreement and International Data Transfer Addendum to the EU SCCs. The U.K. Information Commissioner’s Office has also published its version of the transfer impact assessment and revised guidance on international transfers, although entities may choose to adopt either the EU or U.K. style transfer impact assessment. In terms of international data transfers between the U.K. and U.S., it is understood that the U.K. and the U.S. are negotiating an adequacy agreement.

ESG Considerations. A comprehensive package of measures to facilitate the progression towards sustainable economic activities was approved in principle by the European Commission in April 2021. In August 2021, two delegated regulations (the “EC Regulations”) amending sectoral legislation, including the Solvency II Directive and the Insurance Distribution Directive, were published. The EC Regulations focus on the integration of sustainability into key activities including product oversight and governance, risk management and suitability assessment procedures. The EC Regulations apply from August 2022.

The Corporate Sustainability Reporting Directive (“CSRD”), which replaces the Non-Financial Reporting Directive (“NFRD”), was published in the Official Journal of the EU in November 16, 2022 and enters into effect on January 5, 2023. Certain of our European subsidiaries are subject to NFRD. The CSRD expands the scope of sustainability reporting obligations to any European listed company or any company (including (re)insurers) meeting certain criteria. Companies which are already subject to NFRD must start reporting relevant information for financial years starting on or after January 1, 2024 beginning in 2025. Reporting obligations for other companies fulfilling certain criteria will commence in 2026 for financial years starting on or after January 1, 2025. In addition, the reporting standards under the CSRD, which provides in-scope companies with the technical detail on the information that will need to be disclosed and reported, are currently anticipated to be adopted by the European Commission by June 2023.

An additional ESG framework, the EU Taxonomy, came into force in July 2020, with in-scope companies required to comply with certain reporting obligations from January 1, 2022. The EU Taxonomy (which is a classification standard for reporting) sets out six environmental objectives with which companies' economic activities must comply if they

are to be described as environmentally sustainable. These six environmental objectives are: (1) climate change mitigation, (2) climate change adaptation, (3) sustainable use and protection of water and marine resources, (4) transition to a circular economy, (5) pollution prevention and control and (6) the protection and restoration of biodiversity and ecosystems. In addition, reporting obligations apply to in-scope companies regarding (1) the financial products they provide and (2) the environmental sustainability of an in-scope company's activities, which is to be disclosed in non-financial statements that are currently required under the NFRD (and subsequently under the CSRD once it is implemented). Certain of our European entities will fall within the scope of certain reporting obligations following the implementation of the CSRD.

In February 2022, the European Commission adopted a proposal for the Corporate Sustainability Due Diligence Directive (“CSDD”) and negotiation is ongoing. While the main focus of this proposal is on conducting due diligence on human rights and environmental impacts within a company and across its value chain, there are also additional sustainability requirements for certain in scope entities. As the CSDD is at an early proposal stage, its applicability to certain of our European entities is unclear, but we will monitor the development of the CSDD closely.

In tandem with all of the above, EIOPA continues to engage with stakeholders in the (re)insurance sector and publish detailed guidelines, recommendations and expectations relating to ESG matters and how these should be managed and considered by the (re)insurance sector.

Russian Sanctions. Since February 2022, the EU has imposed sanctions on the Russian Federation in response to the crisis in Ukraine. Given the evolving situation, we are closely monitoring developments and the sanctions imposed, to ensure our European entities remain in compliance with any sanctions measures imposed.

Cyber Risk. Cyber risk and information security is an area of increasing focus for the EU. The Digital Operational Resilience Act (“DORA”) entered into force in January 2023. The core aim of DORA is to prevent and mitigate cyber threats and sets uniform requirements for the security of network and information systems of financial sector entities (including (re)insurers) as well as critical third parties which provide ICT (information and communication technology)-related services, such as cloud platforms or data analytics services. In scope entities will be required to comply with the obligations set out under DORA from January 2025.

In addition to the above, EIOPA continues to publish detailed guidelines, recommendations and expectations relating to cyber matters and how these should be managed and considered by the (re)insurance sector.

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Inflation. The EU has adopted a range of measures to combat

unprecedented levels of inflation, with EIOPA issuing a supervisory statement outlining its expectations of (re)insurers on inflation-related issues in December 2022. We are monitoring ongoing developments and considering the impact of EU and EIOPA guidance on inflation on its business.

Switzerland

In December 2008, Arch Re Europe opened Arch Re Europe Swiss Branch as a branch office. As Arch Re Europe is domiciled outside of Switzerland and its activities are limited to reinsurance, the Arch Re Europe Swiss Branch in Switzerland is not required to be licensed by the Swiss insurance regulatory authorities.

In August 2014, Arch Underwriters Europe opened a branch office in Zurich (“Arch Underwriters Europe Swiss Branch”) to render reinsurance advisory services to certain group companies. Arch Underwriters Europe Swiss Branch is registered with the commercial register of the Canton of Zurich. Since its activities are limited to advisory services for reinsurance matters, the Arch Underwriters Europe Swiss Branch is not required to be licensed by the Swiss insurance regulatory authorities.

Australia

APRA is an independent statutory authority responsible for prudential supervision of institutions across banking, insurance and superannuation and promotes financial stability in Australia. Arch Indemnity has been authorized to conduct monoline lenders’ mortgage insurance business in Australia since June 2002 and was acquired by Arch Capital on August 30, 2021. Arch LMI, which was formerly authorized by APRA in January 2019 to conduct monoline lenders’ mortgage insurance business in Australia, relinquished its APRA authorization in December 2022 and has been converted to a services company for our Australian lenders mortgage insurance operations. Major regulatory requirements that are applicable to Arch Indemnity as a general insurance provider in Australia include requirements on minimum capital levels and compliance with corporate governance standards, including the risk management strategy for our Australian mortgage insurance business.

Our group also conducts property and casualty insurance business in Australia through Lloyd’s. This insurance business is managed by and distributed through local coverholders and is subject to Lloyd’s Supervision. In addition, the business is subject to local Australian prudential regulatory oversight by APRA, and additional separate financial services market conduct regulation by the Australian Securities and Investments Commission. Arch Indemnity has been licensed by the Australian Securities and

Investments Commission (“ASIC”) since March 2011 to engage in credit activities in Australia.

In addition, there are other Australian legislation and regulations applicable to the financial services sector that our group operates in, such as:

•privacy legislation on the collection, use and storage of personal information and sensitive information of individuals and a mandatory data breach notification regime, which are overseen by the Office of the Australian Information Commissioner;

•cyber security obligations imposed by APRA and ASIC and also on larger insurers in Australia under Australian security of critical infrastructure legislation;

•modern slavery legislation which imposes a statutory reporting regime for larger companies operating in Australia; and

•anti-money laundering and counter-terrorism financing legislation, which is administered by the Australian Transaction Reports and Analysis Centre.

Hong Kong

The insurance industry is regulated by Hong Kong Insurance Authority (“HKIA”), whose principal function is to regulate and supervise the insurance industry for the promotion of the general stability of the insurance industry and for the protection of existing and potential policyholders. Arch MI Asia Limited (“Arch MI Asia”) is not writing new business but is authorized to carry on general business Class 14 (Credit) and Class 16 (Miscellaneous Financial Loss), in or from Hong Kong.

Major regulatory requirements that are applicable to Arch MI Asia as a general business insurer include requirements on minimum paid-up capital, minimum solvency margin and maintenance of assets in Hong Kong.

TAX MATTERS

The following summary of the taxation of Arch Capital and the taxation of our shareholders is based upon current law and is for general information only. Legislative, judicial or administrative changes may be forthcoming that could affect this summary.

The following legal discussion (including and subject to the matters and qualifications set forth in such summary) of certain tax considerations (a) under “—Taxation of Arch Capital—Bermuda” and “—Taxation of Shareholders—Bermuda” is based upon the advice of Conyers Dill & Pearman Limited, Hamilton, Bermuda and (b) under “—Taxation of Arch Capital-United States,” “—Taxation of Shareholders-United States Taxation,” “—Taxation of Our U.S. Shareholders” and “—United States Taxation of Non-

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U.S. Shareholders” is based upon the advice of Cahill Gordon & Reindel LLP, New York, New York (the advice of such firms does not include accounting matters, determinations or conclusions relating to the business or activities of Arch Capital). The summary is based upon current law and is for general information only. The tax treatment of a holder of our common or preferred shares, or of a person treated as a holder of our shares for U.S. federal income, state, local or non-U.S. tax purposes, may vary depending on the holder’s particular tax situation. Legislative, judicial or administrative changes or interpretations may be forthcoming that could be retroactive and could affect the tax consequences to us or to holders of our shares.

Taxation of Arch Capital

Bermuda. Under current Bermuda law, Arch Capital is not subject to tax on income or profits, withholding, capital gains or capital transfers. Arch Capital has obtained from the Minister of Finance under the Exempted Undertakings Tax Protection Act 1966 of Bermuda an assurance that, in the event that Bermuda enacts legislation imposing tax computed on profits, income, any capital asset, gain or appreciation, or any tax in the nature of estate duty or inheritance, the imposition of any such tax shall not be applicable to Arch Capital or to any of our operations or our shares, debentures or other obligations until March 31, 2035. Given the limited duration of the Minister of Finance's assurance, we could be subject to taxes in Bermuda after that date. This assurance will be subject to the proviso that it is not to be construed so as to prevent the application of any tax or duty to such persons as are ordinarily resident in Bermuda (we are not so currently affected) or to prevent the application of any tax payable in accordance with the provisions of the Land Tax Act 1967 of Bermuda or otherwise payable in relation to any property leased to us or our insurance subsidiary. We pay annual Bermuda government fees, and our Bermuda insurance and reinsurance subsidiary pays annual insurance license fees. In addition, all entities employing individuals in Bermuda are required to pay a payroll tax and other sundry taxes payable, directly or indirectly, to the Bermuda government.

United States. Arch Capital and its non-U.S. subsidiaries believe they have conducted their operations and currently intend to conduct their operations going forward in a manner that has not caused them and will not cause them to be treated as engaged in a trade or business in the U.S. and, therefore, has not been and will not be required to pay U.S. federal income taxes (other than U.S. excise taxes on insurance and reinsurance premiums and withholding taxes on dividends and certain other U.S. source investment income). However, because definitive identification of activities which constitute being engaged in a trade or business in the U.S. is not provided by the Internal Revenue Code of 1986, as amended

(the “Code”), U.S. Treasury regulations (“Treasury Regulations”) or court decisions, there can be no assurance that our position on being engaged in a trade or business in the U.S. is correct. A foreign corporation deemed to be so engaged would be subject to U.S. federal income tax, as well as the branch profits tax, on its income, which is treated as effectively connected with the conduct of that trade or business unless the corporation is entitled to relief under the permanent establishment provisions of a tax treaty. Such income tax, if imposed, would be based on effectively connected income computed in a manner generally analogous to that applied to the income of a domestic corporation, except that deductions and credits generally are not permitted unless the foreign corporation has timely filed a U.S. federal income tax return in accordance with applicable Treasury Regulations. Penalties may be assessed for failure to file tax returns. In addition, in such case, a 30% branch profits tax would be imposed on net income after subtracting the regular corporate tax and making certain other adjustments.

Under the income tax treaty between Bermuda and the U.S. (the “Treaty”), Arch Capital's Bermuda insurance subsidiaries will be subject to U.S. income tax on any insurance premium income that is effectively connected with a U.S. trade or business only if that trade or business is conducted through a permanent establishment in the U.S. No Treasury Regulations interpreting the Treaty have been issued. While there can be no assurances, Arch Capital does not believe that any of its Bermuda insurance subsidiaries has a permanent establishment in the U.S. Such subsidiaries would not be entitled to the benefits of the Treaty if (i) 50% or less of Arch Capital's shares were beneficially owned, directly or indirectly, by Bermuda residents or U.S. citizens or residents, or (ii) any such subsidiary's income were used in substantial part to make disproportionate distributions to, or to meet certain liabilities to, persons who are not Bermuda residents or U.S. citizens or residents. While Arch Capital believes that its Bermuda insurance subsidiaries have been eligible for Treaty benefits to date, there can be no assurance that this is the case or that the Bermuda insurance subsidiaries will continue to be eligible for Treaty benefits.

The Treaty clearly applies to premium income but may be construed as not protecting investment income. If Arch Capital’s Bermuda insurance subsidiaries were considered to be engaged in a U.S. trade or business and were entitled to the benefits of the Treaty in general, but the Treaty were not found to protect investment income, a portion of such subsidiaries’ investment income could be subject to U.S. federal income tax.

Non-U.S. insurance companies carrying on an insurance business within the U.S. have a certain minimum amount of effectively connected net investment income, determined in accordance with a formula that depends, in part, on the amount of U.S. risk insured or reinsured by such companies.

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If any of Arch Capital's non-U.S. insurance subsidiaries is considered to be engaged in the conduct of an insurance business in the U.S., a significant portion of such subsidiary’s investment income could be subject to U.S. federal income tax.

Non-U.S. corporations not engaged in a trade or business in the U.S. are nonetheless subject to U.S. income tax on certain “fixed or determinable annual or periodic gains, profits and income” derived from sources within the U.S. as enumerated in Section 881(a) of the Code (such as dividends and certain interest on investments), subject to exemption under the Code or reduction by an applicable treaty.

The U.S. also imposes an excise tax on insurance and reinsurance premiums paid to non-U.S. insurers or reinsurers with respect to risks located in the U.S. The rates of tax, unless reduced by an applicable U.S. tax treaty, are 4% for non-life insurance premiums and 1% for life insurance and all reinsurance premiums.

The Tax Cuts and Jobs Act of 2017 (the “Tax Cuts Act”) was signed into law by the President of the United States in 2017. For taxable years beginning after 2017, the Tax Cuts Act imposes a 10% minimum base erosion and anti-abuse tax (increased to 12.5% for taxable years after 2025) on the “modified taxable income” of a U.S. corporation (or a non-U.S. corporation engaged in a U.S. trade or business) over such corporation’s regular U.S. federal income tax, reduced by certain tax credits. The “modified taxable income” of a corporation is determined without deduction for certain payments by such corporation to its non-U.S. affiliates (including reinsurance premiums). Final Treasury Regulations interpreting the base erosion and anti-abuse tax were issued in December 2019.

United Kingdom. Our U.K. subsidiaries are companies that are incorporated and have their central management and control in the U.K. and are therefore resident in the U.K. for corporation tax purposes. As a result, they will be subject to U.K. corporation tax on their respective profits. The U.K. branches of Arch Re Europe and Arch Insurance (EU) will be subject to U.K. corporation tax on the profits (both income profits and chargeable gains) attributable to each branch. The rate of U.K. corporation tax for the financial year is 19% on profits (increasing to 25% with effect from April 1, 2023).

Canada. Arch Insurance Canada is taxed on its worldwide income. Arch Re U.S. is taxed on its net business income earned in Canada. The general federal corporate income tax rate in Canada is currently 15%. Provincial and territorial corporate income tax rates are added to the general federal corporate income tax rate and generally vary between 8% and 16%.

Ireland. Each of Arch Re Europe, Arch Insurance (EU) and Arch Underwriters Europe is incorporated and resident in Ireland for corporation tax purposes and will be subject to Irish corporate tax on worldwide profits, including the profits of the branches of Arch Re Europe, Arch Insurance (EU) and Arch Underwriters Europe. Any foreign branch corporate tax payable will be creditable against Arch Re Europe’s Irish corporate tax liability on the results of Arch Re Europe’s branches with the same principle applied to Arch Insurance (EU)’s branches and Arch Underwriters Europe’s branches. The current rate of Irish corporation tax applicable to such trading profits is 12.5%.

Switzerland. Arch Re Europe Swiss Branch and Arch Underwriters Europe Swiss Branch are subject to Swiss corporation tax on the profit which is allocated to each branch. The effective tax rate is approximately 19.65% for Swiss federal, cantonal and communal corporation taxes on the profit. The effective tax rate of the annual cantonal and communal capital taxes on the equity which is allocated to Arch Re Europe Swiss Branch and Arch Underwriters Europe Swiss Branch is approximately 0.17%.

Denmark. Arch Re Denmark, established as a subsidiary of Arch Re Bermuda, is subject to Danish corporation taxes on its profits at a rate of 22%.

Hong Kong. Arch MI Asia is subject to Hong Kong corporate tax on its assessable profits at a rate of 16.5%. Assessable profits are the net profits for the basis period, arising in or derived from Hong Kong.

Australia. Arch LMI and Arch Indemnity, Australian incorporated and tax resident companies, are subject to Australian corporate tax on its worldwide profits. The current rate of Australian corporation tax applicable to such profits is 30%.

Taxation of Shareholders

Bermuda. Currently, there is no Bermuda withholding tax on dividends paid by us.

United States—General. The following summary sets forth certain U.S. federal income tax considerations related to the purchase, ownership and disposition of our common shares and our non-cumulative preferred shares (“preferred shares”). Unless otherwise stated, this summary deals only with shareholders (“U.S. holders”) that are U.S. Persons (as defined below) and to common shares and preferred shares beneficially owned by such holder and held as capital assets. The following discussion is only a general summary of the U.S. federal income tax matters described herein and does not purport to address all of the U.S. federal income tax consequences that may be relevant to a particular shareholder in light of such shareholder’s specific circumstances. In

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addition, the following summary does not describe the U.S. federal income tax consequences that may be relevant to certain types of shareholders, such as banks, insurance companies, regulated investment companies, real estate investment trusts, financial asset securitization investment trusts, dealers in securities or traders that adopt a mark-to-market method of tax accounting, tax exempt entities, expatriates, U.S. holders that hold our common shares or preferred shares through a non-U.S. broker or other non-U.S. intermediary, persons who hold the common shares or preferred shares as part of a hedging or conversion transaction or as part of a straddle, who may be subject to special rules or treatment under the Code or persons required for U.S. federal income tax purposed to recognize income no later than such income is reported on such persons’ applicable financial statements. This discussion is based upon the Code, the Treasury Regulations promulgated there under and any relevant administrative rulings or pronouncements or judicial decisions, all as in effect on the date of this annual report and as currently interpreted and does not take into account possible changes in such tax laws or interpretations thereof, which may apply retroactively. This discussion does not include any description of the tax laws of any state or local governments within the U.S., or of any foreign government, that may be applicable to our common shares or preferred shares or the shareholders. Persons holding or considering an investment in the common shares or preferred shares should consult their own tax advisors concerning the application of the U.S. federal tax laws to their particular situations as well as any tax consequences arising under the laws of any state, local or foreign taxing jurisdiction prior to making such investment.

If an entity that is treated as a partnership holds our common shares or preferred shares, the tax treatment of a partner will generally depend upon the status of the partner and the activities of the partnership. If you are a partnership holding or considering an investment in our common shares or preferred shares or a partner therein, you should consult your tax advisor.

For purposes of this discussion, the term “U.S. Person” means a person that is, for U.S. federal income tax purposes:

•an individual who is a citizen or resident of the U.S.;

•a corporation created or organized under the laws of the U.S., any state thereof or the District of Columbia;

•an estate, the income of which is subject to U.S. federal income taxation regardless of its source; or

•a trust, if either (i) a court within the U.S. is able to exercise primary supervision over the administration of such trust and one or more U.S. persons have the authority to control all substantial decisions of such trust or (ii) the trust has a valid election in effect to be treated as a U.S. person for U.S. federal income tax purposes.

United States—Taxation of Dividends. The preferred shares should be properly classified as equity rather than debt for U.S. federal income tax purposes. Subject to the discussions below relating to the potential application of the controlled foreign corporation (“CFC”), “related person insurance income” (“RPII”) and passive foreign investment company (“PFIC”) rules, as defined below, cash distributions, if any, made with respect to our common shares or preferred shares will constitute dividends for U.S. federal income tax purposes to the extent paid out of our current or accumulated earnings and profits (as computed using U.S. tax principles). If a U.S. holder of our common shares or our preferred shares is an individual or other non-corporate holder, dividends paid, if any, to that holder that constitute qualified dividend income generally will be taxable at the rate applicable for long-term capital gains (generally up to 20%), provided that such person meets a holding period requirement. Generally, in order to meet the holding period requirement, the U.S. holder must hold the common shares for more than 60 days during the 121-day period beginning 60 days before the ex-dividend date and must hold preferred shares for more than 90 days during the 181-day period beginning 90 days before the ex-dividend date. Dividends paid, if any, with respect to common shares or preferred shares generally will be qualified dividend income, provided the common shares or preferred shares are readily tradable on an established securities market in the U.S. in the year in which the shareholder receives the dividend (which should be the case for shares that are listed on the NASDAQ Stock Market or the New York Stock Exchange) and Arch Capital is not considered to be a passive foreign investment company in either the year of the distribution or the preceding taxable year. No assurance can be given that the preferred shares will be considered readily tradable on an established securities market in the U.S. See “—Taxation of Our U.S. Shareholders” below.

A U.S. holder that is an individual, estate or a trust that does not fall into a special class of trusts that is exempt from such tax, will be subject to a 3.8% tax on the lesser of (1) the U.S. holder’s “net investment income” for the relevant taxable year and (2) the excess of the U.S. holder’s modified adjusted gross income for the taxable year over a certain threshold (which in the case of individual will be between $125,000 and $250,000, depending on the individual’s circumstances). A U.S. holder’s net investment income generally will include its dividend income and its net gains from the disposition of our common shares and preferred shares, unless such dividend income or net gains are derived in the ordinary course of the conduct of a trade or business (other than a trade or business that consists of certain passive or trading activities).

Distributions with respect to the common shares and the preferred shares will not be eligible for the dividends received deduction allowed to U.S. corporations under the Code. To the extent distributions on our common shares and

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preferred shares exceed our earnings and profits, they will be treated first as a return of the U.S. holder's basis in our common shares and our preferred shares to the extent thereof, and then as gain from the sale of a capital asset.

United States—Sale, Exchange or Other Disposition. Subject to the discussions below relating to the potential application of the CFC, RPII and PFIC rules, U.S holders of common shares and preferred shares generally will recognize capital gain or loss, if any, for U.S. federal income tax purposes on the sale, exchange or other taxable disposition of common shares or preferred shares, as applicable.

United States—Redemption of Preferred Shares. A redemption of the preferred shares will be treated under Section 302 of the Code as a dividend to the extent we have earnings and profits allocable to such shares, unless the redemption satisfies one of the tests set forth in Section 302(b) of the Code enabling the redemption to be treated as a sale or exchange, subject to the discussion herein relating to the potential application of the CFC, RPII and PFIC rules. Under the relevant Code Section 302(b) tests, the redemption should be treated as a sale or exchange only if it (1) is substantially disproportionate, (2) constitutes a complete termination of the holder's stock interest in us or (3) is “not essentially equivalent to a dividend.” In determining whether any of these tests are met, shares considered to be owned by the holder by reason of certain constructive ownership rules set forth in the Code, as well as shares actually owned, must generally be taken into account. It may be more difficult for a U.S. holder who owns, actually or constructively by operation of the attribution rules, any of our other shares to satisfy any of the above requirements. The determination as to whether any of the alternative tests of Section 302(b) of the Code is satisfied with respect to a particular holder of the preferred shares depends on the facts and circumstances as of the time the determination is made.

Taxation of Our U.S. Shareholders

Controlled Foreign Corporation Rules. We or any of our non-U.S. subsidiaries generally will be treated as a CFC with respect to any taxable year if at any time during such taxable year, one or more “10% U.S. Shareholders” (as defined below) collectively own more than 50% of us or such non-U.S. subsidiary (as applicable) by vote or value (taking into account shares actually owned by such U.S. holder as well as shares attributed to such U.S. holder under the Code or the Treasury Regulations thereunder). Moreover, with respect to insurance income (including reinsurance income), the “more than 50%” requirement described in the preceding sentence is replaced with a more expansive “more than 25%” requirement. For taxable years beginning on or before December 31, 2017, a 10% U.S. Shareholder means any U.S. Person who was considered to own, actually or constructively, 10% or more of the total combined voting

power of our shares or those of our non-U.S. subsidiaries (as applicable). Under the Tax Cuts Act, for taxable years beginning after December 31, 2017, a 10% U.S. Shareholder also includes any U.S. Person who is considered to own, actually or constructively, 10% or more of the value of our shares or those of our non-U.S. subsidiaries (as applicable). As a result, for taxable years beginning after December 31, 2017, the voting cut-back limitation contained in our bye-laws that limits the votes conferred by the Controlled Shares (as defined in our bye-laws) of any U.S. Person to 9.9% of the total voting power of all our shares entitled to vote will not prevent any U.S. holder from being treated as a 10% U.S. Shareholder. Due to the repeal of Section 958(b)(4) of the Code under the Tax Cuts Act, all non-U.S. subsidiaries directly or indirectly owned by Arch Capital are treated as constructively owned by its U.S. subsidiaries, and therefore are treated as CFCs.

Status as a CFC would not cause us or any of our non-U.S. subsidiaries to be subject to U.S. federal income tax. Such status also would have no adverse U.S. federal income tax consequences for any U.S. holder that is not a 10% U.S. Shareholder with respect to us or any such non-U.S. subsidiary (as applicable). If we or any of our non-U.S. subsidiaries are or were a CFC with respect to any taxable year, a U.S. holder that is considered a 10% U.S. Shareholder would be subject to current U.S. federal income taxation (at ordinary income tax rates) to the extent of all or a portion of the undistributed earnings and profits of Arch Capital and our subsidiaries attributable to “subpart F income” (including certain insurance premium income and investment income) or global intangible low-taxed income and may be taxable at ordinary income tax rates on any gain recognized on a sale or other disposition (including by way of repurchase or liquidation) of our common shares or preferred shares to the extent of the current and accumulated earnings and profits attributable to such common shares or preferred shares. For taxable years beginning after December 31, 2017, a helpful limitation, which provides that a U.S. shareholder would not be subject to the current inclusion rules of Subpart F for a taxable year unless the non-U.S. corporation was a CFC for an uninterrupted period of 30 days or more during such taxable year, will no longer apply.

Related Person Insurance Income Rules. In general, with respect to RPII (a limited category of insurance income, as defined below), the CFC rules are expanded in two significant respects. First, in determining CFC status, as well as determining which U.S. shareholders are subject to current taxation with respect to a CFC’s RPII (whether or not currently distributed), all U.S. shareholders (as opposed to only 10% U.S. Shareholders) are taken into account. Second, the amount of stock in a foreign corporation that all U.S. shareholders, in the aggregate, must own for such corporation to be treated as a CFC is reduced from more than 50% (by

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vote or value), and more than 25% (by vote or value) with respect to insurance income generally, to 25% or more (by vote or value). Generally, RPII is insurance income (including reinsurance income) of a foreign corporation with respect to which the insured is a United States shareholder of the foreign corporation or a related person to such a shareholder.

Under one exception to the foregoing RPII rules, U.S. shareholders are not required to include a CFC’s RPII currently in income if the CFC’s gross RPII is less than 20% of its total gross insurance income for the taxable year in question (the “RPII 20% gross income exception”).

Under current law, we currently expect each of our non-U.S. subsidiaries to satisfy the RPII 20% gross income exception, and therefore we currently do not expect any U.S. shareholder to be required to include RPII in income (although there can be no assurance that this is or will continue be the case). However, proposed Treasury Regulations issued on January 24, 2022, if finalized in their current form, would for the first time (on a prospective basis) expand the definition of RPII to include certain intercompany insurance income (including reinsurance income) in a manner that could cause certain of our foreign subsidiaries not to satisfy the RPII 20% gross income exception. In such event, (1) as noted above, all U.S. shareholders (not just 10% U.S. Shareholders) would be required to include RPII in income currently, whether or not distributed, and (2) as noted below, U.S. shareholders that are tax exempt entities would be required to treat such RPII inclusions as unrelated business taxable income. Current and prospective U.S. holders should consult their own tax advisors as to the potential impact of these proposed Treasury Regulations.

Section 953(c)(7) of the Code generally provides that Section 1248 of the Code (which generally would require a U.S. holder to treat certain gains attributable to the sale, exchange or disposition of common shares or preferred shares as a dividend) will apply to the sale or exchange by a U.S. shareholder of shares in a foreign corporation that is characterized as a CFC under the RPII rules if the foreign corporation would be taxed as an insurance company if it were a U.S. corporation, regardless of whether the U.S. shareholder is a 10% U.S. Shareholder or whether the corporation qualifies for the RPII 20% gross income exception. Although existing Treasury Regulations do not address the question, proposed Treasury Regulations issued in April 1991 create some ambiguity as to whether Section 1248 and the requirement to file Form 5471 would apply when the non-U.S. corporation has a foreign insurance subsidiary that is a CFC for RPII purposes and that would be taxed as an insurance company if it were a domestic corporation. We believe that Section 1248 and the requirement to file Form 5471 will not apply to a less than

10% U.S. Shareholder because Arch Capital is not directly engaged in the insurance business. There can be no assurance, however, that the IRS will interpret the proposed Treasury Regulations in this manner or that the Treasury will not take the position that Section 1248 and the requirement to file Form 5471 will apply to dispositions of our common shares or our preferred shares.

If the IRS or U.S. Treasury were to make Section 1248 of the Code and the Form 5471 filing requirement applicable to the sale of our shares, we would notify shareholders that Section 1248 of the Code and the requirement to file Form 5471 will apply to dispositions of our shares. Thereafter, we would send a notice after the end of each calendar year to all persons who were shareholders during the year notifying them that Section 1248 of the Code and the requirement to file Form 5471 apply to dispositions of our shares by U.S. holders. We would attach to this notice a copy of Form 5471 completed with all our information and instructions for completing the shareholder information.

Tax-Exempt Shareholders. Tax-exempt entities may be required to treat certain Subpart F insurance income, including RPII, that is includible in income by the tax-exempt entity as unrelated business taxable income. Current and prospective U.S. holders that are tax exempt entities should consult their own tax advisors as to the potential impact of the unrelated business taxable income provisions of the Code.

Passive Foreign Investment Companies. Sections 1291 through 1298 of the Code contain special rules applicable with respect to foreign corporations that are PFICs. In general, a foreign corporation will be a PFIC if 75% or more of its income constitutes “passive income” or 50% or more of its assets produce passive income. If we were to be characterized as a PFIC, U.S. holders would be subject to a penalty tax at the time of their sale of (or receipt of an “excess distribution” with respect to) their common shares or preferred shares imposed at the highest applicable rate under the Code for the applicable tax year. In general, a shareholder receives an “excess distribution” if the amount of the distribution is more than 125% of the average distribution with respect to the shares during the three preceding taxable years (or shorter period during which the taxpayer held the stock). In general, the penalty tax is equivalent to an interest charge on taxes that are deemed due during the period the shareholder owned the shares, computed by assuming that the excess distribution or gain (in the case of a sale) with respect to the shares was taxable in equal portions throughout the holder’s period of ownership. The interest charge is equal to the applicable rate imposed on underpayments of U.S. federal income tax for such period. A U.S. shareholder may avoid some of the adverse tax consequences of owning shares in a PFIC by making a qualified electing fund (“QEF”) election. A QEF election is revocable only with the consent of the IRS and has the following consequences to a shareholder:

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•For any year in which Arch Capital is not a PFIC, no income tax consequences would result.

•For any year in which Arch Capital is a PFIC, the shareholder would include in its taxable income a proportionate share of the net ordinary income and net capital gains of Arch Capital and certain of its non-U.S. subsidiaries.

For taxable years beginning on or before December 31, 2017, the determination of whether the active insurance company exception applies to an insurance company was made on a case-by-case basis and the analysis was inherently subjective. Under the Tax Cuts Act, for taxable years beginning after December 31, 2017, the active insurance company exception applies only if (i) the company would be taxed as an insurance company were it a U.S. corporation and (ii) either (A) loss and loss adjustment expense and certain reserves constitute more than 25% of the company’s gross assets for the relevant year or (B) loss and loss adjustment expenses and certain reserves constitute more than 10% of the company’s gross assets for the relevant year and, based on the applicable facts and circumstances, the company is predominantly engaged in an insurance business and the failure of the company to satisfy the preceding 25% test is due solely to run-off related or other specified circumstances involving the insurance business. The PFIC statutory provisions contain a look-through rule that states that, for purposes of determining whether a foreign corporation is a PFIC, such foreign corporation shall be treated as if it “received directly its proportionate share of the income” and as if it “held its proportionate share of the assets” of any other corporation in which it owns at least 25% of the stock. We believe that we were not a PFIC for any taxable year ended on or before December 31, 2022 and we currently are not expecting to become a PFIC for any subsequent taxable year. However, due to the complexity and uncertainty of the PFIC rules and the limited guidance interpreting them, there can be no assurance that we have not been a PFIC to date or that we will not become a PFIC at some time in the future.

On December 4, 2020, the IRS issued certain final Treasury Regulations (the “2020 final PFIC insurance regulations”) and revised proposed Treasury Regulations (the “2020 proposed PFIC insurance regulations”) regarding the application of the insurance company exception. While we believe that the 2020 final PFIC insurance regulations and the 2020 proposed PFIC insurance regulations should not adversely impact the our ability to satisfy the insurance company exception and avoid being treated as a PFIC, there can be no assurance that such exception will in fact apply and/or will continue to apply at all times in the future. Each U.S. holder should consult its own tax advisor as to the effects of these rules.

United States Taxation of Non-U.S. Shareholders

Taxation of Dividends. Cash distributions, if any, made with respect to common shares or preferred shares held by a holder that is, for U.S. federal income tax purposes, an individual, corporation, estate or trust that is not a U.S. holder (a “Non-U.S. holder”) generally will not be subject to U.S. withholding tax.

Sale, Exchange or Other Disposition. Non-U.S. holders of common shares or preferred shares generally will not be subject to U.S. federal income tax with respect to gain recognized upon the sale, exchange or other disposition of such shares unless such gain is effectively connected with a U.S. trade or business of the Non-U.S. holder or such person is present in the U.S. for 183 days or more in the taxable year the gain is recognized and certain other requirements are satisfied.

Information Reporting and Backup Withholding. Non-U.S. holders of common shares or preferred shares will not be subject to U.S. information reporting or backup withholding with respect to dispositions of common shares effected through a non-U.S. office of a broker, unless the broker has certain connections to the U.S. or is a U.S. person. No U.S. backup withholding will apply to payments of dividends, if any, on our common shares or our preferred shares.

FATCA Withholding. Sections 1471 through 1474 to the Code, known as the Foreign Account Tax Compliance Act (“FATCA”), impose a withholding tax of 30% on U.S.-source interest, dividends and certain other types of income, which is received by a foreign financial institution (“FFI”), unless such FFI enters into an agreement with the IRS to obtain certain information as to the identity of the direct and indirect owners of accounts in such institution. In addition, a 30% withholding tax may be imposed on the above payments to certain non-financial foreign entities which do not (i) certify to each applicable withholding agent that they have no “substantial U.S. owners” (i.e., a U.S. 10% direct or indirect shareholder), or (ii) provide such withholding agent with the certain information as to the identity of such substantial U.S. owners. The U.S. has entered into intergovernmental agreements to implement FATCA (“IGAs”) with a number of jurisdictions. Bermuda has signed an IGA with the U.S. Different rules than those described above may apply under such an IGA.

Although dividends with respect to our common shares or preferred shares generally will be treated as foreign source for U.S. federal withholding tax purposes, it is unclear whether, for FATCA purposes, some or all of our dividends may be recharacterized as U.S. source dividends. Treasury Regulations addressing this topic have not yet been issued.

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Current and prospective investors should consult their own tax advisors as to the filing and information requirements that may be imposed on them in respect of their ownership of our common share or preferred shares.

Other Tax Laws. Shareholders should consult their own tax advisors with respect to the applicability to them of the tax laws of other jurisdictions.

ITEM 1A. RISK FACTORS

Set forth below are risk factors relating to our business. These risks and uncertainties are not the only ones we face. There may be additional risks that we currently consider not to be material or of which we are not currently aware, and any of these risks could cause our actual results to differ materially from historical or anticipated results. You should carefully consider these risks along with the other information provided in this report, including our “Management’s Discussion and Analysis of Financial Condition and Results of Operations” and our accompanying consolidated financial statements, as well as the information under the heading “Cautionary Note Regarding Forward-Looking Statements” before investing in any of our securities. We may amend, supplement or add to the risk factors described below from time to time in future reports filed with the SEC.

RISK FACTORS SUMMARY

The following is a summary description of the material risks and uncertainties to which we may be exposed. Each of these risks could adversely affect our business, financial condition and results of operations, and any such effects may be material. These and other risks are more fully described after this summary description.

Risks Relating to Our Industry, Business and Operations

•We operate in a highly competitive environment.

•The insurance and reinsurance industry is highly cyclical, and we may at times experience periods characterized by excess underwriting capacity and unfavorable premium rates.

•The effects of inflation and global recessionary conditions impact the insurance and reinsurance industry in ways which may negatively impact our business, financial condition and results of operations.

•Claims for natural and man-made catastrophic events could cause large losses and substantial volatility in our results of operations and could have a material adverse effect on our financial position and results of operations.

•The impacts of the COVID-19 pandemic, the shift to a COVID-19 endemic approach and related risks could materially affect our results of operations, financial position and/or liquidity.

•The impact of climate change will affect our loss limitation methods, such as the purchase of third party reinsurance and catastrophe risk modeling and risk selection in ways which may adversely impact our business, financial condition and results of operations.

•Our insurance and reinsurance subsidiaries are subject to supervision and regulation. Changes to existing regulation and supervisory standards, or failure to comply with applicable requirements, could adversely affect our business and results of operations.

•We are subject to ongoing legal and policy actions around climate change which may result in implications or additional requirements that could prompt us to shift our risk selection and business strategy in ways which may adversely impact our results of operations.

•The Russian invasion of Ukraine has created global instability and also resulted in the imposition of sanctions by the U.S., U.K. and EU on Russia and Russia-related businesses.

•Our customers and policyholders may also be impacted by regulatory, technological, market or other risks relating to climate change in ways which we cannot predict with certainty and adversely impact our results of operations.

•As we continue to incorporate climate change in our business strategy, we cannot be certain that shareholders, investors and other influential environmental groups will agree with our approach, which may adversely impact our ability to raise funds in the capital markets, our share price and our results of operations.

•Governmental, regulatory and rating actions in response to the COVID-19 pandemic have impacted us, and the continuation or reinstatement of such actions may adversely affect our financial performance.

•We could face unanticipated losses from war, terrorism, cyber attacks, pandemics and political instability, and these or other unanticipated losses could have a material adverse effect on our financial condition and results of operations.

•Underwriting risks and reserving for losses are based on probabilities and related modeling, which are subject to inherent uncertainties.

•The failure of any of the loss limitation methods we employ could have a material adverse effect on our financial condition or results of operations.

•The availability of reinsurance, retrocessional coverage and capital market transactions to limit our exposure to risks may be limited, and counterparty credit and other risks associated with our reinsurance arrangements may result in losses which could adversely affect our financial condition

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and results of operations.

•We could be materially adversely affected to the extent that important third parties with whom we do business do not adequately or appropriately manage their risks, commit fraud or otherwise breach obligations owed to us.

•Emerging claim and coverage issues, including issues relating to the COVID-19 pandemic, may adversely affect our business.

•Acquisitions, the addition of new lines of insurance or reinsurance business, expansion into new geographic regions and/or entering into joint ventures or partnerships expose us to risks.

•Our information technology systems may be unable to meet the demands of customers and our workforce.

•Technology failures and cyber attacks, including, but not limited to, ransomware, exploitation in software or code with malicious intent, state-sponsored cyber attacks, may impact us or our business partners and service providers, causing a disruption in service and operations which would negatively impact our business and/or expose us to litigation.

•Cyber incidents or data breaches caused by bad actors or unintentional human error impacting data, including personal data, we maintain or use during our business operations may result in regulatory fines or action, reputation damage and a disruption in our business operations.

•A downgrade in our ratings or our inability to obtain a rating for our operating insurance and reinsurance subsidiaries may adversely affect our relationships with clients and brokers and negatively impact sales of our products.

•Our ability to execute successfully our business strategy, continue to grow and innovate and offer our employees a dynamic and supportive workplace depends on the recruitment, retention and promotion of talented, agile, diverse and resilient employees at all levels of our organization.

•Our success will depend on our ability to maintain and enhance effective operating procedures and internal controls and our ERM program.

•We are exposed to credit risk in certain of our business operations.

•Our business is subject to applicable laws and regulations relating to economic trade sanctions and foreign bribery laws, the violation of which could adversely affect our operations.

•New legislation or regulations relating to the U.K.’s withdrawal from the EU could adversely affect us.

Risks Relating to Financial Markets and Investments

•Adverse developments in the financial markets could have a material adverse effect on our results of operations, financial position and our businesses, and may also limit our access to capital; our policyholders, reinsurers and retrocessionaires may also be affected by such developments, which could adversely affect their ability to meet their obligations to us.

•Disruption to the financial markets and weak economic conditions resulting from situations such as post pandemic imbalances, inflation and geopolitical conflict may adversely and materially impact our investments, financial condition and results of operation.

•Foreign currency exchange rate fluctuation may adversely affect our financial results.

•Uncertainty relating to the determination of the London Interbank Offered Rate (“LIBOR”) and the phasing out and replacement of LIBOR with alternative benchmark rates may adversely impact us.

•The determination of the amount of current expected credit losses (“CECL”) allowances taken on our investments is highly subjective and could materially impact our results of operations or financial position.

•Our reinsurance subsidiaries may be required to provide collateral to ceding companies, by applicable regulators, their contracts or other commercial considerations. Their ability to conduct business could be significantly and negatively affected if they are unable to do so.

Risks Relating to Our Mortgage Operations

•The ultimate performance of the Arch MI U.S. mortgage insurance portfolio remains uncertain.

•If the volume of low down payment mortgage originations declines, or if other government housing policies, practices or regulations change, the amount of mortgage insurance we write in the U.S. could decline, which would reduce our mortgage insurance revenues.

•Changes to the role of the GSEs in the U.S. housing market or to GSE eligibility requirements for mortgage insurers could negatively impact our results of operations and financial condition or reduce our operating flexibility.

•The implementation of the Basel III Capital Accord and FHFA’s Enterprise Capital Rule may adversely affect the use of mortgage insurance and CRT opportunities.

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Risk Relating to Our Company

•Some of the provisions of our bye-laws and our shareholders agreement may have the effect of hindering, delaying or preventing third party takeovers or changes in management initiated by shareholders. These provisions may also prevent our shareholders from receiving premium prices for their shares in an unsolicited takeover.

•There are regulatory limitations on the ownership and transfer of our common shares.

•Arch Capital is a holding company and is dependent on dividends and other distributions from its operating subsidiaries.

•General market conditions and unpredictable factors could adversely affect market prices for our outstanding preferred shares.

•Dividends on our preferred shares are non-cumulative.

•Our preferred shares are equity and are subordinate to our existing and future indebtedness.

•The voting rights of holders of our preferred shares are limited.

Risks Relating to Taxation

•We and our non-U.S. subsidiaries may become subject to U.S. federal income taxation and/or the U.S. federal income tax liabilities of our U.S. subsidiaries may increase, including as a result of changes in tax law.

•The continuing implementation of the Tax Cuts Act may have a material and adverse impact on our operations and financial condition.

•Proposed Treasury Regulations issued on January 24, 2022, if finalized in their current form, could (on prospective basis) cause our U.S. shareholders (including tax-exempt U.S. shareholders) to be subject to current U.S. federal income tax on the portion of our earnings attributable to certain intercompany reinsurance income (whether or not such income is distributed).

•We may become subject to taxes in Bermuda after March 31, 2035, which may have a material adverse effect on our results of operations.

•The impact of Bermuda's letter of commitment to the OECD to eliminate harmful tax practices is uncertain and could adversely affect our tax status in Bermuda.

•Legislation enacted in Bermuda as to Economic Substance may affect our operations.

•We may become subject to increased taxation in Bermuda and other countries as a result of the OECD's plan on “Base erosion and profit shifting.”

•Application of the EU Anti-Tax Avoidance Directives.

Risks Relating to Our Industry, Business and Operations

We operate in a highly competitive environment, and we may not be able to compete successfully in our industry.

The insurance and reinsurance industry is highly competitive. We compete on an international and regional basis with major U.S. and non-U.S. insurers and reinsurers, many of which have greater financial, marketing and management resources than we do. See “Competition” in Item 1 for details on our competitors in each of the major segments we operate in. There has been significant consolidation in the insurance and reinsurance sector in recent years and we may experience increased competition as a result of that consolidation, with consolidated entities having enhanced market power. These consolidated entities may use their enhanced market power and broader capital base to negotiate price reductions for products and services that compete with ours, and we may experience rate declines and possibly write less business. We also compete on the basis of product offerings and other factors, such as our approach to ESG, and customers may be drawn to our competitors based on these factors. Any failure by us to effectively compete could adversely affect our financial condition and results of operations.

The insurance and reinsurance industry is highly cyclical, and we may at times experience periods characterized by excess underwriting capacity and unfavorable premium rates.

Historically, insurers and reinsurers have experienced significant fluctuations in operating results due to competition, frequency of occurrence or severity of catastrophic events, levels of capacity, general economic conditions, inflation, changes in equity, debt and other investment markets, changes in legislation, case law and prevailing concepts of liability and other factors. Demand for reinsurance is influenced significantly by the underwriting results of primary insurers and prevailing general economic conditions. The supply of insurance and reinsurance is related to prevailing prices and levels of surplus capacity that, in turn, may fluctuate in response to changes in rates of return being realized in the insurance and reinsurance industry on both underwriting and investment sides. As a result, the insurance and reinsurance business historically has been a cyclical industry characterized by periods of intense price competition due to excessive underwriting capacity as well as periods when shortages of capacity permitted favorable premium levels and changes in terms and conditions. Until recently, the supply of insurance and reinsurance had increased over the past several years, and may again in the future, either as a result of capital provided by new entrants or by the commitment of additional capital by existing insurers or reinsurers. Continued increases in the supply of insurance and reinsurance may have consequences for us, including fewer contracts written, lower premium rates, increased expenses for customer acquisition and retention, and less favorable policy terms and conditions.

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The effects of inflation and global recessionary conditions impact the insurance and reinsurance industry in ways which may negatively impact our business, financial condition and results of operations.

General economic inflation has increased in recent quarters and may continue to remain at elevated levels for an extended period of time. The potential also exists, after a catastrophe loss or pandemic events like COVID-19, for the development of inflationary pressures in a local economy. This may have a material effect on the adequacy of our reserves for losses and loss adjustment expenses, especially in longer-tailed lines of business. In addition, governmental actions in response to inflationary pressures, such as increasing interest rates, may have a material impact on the market value of our investment portfolio. While we consider the anticipated effects of inflation in our pricing models, reserving processes and exposure management across all lines of business and types of loss including natural catastrophe events, the actual effects of inflation on our results cannot be accurately known until claims are settled. In addition, there are different types of inflation relevant to certain lines of business, the impact of which is difficult to accurately assess at this time. For example, in our mortgage business, the failure of general wages to keep pace with economic inflation, or increases in unemployment due to prolonged recessionary conditions, could prevent borrowers from being able to afford their mortgage payments and thereby increase the frequency of claims beyond our modeled results. Global recessionary conditions, including inflation, the slow recovery of certain sectors from the pandemic, predicted slow growth rates across key markets and other factors, will impact the insurance and reinsurance industry. There is great uncertainty around how severe and how long a recession will last on a global and local basis. While our risk management and business strategy take recessionary conditions into account, we cannot accurately predict the full impact of a recession on our results of business operations.

Claims for natural and man-made catastrophic events could cause large losses and substantial volatility in our results of operations and could have a material adverse effect on our financial position and results of operations.

We have large aggregate exposures to natural and man-made catastrophic events. Natural catastrophes can be caused by various events, including hurricanes, floods, wildfires, tsunamis, windstorms, earthquakes, hailstorms, tornadoes, explosions, severe winter weather, fires, droughts and other natural disasters. The frequency and severity of natural catastrophe activity has also been greater in recent years due to climate change caused in part by human actions and other related factors. Catastrophic events caused by humans may include acts of war, acts of terrorism and political instability. Catastrophes can cause losses in non-property business such as workers’ compensation or general liability. In addition to

the nature of the property business, we believe that economic and geographic trends affecting insured property, including inflation, property value appreciation and geographic concentration tend to generally increase the size of losses from catastrophic events over time. Actual losses from future catastrophic events may vary materially from estimates due to the inherent uncertainties in making such determinations resulting from several factors, including the potential inaccuracies and inadequacies in the data provided by clients, brokers and ceding companies, the modeling techniques and the application of such techniques, the contingent nature of business interruption exposures, the effects of any resultant demand surge on claims activity and attendant coverage issues. In estimating our losses from catastrophic events our considerations can include factors such as overall market losses, additional claims information from our clients, multiple model views and proprietary scenario testing.

The impact of the COVID-19 pandemic, the shift to a COVID-19 endemic approach and related risks could materially affect our results of operations, financial position and/or liquidity.

The COVID-19 pandemic resulted in a global slowdown of economic activity and disruption of normal business travel and working habits. While we are shifting to a COVID-19 endemic approach, there is still uncertainty about the impact of COVID-19 variants in the long-term. The COVID-19 pandemic impacted our results of operations and a reversion to the COVID-19 restrictions could have a significant effect on our future business, results of operations and financial performance. We may experience higher levels of loss and claims activity in certain lines of business, and our premiums written and earned could also be adversely affected by a suppression of global commercial activity that results in a reduction in insurable assets and other exposure. The pandemic initially resulted in a sharp contraction in the global economy, tightening liquidity and increasing volatility and uncertainty in the capital markets. Coincident global mitigation responses stabilized markets and stimulated economic recovery. During the second quarter of 2020, pandemic-driven dislocations had a negative effect on the performance of our investment portfolio, after which valuations recovered. Continued macroeconomic volatility may persist affecting our businesses and related market opportunities. Certain lines of our business may require additional forms of collateral in the event of a decline in the fair value of securities and benchmarks to which those repayment mechanisms are linked. The impact of an ongoing pandemic on the financial markets may also adversely affect our ability to fund through public or private equity offerings, debt financings, and through other means at acceptable terms.

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The impact of climate change will affect our loss limitation methods, such as the purchase of third party reinsurance and catastrophe risk modeling and risk selection in ways which may adversely impact our business, financial condition and results of operations.

Changing weather patterns and climatic conditions, such as global warming, have added to the unpredictability, severity and frequency of natural disasters. Uncertainty about complexities of climate change affects our ability to assess with certainty the full impact of climate change and creates uncertainty about future trends and exposures. Although the loss experience of catastrophe insurers and reinsurers has historically been characterized as low frequency, climate change has impacted the frequency and severity of extreme weather events and natural catastrophes such as hurricanes, tornado activity, other windstorms, floods and wildfires in recent years and may continue to increase in the future.

Claims for catastrophic events, or an unusual frequency of smaller losses in a particular period, could expose us to large losses, cause substantial volatility in our results of operations and could have a material adverse effect on our ability to write new business if we are not able to adequately assess and reserve for the increased frequency and severity of catastrophes resulting from these environmental factors. Climate change and increasing catastrophic events could increase property damage to residential real estate secured by mortgages owned by the GSEs, and by extension could increase losses to CRT investors. Additionally, climate change may make modeled outcomes less certain or produce new, non-modeled risks. Additionally, catastrophic events could result in increased credit exposure to reinsurers and other counterparties we transact business with, declines in the value of investments we hold and significant disruptions to our physical infrastructure, systems and operations. Climate change-related risks may also specifically adversely impact the value of the securities that we hold. The effects of climate change could also lead to increased credit risk of other counterparties we transact business with, including reinsurers.

Changes in security asset prices may impact the value of our fixed income, real estate and commercial mortgage investments, resulting in realized or unrealized losses on our invested assets. These risks are not limited to, but can include: (i) changes in supply/demand characteristics for fossil fuels (e.g., coal, oil, natural gas); (ii) advances in low-carbon technology and renewable energy development; and (iii) effects of extreme weather events on the physical and operational exposure of industries and issuers, and the transition that these companies make towards addressing climate risk in their own businesses.

We attempt to manage our exposure to these risks relating to climate change through the use of underwriting controls,

proprietary and third-party risk models, and the purchase of third-party reinsurance. Underwriting controls can include more restrictive underwriting criteria such as higher premiums and deductibles, reduction in limits offered or losses retained, and more specifically excluded policy risks. Our exposure in connection with a catastrophic event is determined by market capacity, pricing conditions, regulatory capital requirements, our perceptions of underlying risk and surplus preservation. There can be no assurance that our reinsurance coverage and other measures taken will be sufficient to mitigate losses resulting from one or more catastrophic events. As a result, the occurrence of one or more catastrophic events and the continuation and worsening of recent trends could have an adverse effect on our results of operations and financial condition.

Our insurance and reinsurance subsidiaries are subject to supervision and regulation. Changes to existing regulation and supervisory standards, or failure to comply with applicable requirements, could adversely affect our business and results of operation.

Our insurance and reinsurance subsidiaries conduct business globally and are subject to varying degrees of regulation in the various jurisdictions in which they conduct business, including by state, federal and national insurance regulators. The purpose of insurance laws and regulations generally is to protect policyholders and ceding insurance companies, not our shareholders. See “Regulation” in Item 1.

We may not be able to comply fully with, or obtain appropriate exemptions from, these statutes and regulations, which could result in restrictions on our ability to do business or undertake activities that are regulated in one or more of the jurisdictions in which we conduct business and could subject us to fines and other sanctions. Regulatory authorities also may seek to exercise their supervisory or enforcement authority in new or more extensive ways, such as imposing increased capital requirements. These actions, if they occur, could affect the competitive market and the way we conduct our business and manage our capital and could result in lower revenues and higher costs. As a result, such actions could have a material effect on our results of operations and financial condition.

We are subject to ongoing legal and policy actions around climate change which may result in implications or additional requirements which could prompt us to shift our risk selection and business strategy in ways which may adversely impact our results of operations.

Governments, regulators, legislators and influential non-governmental organizations continue to focus on enacting laws, regulations and other requirements relating to climate change. We are subject to some of these changing laws, regulations and public policy debates, which are difficult to

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predict and quantify and may have an adverse impact on our business. Legislative and regulatory initiatives and court decisions following major catastrophes could force expansion of certain insurance coverages for catastrophe claims or otherwise adversely impact our business. Additionally, changes in regulations or policies relating to climate change or our own leadership decisions implemented as a result of assessing the impact of climate change on our business may result in an increase in the cost of doing business, or a decrease in premiums in certain lines of business.

Our efforts to address these exposures are based in part on the outcomes of our loss mitigation measures and risk modeling, our financial results of operations and our communications with our customers and shareholders. We also continue to monitor changes across our industry and geographies and the Board considers these exposures regularly. We may make strategic business decisions to address or respond to some of the legal and policy changes relating to climate change, but there is no assurance that these decisions will adequately address these exposures or that they will not result in a material adverse effect on our results of operations, financial condition or share price.

The Russian invasion of Ukraine has created global instability and also resulted in the imposition of sanctions by the U.S., U.K. and EU on Russia and Russia-related businesses.

The Russian invasion of Ukraine and ongoing hostilities have created a high level of uncertainty as well as disruption in certain sectors of the global economy. It is impossible to predict whether Russia will expand hostilities to other countries in Europe or elsewhere. A further prolonged war may also create uncertainty in the global economy in the form of oil shortages, inflationary pressures, loss of confidence and general increase in risks worldwide. In response to this aggression, the governments of the U.S., U.K., EU and other countries have implemented several sanctions programs relating to, among other things, the import and transportation of Russian oil and gas and other goods originating in Russia. Certain lines of business we write have been impacted by the sanctions, such as the marine and energy lines of business, although the extent of the impact will depend on the outcome of the war in Ukraine and the nature of future sanctions packages.

Our customers and policyholders may also be impacted by regulatory, technological, market or other risks relating to climate change in ways which we cannot predict with certainty and adversely impact our results of operations.

Our policyholders and customers are located primarily in countries and regions, such as the U.S., U.K. and EU, where there are regulatory, policy, legal and technological changes resulting from actions relating to climate change. In some

cases, those policyholders and customers may not be able to shift their business strategies or adjust adequately to these changes, and their businesses may be negatively impacted or, in some cases, cease to exist. As a result, our results of operations may be impacted by the loss of those customers or a shift in their patterns or levels of insurance coverage in ways we cannot predict.

As we continue to incorporate climate change in our business strategy, we cannot be certain that shareholders, investors and other influential environmental groups will agree with our approach, which may adversely impact our ability to raise funds in the capital markets, our share price and our results of operations.

Shareholders and investors have placed increased importance on how we are addressing ESG issues. ESG encompass a wide range of issues, including climate change and other environmental risks. Our leadership and Board are actively engaged in understanding the ever-changing ESG landscape and assessing our business operations to ensure that our business strategy reflects our values, that our success depends on our commitment to a diverse workforce, an informed and active dialogue about ESG issues with our customers and shareholders and the strength of our ERM framework. We cannot predict whether our business decisions, business strategy and disclosures relating to climate change and other ESG issues will meet the expectations or particular requirements of certain key institutional shareholders in particular. We may be adversely impacted if shareholders or investors do not agree with, or are not satisfied with, our business strategy and approach to climate change and decide to sell or not purchase our equity or debt instruments or to publicize their dissatisfaction.

Governmental, regulatory and rating actions in response to the COVID-19 pandemic have impacted us, and the continuation or reinstatement of such actions may adversely affect our financial performance.

Actions of the federal, state and local government in the U.S. and other countries where we do business, to address and mitigate the impact of COVID-19 impacted us. While many of those actions have expired, been repealed or removed, it is difficult to predict whether such legislative bodies may choose to reintroduce legislation relating to the pandemic or continue to update existing regulations. For example, we are potentially subject to legislative and/or regulatory action that seeks to retroactively mandate coverage for losses which our insurance policies were not designed or priced to cover. There is proposed legislation in some states to require insurers to cover business interruption claims retroactively irrespective of terms, exclusions or other conditions included in the policies that would otherwise preclude coverage. Some proposed bills would require policies providing business

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interruption coverage to cover losses prospectively for pandemic-related losses. Insurance regulators in some states will not approve policy exclusions for losses from COVID-19, viruses or pandemics. In addition, a number of states have instituted, and other states are considering instituting, changes designed to effectively expand workers' compensation coverage by creating presumptions of compensability of claims for certain types of workers. Regulatory restrictions or requirements could also impact pricing, risk selection and our rights and obligations with respect to our policies and insureds, including our ability to cancel policies, our ability to increase rates or our right to collect premiums. Some state regulators have issued orders to review insurers’ rates and prevent rate increases, and regulators in other states could take similar actions. It is also possible that changes in economic conditions and steps taken by federal, state and local governments in response to COVID-19 could require an increase in taxes at the federal, state and local levels, which would adversely impact our results of operations.

Mortgage defaults related to the pandemic, if not cured, could remain in our defaulted loan inventory for a protracted period of time including due to forbearance programs and foreclosure moratoria, potentially resulting in higher frequency (claim rate) and severity (amount of the claim) for those loans that ultimately result in a claim. Accordingly, extended or extensive forbearance programs, foreclosure moratoria and other changes in regulations or laws may adversely impact our mortgage insurance operations.

In addition, the rating agencies continually review the financial strength ratings assigned to the Company and its subsidiaries, and the ratings are subject to change. The COVID-19 pandemic and its impact on financial results and condition, could cause one or more of the rating agencies to downgrade the ratings assigned to the Company and its subsidiaries. The pandemic has resulted, and may continue to result, in a material increase in new defaults as borrowers fail to make timely payments on their mortgages, including as a result of increases in unemployment and entering mortgage forbearance programs that allow borrowers to defer mortgage payments, which may have an adverse impact on our results or operations.

We could face unanticipated losses from war, terrorism, cyber attacks, pandemics and political instability, and these or other unanticipated losses could have a material adverse effect on our financial condition and results of operations.

We have substantial exposure to unexpected, large losses resulting from future man-made catastrophic events, such as acts of war, acts of terrorism, pandemics similar to the COVID-19 pandemic, political instability and social unrest. These risks are inherently unpredictable. It is difficult to predict the timing of such events with statistical certainty or

estimate the amount of loss any given occurrence will generate. In certain instances, we specifically insure and reinsure risks resulting from acts of terrorism. We may also insure against risk related to cybersecurity and cyber attacks. In addition, our exposure to cyber attacks includes exposure to ‘silent cyber’ risks, meaning risks and potential losses associated with policies where cyber risk is not specifically included nor excluded in the policies. Even in cases where we attempt to exclude losses from terrorism, cybersecurity and certain other similar risks from some coverages written by us, we may not be successful in doing so. Moreover, irrespective of the clarity and inclusiveness of policy language, there can be no assurance that a court or arbitration panel will not limit enforceability of policy language or otherwise issue a ruling adverse to us. Accordingly, while we believe our reinsurance programs, together with the coverage provided under the Terrorism Risk Insurance Act of 2002, as amended (“TRIP”) are sufficient to reasonably limit our net losses relating to potential future terrorist attacks, we can offer no assurance that our available capital will be adequate to cover losses when they materialize. To the extent that an act of terrorism is certified by the Secretary of the Treasury and aggregate industry insured losses resulting from the act of terrorism exceeds the prescribed program trigger, our U.S. insurance operations may be covered under TRIP for up to 80% subject to (i) a mandatory deductible of 20% of our prior year’s direct earned premium for covered property and liability coverages, and (ii) an industry aggregate retention of $37.5 billion. The program trigger for calendar year 2022 and any program year thereafter through 2027 is $200 million. If an act (or acts) of terrorism result in covered losses exceeding the $100 billion annual limit, insurers with losses exceeding their deductibles will not be responsible for additional losses. It is not possible to completely eliminate our exposure to unforecasted or unpredictable events, and to the extent that losses from such risks occur, our financial condition and results of operations could be materially adversely affected.

Underwriting risks and reserving for losses are based on probabilities and related modeling, which are subject to inherent uncertainties.

Our success is dependent upon our ability to assess accurately the risks associated with the businesses that we insure and reinsure. We establish reserves for losses and loss adjustment expenses which represent estimates based on actuarial and statistical projections, at a given point in time, of our expectations of the ultimate future settlement and administration costs of losses incurred. We utilize actuarial models as well as available historical insurance industry loss ratio experience and loss development patterns to assist in the establishment of loss reserves. Most or all of these factors are not directly quantifiable, particularly on a prospective basis, and the effects of these and unforeseen factors could negatively impact our ability to accurately assess the risks of the policies that we write. Changes in the assumptions used

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by these models or by management could lead to an increase in our estimate of ultimate losses in the future. In addition, there may be significant reporting lags between the occurrence of the insured event and the time it is reported to the insurer and additional lags between the time of reporting and final settlement of claims. In addition, the estimation of loss reserves is more difficult during times of adverse economic and market conditions due to unexpected changes in behavior of claimants and policyholders, including an increase in fraudulent reporting of exposures and/or losses, reduced maintenance of insured properties or increased frequency of small claims. Changes in the level of inflation also result in an increased level of uncertainty in our estimation of loss reserves. As a result, actual losses and loss adjustment expenses paid can deviate, perhaps substantially, from the reserve estimates reflected in our financial statements.

If our loss reserves are determined to be inadequate, we will be required to increase loss reserves at the time of such determination with a corresponding reduction in our net income in the period when the deficiency becomes known. It is possible that claims in respect of events that have occurred could exceed our claim reserves and have a material adverse effect on our results of operations, in a particular period, or our financial condition in general. As a compounding factor, although most insurance contracts have policy limits, the nature of property and casualty insurance and reinsurance is such that losses and the associated expenses can exceed policy limits for a variety of reasons and could significantly exceed the premiums received on the underlying policies, thereby further adversely affecting our financial condition.

As of December 31, 2022, our consolidated reserves for unpaid losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable, were approximately $13.8 billion. Such reserves were established in accordance with applicable insurance laws and GAAP. Loss reserves are inherently subject to uncertainty. In establishing the reserves for losses and loss adjustment expenses, we have made various assumptions relating to the pricing of our reinsurance contracts and insurance policies and have also considered available historical industry experience and current industry conditions. Any estimates and assumptions made as part of the reserving process could prove to be inaccurate due to several factors, including the fact that for certain lines of business relatively limited historical information has been reported to us through December 31, 2022.

The failure of any of the loss limitation methods we employ could have a material adverse effect on our financial condition or results of operations.

We seek to limit our loss exposure by writing a number of our reinsurance contracts on an excess of loss basis, adhering to maximum limitations on reinsurance written in defined geographical zones, limiting program size for each client and prudent underwriting of each program written. In the case of proportional treaties, we may seek per occurrence limitations or loss ratio caps to limit the impact of losses from any one or series of events. In our insurance operations, we seek to limit our exposure through the purchase of reinsurance. For our U.S. mortgage insurance business, in addition to utilizing reinsurance, we have developed a proprietary risk model that simulates the maximum probable loss resulting from a severe economic event impacting the housing market. We also seek to limit our loss exposure by geographic diversification, including by pricing adjustments in our U.S. mortgage insurance business. Geographic pricing decisions and zone limitations involve significant underwriting judgments, including the determination of the area of the zones and the inclusion of a particular policy within a particular zone’s limits. Various provisions of our policies, negotiated to limit our risk, such as limitations or exclusions from coverage or choice of forum, may not be enforceable in the manner we intend, as it is possible that a court or regulatory authority could nullify or void an exclusion or limitation, or legislation could be enacted modifying or barring the use of these exclusions and limitations. Disputes relating to coverage and choice of legal forum may also arise. Underwriting is inherently a matter of judgment, involving important assumptions about matters that are inherently unpredictable and beyond our control, and for which historical experience and probability analysis may not provide sufficient guidance. One or more catastrophic events or severe economic events could result in claims that substantially exceed our expectations, or the protections set forth in our policies could be voided, which, in either case, could have a material adverse effect on our financial condition or our results of operations, possibly to the extent of eliminating our shareholders’ equity. In addition, factors such as global climate change limit the value of historical experience and therefore further limit the effectiveness of our loss limitation methods. See “Catastrophic Events and Severe Economic Events” in Item 7 for further details. Depending on business opportunities and the mix of business that may comprise our insurance, reinsurance and mortgage insurance portfolio, we may seek to adjust our self-imposed limitations on probable maximum pre-tax loss for catastrophe exposed business and mortgage default exposed business.

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The availability of reinsurance, retrocessional coverage and capital market transactions to limit our exposure to risks may be limited, and counterparty credit and other risks associated with our reinsurance arrangements may result in losses which could adversely affect our financial condition and results of operations.

We manage risk using reinsurance, retrocessional coverage and capital markets transactions. Our insurance subsidiaries typically cede a portion of their premiums through pro rata, excess of loss and facultative reinsurance agreements. Our reinsurance subsidiaries purchase a limited amount of retrocessional coverage as part of their aggregate risk management program. In addition, our reinsurance subsidiaries participate in “common account” retrocessional arrangements for certain pro rata treaties. Such arrangements reduce the effect of individual or aggregate losses to all companies participating on such treaties, including the reinsurers, such as our reinsurance subsidiaries, and the ceding company. Economic conditions, including but not limited to recessionary conditions, inflation, declining home prices or the impact of climate change could also have a material impact on our ability to manage our risk aggregations through reinsurance or capital markets transactions. As a result of these factors, we may not be able to successfully mitigate risk through reinsurance and retrocessional arrangements.

Further, we are subject to credit risk with respect to our reinsurance and retrocessions because the ceding of risk to reinsurers and retrocessionaires does not relieve us of our liability to the clients or companies we insure or reinsure. We monitor the financial condition of our reinsurers and attempt to place coverages only with carriers we view as substantial and financially sound. An inability of our reinsurers or retrocessionaires to meet their obligations to us could have a material adverse effect on our financial condition and results of operations. Our losses for a given event or occurrence may increase if our reinsurers or retrocessionaires dispute or fail to meet their obligations to us or the reinsurance or retrocessional protections purchased by us are exhausted or are otherwise unavailable for any reason. In certain instances, we also require collateral to mitigate our credit risk to our reinsurers or retrocessionaires. We are at risk that losses could exceed the collateral we have obtained. Our failure to establish adequate reinsurance or retrocessional arrangements or the failure of our existing reinsurance or retrocessional arrangements to protect us from overly concentrated risk exposure could adversely affect our financial condition and results of operations.

We could be materially adversely affected to the extent that important third parties with whom we do business do not adequately or appropriately manage their risks, commit fraud or otherwise breach obligations owed to us.

For certain lines of our insurance business, we authorize managing general agents, general agents and other producers to write business on our behalf within underwriting authorities prescribed by us. In addition, our mortgage group delegates the underwriting of a significant percentage of its primary new insurance written to certain mortgage lenders. Under this delegated underwriting program, the approved customer may determine whether mortgage loans meet our mortgage insurance program guidelines and commit us to issue mortgage insurance. We rely on the underwriting controls of these agents to write business within the underwriting authorities provided by us. Although we have contractual protections in some instances and we monitor such business on an ongoing basis, our monitoring efforts may not be adequate or our agents may exceed their underwriting authorities or otherwise breach obligations owed to us. In addition, our agents, our insureds or other third parties may commit fraud or otherwise breach their obligations to us. Our financial condition and results of operations could be materially adversely affected by any one of these issues.

While we conduct underwriting, financial, claims and information technology due diligence reviews and apply rigorous standards in the selection of these counterparties, there is no assurance they have provided us accurate or complete information to assess their risk or that they can manage effectively their own risks. The counterparties are also subject to the same global increase in cyber incidents, including ransomware, and we cannot offer assurances that these counterparties have sufficient technical and organizational controls to mitigate these risks. Consequently, we assume a degree of credit and operational risk of those parties, and a material failure to manage their risks may result in material losses or damage to us.

Emerging claim and coverage issues, including issues relating to the COVID-19 pandemic, may adversely affect our business.

As industry practices and legal, social and other environmental conditions change, unexpected and unintended issues related to claims and coverage may emerge, including new or expanded theories of liability. These or other changes could impose new financial obligations on us by extending coverage beyond our underwriting intent or otherwise require us to make unplanned modifications to the products and services that we provide, or cause the delay or cancellation of products and services that we provide. In some instances, these changes may not become apparent until sometime after we have issued insurance or reinsurance contracts that are

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affected by the changes. As a result, the full extent of liability under our insurance or reinsurance contracts may not be known for many years after a contract is issued. The effects of unforeseen developments or substantial government intervention could adversely impact us.

While we had exposure to a number of lines of business, such as trade credit, travel, workers compensation and property where business interruption coverage under a pandemic such as COVID-19 was at issue, the number of claims in this area has decreased greatly in 2022. In May 2020, FCA commenced court proceedings against a number of insurance companies, including Arch Insurance (U.K.), to test how certain business interruption insurance policies respond to claims arising from COVID-19. The High Court in September 2020 handed down its judgment which, found in favor of policyholders on the majority of the key coverage issues in the representative sample of policies submitted by the defendants. Appeals were filed by six insurers, including Arch Insurance (U.K.), and in January 2021, the Supreme Court in the U.K. broadly confirmed the High Court’s rulings on the business wordings. The impact of this case on Arch Insurance (U.K.)’s results of operations has been modest, and no further litigation has flowed from it that has significantly impacted Arch Insurance (U.K.). Whilst the judgment amended the law in some respects (namely the tests for causation in English litigation), to date this has not had a significant impact on Arch Insurance (U.K.) claims and it is not anticipated to do so, however this cannot be ruled out entirely. See “Risks Relating to Our Mortgage Operations” for further details on our mortgage operations.

Acquisitions, the addition of new lines of insurance or reinsurance business, expansion into new geographic regions and/or entering into joint ventures or partnerships expose us to risks.

We may seek, from time to time, to acquire other companies, acquire selected blocks of business, expand our business lines, expand into new geographic regions and/or enter into joint ventures or partnerships. Such activities expose us to challenges and risks, including: integrating financial and operational reporting systems; establishing satisfactory budgetary and other financial controls; funding increased capital needs, overhead expenses or cash flow shortages that may occur if anticipated sales and revenues are not realized or are delayed, whether by general economic or market conditions or unforeseen internal difficulties; obtaining management personnel required for expanded operations; obtaining necessary regulatory permissions; and establishing adequate reserves for any acquired book of business. In addition, the value of assets acquired may be lower than expected or may diminish due to credit defaults or changes in interest rates; the liabilities assumed may be greater than expected; and assets and liabilities acquired may be subject to foreign currency exchange rate fluctuation. We may also be

subject to financial exposures in the event that the sellers of the entities or business we acquire are unable or unwilling to meet their indemnification, reinsurance and other contractual obligations to us. Our failure to manage successfully any of the foregoing challenges and risks may adversely impact our results of operations.

Our information technology systems may be unable to meet the demands of customers and our workforce.

Our information technology systems service our insurance portfolios. Accordingly, we are highly dependent on the effective operation of these systems. While we believe that the systems are adequate to service our insurance portfolios, there can be no assurance that they will operate in all manners in which we intend or possess all of the functionality required by customers currently or in the future.

Our customers, especially our mortgage insurance customers, require that we conduct our business in a secure manner, electronically via the Internet or via electronic data transmission. We must continually invest significant resources in establishing and maintaining electronic connectivity with customers. In order to integrate electronically with customers in the mortgage insurance industry, we require electronic connections between our systems and those of the industry's largest mortgage servicing systems and leading pricing and loan origination systems. Our mortgage group currently possesses connectivity with certain of these external systems, but there is no assurance that such connectivity is sufficient, and we are continually undertaking new electronic integration efforts with third-party loan servicing, pricing and origination systems. We also rely on electronic integrations in our insurance operations with third parties and customers. Inflation and supply chain issues for components to support our informational technology systems or those of our vendors pose risks which are beyond our control and may be difficult to manage.

Our business, financial condition and operating results may be adversely affected if we do not possess or timely acquire the requisite set of electronic integrations necessary to keep pace with the technological demands of customers. Additionally, attracting and retaining talented information technology employees who support our systems and those of our vendors has been challenging, although the recent easing of this trend may mitigate this risk.

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Technology failures and cyber attacks, including, but not limited to, ransomware, exploitation in software or code with malicious intent, state-sponsored cyber attacks, may impact us or our business partners and service providers, causing a disruption in service and operations which would negatively impact our business and/or expose us to litigation.

We rely on information technology systems to process, transmit, store and protect the electronic information, financial data and proprietary models that are critical to our business. Furthermore, a significant portion of the communications between our employees and our business partners and service providers depends on information technology and electronic information exchange. Like all companies, our information technology systems are vulnerable to data breaches, interruptions or failures due to events that may be beyond our control, including, but not limited to, natural disasters, power outages, theft, terrorist attacks, computer viruses, malicious actors, errors in usage or through social engineering or phishing and general technology failures. Security breaches by third parties could expose us to the loss or misuse of our information, litigation, financial losses and potential liability. In addition, cyber incidents that impact the availability, reliability, speed, accuracy or other proper functioning of these systems could have a significant negative impact on our operations and possibly our results.

We are dependent on certain third party technology service providers and other service providers to operate our business, notably major cloud providers, Software-as-a-Service (or SaaS) solutions, and on-premise software, including proprietary and open source solutions. We also outsource certain business process functions to third parties and may continue do so in the future. This practice exposes us to increased risks related to data security, service disruptions, supply chain issues or the effectiveness of our control system, which could result in our ability to conduct business operations, monetary and reputational damage or harm to our competitive position.

Cyber incidents or data breaches caused by bad actors or unintentional human error impacting data, including personal data, we maintain or use during our business operations may result in regulatory fines or action, reputation damage and a disruption in our business operations.

We collect, process and store data, including the personal data of our employees, customers and policyholders, as part of our business operations. While we believe we have effective technical and organizational measures in place to prevent, detect, manage and mitigate the impact of data breaches caused by malicious actors, systemic failures or human error, we cannot offer complete assurances that

significant data breaches will not occur. A cyber incident could also result in a violation of applicable privacy, data protection or other laws, damage our reputation, cause a loss of customers, adversely affect our stock price, cause us to incur remediation costs, increased insurance premiums, and/or give rise to monetary fines and penalties, any of which could adversely affect our business.

A downgrade in our ratings or our inability to obtain a rating for our operating insurance and reinsurance subsidiaries may adversely affect our relationships with clients and brokers and negatively impact sales of our products.

Similar to our competitors, a ratings downgrade or the potential for such a downgrade, or failure to obtain a necessary rating, could adversely affect our relationships with agents, brokers, wholesalers, intermediaries, clients and other distributors of our existing and new products and services. Some of the reinsurance agreements assumed by our reinsurance operations include provisions that a ratings downgrade or other specified triggering event with respect to our reinsurance operations, such as a reduction in surplus by specified amounts during specified periods, provide our ceding company clients certain rights, including, the right to terminate the subject reinsurance agreement and/or to require us to post additional collateral. Any ratings downgrade or failure to obtain a necessary rating could adversely affect our ability to compete in our markets, could cause our premiums and earnings to decrease and could have a material adverse impact on our financial condition and results of operations. In some cases, a downgrade in ratings of certain of our operating subsidiaries may constitute an event of default under our credit facilities.

We can offer no assurances that our ratings will remain at their current levels or that any of our ratings which are under review or watch by ratings agencies will remain unchanged. It is possible that rating agencies may modify their evaluation criteria, heighten the level of scrutiny they apply when analyzing companies in our industry, adjust upward the capital and other requirements employed in their models and/or discontinue credit and debt instruments or other structures deployed for maintenance of certain rating levels. We may need to raise additional funds through equity or debt financings. Any equity or debt financing, if available at all, may be on terms that are unfavorable to us. Equity financings could be dilutive to our existing shareholders and could result in the issuance of securities that have rights, preferences and privileges that are senior to those of our outstanding securities. If we are not able to obtain adequate capital, our business, results of operations and financial condition could be adversely affected. See “Capital Resources” in Item 7 for further details.

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For further information on our financial strength and/or issuer ratings, see “Ratings” in Item 1. For further information on our letter of credit facilities, see the Letter of Credit and Revolving Credit Facilities section of “Contractual Obligations and Commercial Commitments” in Item 7.

Our ability to execute successfully our business strategy, continue to grow and innovate and offer our employees a dynamic and supportive workplace depends on the recruitment, retention and promotion of talented, agile, diverse and resilient employees at all levels of our organization.

With the easing of restrictions relating to the COVID-19 pandemic, we have adopted a hybrid work model in most of our offices with employees returning to the office for part of the work week. The pandemic impacted employee work models and, in some cases, also impacted employee workloads and attitudes about work. We provide a work environment and culture which reflects our goal to “Enable Possibility”. We offer flexible work arrangements, when possible, for our employees globally, as well as competitive compensation packages which include participation in our Employee Stock Purchase Plan and the possibility of equity awards at certain job levels. Over the past few years, we have also implemented and expanded our learning programs, career leveling and employee networks, all of which we believe will help us retain talent. Our leadership and Board promote the goals of building a diverse employee population and fostering an environment that allows us to fully leverage and engage that diversity as a competitive edge which benefits both our employees and our business. While our efforts to attract, develop and retain talented employees continues to be a top priority, current job market conditions present challenges for us and may adversely impact our ability to fully realize our business strategy.

Our success will depend on our ability to maintain and enhance effective operating procedures and internal controls and our ERM program.

We operate within an ERM framework designed to identify, assess and monitor our risks. We consider underwriting, reserving, investment, credit and operational risk in our ERM framework. Losses, reputational damage, regulatory fines and litigation are among the adverse impacts which can arise if we fail to operate an effective ERM framework. Operational risk and losses can result from, among other things, fraud, errors, failure to document transactions properly or to obtain proper internal authorization, failure to comply with regulatory requirements, information technology or information security failures and failure to train employees appropriately or adequately. We continuously enhance our operating procedures and internal controls to effectively support our business and our regulatory and reporting

requirements. As a result of the inherent limitations in all control systems, no evaluation of controls can provide absolute assurance that all control issues and instances of fraud, if any, within the company have been detected. These inherent limitations include the realities that judgments in decision making can be faulty, and that breakdowns can occur because of simple error or mistake or circumvention of controls. There can be no assurance that our control system will succeed in achieving its stated goals under all potential future conditions. Any ineffectiveness in our controls or procedures could have a material adverse effect on our business. For further information on our ERM framework, see “Enterprise Risk Management” in Item 1.

We are exposed to credit risk in certain of our business operations.

In addition to exposure to credit risk related to our investment portfolio, reinsurance recoverables and reliance on brokers and other agents, we are exposed to credit risk in other areas of our business related to policyholders. We are exposed to credit risk in our insurance group’s surety unit where we guarantee to a third party that our policyholder will satisfy certain performance or financial obligations. If our policyholder defaults, we may suffer losses and be unable to be reimbursed by our policyholder. We are also exposed to credit risk from policyholders on smaller deductibles in other insurance group lines, such as healthcare and excess and surplus casualty. Although we have not experienced any material credit losses to date, an increased inability of our policyholders to meet their obligations to us could have a material adverse effect on our financial condition and results of operations. See note 3, “Significant Accounting Policy.”

Our business is subject to applicable laws and regulations relating to economic trade sanctions and foreign bribery laws, the violation of which could adversely affect our operations.

We must comply with all applicable economic sanctions and anti-bribery laws and regulations of the U.S. and other foreign jurisdictions where we operate. U.S. laws and regulations applicable to us and others who provide insurance and reinsurance include the economic trade sanctions laws and regulations administered by the Treasury’s Office of Foreign Assets Control as well as certain laws administered by the U.S. Department of State. New sanction regimes may be initiated, or existing sanctions expanded, at any time, which can immediately impact our business activities. Since the Russian invasion of Ukraine in February 2022, there have been several sanctions packages imposed by the U.S., U.K. and EU which impact our business. The sanctions are complex, numerous and nuanced, requiring close review and assessment as they pertain to our business. We are also subject to the U.S. Foreign Corrupt Practices Act and other anti-bribery laws such as the U.K. Bribery Act that generally

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bar corrupt payments or unreasonable gifts to foreign governments or officials. Although we have policies and controls in place designed to ensure compliance with these laws and regulations, it is possible that an employee or intermediary could fail to comply with applicable laws and regulations. In addition, we may interpret a complex sanction in a way which may differ from a regulator. In these cases, we could be exposed to fines, criminal penalties and other sanctions. Such violations could limit our ability to conduct business and/or damage our reputation, resulting in a material adverse effect on our financial condition and results of operations.

New legislation or regulations relating to the U.K.’s Withdrawal from the EU could adversely affect us.

The U.K. ceased to be a member state of the European Union in January 2020. Although the EU and U.K. reached a limited agreement in relation to certain matters, U.K. insurers and reinsurers no longer have automatic access to EU markets and vice versa. Our U.K. domiciled entities and our Lloyd’s Syndicates may no longer “passport” within the EU and are now part of the U.K. temporary permissions regime which allows firms to operate in the U.K. for a limited period while they seek authorization from the U.K. regulators. We have implemented changes in our operations to accommodate Brexit; however we remain subject to new proposals and regulations which may negatively impact U.K. underwriting activities in respect of EU risks and policyholders.

Risks Relating to Financial Markets and Investments

Adverse developments in the financial markets could have a material adverse effect on our results of operations, financial position and our businesses, and may also limit our access to capital; our policyholders, reinsurers and retrocessionaires may also be affected by such developments, which could adversely affect their ability to meet their obligations to us.

Adverse developments in the financial markets, resulting from inflation, global recessionary pressures, geopolitical conflict, among other factors, has increased uncertainty levels and heightened volatility in the capital and credit markets. These developments may result in realized and unrealized losses on our investment portfolio that could have a material adverse effect on our results of operations, financial position and our businesses, and may also limit our access to capital required to operate our business. More specifically, economic conditions could also have a material impact on the frequency and severity of claims and therefore could negatively impact our underwriting returns. In addition, our policyholders, reinsurers and retrocessionaires may be affected by developments in the financial markets, which could adversely affect their ability to meet their obligations to us. The volatility in the financial markets could continue to significantly affect our investment returns, reported results and shareholders’ equity.

The capital requirements of our businesses depend on many factors, including regulatory and rating agency requirements, the performance of our investment portfolio, our ability to write new business successfully, the frequency and severity of catastrophe events and our ability to establish premium rates and reserves at levels sufficient to cover losses.

Disruption to the financial markets and weak economic conditions resulting from situations such as post pandemic imbalances, inflation and geopolitical conflict may adversely and materially impact our investments, financial condition and results of operation.

Disruption in the financial markets and the downturn in global economic activity resulting from the geopolitical conflict, elevated financing rates, housing market declines or other macro-and micro-economic conditions could adversely affect the valuation of securities in our investment portfolio. Credit spread widening and/or equity market volatility could result in temporary or permanent impairment. Elevated levels of inflation could drive higher U.S. and global interest rates, negatively impacting asset prices, particularly in fixed income. In addition, a lack of pricing transparency, decreased market liquidity, the strengthening or weakening of foreign currencies against the U.S. Dollar, individually or in tandem, could have a material adverse effect on our results through realized losses, impairments and changes in unrealized positions in our investment portfolio. Furthermore, issuers of the investments we hold under the equity method of accounting report their financial information to us one month to three months following the end of the reporting period. Accordingly, the adverse impact of any disruptions in global financial markets on equity method income from these investments would likely not be reflected in our current quarter results and would instead be reported in the subsequent quarter.

Our operating results depend in part on the performance of our investment portfolio. A significant portion of cash and invested assets held by Arch consists of fixed maturities (72.1% as of December 31, 2022). Although our current investment guidelines and approach stress preservation of capital, market liquidity and diversification of risk, our investments are subject to market-wide risks and fluctuations. In addition, we are subject to risks inherent in particular securities or types of securities, as well as sector concentrations. We may not be able to realize our investment objectives, which could have a material adverse effect on our financial results. In the event that we are unsuccessful in calibrating the liquidity of our investment portfolio with our expected insurance and reinsurance liabilities, we may be forced to liquidate our investments at times and prices that are not optimal, which could have a material adverse effect on our financial results and ability to conduct our business.

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Foreign currency exchange rate fluctuation may adversely affect our financial results.

We write business on a worldwide basis, and our results of operations may be affected by fluctuations in the value of currencies other than the U.S. Dollar. The primary foreign currencies in which we operate are the Euro, the British Pound Sterling, the Australian Dollar and the Canadian Dollar. In order to minimize the possibility of losses we may suffer as a result of our exposure to foreign currency fluctuations in our net insurance liabilities, we invest in securities denominated in currencies other than the U.S. Dollar. In addition, we may replicate investment positions in foreign currencies using derivative financial instruments. Changes in the value of available-for-sale investments due to foreign currency rate movements are reflected as a direct increase or decrease to shareholders' equity and are not included in the statement of income.

Uncertainty relating to the determination of LIBOR and the phasing out and replacement of LIBOR with alternative benchmark rates may adversely impact us.

In order to mitigate the potential adverse effects on our cost of capital caused by the uncertainty of the timing and impact of the phase-out of LIBOR, we entered into certain amendments to our credit facilities in 2021 in order to replace the LIBOR-based benchmarks for borrowings and letters of credit denominated in British Pounds Sterling and Euros with the Sterling Overnight Index Average (“SONIA”) and the Euro Inter-bank Offered Rate (“EURIBOR”), respectively, as SONIA and EURIBOR have emerged as preferred alternative benchmarks with respect to certain indebtedness and other financial instruments denominated in these currencies. Similarly, in April 2022, we entered into an amendment to our credit facilities in order to replace the LIBOR-based benchmark for borrowings and letters of credit denominated in U.S. Dollars with a rate based on Secured Overnight Financing Rate (“SOFR”). However, there can be no assurance that these mitigation efforts will adequately protect against increases or volatility in our cost of capital. Although we believe we have taken appropriate measures to adjust to the replacement of LIBOR, the transition from LIBOR to SOFR and other alternative reference rates may adversely impact our investment portfolio, our cost of capital and our cost of issuing Bellemeade mortgage risk transfer securities and could require changes to our current asset liability strategies.

The determination of the amount of current expected CECL allowances taken on our investments is highly subjective and could materially impact our results of operations or financial position.

On a quarterly basis, we review our investments by applying an approach based on the CECL and whether declines in fair value below the cost basis requires an estimate of the expected credit loss. There can be no assurance that our management has accurately assessed the level of the credit loss allowance taken reflected in our financial statements. Furthermore, additional allowance may need to be taken or allowances provided for in the future. Further, rapidly changing and unpredictable credit and equity market conditions could materially affect the valuation of securities carried at fair value as reported within our consolidated financial statements and the period-to-period changes in value could vary significantly.

Our reinsurance subsidiaries may be required to provide collateral to ceding companies, by applicable regulators, their contracts or other commercial considerations. Their ability to conduct business could be significantly and negatively affected if they are unable to do so.

Arch Re Bermuda is a registered Bermuda insurance company and is not licensed or admitted as an insurer in any jurisdiction in the U.S., although Arch Re Bermuda has been approved as a “certified reinsurer” in certain U.S. states that allow reduced collateral for reinsurance ceded to such reinsurers. Arch Re Bermuda's contracts generally require it to post a letter of credit or provide other security, even in U.S. states where it has been approved for reduced collateral. State credit for reinsurance rules also generally provide that certified reinsurers such as Arch Re Bermuda must provide 100% collateral in the event their certified status is “terminated” or upon the entry of an order of rehabilitation, liquidation or conservation against a ceding insurer.

Although, to date, Arch Re Bermuda has not experienced any difficulties in providing collateral when required, if we are unable to post security in the form of letters of credit or trust funds when required, the operations of Arch Re Bermuda could be significantly and negatively affected.

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Risks Relating to Our Mortgage Operations

The ultimate performance of the Arch MI U.S. mortgage insurance portfolio remains uncertain.

The mix of business in our insured loan portfolio may affect losses. The presence of multiple higher-risk characteristics in a loan materially increases the likelihood of a claim on such a loan unless there are other characteristics to mitigate the risk. The mix of higher-risk loans, including affordable housing loans which often have higher-risk characteristics, could increase losses and harm our financial performance. The geographic mix of Arch MI U.S.’s business could increase losses and harm our financial performance.

Mortgage insurance premiums are set at the time coverage is procured, based in part on the expected duration of the coverage. We cannot cancel mortgage insurance coverage or adjust renewal premiums during the life of the policy. To the extent that the insured cancels coverage as a result of prior home price appreciation, the duration of coverage will be shorter, and we will receive less premium. Further, higher than anticipated claims generally cannot be offset by premium increases on policies in force or mitigated by our non-renewal or cancellation of insurance coverage. The premiums charged, and the associated investment income, may not be adequate to compensate us for the risks and costs associated with the insurance coverage provided to customers. A decrease in the amount of premium received or an increase in the number or size of claims, compared to what we anticipate, could adversely affect Arch MI U.S.’s results of operations and financial condition.

The frequency and severity of claims we incur is uncertain and will depend largely on general economic factors outside of our control, including, among others, changes in unemployment, home prices and interest rates in the U.S. Inflated home prices followed by a decline in home values could significantly decrease a borrower’s equity in their home, which would limit their ability to sell the property without incurring a loss, and could increase the frequency and severity of claims. Deteriorating economic conditions in the U.S., potentially due to prolonged recessionary conditions increasing levels of unemployment and inflation, could adversely affect the performance of our U.S. mortgage insurance portfolio and could adversely affect our results of operations and financial condition.

If the volume of low down payment mortgage originations declines, or if other government housing policies, practices or regulations change, the amount of mortgage insurance we write in the U.S. could decline, which would reduce our mortgage insurance revenues.

The size of the U.S. mortgage insurance market depends in large part upon the volume of low down payment home mortgage originations. Factors affecting the volume of low down payment mortgage originations include, among others: restrictions on mortgage credit due to stringent underwriting standards and liquidity issues affecting lenders; changes in mortgage interest rates and home prices, and other economic conditions in the U.S. and regional economies; population trends, including the rate of household formation; and U.S. government housing policy. Increases to mortgage interest rates have materially increased financing costs, and as a result may decrease the number of qualified borrowers and the volume of low down payment mortgage originations.

The private mortgage insurers’ principal government competitor is the Federal Housing Administration (“FHA”). Future changes to the FHA program, including any reduction to mortgage insurance premiums charged may negatively impact the amount of mortgage insurance we write in the U.S.

The Federal Housing Finance Agency (“FHFA”) as conservator of the GSEs continues to evaluate loan level price adjustments (“LLPAs”) assessed by the GSEs when purchasing loans. Effective on April 1, 2022, Fannie Mae and Freddie Mac increased upfront fees for “high-balance loans” (mortgages in excess of $647,000) and mortgages on second homes. On October 24, 2022, FHFA announced that the GSEs are eliminating upfront fees for certain first-time homebuyers, low-income borrowers, and underserved communities and is increasing fees for cash out refinance loans. On January 19, 2023, FHFA announced three new pricing grids that broadly adjusted pricing to GSE purchases. These, and future actions could cause a decline in the volume of low-down payment home mortgage purchases by the GSEs, could decrease demand for mortgage insurance, and could decrease our U.S. new insurance written and reduce mortgage insurance revenues.

On June 8, 2022, the FHFA announced the GSEs release of Fannie Mae's and Freddie Mac's Equitable Housing Finance Plans for 2022-2024. These plans are designed to foster housing finance markets that provide equitable access to affordable and sustainable housing, including through the use of special purpose credit programs (“SPCPs”). SPCPs are lending programs designed to expand access to credit among disadvantaged groups to address special social needs that exist today. The Consumer Finance Protection Bureau, the Department of Housing and Urban Development, and other federal agencies have issued guidance encouraging the use of

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SPCPs and providing assurances that properly structured SPCPs are permissible under federal law. New practices or programs implemented under the GSEs’ Equitable Housing Plans, may impact the underwriting and servicing standards on mortgages purchased by the GSEs and could increase the presence of multiple higher-risk characteristics in our insured loan portfolio. Further, the legal landscape applicable to SPCPs remains untested and loans originated under these programs could be subject to increased risk of private litigation or enforcement actions under state and federal law.

Changes to the role of the GSEs in the U.S. housing market or to GSE eligibility requirements for mortgage insurers could negatively impact our results of operations and financial condition, or reduce our operating flexibility.

Substantially all of Arch MI U.S.’s insurance written has been for loans sold to the GSEs. The charters of the GSEs require credit enhancement for low down payment mortgages to be eligible for purchase or guarantee by the GSEs. Any changes to the charters or statutory authorities of the GSEs would require congressional action to implement. If the charters of the GSEs were amended to change or eliminate the acceptability of private mortgage insurance, our mortgage insurance business could decline significantly.

In January 2021, the U.S. Department of Treasury (the “Treasury Department”) and FHFA announced an agreement to amend the preferred stock purchase agreements between the Treasury Department and the GSEs, originally entered into in September 2008, in order to, among other things, codify several existing FHFA conservatorship practices for the GSEs and outline a plan for the Treasury Department, in consultation with FHFA, to develop a proposal for continued GSE reform. If any GSE reform is adopted, whether through legislation or administrative action, it could impact the current role of private mortgage insurance as credit enhancement, including its reduction or elimination. Passage and timing of any comprehensive GSE reform or incremental change (legislative or administrative) is uncertain, making the actual impact on the mortgage insurance industry difficult to predict. Any such changes that come to pass could have a material adverse impact on the Company.

The PMIERs apply to Arch Mortgage Insurance Company and United Guaranty Residential Insurance Company, which are GSE-approved mortgage insurers (“eligible mortgage insurers”). The PMIERs impose limitations on the type of risk insured, the forms and insurance policies issued, standards for the geographic and customer diversification of risk, acceptable underwriting practices, quality assurance, loss mitigation, claims handling, standards for certain reinsurance cessions and financial requirements, among other things. The financial requirements require a mortgage insurer’s available assets, which generally include only the most liquid assets, to meet or exceed “minimum required

assets” as of each quarter end. Arch MI U.S.’s minimum required assets under the PMIERs will be determined, in part, by the particular risk profiles of the loans it insures. If, absent other changes, Arch MI U.S.’s mix of business changes to include more loans with higher loan-to-value ratios or lower credit scores, it will have a higher minimum required asset amount under the PMIERs and, accordingly, be required to hold more capital in order to maintain GSE eligibility. Our eligible mortgage insurers each satisfied the PMIERs’ financial requirements as of December 31, 2022. While we intend to continue to comply with these requirements, there can be no assurance that the GSEs will not change the PMIERs or that Arch Mortgage Insurance Company or United Guaranty Residential Insurance Company will continue as eligible mortgage insurers. If either or both of the GSEs were to cease to consider Arch Mortgage Insurance Company or United Guaranty Residential Insurance Company as eligible mortgage insurers and, therefore, cease accepting our mortgage insurance products, our results of operations and financial condition would be adversely affected.

The implementation of the Basel III Capital Accord and FHFA’s Enterprise Capital Rule may adversely affect the use of mortgage insurance and CRT opportunities.

With certain exceptions, the Basel III Rules became effective on January 1, 2014. In December 2017, the Basel Committee published final revisions to the Basel Capital Accord which is informally denominated in the U.S. as “Basel IV.” The Basel Committee expects the new rules to be fully implemented by January 2027. On September 9, 2022, the Federal banking agencies issued a statement reaffirming their commitment to implementing the 2017 revisions and stated that a request for public comment on new regulatory standards would be forthcoming. Under the Basel IV protocols, banks using the standardized approach for credit risk management will determine the risk-weight for residential mortgages based on the loan-to-value ratio at loan origination, without consideration of mortgage insurance. The U.S. regulatory agencies could determine that current U.S. rules for residential mortgages are “at least as stringent” as the Basel IV provisions, and therefore do not need to be modified. However, if U.S. regulators decide to adopt the Basel IV approach to mortgage assets, the capital relief benefits of mortgage insurance would be diminished, which could adversely affect the demand for mortgage insurance.

On December 17, 2020, the FHFA published a new capital framework for Fannie Mae and Freddie Mac that significantly increases minimum capital requirements for these GSEs. The new rule requires each GSE to maintain both higher minimum capital ratios and capital “buffers” to avoid restrictions on capital distributions and discretionary bonus payments. The rule also imposes a risk-weight floor of 10 percent on retained CRT positions. In a 2022 amendment,

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the risk-weight floor was reduced to 5 percent, and other changes were made to incentivize CRT transactions.

The new framework continues to take into account the benefits of mortgage insurance, provided the mortgage insurer is compliant with the PMIERs. The amount of capital relief afforded for mortgage insurers will depend on a number of factors, including the GSEs’ determination of the creditworthiness of the mortgage insurer. It is possible that the higher capital standards imposed on the GSEs will result in increased fees for homebuyers that will reduce the demand for mortgage loans, and therefore the demand for mortgage insurance. Further, the GSEs will independently determine the creditworthiness of mortgage insurance counterparties, which could affect the competitive position of individual mortgage insurance providers. Moreover, the higher risk-capital charges for residential mortgages could be incorporated into the PMIERs standards, thereby requiring mortgage insurers to hold higher capital levels in order to be recognized as approved counterparties for the GSEs. This could have a negative impact on our return on equity.

On January 4, 2023, the unified regulatory agenda issued by the Office of Management and Budget referenced that FHFA targets February 2023 for a notice of proposed rulemaking addressing capital requirements for derivatives; market risk; multifamily loans in general and multifamily loans with government subsidies specifically, and exposures of an Enterprise to the other Enterprise. There is a risk that future changes to the capital framework could adversely impact credit for credit risk transfer or the capital relief afforded for mortgage insurance.

Risk Relating to Our Company and Our Shares

Some of the provisions of our bye-laws and our shareholders agreement may have the effect of hindering, delaying or preventing third party takeovers or changes in management initiated by shareholders. These provisions may also prevent our shareholders from receiving premium prices for their shares in an unsolicited takeover.

Some provisions of our bye-laws could have the effect of discouraging unsolicited takeover bids from third parties or changes in management initiated by shareholders. These provisions may encourage companies interested in acquiring us to negotiate in advance with our Board, since the Board has the authority to overrule the operation of several of the limitations.

Among other things, our bye-laws provide: for a classified Board, in which the directors of the class elected at each annual general meeting holds office for a term of three years, with the term of each class expiring at successive annual general meetings of shareholders; that the number of directors is determined by the Board from time to time by a

vote of the majority of the Board; that directors may only be removed for cause, and cause removal shall be deemed to exist only if the director whose removal is proposed has been convicted of a felony or been found by a court to be liable for gross negligence or misconduct in the performance of his or her duties; that the Board has the right to fill vacancies, including vacancies created by an expansion of the Board; and for limitations on a shareholder’s right to raise proposals or nominate directors at general meetings. Our bye-laws provide that certain provisions that may have anti-takeover effects may be repealed or altered only with prior Board approval and upon the affirmative vote of holders of shares representing at least 65% of the total voting power of our shares entitled generally to vote at an election of directors.

The bye-laws also contain a provision limiting the rights of any U.S. person (as defined in section 7701(a)(30) of the Internal Revenue Code of 1986, as amended (the “Code”)) that owns shares of Arch Capital, directly, indirectly or constructively (within the meaning of section 958 of the Code), representing more than 9.9% of the voting power of all shares entitled to vote generally at an election of directors. The votes conferred by such shares of such U.S. person will be reduced by whatever amount is necessary so that after any such reduction the votes conferred by the shares of such person will constitute 9.9% of the total voting power of all shares entitled to vote generally at an election of directors. Notwithstanding this provision, the Board may make such final adjustments to the aggregate number of votes conferred by the shares of any U.S. person that the Board considers fair and reasonable in all circumstances to ensure that such votes represent 9.9% of the aggregate voting power of the votes conferred by all shares of Arch Capital entitled to vote generally at an election of directors. Arch Capital will assume that all shareholders (other than specified persons) are U.S. persons unless we receive assurance satisfactory to us that they are not U.S. persons.

The bye-laws also provide that the affirmative vote of at least 66 2/3% of the outstanding voting power of our shares (excluding shares owned by any person (and such person’s affiliates and associates) that is the owner of 15% or more (a “15% Holder”) of our outstanding voting shares) shall be required for various corporate actions, including: merger or consolidation of the company into a 15% Holder; sale of any or all of our assets to a 15% Holder; the issuance of voting securities to a 15% Holder; or amendment of these provisions; provided, however, the super majority vote will not apply to any transaction approved by the Board.

The provisions described above may have the effect of making more difficult or discouraging unsolicited takeover bids from third parties. To the extent that these effects occur, shareholders could be deprived of opportunities to realize takeover premiums for their shares and the market price of their shares could be depressed. In addition, these provisions

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could also result in the entrenchment of incumbent management.

There are regulatory limitations on the ownership and transfer of our common shares.

The jurisdictions where we operate have laws and regulations that require regulatory approval of a change in control of an insurer or an insurer's holding company. Where such laws apply to us, there can be no effective change in our control unless the person seeking to acquire control has filed a statement with the regulators and obtained prior approval for the proposed change. Certain regulators may at any time, by written notice, object to a person holding shares in an insurer or an insurer's holding company if it appears to the regulator that the person is not or is no longer fit and proper to be such a holder. The regulator may require the shareholder to reduce its holding in the insurer or an insurer's holding company and direct, among other things, that such shareholder’s voting rights attaching to the shares in an insurer or an insurer's holding company shall not be exercisable.

Arch Capital is a holding company and is dependent on dividends and other distributions from its operating subsidiaries.

Arch Capital is a holding company whose assets primarily consist of the shares in our subsidiaries. Generally, Arch Capital depends on its available cash resources, liquid investments and dividends or other distributions from subsidiaries to make payments, including the payment of debt service obligations and operating expenses it may incur and any payments of dividends, redemption amounts or liquidation amounts with respect to our preferred shares and common shares, and to fund the share repurchase program. The ability of our regulated insurance and reinsurance subsidiaries to pay dividends or make distributions is subject to legislative constraints and dependent on their ability to meet applicable regulatory standards. In addition, the ability of our insurance and reinsurance subsidiaries to pay dividends to Arch Capital and to intermediate parent companies owned by Arch Capital could be constrained by our dependence on financial strength ratings from independent rating agencies. Our ratings from these agencies depend to a large extent on the capitalization levels of our insurance and reinsurance subsidiaries.

General market conditions and unpredictable factors could adversely affect market prices for our outstanding preferred shares.

There can be no assurance about the market prices for our series of preferred shares that are traded publicly. Several factors, many of which are beyond our control, will influence the fair value of our preferred shares, including, but not limited to:

•whether dividends have been declared and are likely to be declared on any series of our preferred shares from time to time;

•our creditworthiness, financial condition, performance and prospects;

•whether the ratings on any series of our preferred shares provided by any ratings agency have changed;

•the market for similar securities; and

•economic, financial, geopolitical, social, regulatory or judicial events that affect us and/or the insurance or financial markets generally.

Dividends on our preferred shares are non-cumulative.

Dividends on our preferred shares are non-cumulative and payable only out of lawfully available funds of Arch Capital under Bermuda law. Consequently, if the Board (or a duly authorized committee of the Board) does not authorize and declare a dividend for any dividend period with respect to any series of our preferred shares, holders of such preferred shares would not be entitled to receive any such dividend, and such unpaid dividend will not accrue and will never be payable. Arch Capital will have no obligation to pay dividends for a dividend period on or after the dividend payment date for such period if the Board (or a duly authorized committee of the Board) has not declared such dividend before the related dividend payment date; if dividends on our series F or series G preferred shares are authorized and declared with respect to any subsequent dividend period, Arch Capital will be free to pay dividends on any other series of preferred shares and/or our common shares. In the past, we have not paid dividends on our common shares.

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Our preferred shares are equity and are subordinate to our existing and future indebtedness.

Our preferred shares are equity interests and do not constitute indebtedness. As such, these preferred shares will rank junior to all of our indebtedness and other non-equity claims with respect to assets available to satisfy our claims, including in our liquidation. Our existing and future indebtedness may restrict payments of dividends on our preferred shares. Additionally, unlike indebtedness, where principal and interest would customarily be payable on specified due dates, in the case of preferred shares, (1) dividends are payable only if declared by the Board (or a duly authorized committee of the Board) and (2) as described under “Risks Relating to Our Company—Arch Capital is a holding company and is dependent on dividends and other distributions from its operating subsidiaries,” we are subject to certain regulatory and other constraints affecting our ability to pay dividends and make other payments.

We may issue additional securities that rank equally with or senior to our series F and series G preferred shares without limitation. The issuance of securities ranking equally with or senior to our preferred shares may reduce the amount available for dividends and the amount recoverable by holders of such series in the event of a liquidation, dissolution or winding-up of Arch Capital.

The voting rights of holders of our preferred shares are limited.

Holders of our preferred shares have no voting rights with respect to matters that generally require the approval of voting shareholders. The limited voting rights of holders of our preferred shares include the right to vote as a class on certain fundamental matters that affect the preference or special rights of our preferred shares as set forth in the certificate of designations relating to each series of preferred shares. In addition, if dividends on our series F or series G preferred shares have not been declared or paid for the equivalent of six dividend payments, whether or not for consecutive dividend periods, holders of the outstanding series F or series G preferred shares will be entitled to vote for the election of two additional directors to the Board subject to the terms and to the limited extent as set forth in the certificate of designations relating to such series of preferred shares.

Risks Relating to Taxation

We and our non-U.S. subsidiaries may become subject to U.S. federal income taxation and/or the U.S. federal income tax liabilities of our U.S. subsidiaries may increase, including as a result of changes in tax law.

Arch Capital and its non-U.S. subsidiaries intend to operate their business in a manner that will not cause them to be treated as engaged in a trade or business in the U.S. and, thus, will not be required to pay U.S. federal income taxes (other than U.S. excise taxes on insurance and reinsurance premiums and withholding taxes on certain U.S. source investment income) on their income. However, because there is uncertainty as to the activities which constitute being engaged in a trade or business in the U.S., there can be no assurance that the IRS will not contend successfully that Arch Capital or its non-U.S. subsidiaries are engaged in a trade or business in the U.S., in which case our shareholders' equity and earnings could be adversely affected.

Congress has been considering several legislative proposals intended to eliminate certain perceived tax advantages of Bermuda and other non-U.S. jurisdictions. There is no assurance that any such legislative proposal will not be enacted into law or that any such enacted law would not materially increase our income tax liabilities or those of our subsidiaries.

The continuing implementation of the Tax Cuts Act may have a material and adverse impact on our operations and financial condition.

Certain provisions in the Tax Cuts Act could have a material and adverse impact on our financial condition and business operation. One such provision imposes a 10% minimum base erosion and anti-abuse tax (increased to 12.5% for taxable years after 2025) on the “modified taxable income” of a U.S. corporation (or a non-U.S. corporation engaged in a U.S. trade or business) over such corporation’s regular U.S. federal income tax, reduced by certain tax credits. The “modified taxable income” of a corporation is determined without deduction for certain payments by such corporation to its non-U.S. affiliates (including reinsurance premiums). Other provisions of the Tax Cuts Act that could have a material and adverse impact on us include a provision that defers or disallows a U.S. corporation’s deduction of interest expense to the extent such interest expense exceeds a specified percentage of such U.S. corporation’s “adjusted taxable income” and a provision that adjusts the manner in which a U.S. property and casualty insurance company computes its loss reserve.

In addition, there is no assurance that subsequent changes in tax laws or regulations will not materially and adversely affect our operations and financial condition.

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Proposed Treasury Regulations issued on January 24, 2022, if finalized in their current form, could (on prospective basis) cause our U.S. shareholders (including tax-exempt U.S. shareholders) to be subject to current U.S. federal income tax on the portion of our earnings attributable to certain intercompany reinsurance income (whether or not such income is distributed).

Unless an exception applies, U.S. shareholders generally are required to include currently in income a portion of any RPII recognized by our foreign subsidiaries, whether or not distributed. Generally, RPII is insurance income (including reinsurance income) of a foreign corporation with respect to which the insured is a United States shareholder of the foreign corporation or a related person to such a shareholder.

Under one exception to the foregoing RPII rules, U.S. shareholders are not required to include a CFC’s RPII currently in income if the CFC’s gross RPII is less than 20% of its total gross insurance income for the taxable year in question (the “RPII 20% gross income exception”).

Under current law, we currently expect each of our non-U.S. subsidiaries to satisfy the RPII 20% gross income exception, and therefore we currently do not expect any U.S. shareholder to be required to currently include RPII in income (although there can be no assurance that this is or will continue be the case). However, proposed Treasury Regulations issued on January 24, 2022, if finalized in their current form, would for the first time (on a prospective basis) expand the definition of RPII to include certain intercompany insurance income (including reinsurance income) in a manner that could cause certain of our foreign subsidiaries not to satisfy the RPII 20% gross income exception. In such event, (1) all U.S. shareholders (not just 10% U.S. shareholders) would be required to include RPII in income currently, whether or not distributed, and (2) U.S. shareholders that are tax exempt entities would be required to treat such RPII inclusions as unrelated business taxable income. Current and prospective U.S. shareholders should consult their own tax advisors as to the potential impact of these recently proposed Treasury Regulations.

We may become subject to taxes in Bermuda after March 31, 2035, which may have a material adverse effect on our results of operations.

Under current Bermuda law, we are not subject to tax on income, profits, withholding, capital gains or capital transfers. Furthermore, we have obtained from the Minister of Finance of Bermuda under the Exempted Undertakings Tax Protection Act 1966 of Bermuda, an assurance that, in the event that Bermuda enacts legislation imposing tax computed on profits, income, any capital asset, gain or appreciation, or any tax in the nature of estate duty or inheritance tax, then the imposition of the tax will not be

applicable to us or our operations until March 31, 2035. Given the limited duration of the Minister of Finance's assurance we cannot be certain that we will not be subject to any Bermuda tax after that date, which may have a material adverse effect on our results of operations. This assurance does not, however, prevent the imposition of taxes on any person ordinarily resident in Bermuda or any company in respect of its ownership of real property or leasehold interests in Bermuda.

The impact of Bermuda's letter of commitment to the OECD to eliminate harmful tax practices is uncertain and could adversely affect our tax status in Bermuda

OECD has published reports and launched a global initiative among member and non-member countries on measures to limit harmful tax competition. These measures are largely directed at counteracting the effects of tax havens and preferential tax regimes in countries around the world. Bermuda was not listed in the most recent report as an uncooperative tax haven jurisdiction because it has substantially implemented the internationally agreed tax standard and previously committed to eliminate harmful tax practices, to embrace international tax standards for transparency, to exchange information and to eliminate an environment that attracts business with no substantial domestic activity. We are not able to predict what changes will arise from the commitment or whether such changes will subject us to additional taxes.

Legislation enacted in Bermuda as to Economic Substance may affect our operations.

Pursuant to the Economic Substance Act 2018 (as amended) of Bermuda and related regulations (the “ES Act”), which came into force on January 1, 2019, a registered entity other than an entity which is resident for tax purposes in certain jurisdictions outside Bermuda (“non-resident entity”) that carries on as a business any one or more of the “relevant activities” referred to in the ES Act must comply with economic substance requirements. The ES Act may require in-scope Bermuda entities which are engaged in such “relevant activities” to be directed and managed in Bermuda, have an adequate level of qualified employees in Bermuda, incur an adequate level of annual expenditure in Bermuda, maintain physical offices and premises in Bermuda or perform core income-generating activities in Bermuda. The list of “relevant activities” includes carrying on any one or more of the following activities: banking, insurance, fund management, financing, leasing, headquarters, shipping, distribution and service center, intellectual property and holding entities. An in-scope Bermuda entity that carries on a relevant activity is obliged under the ES Act to file a declaration with the Bermuda Registrar of Companies on an annual basis containing certain information. Any entity found to be lacking adequate economic substance may be fined or ordered by a court to take action to remedy such failure (or

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face being struck off the companies register). As a result, there is a risk that non-compliance with its economic substance requirements under the ES Act could require Arch to enhance its infrastructure in Bermuda, and this may result in some additional operational expenditures, increased tax liabilities and/or compliance costs for Arch.

We may become subject to increased taxation in Bermuda and other countries as a result of the OECD's plan on “Base erosion and profit shifting.”

The OECD, with the support of the G20, initiated the “base erosion and profit shifting” (“BEPS”) project in 2013 in response to concerns that changes are needed to international tax laws to address situations where multinationals may pay little or no tax in certain jurisdictions by shifting profits away from jurisdictions where the activities creating those profits may take place. In November 2015, “final reports” were approved for adoption by the G20 finance ministers. The final reports provide the basis for international standards for corporate taxation that are designed to prevent, among other things, the artificial shifting of income to tax havens and low-tax jurisdictions, the erosion of the tax base through interest deductions on intercompany debt and the artificial avoidance of permanent establishments (i.e., tax nexus with a jurisdiction).

Legislation to adopt and implement these standards, including country by country reporting, has been enacted or is currently under consideration in a number of jurisdictions. As a result, our income may be taxed in jurisdictions where it is not currently taxed and at higher rates of tax than currently taxed, which may substantially increase our effective tax rate. Also, the continued adoption of these standards may increase the complexity and costs associated with tax compliance and adversely affect our financial position and results of operations.

In May 2019, the OECD published a “Programme of Work,” divided into two pillars, which is designed to address the tax challenges created by an increasing digitalized economy. Pillar I addresses the broader challenge of a digitalized economy and focuses on the allocation of group profits among taxing jurisdictions based on a market-based concept rather than historical “permanent establishment” concepts. In January 2020, the OECD released a statement excluding most financial services activities, including insurance activities, from the scope of the profit reallocation mechanism in Pillar I. The OECD statement cited the presence of commercial (rather than consumer) customers as grounds for the carve-out, but also acknowledged that a “compelling case” could be made that the consumer-facing business lines of insurance companies should be excluded from the scope of Pillar I given the impact of regulations and licensing requirements that typically ensure that residual profits are largely realized in local customer markets. However, profits from

“unregulated elements of the financial services sector” remain in scope but only where revenue exceeds €20 billion. Pillar II addresses the remaining BEPS risk of profit shifting to entities in low tax jurisdictions by introducing a global minimum tax (15%) and a proposed tax on base eroding payments, which would operate through a denial of a deduction or imposition of source-based taxation (including withholding tax) on certain payments. In October 2021, 136 jurisdictions agreed on a two-pillar solution to address the tax challenges arising from the digitalization of the economy. In December 2021, the OECD released Model Rules for implementation of Pillar II followed by the release of detailed commentary in March 2022. Further details of the Implementation Package and related topics is expected in early 2023. The OECD expects the rules to be enacted into domestic legislation in 2023 in order for the rules to be effective from 2023 (with a key element of the rules, the UTPR, deferred for one year until 2025).

On December 15, 2022, the EU formally adopted Council Directive on ensuring a global minimum level of taxation for groups operating in the Union. Member States are required to transpose the Directive into their domestic law by December 31, 2023.The OECD expects the rules to be enacted into domestic legislation in 2023 in order for the rules to be effective from 2023 (with a key element of the rules, the UTPR, deferred for one year until 2025). The adoption of these rules may increase the complexity and costs associated with tax compliance and may adversely affect our financial position and results of operations.

Application of the EU Anti-Tax Avoidance Directives

As part of the BEPS project, the EU Council adopted on 12 July 2016 Council Directive (EU) 2016/1164 (“ATAD I”), as amended by Council Directive (EU) 2017/952 (“ATAD II”, together with ATAD I, “ATAD”), to provide for minimum standards across EU Member States for tackling aggressive tax planning involving hybrid tax mismatches and interest deductibility. ATAD I was required to be transposed into domestic Member State law with effect from January 1, 2019, whilst ATAD II was required to be transposed into domestic Member State law with effect from January 1, 2020 (with an exception in respect of reverse hybrid mismatch provisions, which will take effect on January 1, 2022). On December 22, 2021, the European Commission published a proposal for a Directive (“ATAD III”) laying down rules to prevent the misuse of shell entities for improper tax purposes and amending the Directive on administrative cooperation (Directive 2011/16/EU). If adopted, ATAD III will be effective from January 1, 2024. ATAD and ATAD III could result in increased tax liabilities and/or compliance costs and administrative burden for us.

ARCH CAPITAL 57 2022 FORM 10-K

ITEM 1B. UNRESOLVED STAFF COMMENTS

None.

ITEM 2. PROPERTIES

We lease office space in Bermuda where our principal offices are located. Our insurance group leases space for offices in the U.S., Canada, Bermuda, U.K., Europe and Australia. Our reinsurance group leases space for offices in the U.S., Bermuda, U.K., Europe, Canada and Dubai. Our mortgage group leases space for offices in the U.S., Hong Kong and Australia. We believe that the above described office space is adequate for our needs. However, as we continue to develop our business, we may open additional office locations in 2023.

ITEM 3. LEGAL PROCEEDINGS

We, in common with the insurance industry in general, are subject to litigation and arbitration in the normal course of our business. As of December 31, 2022, we were not a party to any litigation or arbitration which is expected by management to have a material adverse effect on our results of operations and financial condition and liquidity.

ITEM 4. MINE SAFETY DISCLOSURES

Not applicable.

ARCH CAPITAL 58 2022 FORM 10-K

PART II

ITEM 5. MARKET FOR REGISTRANT’S COMMON EQUITY, RELATED STOCKHOLDER MATTERS AND ISSUER PURCHASES OF EQUITY SECURITIES

HOLDERS

As of February 17, 2023, and based on information provided to us by our transfer agent and proxy solicitor, there were 1,150 holders of record of our common shares (NASDAQ: ACGL) and approximately 215,000 beneficial holders of our common shares.

ISSUER PURCHASES OF EQUITY SECURITIES

The following table summarizes our purchases of common shares for the 2022 fourth quarter:

	Issuer Purchases of Common Shares
Period	Total Number of Shares Purchased (1)	Average Price Paid per Share		Total Number of Shares Purchased as Part of Publicly Announced Plans or Programs	Approximate Dollar Value of Shares that May Yet be Purchased Under the Plan or Programs ($000’s) (2)
10/1/2022-10/31/2022	59,926	$	53.08	—	$	596,411
11/1/2022-11/30/2022	29,362	$	56.43	—	$	596,411
12/1/2022-12/31/2022	3,420	$	60.61	—	$	1,000,000
Total	92,708	$	54.42	—	$	1,000,000

(1)    Includes repurchases by Arch Capital of shares, from time to time, from employees in order to facilitate the payment of withholding taxes on restricted shares granted and the exercise of stock appreciation rights. We purchased these shares at their fair market value, as determined by reference to the closing price of our common shares on the day the restricted shares vested or the stock appreciation rights were exercised.

(2)    Remaining amount available at December 31, 2022 under Arch Capital’s $1.0 billion share repurchase authorization, authorized by the Board of Directors of ACGL on December 19, 2022. Repurchases under this authorization may be effected from time to time in open market or privately negotiated transactions through December 31, 2024.

ARCH CAPITAL 59 2022 FORM 10-K

PERFORMANCE GRAPH

The following graph compares the cumulative total shareholder return on our common shares for each of the last five years through December 31, 2022 to the cumulative total return, assuming reinvestment of dividends, of (1) S&P 500 Composite Stock Index (“S&P 500 Index”) and (2) the S&P 500 Property & Casualty Insurance Index. The share price performance presented below is not necessarily indicative of future results.

CUMULATIVE TOTAL SHAREHOLDER RETURN (1)(2)(3)

		Base Period
	Company Name/Index	12/31/17	12/31/18	12/31/19	12/31/20	12/31/21	12/31/22
l	Arch Capital Group Ltd.	$100.00	$88.31	$141.75	$119.21	$146.91	$207.49
n	S&P 500 Index	$100.00	$95.62	$125.72	$148.85	$191.58	$156.88
p	S&P 500 Property & Casualty Insurance Index	$100.00	$95.31	$119.97	$128.31	$153.05	$181.93

(1)    Stock price appreciation plus dividends.

(2)    The above graph assumes that the value of the investment was $100 on December 31, 2017.

(3)    This graph is not “soliciting material,” is not deemed filed with the SEC and is not to be incorporated by reference in any filing by us under the Securities Act of 1933 or the Securities and Exchange Act of 1934, whether made before or after the date hereof and irrespective of any general incorporation language in any such filing.

ITEM 6. [RESERVED]

ARCH CAPITAL 60 2022 FORM 10-K

ITEM 7. MANAGEMENT’S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS OF OPERATIONS

The following is a discussion and analysis of the financial condition and results of operations for the year ended December 31, 2022 and 2021. Comparisons between 2021 and 2020 have been omitted from this Form 10-K, but may be found in "Management's Discussion and Analysis of Financial Condition and Results of Operations" in Part II, Item 7 of the Company's Annual Report on Form 10-K year ended December 31, 2021 filed with the SEC. This discussion and analysis contains forward-looking statements which involve inherent risks and uncertainties. All statements other than statements of historical fact are forward-looking statements. These statements are based on our current assessment of risks and uncertainties. Actual results may differ materially from those expressed or implied in these statements and, therefore, undue reliance should not be placed on them. Important factors that could cause actual events or results to differ materially from those indicated in such statements are discussed in this report, including the sections entitled “Cautionary Note Regarding Forward-Looking Statements,” and “Risk Factors.”

This discussion and analysis should be read in conjunction with our audited consolidated financial statements and notes thereto presented under Item 8. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.

		Page No.
Overview		62
Current Outlook		62
Financial Measures		63
Comments on Non-GAAP Measures		64
Results of Operations		66
	Insurance Segment	67
	Reinsurance Segment	68
	Mortgage Segment	69
	Corporate Segment	71
Summary of Critical Accounting Estimates		72
Financial Condition		80
Liquidity		83
Capital Resources		85
Contractual Obligations and Commitments		88
Ratings		89
Catastrophic Events and Severe Economic Events		89
Market Sensitive Instruments and Risk Management		91

ARCH CAPITAL 61 2022 FORM 10-K

OVERVIEW

Arch Capital Group Ltd. (“Arch Capital” and, together with its subsidiaries, “we” or “us”) is a publicly listed Bermuda exempted company with approximately $15.6 billion in capital at December 31, 2022 and is part of the S&P 500 index. Through operations in Bermuda, the United States, United Kingdom, Europe, Canada and Australia, we write specialty lines of property and casualty insurance and reinsurance, as well as mortgage insurance and reinsurance, on a worldwide basis. It is our belief that our underwriting platform, our experienced management team and our strong capital base have enabled us to establish a strong presence in the insurance and reinsurance markets.

The worldwide property casualty insurance and reinsurance industry is highly competitive and has traditionally been subject to an underwriting cycle. In that cycle, a “hard” market is evidenced by high premium rates, restrictive underwriting standards, narrow terms and conditions, and strong underwriting profits for insurers. A “hard” market typically attracts new capital and new entrants to the market and is eventually followed by a “soft” market, which has characteristics of low premium rates, relaxed underwriting standards, broader terms and conditions, and lower underwriting profits for insurers. Market conditions in the property and casualty arena may affect, among other things, the demand for our products, our ability to increase premium rates, the terms and conditions of the insurance policies we write, changes in the products offered by us or changes in our business strategy.

The financial results of the property casualty insurance and reinsurance industry are influenced by factors such as the frequency and/or severity of claims and losses, including natural disasters or other catastrophic events, variations in interest rates and financial markets, changes in the legal, regulatory and judicial environments, inflationary pressures and general economic conditions. These factors influence, among other things, the demand for insurance or reinsurance, the supply of which is generally related to the total capital of competitors in the market.

Mortgage insurance and reinsurance is subject to similar cycles to property casualty except that they have historically been more dependent on macroeconomic conditions.

CURRENT OUTLOOK

As we head into 2023, our objective remains the same, to deliver long term value for our shareholders. Underwriting discipline is core to our culture and we are committed to agile cycle management with a focus on risk-adjusted returns. 2022 was our third consecutive year of sustained premium and revenue growth, supporting stronger and more stable earnings power for the near term. Reinsurance segment’s net premiums written grew 51% as the team seized on market dislocations while our insurance segment grew a robust 21%. We continue to see a broad array of opportunities to allocate capital where rates and terms and conditions allow for growth in attractive returns.

We continue to execute our cycle management strategy by actively allocating capital across a diversified, specialty portfolio where rates allow for returns that are higher than our cost of capital. While we continue to allocate more capital to our property and casualty segments, it is important to note that we have capitalized on attractive returns from our mortgage segment with $1.3 billion of underwriting income in 2022.

The catastrophic activity in 2022 has significantly increased pressure on property catastrophe markets, which could have a ripple effect across all property and casualty lines. As a result, we continue to show improved underwriting margins, partially due to the compounding of rate-on-rate increases and the rebalancing of our mix of business. We believe that this proven strategy of protecting capital through soft markets and increasing writings in hard markets gives us the best chance to generate superior risk adjusted returns over time.

In reinsurance, pricing for the January 1 renewals was strong. Property catastrophe pricing and terms both improved, leading to the effective rate changes in the 30% to 50% range. We anticipate that these trends will continue to the mid-year property catastrophe renewal period and should translate to strong property growth in 2023. As long as rate increases support returns above our required thresholds, we expect to continue to grow our writings. Rate improvements have enabled us to continue to expand writings in our property casualty segments.

In insurance, underwriting conditions remain opportunistic as pricing discipline, terms and conditions, and limits management are stable across most lines. This stability, combined with the uncertainties in the insurance market, should keep the market disciplined and sustain rate increases in most lines of business. Our specialty business in the U.K. and the U.S. operations benefited from growth in professional liability, including cyber insurance, as well as travel where we believe relative returns are attractive.

ARCH CAPITAL 62 2022 FORM 10-K

Inflation continues to be a focus for our industry. We proactively analyze available data and we incorporate emerging trends into our pricing and reserving. We believe that this discipline, coupled with increases in future investment returns and prudent reserving, helps us somewhat mitigate inflation’s impact.

In mortgage, we continue to be thoughtful in how we manage our portfolio and, because of our diversified model, we have the ability to take a measured view of the business as just one component of our diversified enterprise. Our mortgage business continues to deliver consistent underwriting results, once again demonstrating its sustainable earnings model. Although higher interest rates affected new loan origination volume, our U.S. primary mortgage insurance in force grew to nearly $296 billion, reflecting a higher persistency rate. The credit quality of homebuyers remains excellent and we believe our portfolio is well positioned for a variety of economic scenarios.

We remain committed to providing solutions across many offerings as the marketplace evolves, including the mortgage credit risk transfer programs initiated by government sponsored enterprises, or (“GSEs”). In addition, we have entered into aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda and have issued mortgage insurance linked notes, increasing our protection for mortgage tail risk. The Bellemeade structures provided approximately $4.0 billion of aggregate reinsurance coverage at December 31, 2022.

FINANCIAL MEASURES

Management uses the following three key financial indicators in evaluating our performance and measuring the overall growth in value generated for Arch Capital’s common shareholders:

Book Value per Share

Book value per share represents total common shareholders’ equity available to Arch divided by the number of common shares and common share equivalents outstanding. Management uses growth in book value per share as a key measure of the value generated for our common shareholders each period and believes that book value per share is the key driver of Arch Capital’s share price over time. Book value per share is impacted by, among other factors, our underwriting results, investment returns and share repurchase activity, which has an accretive or dilutive impact on book value per share depending on the purchase price. Book value per share was $32.62 at December 31, 2022, a 2.8% decrease from $33.56 at December 31, 2021. The decline in 2022 reflected negative total return on investments driven by rising interest rates on fixed maturities.

Operating Return on Average Common Equity

Operating return on average common equity (“Operating ROAE”) represents annualized after-tax operating income available to Arch common shareholders divided by average common shareholders’ equity available to Arch during the period. After-tax operating income available to Arch common shareholders, a “non-GAAP measure” as defined in the SEC rules, represents net income available to Arch common shareholders, excluding net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings), equity in net income or loss of investments accounted for using the equity method, net foreign exchange gains or losses, transaction costs and other, loss on redemption of preferred shares and income taxes. Management uses Operating ROAE as a key measure of the return generated to Arch common shareholders. See “Comment on Non-GAAP Financial Measures.”

Our annualized net income return on average common equity was 11.6% for 2022, compared to 16.7% for 2021, with the lower return in 2022 primarily resulting from net realized losses and a lower level of income from equity method investments. Our Operating ROAE was 14.8% for 2022, compared to 11.5% for 2021, with the higher return in 2022 primarily resulting from strong underwriting performance and growth in net investment income, reflecting higher yields available on fixed income securities.

ARCH CAPITAL 63 2022 FORM 10-K

Total Return on Investments

Total return on investments includes investment income, equity in net income or loss of investments accounted for using the equity method, net realized gains or losses and the change in unrealized gains or losses generated by Arch’s investment portfolio. Total return is calculated on a pre-tax basis before investment expenses, excluding amounts reflected in the ‘other’ segment, and reflects the effect of financial market conditions along with foreign currency fluctuations. Management uses total return on investments as a key measure of the return generated for Arch common shareholders on the capital held in the business, and compares the return generated by our investment portfolio against benchmark returns. See “Comment on Non-GAAP Financial Measures.”

The following table summarizes the pre-tax total return (before investment expenses) of investments held by Arch compared to the benchmark return (both based in U.S. Dollars) against which we measured our portfolio during the periods:

	Arch Portfolio (1)		Benchmark  Return
Year Ended December 31, 2022	-6.45	%	-9.60	%
Year Ended December 31, 2021	1.90	%	1.20	%

(1) Our investment expenses were approximately 0.28% and 0.32%, respectively, of average invested assets in 2022 and 2021.

Total return for the 2022 period reflected rising interest rates on fixed maturities and weak equity markets. The overall position of our investment portfolio remains relatively unchanged as we remain cautious relative to duration, credit and equity risk.

The benchmark return index is a customized combination of indices intended to approximate a target portfolio by asset mix and average credit quality while also matching the approximate estimated duration and currency mix of our insurance and reinsurance liabilities. Although the estimated duration and average credit quality of this index will move as the duration and rating of its constituent securities change, generally we do not adjust the composition of the benchmark return index except to incorporate changes to the mix of liability currencies and durations noted above. The benchmark return index should not be interpreted as expressing a preference for or aversion to any particular sector or sector weight. The index is intended solely to provide, unlike many master indices that change based on the size of their constituent indices, a relatively stable basket of investable indices. At December 31, 2022, the benchmark return index had an average credit quality of “Aa3” by Moody’s, an estimated duration of 3.16 years.

The benchmark return index included weightings to the following indices:

	%
ICE BofAML US Corporates, A - AAA Rated 1-5 Yr Index	13.00	%
ICE BofAML 1-5 Year US Treasury Index	12.00
ICE BofAML US Corporates, AAA-A 5-10 Year Index	11.00
ICE BofAML US Corporates, BBB Rated 1-10 Yr Index	5.00
JPM CLOIE Investment Grade	5.00
ICE BofAML 1-5 Year UK Gilt Index	4.25
ICE BofAML AAA US Fixed Rate CMBS Index	4.00
ICE BofAML US Mortgage Backed Securities Index	4.00
ICE BofAML German Government 1-10 Year Index	4.00
MSCI ACWI Net Total Return USD Index	4.00
Equity (MSCI ACWI)	3.30
ICE BofAML 0-3 Month US Treasury Bill Index	3.00
ICE BofAML 5-10 Year US Treasury Index	3.00
ICE BofAML 1-10 Year US Municipal Securities Index	3.00
Bloomberg Barclays ABS Aaa Total Return Index	3.00
ICE BofAML 1-5 Year Canada Government Index	2.50
ICE BofAML 1-5 Year Australia Government Index	2.50
Morningstar LSTA US Leveraged Loan TR USD	2.50
ICE BofAML US High Yield Constrained Index	2.50
Senior Lending (S&P Leveraged Loan)	2.48
Opportunistic Credit (Barclays Global HY)	1.38
Distressed (Ice BofA CCC and Lower)	1.38
Int'l Equity RE (DJ International RE)	0.83
US RE Mezz (FTSE NAREIT Mortgage Plus Capped Index)	0.83
US RE Senior (Barclays CMBS Erisa Eligible)	0.83
ICE BofAML 15+ Year Canada Government Index	0.50
ICE BofA 1-5 Year Japan Government Index	0.25
Total	100.0	%

COMMENT ON NON-GAAP FINANCIAL MEASURES

Throughout this filing, we present our operations in the way we believe will be the most meaningful and useful to investors, analysts, rating agencies and others who use our financial information in evaluating the performance of our company. This presentation includes the use of after-tax operating income available to Arch common shareholders, which is defined as net income available to Arch common shareholders, excluding net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings), equity in net income or loss of investments accounted for using the equity method, net foreign exchange gains or losses, transaction costs and other, loss on redemption of preferred shares and income taxes, and the use of annualized operating return on average common equity. The presentation of after-tax operating income available to Arch common shareholders and annualized operating return on average common equity are non-GAAP financial measures as defined in Regulation G. The reconciliation of such measures to net income available to Arch common

ARCH CAPITAL 64 2022 FORM 10-K

shareholders and annualized net income return on average common equity (the most directly comparable GAAP financial measures) in accordance with Regulation G is included under “Results of Operations” below.

We believe that net realized gains or losses, equity in net income or loss of investments accounted for using the equity method, net foreign exchange gains or losses and transaction costs and other in any particular period are not indicative of the performance of, or trends in, our business. Although net realized gains or losses, equity in net income or loss of investments accounted for using the equity method and net foreign exchange gains or losses are an integral part of our operations, the decision to realize these items are independent of the insurance underwriting process and result, in large part, from general economic and financial market conditions. Furthermore, certain users of our financial information believe that, for many companies, the timing of the realization of investment gains or losses is largely opportunistic. In addition, changes in the allowance for credit losses and net impairment losses recognized in earnings on the Company’s investments represent other-than-temporary declines in expected recovery values on securities without actual realization.

The use of the equity method on certain of our investments in certain funds that invest in fixed maturity securities is driven by the ownership structure of such funds (either limited partnerships or limited liability companies). In applying the equity method, these investments are initially recorded at cost and are subsequently adjusted based on our proportionate share of the net income or loss of the funds (which include changes in the market value of the underlying securities in the funds). This method of accounting is different from the way we account for our other investments and the timing of the recognition of equity in net income or loss of investments accounted for using the equity method may differ from gains or losses in the future upon sale or maturity of such investments.

Transaction costs and other include advisory, financing, legal, severance, incentive compensation and other transaction costs related to acquisitions. We believe that transaction costs and other, due to their non-recurring nature, are not indicative of the performance of, or trends in, our business performance. The loss on redemption of preferred shares related to the redemption of the Company’s preferred shares had no impact on shareholders' equity or cash flows.

Due to these reasons noted above, we exclude net realized gains or losses, equity in net income or loss of investments accounted for using the equity method, net foreign exchange gains or losses, transaction costs and other and loss on redemption of preferred shares from the calculation of after-tax operating income available to Arch common shareholders.

We believe that showing net income available to Arch common shareholders exclusive of the items referred to above reflects the underlying fundamentals of our business since we evaluate the performance of and manage our business to produce an underwriting profit. In addition to presenting net income available to Arch common shareholders, we believe that this presentation enables investors and other users of our financial information to analyze our performance in a manner similar to how management analyzes performance. We also believe that this measure follows industry practice and, therefore, allows the users of financial information to compare our performance with our industry peer group. We believe that the equity analysts and certain rating agencies that follow us and the insurance industry as a whole generally exclude these items from their analyses for the same reasons.

Our segment information includes the presentation of consolidated underwriting income or loss and a subtotal of underwriting income or loss before the contribution from the ‘other’ segment. Such measures represent the pre-tax profitability of our underwriting operations and include net premiums earned plus other underwriting income, less losses and loss adjustment expenses, acquisition expenses and other operating expenses. Other operating expenses include those operating expenses that are incremental and/or directly attributable to our individual underwriting operations. Underwriting income or loss does not incorporate items included in our corporate segment. While these measures are presented in note 4, “Segment Information,” to our consolidated financial statements in Item 8, they are considered non-GAAP financial measures when presented elsewhere on a consolidated basis. The reconciliations of underwriting income or loss to income before income taxes (the most directly comparable GAAP financial measure) on a consolidated basis and a subtotal before the contribution from the ‘other’ segment, in accordance with Regulation G, is shown in note 4, “Segment Information,” to our consolidated financial statements in Item 8.

We measure segment performance for our three underwriting segments based on underwriting income or loss. We do not manage our assets by underwriting segment, with the exception of goodwill and intangible assets, and, accordingly, investment income, income from operating affiliates and other non-underwriting related items are not allocated to each underwriting segment.

Along with consolidated underwriting income, we provide a subtotal of underwriting income or loss before the contribution from the ‘other’ segment. Through June 30, 2021, the ‘other’ segment included the results of Somers Holdings Ltd. (formerly Watford Holdings Ltd.). Somers Holdings Ltd. is the parent of Somers Re Ltd., a multi-line Bermuda reinsurance company (together with Somers Holdings Ltd., “Somers”). Pursuant to GAAP, Somers was

ARCH CAPITAL 65 2022 FORM 10-K

considered a variable interest entity and we concluded that we were the primary beneficiary of Somers. As such, we consolidated the results of Somers in our consolidated financial statements through June 30, 2021. In the 2020 fourth quarter, Arch Capital, Somers, and Greysbridge Ltd., a wholly-owned subsidiary of Arch Capital, entered into an Agreement and Plan of Merger (as amended, the “Merger Agreement”). Arch Capital assigned its rights under the Merger Agreement to Greysbridge Holdings Ltd. (“Greysbridge”). The merger and the related Greysbridge equity financing closed on July 1, 2021. Effective July 1, 2021, Somers is wholly owned by Greysbridge, and Greysbridge is owned 40% by Arch and 30% by certain funds managed by Kelso and 30% by certain funds managed by Warburg. Based on the governing documents of Greysbridge, we concluded that, while we retain significant influence over Greysbridge, Greysbridge does not constitute a variable interest entity. Accordingly, effective July 1, 2021, we no longer consolidate the results of Somers in our consolidated financial statements and footnotes. See note 12, “Variable Interest Entities and Noncontrolling Interests” and note 4, “Segment Information,” to our consolidated financial statements for additional information on Somers.

Our presentation of segment information includes the use of a current year loss ratio which excludes favorable or adverse development in prior year loss reserves. This ratio is a non-GAAP financial measure as defined in Regulation G. The reconciliation of such measure to the loss ratio (the most directly comparable GAAP financial measure) in accordance with Regulation G is shown on the individual segment pages. Management utilizes the current year loss ratio in its analysis of the underwriting performance of each of our underwriting segments.

Total return on investments includes investment income, equity in net income or loss of investments accounted for using the equity method, net realized gains or losses (excluding changes in the allowance for credit losses on non-investment related financial assets) and the change in unrealized gains or losses generated by Arch’s investment portfolio. Total return is calculated on a pre-tax basis and before investment expenses, excludes amounts reflected in the ‘other’ segment, and reflects the effect of financial market conditions along with foreign currency fluctuations. In addition, total return incorporates the timing of investment returns during the periods. There is no directly comparable GAAP financial measure for total return. Management uses total return on investments as a key measure of the return generated to Arch common shareholders on the capital held in the business, and compares the return generated by our investment portfolio against benchmark returns which we measured our portfolio against during the periods.

RESULTS OF OPERATIONS

The following table summarizes our consolidated financial data, including a reconciliation of net income available to Arch common shareholders to after-tax operating income available to Arch common shareholders. See “Comment on Non-GAAP Financial Measures.”

	Year Ended December 31,
	2022		2021
Net income available to Arch common shareholders	$	1,436,197	$	2,093,405
Net realized (gains) losses	662,735		(307,466)
Equity in net (income) loss of investments accounted for using the equity method	(115,856)		(366,402)
Net foreign exchange (gains) losses	(100,988)		(42,743)
Transaction costs and other	1,092		1,199
Loss on redemption of preferred shares	—		15,101
Income tax expense (benefit) (1)	(42,791)		41,836
After-tax operating income available to Arch common shareholders	$	1,840,389	$	1,434,930
Beginning common shareholders’ equity	$	12,715,896	$	12,325,886
Ending common shareholders’ equity	12,080,073		12,715,896
Average common shareholders’ equity	$	12,397,985	$	12,520,891
Annualized net income return on average common equity %	11.6		16.7
Annualized operating return on average common equity %	14.8		11.5

(1) Income tax on net realized gains or losses, equity in net income or loss of investments accounted for using the equity method, net foreign exchange gains or losses and transaction costs and other reflects the relative mix reported by jurisdiction and the varying tax rates in each jurisdiction.

ARCH CAPITAL 66 2022 FORM 10-K

Segment Information

We classify our businesses into three underwriting segments – insurance, reinsurance and mortgage – and two operating segments – corporate and ‘other.’ Our insurance, reinsurance and mortgage segments each have managers who are responsible for the overall profitability of their respective segments and who are directly accountable to our chief operating decision makers, the Chief Executive Officer of Arch Capital, Chief Financial Officer and Treasurer of Arch Capital and the President and Chief Underwriting Officer of Arch Capital. The chief operating decision makers do not assess performance, measure return on equity or make resource allocation decisions on a line of business basis. Management measures segment performance for our three underwriting segments based on underwriting income or loss. We do not manage our assets by underwriting segment, with the exception of goodwill and intangible assets and accordingly, investment income is not allocated to each underwriting segment.

We determined our reportable segments using the management approach described in accounting guidance regarding disclosures about segments of an enterprise and related information. The accounting policies of the segments are the same as those used for the preparation of our consolidated financial statements. Intersegment business is allocated to the segment accountable for the underwriting results.

Insurance Segment

The following tables set forth our insurance segment’s underwriting results:

	Year Ended December 31,
	2022			2021			% Change
Gross premiums written	$	6,930,864		$	5,867,734		18.1
Premiums ceded	(1,910,222)			(1,719,541)
Net premiums written	5,020,642			4,148,193			21.0
Change in unearned premiums	(461,307)			(521,725)
Net premiums earned	4,559,335			3,626,468			25.7
Losses and loss adjustment expenses	(2,782,945)			(2,344,365)
Acquisition expenses	(885,866)			(606,265)
Other operating expenses	(665,472)			(558,906)
Underwriting income (loss)	$	225,052		$	116,932		92.5
Underwriting Ratios							% Point Change
Loss ratio	61.0		%	64.6		%	(3.6)
Acquisition expense ratio	19.4		%	16.7		%	2.7
Other operating expense ratio	14.6		%	15.4		%	(0.8)
Combined ratio	95.0		%	96.7		%	(1.7)

The insurance segment consists of our insurance underwriting units which offer specialty product lines on a worldwide basis, as described in note 4, “Segment Information,” to our consolidated financial statements in Item 8.

Net Premiums Written.

The following tables set forth our insurance segment’s net premiums written by major line of business:

	Year Ended December 31,
	2022			2021
	Amount		%	Amount		%
Professional lines	$	1,502,448	29.9	$	1,177,144	28.4
Property, energy, marine and aviation	878,067		17.5	722,582		17.4
Programs	611,922		12.2	595,824		14.4
Travel, accident and health	484,847		9.7	305,390		7.4
Construction and national accounts	469,717		9.4	431,952		10.4
Excess and surplus casualty	460,798		9.2	359,458		8.7
Warranty and lenders solutions	139,247		2.8	146,984		3.5
Other	473,596		9.4	408,859		9.9
Total	$	5,020,642	100.0	$	4,148,193	100.0

Net premiums written by the insurance segment were 21.0% higher in 2022 than in 2021. The increase in net premiums written reflected growth in professional lines and in property, primarily due to rate increases, new business opportunities and growth in existing accounts, and in travel, primarily due to new business and growth in existing accounts.

Net Premiums Earned.

The following tables set forth our insurance segment’s net premiums earned by major line of business:

	Year Ended December 31,
	2022			2021
	Amount		%	Amount		%
Professional lines	$	1,314,236	28.8	$	942,817	26.0
Property, energy, marine and aviation	772,388		16.9	667,892		18.4
Programs	589,860		12.9	506,867		14.0
Travel, accident and health	491,847		10.8	255,590		7.0
Construction and national accounts	432,020		9.5	416,107		11.5
Excess and surplus casualty	393,353		8.6	318,027		8.8
Warranty and lenders solutions	127,222		2.8	153,958		4.2
Other	438,409		9.6	365,210		10.1
Total	$	4,559,335	100.0	$	3,626,468	100.0

Net premiums written are primarily earned on a pro rata basis over the terms of the policies for all products, usually 12 months. Net premiums earned by the insurance segment were 25.7% higher in 2022 than in 2021, reflecting changes in net premiums written over the previous five quarters.

ARCH CAPITAL 67 2022 FORM 10-K

Losses and Loss Adjustment Expenses.

The table below shows the components of the insurance segment’s loss ratio:

	Year Ended December 31,
	2022		2021
Current year	61.6	%	65.0	%
Prior period reserve development	(0.6)	%	(0.4)	%
Loss ratio	61.0	%	64.6	%

Current Year Loss Ratio.

The insurance segment’s current year loss ratio was 3.4 points lower in 2022 than in 2021. The 2022 loss ratio included 5.2 points of current year catastrophic event activity, primarily related to Hurricane Ian, Russia’s invasion of Ukraine and other natural catastrophes, compared to 5.6 points in 2021, primarily related to Hurricane Ida and winter storms Uri and Viola. The balance of the change in the 2022 loss ratios resulted, in part, from changes in mix of business.

Prior Period Reserve Development.

The insurance segment’s net favorable development was $25.3 million, or 0.6 points, for 2022, compared to $16.2 million, or 0.4 points, for 2021. See note 5, “Reserve for Losses and Loss Adjustment Expenses,” to our consolidated financial statements in Item 8 for information about the insurance segment’s prior year reserve development.

Underwriting Expenses.

The insurance segment’s underwriting expense ratio was 34.0% in 2022, compared to 32.1% in 2021, with the increase primarily due to changing mix of business and growth in lines with higher acquisition costs.

Reinsurance Segment 

The following tables set forth our reinsurance segment’s underwriting results:

	Year Ended December 31,
	2022			2021			% Change
Gross premiums written	$	6,948,438		$	5,093,930		36.4
Premiums ceded	(2,024,462)			(1,839,556)
Net premiums written	4,923,976			3,254,374			51.3
Change in unearned premiums	(964,595)			(413,931)
Net premiums earned	3,959,381			2,840,443			39.4
Other underwriting income (loss)	4,871			3,669
Losses and loss adjustment expenses	(2,568,843)			(1,924,719)
Acquisition expenses	(813,555)			(536,754)
Other operating expenses	(267,531)			(212,810)
Underwriting income	$	314,323		$	169,829		85.1
Underwriting Ratios							% Point Change
Loss ratio	64.9		%	67.8		%	(2.9)
Acquisition expense ratio	20.5		%	18.9		%	1.6
Other operating expense ratio	6.8		%	7.5		%	(0.7)
Combined ratio	92.2		%	94.2		%	(2.0)

The reinsurance segment consists of our reinsurance underwriting units which offer specialty product lines on a worldwide basis, as described in note 4, “Segment Information,” to our consolidated financial statements in Item 8.

Net Premiums Written.

The following tables set forth our reinsurance segment’s net premiums written by major line of business:

	Year Ended December 31,
	2022			2021
	Amount		%	Amount		%
Other specialty	$	1,982,594	40.3	$	955,474	29.4
Property excluding property catastrophe	1,276,083		25.9	1,004,086		30.9
Casualty	973,948		19.8	808,164		24.8
Property catastrophe	415,725		8.4	233,260		7.2
Marine and aviation	166,933		3.4	171,753		5.3
Other	108,693		2.2	81,637		2.5
Total	$	4,923,976	100.0	$	3,254,374	100.0

Net premiums written by the reinsurance segment were 51.3% higher in 2022 than in 2021. The growth in net premiums written reflected increases in most lines of business, primarily due to growth in existing accounts, new business, and rate increases. The 2022 fourth quarter was affected by a few non-recurring transactions, primarily impacting the other specialty line of business.

ARCH CAPITAL 68 2022 FORM 10-K

Net Premiums Earned.

The following tables set forth our reinsurance segment’s net premiums earned by major line of business:

	Year Ended December 31,
	2022			2021
	Amount		%	Amount		%
Other specialty	$	1,377,880	34.8	$	818,801	28.8
Property excluding property catastrophe	1,091,440		27.6	836,573		29.5
Casualty	854,543		21.6	666,754		23.5
Property catastrophe	366,991		9.3	280,738		9.9
Marine and aviation	159,401		4.0	152,955		5.4
Other	109,126		2.8	84,622		3.0
Total	$	3,959,381	100.0	$	2,840,443	100.0

Net premiums earned in 2022 were 39.4% higher than in 2021, reflecting changes in net premiums written over the previous five quarters, including the mix and type of business written.

Other Underwriting Income (Loss).

Other underwriting income in 2022 was $4.9 million, compared to $3.7 million in 2021.

Losses and Loss Adjustment Expenses.

The table below shows the components of the reinsurance segment’s loss ratio:

	Year Ended December 31,
	2022		2021
Current year	69.7	%	74.1	%
Prior period reserve development	(4.8)	%	(6.3)	%
Loss ratio	64.9	%	67.8	%

Current Year Loss Ratio.

The reinsurance segment’s current year loss ratio was 4.4 points lower in 2022 than in 2021. The 2022 loss ratio included 13.9 points for current year catastrophic event activity, primarily related to Hurricane Ian, Russia’s invasion of Ukraine and other global events, compared to 16.5 points in 2021. The balance of the change in the 2022 current year loss ratio resulted, in part, from the effect of rate increases, changes in mix of business and the level of attritional losses.

Prior Period Reserve Development.

The reinsurance segment’s net favorable development was $191.6 million, or 4.8 points, for 2022, compared to $178.8 million, or 6.3 points, for 2021, See note 5, “Reserve for Losses and Loss Adjustment Expenses,” to our consolidated financial statements in Item 8 for information about the reinsurance segment’s prior year reserve development.

Underwriting Expenses.

The underwriting expense ratio for the reinsurance segment was 27.3% in 2022, compared to 26.4% in 2021, with the increase primarily resulting from changes in mix of business to lines with higher acquisition costs and expenses related to favorable development of prior year loss reserves.

Mortgage Segment

The following tables set forth our mortgage segment’s underwriting results.

	Year Ended December 31,
	2022			2021			% Change
Gross premiums written	$	1,454,971		$	1,507,825		(3.5)
Premiums ceded	(322,400)			(246,757)
Net premiums written	1,132,571			1,261,068			(10.2)
Change in unearned premiums	26,790			22,351
Net premiums earned	1,159,361			1,283,419			(9.7)
Other underwriting income	8,356			17,665
Losses and loss adjustment expenses	324,271			(56,677)
Acquisition expenses	(40,159)			(97,418)
Other operating expenses	(195,172)			(194,010)
Underwriting income	$	1,256,657		$	952,979		31.9
Underwriting Ratios							% Point Change
Loss ratio	(28.0)		%	4.4		%	(32.4)
Acquisition expense ratio	3.5		%	7.6		%	(4.1)
Other operating expense ratio	16.8		%	15.1		%	1.7
Combined ratio	(7.7)		%	27.1		%	(34.8)

Premiums Written.

The following table sets forth our mortgage segment’s net premiums written by underwriting location (i.e., where the business is underwritten):

	Year Ended December 31,
	2022		2021
Net premiums written by underwriting location
United States	$	780,256	$	914,477
Other	352,315		346,591
Total	$	1,132,571	$	1,261,068

Gross premiums written by the mortgage segment in 2022 were 3.5% lower than in 2021. The reduction in gross premiums written primarily reflected a lower U.S. primary mortgage insurance single premium volume and a decrease in monthly premiums. Net premiums written for 2022 were 10.2% lower than in the 2021 period. Net premiums written for the 2022 period reflected a higher level of premiums ceded than in the 2021 period.

ARCH CAPITAL 69 2022 FORM 10-K

The persistency rate of the U.S. primary portfolio of mortgage loans was 79.5% at December 31, 2022 compared to 62.4% at December 31, 2021, with the increase primarily reflecting a lower level of refinancing activity due to a higher interest rate environment. The persistency rate represents the percentage of mortgage insurance in force at the beginning of a 12-month period that remains in force at the end of such period.

Net Premiums Earned.

The following table sets forth our mortgage segment’s net premiums earned by underwriting location (i.e., where the business is underwritten):

	Year Ended December 31,
	2022		2021
Net premiums earned by underwriting location
United States	$	815,519	$	970,507
Other	343,842		312,912
Total	$	1,159,361	$	1,283,419

Net premiums earned for 2022 were 9.7% lower than in 2021 and reflected a decline in monthly premiums and an increase in ceded premiums earned, partially offset by growth in credit risk transfer business.

Other Underwriting Income.

Other underwriting income, which is primarily related to GSE risk-sharing transactions and our whole mortgage loan purchase and sell program, was $8.4 million for 2022, compared to $17.7 million for 2021.

Losses and Loss Adjustment Expenses.

The table below shows the components of the mortgage segment’s loss ratio:

	Year Ended December 31,
	2022		2021
Current year	19.8	%	17.6	%
Prior period reserve development	(47.8)	%	(13.2)	%
Loss ratio	(28.0)	%	4.4	%

Unlike property and casualty business for which we estimate ultimate losses on premiums earned, losses on mortgage insurance business are only recorded at the time a borrower is delinquent on their mortgage, in accordance with primary mortgage insurance industry practice. Because our primary mortgage insurance reserving process does not take into account the impact of future losses from loans that are not delinquent, mortgage insurance loss reserves are not an estimate of ultimate losses. In addition to establishing loss reserves for delinquent loans, under GAAP, we are required to establish a premium deficiency reserve for our mortgage

insurance products if the amount of expected future losses and maintenance costs exceeds expected future premiums, existing reserves and the anticipated investment income for such product. We assess the need for a premium deficiency reserve on a quarterly basis and perform a full analysis annually. No such reserve was established during 2022 or 2021.

Current Year Loss Ratio.

The mortgage segment’s current year loss ratio was 2.2 points higher in 2022 compared to 2021. The higher current year loss ratio for the 2022 period reflected a lower level of premiums earned in the U.S. primary mortgage insurance business combined with an increase in new delinquencies as well as an increase in estimated claim rates.

The percentage of loans in default on U.S. primary mortgage insurance decreased from 2.36% at December 31, 2021 to 1.77% at December 31, 2022.

We insure mortgages for homes in areas that have been impacted by catastrophic events. Generally, mortgage insurance losses occur only when a credit event occurs and, following a physical damage event, when the home is restored to pre-storm condition. Our ultimate claims exposure will depend on the number of delinquency notices received and the ultimate claim rate related to such notices. In the event of natural disasters, cure rates are influenced by the adequacy of homeowners and flood insurance carried on a related property, and a borrower's access to aid from government entities and private organizations, in addition to other factors which generally impact cure rates in unaffected areas.

Prior Period Reserve Development.

The mortgage segment’s net favorable development was $554.1 million, or 47.8 points, for 2022, compared to $169.6 million, or 13.2 points, for 2021. See note 5, “Reserve for Losses and Loss Adjustment Expenses,” to our consolidated financial statements in Item 8 for information about the mortgage segment’s prior year reserve development.

Underwriting Expenses.

The underwriting expense ratio for the mortgage segment was 20.3% for 2022, compared to 22.7% for 2021, with the decrease primarily due to lower acquisition expenses on Australian mortgage insurance following the acquisition of Westpac LMI in the 2021 third quarter and profit commissions adjustments related to favorable development of prior year loss reserves. Such amounts were partially offset by a lower level of net premiums earned in the U.S. primary mortgage insurance business.

ARCH CAPITAL 70 2022 FORM 10-K

Corporate Segment

The corporate segment results include net investment income, net realized gains or losses, equity in net income or loss of investments accounted for using the equity method, other income (loss), corporate expenses, transaction costs and other, amortization of intangible assets, interest expense, net foreign exchange gains or losses, income taxes, income from operating affiliates and items related to our non-cumulative preferred shares. Such amounts exclude the results of the ‘other’ segment.

Net Investment Income.

The components of net investment income were derived from the following sources:

	Year Ended December 31,
	2022		2021
Fixed maturities	$	468,659	$	307,536
Equity securities	22,497		42,094
Short-term investments	29,519		6,799
Other (1)	46,647		68,411
Gross investment income	567,322		424,840
Investment expenses (2)	(70,775)		(78,032)
Net investment income	$	496,547	$	346,808

(1)    Amounts include dividends and other distributions on investment funds, term loan investments, funds held balances, cash balances and other.

(2)    Investment expenses were approximately 0.28% of average invested assets for 2022, compared to 0.32% for 2021.

The pre-tax investment income yield was 1.99% for 2022, compared to 1.41% for 2021. The higher level of net investment income for 2022 compared to 2021 reflected higher yields available in the financial markets. The pre-tax investment income yields were calculated based on amortized cost. Yields on future investment income may vary based on financial market conditions, investment allocation decisions and other factors.

Net Realized Gains (Losses).

We recorded net realized losses of $662.7 million for 2022, compared to net realized gains of $299.2 million for 2021. Currently, our portfolio is actively managed to maximize total return within certain guidelines. The effect of financial market movements on the investment portfolio will directly impact net realized gains or losses as the portfolio is rebalanced. Net realized gains or losses from the sale of fixed maturities primarily results from our decisions to reduce credit exposure, to change duration targets, to rebalance our portfolios or due to relative value determinations.

Net realized gains or losses also include realized and unrealized contract gains and losses on our derivative instruments, changes in the fair value of assets accounted for

using the fair value option and in the fair value of equities, along with changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings. See note 9, “Investment Information—Net Realized Gains (Losses),” and note 9, “Investment Information—Allowance for Credit Losses,” to our consolidated financial statements for additional information.

Equity in Net Income (Loss) of Investments Accounted for Using the Equity Method.

We recorded $115.9 million of equity in net income related to investments accounted for using the equity method for 2022, compared to $366.4 million for 2021. Investments accounted for using the equity method totaled $3.8 billion at December 31, 2022, compared to $3.1 billion at December 31, 2021. See note 9, “Investment Information—Equity in Net Income (Loss) of Investments Accounted For Using the Equity Method,” to our consolidated financial statements in Item 8 for additional information.

Other Income (Loss)

Other loss for the 2022 period was $26.2 million, compared to other income of $10.2 million for the 2021 period. Amounts in both periods primarily reflect changes in the cash surrender value of our investment in corporate-owned life insurance.

Corporate Expenses.

Corporate expenses were $94.4 million for 2022, compared to $77.1 million for 2021. Such amounts primarily represent certain holding company costs necessary to support our worldwide operations and costs associated with operating as a publicly traded company.

Transaction Costs and Other.

Transaction costs and other were $1.1 million for the 2022 period consistent with $1.1 million for 2021. Amounts in both periods are primarily related to acquisition activity.

Amortization of Intangible Assets.

Amortization of intangible assets for 2022 was $106.2 million, compared to $82.1 million for 2021. Amounts in 2022 and 2021 primarily related to amortization of finite-lived intangible assets. The increase in amortization of intangible assets expense was a result of acquisitions closed during the 2021 period. See note 2, “Acquisitions."

Interest Expense.

Interest expense was $130.3 million for 2022, compared to $131.1 million for 2021. Interest expense primarily reflects amounts related to our outstanding senior notes.

ARCH CAPITAL 71 2022 FORM 10-K

Net Foreign Exchange Gains or Losses.

Net foreign exchange gains for 2022 were $100.9 million, compared to net foreign exchange gains for 2021 of $42.9 million. Amounts in such periods were primarily unrealized and resulted from the effects of revaluing our net insurance liabilities required to be settled in foreign currencies at each balance sheet date.

Income Tax Expense.

Our income tax provision on income before income taxes resulted in an expense of 5.1% for 2022, compared to an expense of 5.6% for 2021. The effective tax rate for the 2022 period included discrete income tax benefits of $40.6 million, compared to benefits of $39.3 million for 2021. The discrete tax items in both periods primarily related to the release of valuation allowances on certain deferred tax assets. Our effective tax rate fluctuates from year to year consistent with the relative mix of income or loss reported by jurisdiction and the varying tax rates in each jurisdiction.

See note 15, “Income Taxes,” to our consolidated financial statements in Item 8 for a reconciliation of the difference between the provision for income taxes and the expected tax provision at the weighted average statutory tax rate for 2022 and 2021.

Income (Loss) from Operating Affiliates.

We recorded $73.9 million of net income from our operating affiliates in the 2022 period, compared to income of $264.7 million in the 2021 period. Results for the 2021 period included a one-time gain of $95.7 million recognized from the Company’s investment in Greysbridge and a one-time gain of $74.5 million recognized from the Company’s investment in Coface SA (“Coface”), a France-based leader in the global trade credit insurance market.

Loss on Redemption of Preferred Shares.

In 2021, we redeemed all 5.25% Series E preferred shares and recorded a loss of $15.1 million to remove original issuance costs related to the redeemed shares from additional paid-in capital. Such adjustment had no impact on total shareholders’ equity or cash flows.

SUMMARY OF CRITICAL ACCOUNTING ESTIMATES

The preparation of consolidated financial statements in accordance with GAAP requires us to make many estimates and judgments that affect the reported amounts of assets, liabilities (including reserves), revenues and expenses, and related disclosures of contingent liabilities. On an ongoing basis, we evaluate our estimates, including those related to revenue recognition, insurance and other reserves, reinsurance recoverables, allowance for current expected credit losses, investment valuations, goodwill and intangible assets, bad debts, income taxes, contingencies and litigation. We base our estimates on historical experience, where possible, and on various other assumptions that we believe to be reasonable under the circumstances, which form the basis for our judgments about the carrying values of assets and liabilities that are not readily apparent from other sources. Actual results will differ from these estimates and such differences may be material. We believe that the following critical accounting policies affect significant estimates used in the preparation of our consolidated financial statements.

Loss Reserves

We are required by applicable insurance laws and regulations and GAAP to establish reserves for losses and loss adjustment expenses, or “Loss Reserves”, that arise from the business we underwrite. Loss Reserves for our insurance, reinsurance and mortgage operations are balance sheet liabilities representing estimates of future amounts required to pay losses and loss adjustment expenses for insured or reinsured events which have occurred at or before the balance sheet date. Loss Reserves do not reflect contingency reserve allowances to account for future loss occurrences. Losses arising from future events will be estimated and recognized at the time the losses are incurred and could be substantial. See note 6, “Short Duration Contracts,” to our consolidated financial statements in Item 8 for additional information on our reserving process.

ARCH CAPITAL 72 2022 FORM 10-K

At December 31, 2022 and 2021, our Loss Reserves, net of unpaid losses and loss adjustment expenses recoverable, by type and by operating segment were as follows:

	December 31,
	2022		2021
Insurance segment:
Case reserves	$	2,397,881	$	2,102,891
IBNR reserves	4,934,583		4,269,904
Total net reserves	7,332,464		6,372,795
Reinsurance segment:
Case reserves	1,902,899		1,733,571
Additional case reserves	481,523		426,531
IBNR reserves	3,403,109		2,656,527
Total net reserves	5,787,531		4,816,629
Mortgage segment:
Case reserves	447,018		741,897
IBNR reserves	186,105		226,604
Total net reserves	633,123		968,501
Total:
Case reserves	4,747,798		4,578,359
Additional case reserves	481,523		426,531
IBNR reserves	8,523,797		7,153,035
Total net reserves	$	13,753,118	$	12,157,925

At December 31, 2022 and 2021, the insurance segment’s Loss Reserves by major line of business, net of unpaid losses and loss adjustment expenses recoverable, were as follows:

	December 31,
	2022		2021
Professional lines	$	2,069,912	$	1,673,615
Construction and national accounts	1,558,466		1,490,206
Programs	843,094		793,187
Excess and surplus casualty	786,494		657,307
Property, energy, marine and aviation	763,531		599,093
Travel, accident and health	138,814		96,051
Warranty and lenders solutions	46,733		58,351
Other	1,125,420		1,004,985
Total net reserves	$	7,332,464	$	6,372,795

At December 31, 2022 and 2021, the reinsurance segment’s Loss Reserves by major line of business, net of unpaid losses and loss adjustment expenses recoverable, were as follows:

	December 31,
	2022		2021
Casualty	$	2,342,077	$	2,123,360
Other specialty	1,475,702		1,113,766
Property excluding property catastrophe	993,454		711,859
Property catastrophe	535,844		486,911
Marine and aviation	291,548		246,861
Other	148,906		133,872
Total net reserves	$	5,787,531	$	4,816,629

At December 31, 2022 and 2021, the mortgage segment’s Loss Reserves by major line of business, net of unpaid losses and loss adjustment expenses recoverable, were as follows:

	December 31,
	2022		2021
U.S. primary mortgage insurance (1)	$	415,242	$	710,708
U.S. credit risk transfer (CRT) and other	108,910		112,549
International mortgage insurance/reinsurance	108,971		145,244
Total net reserves	$	633,123	$	968,501

(1)    At December 31, 2022, 33.8% of total net reserves represent policy years 2012 and prior and the remainder from later policy years. At December 31, 2021, 27.9% of total net reserves represent policy years 2012 and prior and the remainder from later policy years.

Potential Variability in Loss Reserves

The following tables summarize the effect of reasonably likely scenarios on the key actuarial assumptions used to estimate our Loss Reserves, net of unpaid losses and loss adjustment expenses recoverable, at December 31, 2022 by underwriting segment and reserving lines. See note 6, “Short Duration Contracts,” to our consolidated financial statements in Item 8 for a description of the lines of business included in each reserving line.

The scenarios shown in the tables summarize the effect of (i) changes to the expected loss ratio selections used at December 31, 2022, which represent loss ratio point increases or decreases to the expected loss ratios used, and (ii) changes to the loss development patterns used in our reserving process at December 31, 2022, which represent claims reporting that is either slower or faster than the reporting patterns used. We believe that the illustrated sensitivities are indicative of the potential variability inherent in the estimation process of those parameters. The results show the impact of varying each key actuarial assumption using the chosen sensitivity on our IBNR reserves, on a net basis and across all accident years.

ARCH CAPITAL 73 2022 FORM 10-K

INSURANCE SEGMENT	Higher Expected Loss Ratios		Slower Loss Development Patterns
Reserving lines selected assumptions:
Property, energy, marine and aviation	5 points		3 months
Third party occurrence business	10		6
Third party claims-made business	10		6
Multi-line and other specialty	10		6
Increase (decrease) in Loss Reserves:
Property, energy, marine and aviation	$	44,139	$	93,943
Third party occurrence business	209,293		100,645
Third party claims-made business	385,410		210,223
Multi-line and other specialty	235,811		104,475

INSURANCE SEGMENT	Lower Expected Loss Ratios		Faster Loss Development Patterns
Reserving lines selected assumptions:
Property, energy, marine and aviation	(5) points		(3) months
Third party occurrence business	(10)		(6)
Third party claims-made business	(10)		(6)
Multi-line and other specialty	(10)		(6)
Increase (decrease) in Loss Reserves:
Property, energy, marine and aviation	$	(44,139)	$	(60,941)
Third party occurrence business	(207,906)		(82,490)
Third party claims-made business	(382,587)		(173,800)
Multi-line and other specialty	(197,682)		(71,891)

REINSURANCE SEGMENT	Higher Expected Loss Ratios		Slower Loss Development Patterns
Reserving lines selected assumptions:
Casualty	10 points		6 months
Other specialty	5		3
Property excluding property catastrophe	5		3
Property catastrophe	5		3
Marine and aviation	5		3
Other	5		3
Increase (decrease) in Loss Reserves:
Casualty	$	192,747	$	220,372
Other specialty	140,889		102,342
Property excluding property catastrophe	41,745		101,294
Property catastrophe	31,774		52,223
Marine and aviation	14,524		25,618
Other	8,541		5,591

REINSURANCE SEGMENT	Lower Expected Loss Ratios		Faster Loss Development Patterns
Reserving lines selected assumptions:
Casualty	(10) points		(6) months
Other specialty	(5)		(3)
Property excluding property catastrophe	(5)		(3)
Property catastrophe	(5)		(3)
Marine and aviation	(5)		(3)
Other	(5)		(3)
Increase (decrease) in Loss Reserves:
Casualty	$	(192,743)	$	(167,558)
Other specialty	(140,889)		(147,647)
Property excluding property catastrophe	(41,745)		(99,642)
Property catastrophe	(31,774)		(32,967)
Marine and aviation	(14,715)		(27,465)
Other	(8,541)		(5,086)

It is not necessarily appropriate to sum the total impact for a specific factor or the total impact for a specific business category as the business categories are not perfectly correlated. In addition, the potential variability shown in the tables above are reasonably likely scenarios of changes in our key assumptions at December 31, 2022 and are not meant to be a “best case” or “worst case” series of outcomes and therefore, it is possible that future variations may be more or less than the amounts set forth above.

For our mortgage segment, we considered the sensitivity of loss reserve estimates at December 31, 2022 by assessing the potential changes resulting from a parallel shift in severity and default to claim rate. For example, assuming all other factors remain constant, for every one percentage point change in primary claim severity (which we estimate to be approximately 30% of the unpaid principal balance at December 31, 2022), we estimated that our loss reserves would change by approximately $21.0 million at December 31, 2022. For every one percentage point change in our primary net default to claim rate (which we estimate to be approximately 37% at December 31, 2022), we estimated a $17.0 million change in our loss reserves at December 31, 2022.

ARCH CAPITAL 74 2022 FORM 10-K

Simulation Results

In order to illustrate the potential volatility in our Loss Reserves, we used a Monte Carlo simulation approach to simulate a range of results based on various probabilities. Both the probabilities and related modeling are subject to inherent uncertainties. The simulation relies on a significant number of assumptions, such as the potential for multiple entities to react similarly to external events, and includes other statistical assumptions. The simulation results shown for each segment do not add to the total simulation results, as the individual segment simulation results do not reflect the diversification effects across our segments.

At December 31, 2022, our recorded Loss Reserves by underwriting segment, net of unpaid losses and loss adjustment expenses recoverable, and the results of the simulation were as follows:

	Insurance Segment	Reinsurance Segment	Mortgage Segment	Total
Loss Reserves (1)	$7,332,464	$5,787,531	$633,123	$13,753,118
Simulation results:
90th percentile (2)	$8,611,623	$7,054,715	$757,900	$16,070,373
10th percentile (3)	$6,091,636	$4,614,229	$517,006	$11,544,929

(1)    Net of reinsurance recoverables.

(2)    Simulation results indicate that a 90% probability exists that the net reserves for losses and loss adjustment expenses will not exceed the indicated amount.

(3)    Simulation results indicate that a 10% probability exists that the net reserves for losses and loss adjustment expenses will be at or below the indicated amount.

For informational purposes, based on the total simulation results, a change in our Loss Reserves to the amount indicated at the 90th percentile would result in a decrease in income before income taxes of approximately $2.3 billion, or $6.14 per diluted share, while a change in our Loss Reserves to the amount indicated at the 10th percentile would result in an increase in income before income taxes of approximately $2.2 billion, or $5.85 per diluted share. The simulation results noted above are informational only, and no assurance can be given that our ultimate losses will not be significantly different than the simulation results shown above, and such differences could directly and significantly impact earnings favorably or unfavorably in the period they are determined. We do not have significant exposure to pre-2002 liabilities, such as asbestos-related illnesses and other long-tail liabilities. It is difficult to provide meaningful trend information for certain liability/casualty coverages for which the claim-tail may be especially long, as claims are often reported and ultimately paid or settled years, or even decades, after the related loss events occur. Any estimates and

assumptions made as part of the reserving process could prove to be inaccurate due to several factors, including the fact that for certain lines of business relatively limited historical information has been reported to us through December 31, 2022. Accordingly, the reserving for incurred losses in these lines of business could be subject to greater variability. See Item 1A, “Risk Factors – Risks Relating to Our Industry, Business & Operations – Underwriting risks and reserving for losses are based on probabilities and related modeling, which are subject to inherent uncertainties.”

Mortgage Operations Supplemental Information

The mortgage segment’s insurance in force (“IIF”) and risk in force (“RIF”) were as follows at December 31, 2022 and 2021:

(U.S. Dollars in millions)	December 31,
	2022			2021
	Amount		%	Amount		%
Insurance In Force (IIF) (1):
U.S. primary mortgage insurance	$	295,651	57.6	$	280,945	61.0
U.S. credit risk transfer (CRT) and other (2)	145,087		28.3	110,018		23.9
International mortgage insurance/reinsurance (3)	72,315		14.1	69,655		15.1
Total	$	513,053	100.0	$	460,618	100.0
Risk In Force (RIF) (4):
U.S. primary mortgage insurance	$	75,806	84.8	$	70,619	84.3
U.S. credit risk transfer (CRT) and other (2)	6,245		7.0	5,120		6.1
International mortgage insurance/reinsurance (3)	7,369		8.2	7,983		9.5
Total	$	89,420	100.0	$	83,722	100.0

(1)    Represents the aggregate dollar amount of each insured mortgage loan’s current principal balance.

(2)    Includes all CRT transactions, which are predominantly with GSEs, and other U.S. reinsurance transactions.

(3)    International mortgage insurance and reinsurance with risk primarily located in Australia and to lesser extent Europe and Asia.

(4)    The aggregate dollar amount of each insured mortgage loan’s current principal balance multiplied by the insurance coverage percentage specified in the policy for insurance policies issued and after contract limits and/or loss ratio caps for risk-sharing or reinsurance transactions.

ARCH CAPITAL 75 2022 FORM 10-K

The insurance in force and risk in force for our U.S. primary mortgage insurance business by policy year were as follows at December 31, 2022:

(U.S. Dollars in millions)	IIF			RIF			Delinquency
	Amount		%	Amount		%	Rate (1)
Policy year:
2012 and prior	$	9,931	3.4	$	2,424	3.2	8.41	%
2013	3,000		1.0	798		1.1	1.85	%
2014	3,696		1.3	1,012		1.3	2.61	%
2015	6,236		2.1	1,680		2.2	2.08	%
2016	10,225		3.5	2,744		3.6	2.66	%
2017	9,508		3.2	2,521		3.3	3.06	%
2018	10,260		3.5	2,625		3.5	4.11	%
2019	19,096		6.5	4,840		6.4	2.36	%
2020	65,141		22.0	16,414		21.7	1.20	%
2021	89,621		30.3	22,740		30.0	0.95	%
2022	68,937		23.3	18,008		23.8	0.20	%
Total	$	295,651	100.0	$	75,806	100.0	1.77	%

(1)Represents the ending percentage of loans in default.

The insurance in force and risk in force for our U.S. primary mortgage insurance business by policy year were as follows at December 31, 2021:

(U.S. Dollars in millions)	IIF			RIF			Delinquency
	Amount		%	Amount		%	Rate (1)
Policy year:
2012 and prior	$	13,030	4.6	$	2,960	4.2	8.48	%
2013	4,206		1.5	1,148		1.6	2.63	%
2014	4,822		1.7	1,328		1.9	3.14	%
2015	8,703		3.1	2,340		3.3	2.67	%
2016	14,344		5.1	3,841		5.4	3.29	%
2017	13,128		4.7	3,436		4.9	4.09	%
2018	14,046		5.0	3,562		5.0	5.28	%
2019	25,841		9.2	6,467		9.2	3.13	%
2020	82,502		29.4	20,341		28.8	0.97	%
2021	100,323		35.7	25,196		35.7	0.29	%
Total	$	280,945	100.0	$	70,619	100.0	2.36	%

(1)Represents the ending percentage of loans in default.

The following tables provide supplemental disclosures on risk in force for our U.S. primary mortgage insurance business at December 31, 2022 and 2021:

(U.S. Dollars in millions)	December 31,
	2022				2021
	Amount			%	Amount			%
Credit quality (FICO):
>=740	$	46,812		61.8	$	42,451		60.1
680-739	24,945			32.9	23,646			33.5
620-679	3,772			5.0	4,196			5.9
<620	277			0.4	326			0.5
Total	$	75,806		100.0	$	70,619		100.0
Weighted average FICO score	750				746
Loan-to-Value (LTV):
95.01% and above	$	7,289		9.6	$	7,538		10.7
90.01% to 95.00%	43,681			57.6	38,829			55.0
85.01% to 90.00%	20,851			27.5	20,006			28.3
85.00% and below	3,985			5.3	4,246			6.0
Total	$	75,806		100.0	$	70,619		100.0
Weighted average LTV	92.8		%		92.8		%
Total RIF, net of external reinsurance	$	57,151			$	54,574

(U.S. Dollars in millions)	December 31,
	2022			2021
	Amount		%	Amount		%
Total RIF by State:
California	$	6,341	8.4	$	5,559	7.9
Texas	6,151		8.1	5,594		7.9
Florida	3,268		4.3	3,303		4.7
Georgia	3,169		4.2	2,902		4.1
North Carolina	3,160		4.2	2,921		4.1
Illinois	3,081		4.1	2,933		4.2
Minnesota	3,003		4.0	2,916		4.1
Massachusetts	2,809		3.7	2,537		3.6
Virginia	2,656		3.5	2,446		3.5
Michigan	2,618		3.5	2,492		3.5
Others	39,550		52.2	37,016		52.4
Total	$	75,806	100.0	$	70,619	100.0

ARCH CAPITAL 76 2022 FORM 10-K

The following table provides supplemental disclosures for our U.S. primary mortgage insurance business related to insured loans and loss metrics for the years ended December 31, 2022 and 2021:

(U.S. Dollars in thousands, except loan and claim count)	Year Ended December 31,
	2022			2021
Rollforward of insured loans in default:
Beginning delinquent number of loans	27,645			52,234
New notices	36,396			35,554
Cures	(42,789)			(59,372)
Paid claims	(685)			(771)
Ending delinquent number of loans (1)	20,567			27,645
Ending number of policies in force (1)	1,160,219			1,171,835
Delinquency rate (1)	1.77		%	2.36		%
Losses:
Number of claims paid	685			771
Total paid claims	$	21,412		$	30,979
Average per claim	$	31.3		$	40.2
Severity (2)	73.2		%	80.8		%
Average reserve per default (in thousands) (1)	$	21.1		$	26.7

(1)    Includes first lien primary and pool policies.

(2)    Represents total paid claims divided by RIF of loans for which claims were paid.

The risk-to-capital ratio, which represents total current (non-delinquent) risk in force, net of reinsurance, divided by total statutory capital, for Arch MI U.S. was approximately 7.2 to 1 at December 31, 2022, compared to 8 to 1 at December 31, 2021.

Ceded Reinsurance

In the normal course of business, our insurance and mortgage insurance operations cede a portion of their premium on a quota share or excess of loss basis through treaty or facultative reinsurance agreements. Our reinsurance operations also obtain reinsurance whereby another reinsurer contractually agrees to indemnify it for all or a portion of the reinsurance risks underwritten by our reinsurance operations. Such arrangements, where one reinsurer provides reinsurance to another reinsurer, are usually referred to as “retrocessional reinsurance” arrangements. In addition, our reinsurance subsidiaries participate in “common account” retrocessional arrangements for certain pro rata treaties. Such arrangements reduce the effect of individual or aggregate losses to all companies participating on such treaties, including the reinsurers, such as our reinsurance operations, and the ceding company. Estimating reinsurance recoverables can be more subjective than estimating the underlying reserves for losses and loss adjustment expenses as discussed above in “—Loss Reserves.” In particular, reinsurance recoverables may be affected by deemed inuring reinsurance, industry losses

reported by various statistical reporting services, and other factors. Reinsurance recoverables are recorded as assets, predicated on the reinsurers’ ability to meet their obligations under the reinsurance agreements. If the reinsurers are unable to satisfy their obligations under the agreements, our insurance or reinsurance operations would be liable for such defaulted amounts.

The availability and cost of reinsurance and retrocessional protection is subject to market conditions, which are beyond our control. Although we believe that our insurance and reinsurance operations have been successful in obtaining adequate reinsurance and retrocessional protection, it is not certain that they will be able to continue to obtain adequate protection at cost effective levels. As a result of such market conditions and other factors, our insurance, reinsurance and mortgage operations may not be able to successfully mitigate risk through reinsurance and retrocessional arrangements and may lead to increased volatility in our results of operations in future periods. See “Risk Factors—Risks Relating to Our Industry, Business and Operations—The failure of any of the loss limitation methods we employ could have a material adverse effect on our financial condition or results of operations.”

For purposes of managing risk, we reinsure a portion of our exposures, paying to reinsurers a part of the premiums received on the policies we write, and we may also use retrocessional protection. On a consolidated basis, ceded premiums written represented 27.7% of gross premiums written for 2022, compared to 29.3% for 2021. We monitor the financial condition of our reinsurers and attempt to place coverages only with substantial, financially sound carriers. If the financial condition of our reinsurers or retrocessionaires deteriorates, resulting in an impairment of their ability to make payments, we will be responsible for probable losses resulting from our inability to collect amounts due from such parties, as appropriate. We evaluate the credit worthiness of all the reinsurers to which we cede business. We report reinsurance recoverables net of an allowance for expected credit loss. The allowance is based upon our ongoing review of amounts outstanding, the financial condition of our reinsurers, amounts and form of collateral obtained and other relevant factors. A ratings based probability-of-default and loss-given-default methodology is used to estimate the allowance for expected credit loss. See “Risk Factors—Risks Relating to Our Industry, Business and Operations—We are exposed to credit risk in certain of our business operations” and “Financial Condition, Liquidity and Capital Resources” for further details.

We have entered into various aggregate excess of loss reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda. These are special purpose variable interest entities that are not consolidated in our financial results because we do not have

ARCH CAPITAL 77 2022 FORM 10-K

the unilateral power to direct those activities that are significant to its economic performance. As of December 31, 2022, our estimated off-balance sheet maximum exposure to loss from such entities was $26.8 million. See note 12, “Variable Interest Entity and Noncontrolling Interests,” to our consolidated financial statements in Item 8 for additional information.

Premium Revenues and Related Expenses

Insurance premiums written are generally recorded at the policy inception and are primarily earned on a pro rata basis over the terms of the policies for all products, usually 12 months. Premiums written include estimates in our insurance operations’ programs, specialty lines, collateral protection business and for participation in involuntary pools. Such premium estimates are derived from multiple sources which include the historical experience of the underlying business, similar business and available industry information. Unearned premium reserves represent the portion of premiums written that relates to the unexpired terms of in-force insurance policies.

Reinsurance premiums written include amounts reported by brokers and ceding companies, supplemented by our own estimates of premiums where reports have not been received. The determination of premium estimates requires a review of our experience with the ceding companies, familiarity with each market, the timing of the reported information, an analysis and understanding of the characteristics of each line of business, and management’s judgment of the impact of various factors, including premium or loss trends, on the volume of business written and ceded to us. On an ongoing basis, our underwriters review the amounts reported by these third parties for reasonableness based on their experience and knowledge of the subject class of business, taking into account our historical experience with the brokers or ceding companies. In addition, reinsurance contracts under which we assume business generally contain specific provisions which allow us to perform audits of the ceding company to ensure compliance with the terms and conditions of the contract, including accurate and timely reporting of information. Based on a review of all available information, management establishes premium estimates where reports have not been received. Premium estimates are updated when new information is received and differences between such estimates and actual amounts are recorded in the period in which estimates are changed or the actual amounts are determined. Premiums written are recorded based on the type of contracts we write. Premiums on our excess of loss and pro rata reinsurance contracts are estimated when the business is underwritten. For excess of loss contracts, premiums are recorded as written based on the terms of the contract. Estimates of premiums written under pro rata contracts are recorded in the period in which the underlying risks incept and are based on information provided by the

brokers and the ceding companies. For multi-year reinsurance treaties which are payable in annual installments, generally, only the initial annual installment is included as premiums written at policy inception due to the ability of the reinsured to commute or cancel coverage during the term of the policy. The remaining annual installments are included as premiums written at each successive anniversary date within the multi-year term.

Reinstatement premiums for our insurance and reinsurance operations are recognized at the time a loss event occurs, where coverage limits for the remaining life of the contract are reinstated under pre-defined contract terms. Reinstatement premiums, if obligatory, are fully earned when recognized. The accrual of reinstatement premiums is based on an estimate of losses and loss adjustment expenses, which reflects management’s judgment, as described above in “—Loss Reserves.”

The amount of reinsurance premium estimates included in premiums receivable and the amount of related acquisition expenses by type of business were as follows at December 31, 2022:

	December 31, 2022
	Gross Amount		Acquisition Expenses		Net Amount
Other specialty	$	1,211,598	$	(381,502)	$	830,096
Property excluding property catastrophe	390,612		(123,720)		266,892
Casualty	388,091		(114,028)		274,063
Marine and aviation	203,125		(43,922)		159,203
Property catastrophe	49,078		(5,850)		43,228
Other	69,297		(5,004)		64,293
Total	$	2,311,801	$	(674,026)	$	1,637,775

Premium estimates are reviewed by management at least quarterly. Such review includes a comparison of actual reported premiums to expected ultimate premiums along with a review of the aging and collection of premium estimates. Based on management’s review, the appropriateness of the premium estimates is evaluated, and any adjustment to these estimates is recorded in the period in which it becomes known. Adjustments to premium estimates could be material and such adjustments could directly and significantly impact earnings favorably or unfavorably in the period they are determined because the estimated premium may be fully or substantially earned.

A significant portion of amounts included as premiums receivable, which represent estimated premiums written, net of commissions, are not currently due based on the terms of the underlying contracts. Based on currently available information, we report premiums receivable net of an allowance for expected credit loss. We monitor credit risk associated with premiums receivable through our ongoing

ARCH CAPITAL 78 2022 FORM 10-K

review of amounts outstanding, aging of the receivable, historical data and counterparty financial strength measures.

Reinsurance premiums assumed, irrespective of the class of business, are generally earned on a pro rata basis over the terms of the underlying policies or reinsurance contracts. Contracts and policies written on a “losses occurring” basis cover claims that may occur during the term of the contract or policy, which is typically 12 months. Accordingly, the premium is earned evenly over the term. Contracts which are written on a “risks attaching” basis cover claims which attach to the underlying insurance policies written during the terms of such contracts. Premiums earned on such contracts usually extend beyond the original term of the reinsurance contract, typically resulting in recognition of premiums earned over a 24-month period.

Certain of our reinsurance contracts include provisions that adjust premiums or acquisition expenses based upon the experience under the contracts. Premiums written and earned, as well as related acquisition expenses, are recorded based upon the projected experience under such contracts.

Retroactive reinsurance reimburses a ceding company for liabilities incurred as a result of past insurable events covered by the underlying policies reinsured. In certain instances, reinsurance contracts cover losses both on a prospective basis and on a retroactive basis and, accordingly, we bifurcate the prospective and retrospective elements of these reinsurance contracts and accounts for each element separately where practical. Underwriting income generated in connection with retroactive reinsurance contracts is deferred and amortized into income over the settlement period while losses are charged to income immediately. Subsequent changes in estimated amount or timing of cash flows under such retroactive reinsurance contracts are accounted for by adjusting the previously deferred amount to the balance that would have existed had the revised estimate been available at the inception of the reinsurance transaction, with a corresponding charge or credit to income.

Mortgage guaranty insurance policies are contracts that are generally non-cancelable by the insurer, are renewable at a fixed price, and provide for payment of premiums on a monthly, annual or single basis. Upon renewal, we are not able to re-underwrite or re-price our policies. Consistent with industry accounting practices, premiums written on a monthly basis are earned as coverage is provided. Premiums written on an annual basis are amortized on a monthly pro rata basis over the year of coverage. Primary mortgage insurance premiums written on policies covering more than one year are referred to as single premiums. A portion of the revenue from single premiums is recognized in premiums earned in the current period, and the remaining portion is deferred as unearned premiums and earned over the estimated expiration of risk of the policy. If single premium policies

related to insured loans are canceled for any reason and the policy is a non-refundable product, the remaining unearned premium related to each canceled policy is recognized as earned premium upon notification of the cancellation.

Unearned premiums represent the portion of premiums written that is applicable to the estimated unexpired risk of insured loans. A portion of premium payments may be refundable if the insured cancels coverage, which generally occurs when the loan is repaid, the loan amortizes to a sufficiently low amount to trigger a lender permitted or legally required cancellation, or the value of the property has increased sufficiently in accordance with the terms of the contract. Premium refunds reduce premiums earned in the consolidated statements of income. Generally, only unearned premiums are refundable.

Acquisition costs that are directly related and incremental to the successful acquisition or renewal of business are deferred and amortized based on the type of contract. For property and casualty insurance and reinsurance contracts, deferred acquisition costs are amortized over the period in which the related premiums are earned. Consistent with mortgage insurance industry accounting practice, amortization of acquisition costs related to the mortgage insurance contracts for each underwriting year’s book of business is recorded in proportion to estimated gross profits. Estimated gross profits are comprised of earned premiums and losses and loss adjustment expenses. For each underwriting year, we estimate the rate of amortization to reflect actual experience and any changes to persistency or loss development.

Acquisition expenses and other expenses related to our underwriting operations that vary with, and are directly related to, the successful acquisition or renewal of business are deferred and amortized based on the type of contract. Our insurance and reinsurance operations capitalize incremental direct external costs that result from acquiring a contract but do not capitalize salaries, benefits and other internal underwriting costs. For our mortgage insurance operations, which include a substantial direct sales force, both external and certain internal direct costs are deferred and amortized. Deferred acquisition costs are carried at their estimated realizable value and take into account anticipated losses and loss adjustment expenses, based on historical and current experience, and anticipated investment income.

A premium deficiency occurs if the sum of anticipated losses and loss adjustment expenses, unamortized acquisition costs and maintenance costs and anticipated investment income exceed unearned premiums. A premium deficiency reserve (“PDR”) is recorded by charging any unamortized acquisition costs to expense to the extent required in order to eliminate the deficiency. If the premium deficiency exceeds unamortized acquisition costs then a liability is accrued for the excess deficiency.

ARCH CAPITAL 79 2022 FORM 10-K

To assess the need for a PDR on our mortgage exposures, we develop loss projections based on modeled loan defaults related to our current policies in force. This projection is based on recent trends in default experience, severity and rates of defaulted loans moving to claim, as well as recent trends in the rate at which loans are prepaid, and incorporates anticipated interest income. Evaluating the expected profitability of our existing mortgage insurance business and the need for a PDR for our mortgage business involves significant reliance upon assumptions and estimates with regard to the likelihood, magnitude and timing of potential losses and premium revenues. The models, assumptions and estimates we use to evaluate the need for a PDR may prove to be inaccurate, especially during an extended economic downturn or a period of extreme market volatility and uncertainty.

No premium deficiency charges were recorded by us during 2022 or 2021.

Fair Value Measurements

We review our securities measured at fair value and discuss the proper classification of such investments with investment advisors and others. See note 10, “Fair Value,” to our consolidated financial statements in Item 8 for a summary of our financial assets and liabilities measured at fair value at December 31, 2022 by valuation hierarchy.

Reclassifications

We have reclassified the presentation of certain prior year information to conform to the current presentation. Such reclassifications had no effect on our net income, shareholders’ equity or cash flows.

Significant Accounting Pronouncements

For all other significant accounting policies see note 3, “Significant Accounting Policies” and note 3(t), “Recent Accounting Pronouncements” to our consolidated financial statements in Item 8 for disclosures concerning our companies significant accounting policies and recent accounting pronouncements.

FINANCIAL CONDITION

Investable Assets

At December 31, 2022, total investable assets held by Arch were $28.1 billion.

Investable Assets Held by Arch 

The Finance, Investment and Risk Committee (“FIR Committee”) of our Board of Directors (the “Board”) establishes our investment policies and sets the parameters for creating guidelines for our investment managers. The FIR reviews the implementation of the investment strategy on a regular basis. Our current approach stresses preservation of capital, market liquidity and diversification of risk. While maintaining our emphasis on preservation of capital and liquidity, we expect our portfolio to become more diversified and, as a result, we may expand into areas which are not currently part of our investment strategy. Our Chief Investment Officer administers the investment portfolio, oversees our investment managers and formulates investment strategy in conjunction with the FIR Committee. At December 31, 2022, approximately $18.8 billion, or 67%, of total investable assets held by Arch were internally managed, compared to $18.5 billion, or 67%, at December 31, 2021.

The following table summarizes the fair value of investable assets held by Arch:

	December 31,
	2022	2021
Average effective duration (in years)	2.89	2.70
Average S&P/Moody’s credit ratings (1)	AA-/Aa3	AA-/Aa3

(1)Average credit ratings on our investment portfolio on securities with ratings by Standard & Poor’s Rating Services (“S&P”) and Moody’s Investors Service (“Moody’s”).

ARCH CAPITAL 80 2022 FORM 10-K

The following table provides the credit quality distribution of our Fixed Maturities. For individual fixed maturities, S&P ratings are used. In the absence of an S&P rating, ratings from Moody’s are used, followed by ratings from Fitch Ratings.

	Estimated Fair Value		% of Total
December 31, 2022
U.S. government and gov’t agencies (1)	$	5,829,279	28.8
AAA	3,616,537		17.9
AA	2,214,494		10.9
A	3,993,471		19.7
BBB	3,324,095		16.4
BB	560,213		2.8
B	377,462		1.9
Lower than B	12,029		0.1
Not rated	309,329		1.5
Total	$	20,236,909	100.0
December 31, 2021
U.S. government and gov’t agencies (1)	$	5,063,191	27.5
AAA	3,783,386		20.5
AA	2,459,413		13.4
A	2,943,594		16.0
BBB	2,936,398		15.9
BB	501,588		2.7
B	371,747		2.0
Lower than B	43,756		0.2
Not rated	311,734		1.7
Total	$	18,414,807	100.0

(1)Includes U.S. government-sponsored agency mortgage backed securities and agency commercial mortgage backed securities.

The following table provides information on the severity of the unrealized loss position as a percentage of amortized cost for all Fixed Maturities which were in an unrealized loss position:

Severity of gross unrealized losses:	Estimated Fair Value		Gross Unrealized Losses		% of Total Gross Unrealized Losses
December 31, 2022
0-10%	$	12,342,899	$	(579,958)	35.2
10-20%	5,331,223		(843,924)		51.3
20-30%	692,100		(198,778)		12.1
Greater than 30%	44,023		(23,739)		1.4
Total	$	18,410,245	$	(1,646,399)	100.0
December 31, 2021
0-10%	$	12,231,146	$	(166,867)	97.6
10-20%	16,884		(2,412)		1.4
20-30%	2,593		(759)		0.4
Greater than 30%	684		(916)		0.5
Total	$	12,251,307	$	(170,954)	100.0

The following table summarizes our top ten exposures to fixed income corporate issuers by fair value at December 31, 2022, excluding guaranteed amounts and covered bonds:

	Estimated Fair Value		Credit Rating (1)
Bank of America Corporation	$	430,071	A-/A2
JPMorgan Chase & Co.	296,901		A-/A1
Morgan Stanley	290,477		A-/A1
Citigroup Inc.	270,074		BBB+/A3
The Goldman Sachs Group, Inc.	249,547		BBB+/A2
Wells Fargo & Company	242,538		BBB+/A1
Blue Owl Capital Inc.	164,098		BBB-/Baa3
Blackstone Inc.	150,691		BBB-/Baa3
UBS Group AG	130,244		A/Aa3
Spring Funding II Llc	121,221		NA/NA
Total	$	2,345,862

(1)Average credit ratings as assigned by S&P and Moody’s, respectively.

ARCH CAPITAL 81 2022 FORM 10-K

The following table provides information on our structured securities, which include residential mortgage-backed securities (“RMBS”), commercial mortgage-backed securities (“CMBS”) and asset backed securities (“ABS”):

	Agencies		Investment Grade		Below Investment Grade		Total
Dec. 31, 2022
RMBS	$	645,008	$	133,958	$	16,425	$	795,391
CMBS	17,680		947,396		82,199		1,047,275
ABS	—		1,787,684		140,785		1,928,469
Total	$	662,688	$	2,869,038	$	239,409	$	3,771,135
Dec. 31, 2021
RMBS	$	268,229	$	129,296	$	10,952	$	408,477
CMBS	22,198		926,302		97,984		1,046,484
ABS	—		2,543,907		152,551		2,696,458
Total	$	290,427	$	3,599,505	$	261,487	$	4,151,419

The following table summarizes our equity securities, which include investments in exchange traded funds:

	December 31,
	2022		2021
Equities (1)	$	569,239	$	883,722
Exchange traded funds
Fixed income (2)	272,407		455,467
Equity and other (3)	32,115		491,474
Total	$	873,761	$	1,830,663

(1)Primarily in healthcare, technology, consumer cyclical and non-cyclical and industrials at December 31, 2022.

(2)Primarily in corporate at December 31, 2022.

(3)Primarily in large cap stocks, foreign equities, healthcare, technology and consumer discretionary at December 31, 2022.

Our investment strategy allows for the use of derivative instruments. We utilize various derivative instruments such as futures contracts to enhance investment performance, replicate investment positions or manage market exposures and duration risk that would be allowed under our investment guidelines if implemented in other ways. See note 11, “Derivative Instruments,” to our consolidated financial statements in Item 8 for additional disclosures concerning derivatives.

Accounting guidance regarding fair value measurements addresses how companies should measure fair value when they are required to use a fair value measure for recognition or disclosure purposes under GAAP and provides a common definition of fair value to be used throughout GAAP. See note 10, “Fair Value,” to our consolidated financial statements in Item 8 for a summary of our financial assets and liabilities measured at fair value at December 31, 2022 and 2021 segregated by level in the fair value hierarchy.

Reinsurance Recoverables

The following table details our reinsurance recoverables at December 31, 2022:

	% of Total	A.M. Best Rating (1)
Somers Re (2)	17.7	A-
Hannover Rück SE	4.6	A+
Lloyd’s syndicates (3)	3.6	A
Swiss Reinsurance America Corporation	3.3	A+
Everest Reinsurance Company	3.2	A+
Munich Reinsurance America, Inc.	3.1	A+
Fortitude Reinsurance Company Ltd.	2.9	A
Partner Reinsurance Company of the U.S.	2.9	A+
XL Re	2.5	A+
Berkley Insurance Company	2.0	A+
All other -- “A-” or better	23.0
All other -- rated carriers	0.1
All other -- not rated (4)	31.1
Total	100.0

(1)    The financial strength ratings are as of February 6, 2023 and were assigned by A.M. Best based on its opinion of the insurer’s financial strength as of such date. An explanation of the ratings listed in the table follows: the rating of “A+” is designated “Superior”; and the “A” rating is designated “Excellent.”

(2)    See note 12, “Variable Interest Entity and Noncontrolling Interests” and note 16, “Transactions with Related Parties.”

(3)    The A.M. Best group rating of “A” (Excellent) has been applied to all Lloyd’s syndicates.

(4)    Over 95% of such amount is collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other.

See note 8, “Reinsurance,” to our consolidated financial statements in Item 8 for further details.

Reserves for Losses and Loss Adjustment Expenses

We establish Loss Reserves which represent estimates involving actuarial and statistical projections, at a given point in time, of our expectations of the ultimate settlement and administration costs of losses incurred. Estimating Loss Reserves is inherently difficult. We utilize actuarial models as well as available historical insurance industry loss ratio experience and loss development patterns to assist in the establishment of Loss Reserves. Actual losses and loss adjustment expenses paid will deviate, perhaps substantially, from the reserve estimates reflected in our financial statements. See “Management’s Discussion and Analysis of Financial Condition and Results of Operations—Summary of Critical Accounting Estimates—Loss Reserves” and see Item 1 “Business—Reserves” for further details.

ARCH CAPITAL 82 2022 FORM 10-K

Shareholders’ Equity and Book Value per Share

Total shareholders’ equity available to Arch was $12.9 billion at December 31, 2022, compared to $13.5 billion at December 31, 2021. The 2022 period primarily reflected the impact of rising interest rates on our fixed income portfolio and the elevated catastrophe activity we experienced during the year.

The following table presents the calculation of book value per share:

(U.S. dollars in thousands, except share data)	December 31,
	2022		2021
Total shareholders’ equity available to Arch	$	12,910,073	$	13,545,896
Less preferred shareholders’ equity	830,000		830,000
Common shareholders’ equity available to Arch	$	12,080,073	$	12,715,896
Common shares and common share equivalents outstanding, net of treasury shares (1)	370,345,997		378,923,894
Book value per share	$	32.62	$	33.56

(1)    Excludes the effects of 14,420,901 and 17,083,160 stock options and 557,003 and 729,636 restricted stock and performance units outstanding at December 31, 2022 and 2021, respectively.

LIQUIDITY

Liquidity is a measure of our ability to access sufficient cash flows to meet the short-term and long-term cash requirements of our business operations.

Arch Capital is a holding company whose assets primarily consist of the shares in its subsidiaries. Generally, Arch Capital depends on its available cash resources, liquid investments and dividends or other distributions from its subsidiaries to make payments, including the payment of debt service obligations and operating expenses it may incur and any dividends or liquidation amounts with respect to our preferred and common shares.

In 2022, Arch Capital received dividends of $0.7 billion from Arch Reinsurance Ltd. (“Arch Re Bermuda”), our Bermuda-based reinsurer and insurer which can pay approximately $3.7 billion to Arch Capital in 2023 without providing an affidavit to the Bermuda Monetary Authority (“BMA”).

Our insurance and reinsurance operations provide liquidity in that premiums are received in advance, sometimes substantially in advance, of the time losses are paid. The period of time from the occurrence of a claim through the settlement of the liability may extend many years into the future. Sources of liquidity include cash flows from operations, financing arrangements or routine sales of investments.

As part of our investment strategy, we seek to establish a level of cash and highly liquid short-term and intermediate-term securities which, combined with expected cash flow, is believed by us to be adequate to meet our foreseeable payment obligations. However, due to the nature of our operations, cash flows are affected by claim payments that may comprise large payments on a limited number of claims and which can fluctuate from year to year. We believe that our liquid investments and cash flow will provide us with sufficient liquidity in order to meet our claim payment obligations. However, the timing and amounts of actual claim payments related to recorded Loss Reserves vary based on many factors, including large individual losses, changes in the legal environment, as well as general market conditions. The ultimate amount of the claim payments could differ materially from our estimated amounts. Certain lines of business written by us, such as excess casualty, have loss experience characterized as low frequency and high severity. The foregoing may result in significant variability in loss payment patterns. The impact of this variability can be exacerbated by the fact that the timing of the receipt of reinsurance recoverables owed to us may be slower than anticipated by us. Therefore, the irregular timing of claim payments can create significant variations in cash flows from operations between periods and may require us to utilize other sources of liquidity to make these payments, which may include the sale of investments or utilization of existing or new credit facilities or capital market transactions. If the source of liquidity is the sale of investments, we may be forced to sell such investments at a loss, which may be material.

We expect that our liquidity needs, including our anticipated insurance obligations and operating and capital expenditure needs, will be met by funds generated from underwriting activities and investment income, as well as by our balance of cash, short-term investments, proceeds on the sale or maturity of our investments, and our credit facilities, for the next twelve months, at a minimum.

Dividend Restrictions 

Arch Capital has no material restrictions on its ability to make distributions to shareholders. However, the ability of our regulated insurance and reinsurance subsidiaries to pay dividends or make distributions or other payments to us is limited by the applicable local laws and relevant regulations of the various countries and states in which we operate. See note 25, “Statutory Information,” to our consolidated financial statements in Item 8 for additional information on dividend restrictions.

The payment of dividends from Arch Re Bermuda is, under certain circumstances, limited under Bermuda law, which requires our Bermuda operating subsidiary to maintain certain measures of solvency and liquidity.

ARCH CAPITAL 83 2022 FORM 10-K

Our U.S. insurance and reinsurance subsidiaries are subject to insurance laws and regulations in the jurisdictions in which they operate. The ability of our regulated insurance subsidiaries to pay dividends or make distributions is dependent on their ability to meet applicable regulatory standards. These regulations include restrictions that limit the amount of dividends or other distributions, such as loans or cash advances, available to shareholders without prior approval of the insurance regulatory authorities. Each state requires prior regulatory approval of any payment of extraordinary dividends.

We also have insurance subsidiaries that are the parent company for other insurance subsidiaries, which means that dividends and other distributions will be subject to multiple layers of regulations in order for our insurance subsidiaries to be able to dividend funds to Arch Capital. The inability of the subsidiaries of Arch Capital to pay dividends and other permitted distributions could have a material adverse effect on Arch Capital’s cash requirements and our ability to make principal, interest and dividend payments on the senior notes, preferred shares and common shares.

In addition to meeting applicable regulatory standards, the ability of our insurance and reinsurance subsidiaries to pay dividends is also constrained by our dependence on the financial strength ratings of our insurance and reinsurance subsidiaries from independent rating agencies. The ratings from these agencies depend to a large extent on the capitalization levels of our insurance and reinsurance subsidiaries. We believe that Arch Capital has sufficient cash resources and available dividend capacity to service its indebtedness and other current outstanding obligations.

Restricted Assets 

Our insurance, reinsurance and mortgage insurance subsidiaries are required to maintain assets on deposit, which primarily consist of fixed maturities, with various regulatory authorities to support their operations. The assets on deposit are available to settle insurance and reinsurance liabilities to third parties. Our insurance and reinsurance subsidiaries maintain assets in trust accounts as collateral for insurance and reinsurance transactions with affiliated companies and also have investments in segregated portfolios primarily to provide collateral or guarantees for letters of credit to third parties. At December 31, 2022 and 2021, such amounts approximated $8.7 billion and $8.2 billion, respectively.

Our investments in certain securities, including certain fixed income and structured securities, investments in funds accounted for using the equity method, other alternative investments and investments in operating affiliates may be illiquid due to contractual provisions or investment market conditions. If we require significant amounts of cash on short notice in excess of anticipated cash requirements, then we

may have difficulty selling these investments in a timely manner or may be forced to sell or terminate them at unfavorable values. Our unfunded investment commitments totaled approximately $2.9 billion at December 31, 2022 and are callable by our investment managers. The timing of the funding of investment commitments is uncertain and may require us to access cash on short notice.

Cash Flows 

The following table summarizes our cash flows from operating, investing and financing activities, excluding amounts related to the ‘other’ segment:

	Year Ended December 31,
	2022		2021
Total cash provided by (used for):
Operating activities	$	3,815,227	$	3,380,700
Investing activities	(3,102,055)		(1,870,885)
Financing activities	(705,726)		(1,243,613)
Effects of exchange rate changes on foreign currency cash	(48,889)		(30,524)
Increase (decrease) in cash	$	(41,443)	$	235,678

Cash provided by operating activities for the 2022 period reflected a higher level of premiums collected than in the 2021 period.

Cash used for investing activities for the 2022 period reflected a higher level of purchases of fixed income securities than in the 2021 period, while the 2021 period reflected cash used for our investment in Coface and Somers.

Cash used for financing activities for the 2022 period primarily reflected $585.8 million of repurchases under our share repurchase program, compared to $1.2 in the 2021 period.

Investments 

At December 31, 2022, our investable assets were $28.1 billion. The primary goals of our asset liability management process are to meet our insurance liabilities, manage the interest rate risk embedded in those insurance liabilities and maintain sufficient liquidity to cover fluctuations in projected liability cash flows, including debt service obligations. Generally, the expected principal and interest payments produced by our fixed income portfolio adequately fund the estimated runoff of our insurance reserves. Although this is not an exact cash flow match in each period, the substantial degree by which the fair value of the fixed income portfolio exceeds the expected present value of the net insurance liabilities, as well as the positive cash flow from newly sold policies and the large amount of high quality liquid bonds, provide assurance of our ability to fund the payment of claims and to service our outstanding debt without having to

ARCH CAPITAL 84 2022 FORM 10-K

sell securities at distressed prices or access credit facilities. Please refer to Item 1A “Risk Factors” for a discussion of other risks relating to our business and investment portfolio.

CAPITAL RESOURCES

The following table provides an analysis of our capital structure:

(U.S. dollars in thousands, except  share data)	December 31,
	2022		2021
Senior notes	$	2,725,410	$	2,724,394
Shareholders’ equity available to Arch:
Series F non-cumulative preferred shares	330,000		330,000
Series G non-cumulative preferred shares	500,000		500,000
Common shareholders’ equity	12,080,073		12,715,896
Total	$	12,910,073	$	13,545,896
Total capital available to Arch	$	15,635,483	$	16,270,290
Senior notes to total capital (%)	17.4		16.7
Revolving credit agreement borrowings to total capital (%)	—		—
Debt to total capital (%)	17.4		16.7
Preferred to total capital (%)	5.3		5.1
Debt and preferred to total capital (%)	22.7		21.8

See note 19, “Debt and Financing Arrangements" and note 21, “Shareholders' Equity”, to our consolidated financial statements in Item 8 for additional information on capital structure.

Capital Adequacy

We monitor our capital adequacy on a regular basis and will seek to adjust our capital base (up or down) according to the needs of our business. The future capital requirements of our business will depend on many factors, including our ability to write new business successfully and to establish premium rates and reserves at levels sufficient to cover losses. Our ability to underwrite is largely dependent upon the quality of our claims paying and financial strength ratings as evaluated by independent rating agencies. In particular, we require (1) sufficient capital to maintain our financial strength ratings, as issued by several ratings agencies, at a level considered necessary by management to enable our key operating subsidiaries to compete; (2) sufficient capital to enable our underwriting subsidiaries to meet the capital adequacy tests performed by statutory agencies in the U.S. and other key markets; and (3) our non-U.S. operating companies are required to post letters of credit and other forms of collateral that are necessary for them to operate as they are “non-admitted” under U.S. state insurance regulations.

In addition, AMIC and UGRIC (together, “Arch MI U.S.”) are required to maintain compliance with the GSE requirements, known as PMIERs. The financial requirements require an eligible mortgage insurer’s available assets, which generally include only the most liquid assets of an insurer, to meet or exceed “minimum required assets” as of each quarter end. Minimum required assets are calculated from PMIERs tables with several risk dimensions (including origination year, original loan-to-value and original credit score of performing loans, and the delinquency status of non-performing loans) and are subject to a minimum amount. Arch MI U.S. satisfied the PMIERs’ financial requirements as of December 31, 2022 with a PMIER sufficiency ratio of 236%, compared to 197% at December 31, 2021.

As part of our capital management program, we may seek to raise additional capital or may seek to return capital to our shareholders through share repurchases, cash dividends or other methods (or a combination of such methods). Any such determination will be at the discretion of the Board and will be dependent upon our profits, financial requirements and other factors, including legal restrictions, rating agency requirements and such other factors as our Board deems relevant.

To the extent that our existing capital is insufficient to fund our future operating requirements or maintain such ratings, we may need to raise additional funds through financings or limit our growth. We can provide no assurance that, if needed, we would be able to obtain additional funds through financing on satisfactory terms or at all. Any adverse developments in the financial markets, such as disruptions, uncertainty or volatility in the capital and credit markets, may result in realized and unrealized capital losses that could have

ARCH CAPITAL 85 2022 FORM 10-K

a material adverse effect on our results of operations, financial position and our businesses, and may also limit our access to capital required to operate our business. In addition to common share capital, we depend on external sources of finance to support our underwriting activities, which can be in the form (or any combination) of debt securities, preference shares, common equity and bank credit facilities providing loans and/or letters of credit.

Arch Capital, through its subsidiaries, provides financial support to certain of its insurance subsidiaries and affiliates, through certain reinsurance arrangements beneficial to the ratings of such subsidiaries. Historically, our insurance, reinsurance and mortgage insurance subsidiaries have entered into separate reinsurance arrangements with Arch Re Bermuda covering individual lines of business.

Except as described in the above paragraph, or where express reinsurance, guarantee or other financial support contractual arrangements are in place, each of Arch Capital’s subsidiaries or affiliates is solely responsible for its own liabilities and commitments (and no other Arch Capital subsidiary or affiliate is so responsible). Any reinsurance arrangements, guarantees or other financial support contractual arrangements that are in place are solely for the benefit of the Arch Capital subsidiary or affiliate involved and third parties (creditors or insureds of such entity) are not express beneficiaries of such arrangements.

Share Repurchase Program 

Our Board has authorized the investment in Arch Capital’s common shares through a share repurchase program. Since the inception of the share repurchase program through December 31, 2022, Arch Capital has repurchased approximately 433.6 million common shares for an aggregate purchase price of $5.9 billion. At December 31, 2022, $1.0 billion of share repurchases were available under the program. Repurchases under the program may be effected from time to time in open market or privately negotiated transactions through December 31, 2024. The timing and amount of the repurchase transactions under this program will depend on a variety of factors, including market conditions, the development of the economy, corporate and regulatory considerations. We will continue to monitor our share price and, depending upon results of operations, market conditions and the development of the economy, as well as other factors, we will consider share repurchases on an opportunistic basis.

GUARANTOR INFORMATION

The below table provides a description of our senior notes payable at December 31, 2022:

	Interest		Principal		Carrying
Issuer/Due	(Fixed)		Amount		Amount
Arch Capital:
May 1, 2034	7.350	%	$	300,000	$	297,618
June 30, 2050	3.635	%	1,000,000		988,949
Arch-U.S.:
Nov. 1, 2043 (1)	5.144	%	500,000		495,188
Arch Finance:
Dec. 15, 2026 (1)	4.011	%	500,000		498,073
Dec. 15, 2046 (1)	5.031	%	450,000		445,582
Total			$	2,750,000	$	2,725,410

(1) Fully and unconditionally guaranteed by Arch Capital.

Our senior notes were issued by Arch Capital, Arch Capital Group (U.S.) Inc. (“Arch-U.S.”) and Arch Capital Finance LLC (“Arch Finance”). Arch-U.S. is a wholly-owned subsidiary of Arch Capital and Arch Finance is a wholly-owned finance subsidiary of Arch-U.S. Our 2034 senior notes and 2050 senior notes issued by Arch Capital are unsecured and unsubordinated obligations of Arch Capital and ranked equally with all of its existing and future unsecured and unsubordinated indebtedness. The 2043 senior notes issued by Arch-U.S. are unsecured and unsubordinated obligations of Arch-U.S. and Arch Capital and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch-U.S. and Arch Capital. The 2026 senior notes and 2046 senior notes issued by Arch Finance are unsecured and unsubordinated obligations of Arch Finance and Arch Capital and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch Finance and Arch Capital.

Arch Capital and Arch-U.S. are each holding companies and, accordingly, they conduct substantially all of their operations through their operating subsidiaries. Arch Finance is a wholly owned subsidiary of Arch U.S. MI Holdings Inc., a U.S. holding company. As a result, Arch Capital, Arch-U.S. and Arch Finance's cash flows and their ability to service their debt depends upon the earnings of their operating subsidiaries and on their ability to distribute the earnings, loans or other payments from such subsidiaries to Arch Capital, Arch-U.S. and Arch Finance, respectively.

During 2022 and 2021, we made interest payments of $128.4 million and $131.0 million respectively, related to our senior notes and other financing arrangements. See note 19, “Debt and Financing Arrangements,” to our consolidated financial statements in Item 8 for additional disclosures concerning our senior notes and revolving credit agreement borrowings. For additional information on our preferred shares, see note 21, “Shareholders’ Equity,” to our consolidated financial statements in Item 8.

ARCH CAPITAL 86 2022 FORM 10-K

The following tables present condensed financial information for Arch Capital (parent guarantor) and Arch-U.S. (subsidiary issuer):

	December 31, 2022				December 31, 2021
	Arch Capital		Arch-U.S.		Arch Capital		Arch-U.S.
Assets
Total investments	$	7,282	$	78,766	$	2,038	$	137,124
Cash	11,393		9,542		16,317		18,392
Investment in operating affiliates	5,259				6,877
Due from subsidiaries and affiliates	1,554		2		11		26,000
Other assets	17,203		30,311		9,604		37,040
Total assets	$	42,691	$	118,621	$	34,847	$	218,556
Liabilities
Senior notes	1,286,567		495,188		1,286,208		495,063
Due to subsidiaries and affiliates	—		991,070		—		521,839
Other liabilities	37,239		36,405		24,767		47,410
Total liabilities	1,323,806		1,522,663		1,310,975		1,064,312
Non-cumulative preferred shares	$	830,000	$	—	$	830,000	$	—

	December 31, 2022				December 31, 2021
Year Ended	Arch Capital		Arch-U.S.		Arch Capital		Arch-U.S.
Revenues
Net investment income	$	2,058	$	1,341	$	1,524	$	11,596
Net realized gains (losses)	29		(346)		—		72,437
Equity in net income (loss) of investments accounted for using the equity method	—		10,228		—		18,149
Total revenues	2,087		11,223		1,524		102,182
Expenses
Corporate expenses	85,997		12,502		71,818		5,875
Interest expense	58,759		48,199		58,741		47,292
Net foreign exchange (gains) losses	(1)		—		7		—
Total expenses	144,755		60,701		130,566		53,167
Income (loss) before income taxes	(142,668)		(49,478)		(129,042)		49,015
Income tax (expense) benefit	—		10,097		—		(12,513)
Income (loss) from operating affiliates	(1,047)		—		(590)		—
Net income available to Arch	(143,715)		(39,381)		(129,632)		36,502
Preferred dividends	(40,736)		—		(48,343)		—
Loss on redemption of preferred shares	—		—		(15,101)		—
Net income available to Arch common shareholders	$	(184,451)	$	(39,381)	$	(193,076)	$	36,502

ARCH CAPITAL 87 2022 FORM 10-K

CONTRACTUAL OBLIGATIONS AND COMMITMENTS

Contractual Obligations

The following table provides an analysis of our contractual commitments at December 31, 2022:

	Payment due by period
	Total		2023		2024 and 2025		2026 and 2027		Thereafter
Operating activities
Estimated gross payments for losses and loss adjustment expenses (1)	$	20,031,943	$	5,687,045	$	6,410,819	$	3,030,790	$	4,903,289
Deposit accounting liabilities (2)	10,376		5,449		1,519		365		3,043
Contractholder payables (3)	1,733,984		549,050		602,897		239,833		342,204
Operating lease obligations	175,284		31,922		54,862		39,918		48,582
Purchase obligations	150,053		83,078		64,952		2,023		—
Investing activities
Unfunded investment commitments (4)	2,922,663		2,922,663		—		—		—
Financing activities
Senior notes (including interest payments)	5,166,889		126,815		253,629		733,574		4,052,871
Total contractual obligations and commitments	$	30,191,192	$	9,406,022	$	7,388,678	$	4,046,503	$	9,349,989

(1)The estimated expected contractual commitments related to the reserves for losses and loss adjustment expenses are presented on a gross basis (i.e., not reflecting any corresponding reinsurance recoverable amounts that would be due to us). It should be noted that until a claim has been presented to us, determined to be valid, quantified and settled, there is no known obligation on an individual transaction basis, and while estimable in the aggregate, the timing and amount contain significant uncertainty.

(2)The estimated expected contractual commitments related to deposit accounting liabilities have been estimated using projected cash flows from the underlying contracts. It should be noted that, due to the nature of such liabilities, the timing and amount contain significant uncertainty.

(3)Certain insurance policies written by our insurance operations feature large deductibles, primarily in construction and national accounts lines. Under such contracts, we are obligated to pay the claimant for the full amount of the claim and are subsequently reimbursed by the policyholder for the deductible amount. In the event we are unable to collect from the policyholder, we would be liable for such defaulted amounts.

(4)Unfunded investment commitments are callable by our investment managers. We have assumed that such investments will be funded in the next year but the funding may occur over a longer period of time, due to market conditions and other factors.

Letter of Credit and Revolving Credit Facilities

In the normal course of its operations, the Company enters into agreements with financial institutions to obtain secured and unsecured credit facilities. On April 7, 2022, Arch Capital and certain of its subsidiaries amended its existing credit agreement into a $925.0 million facility (the “Credit Facility”) with a syndication of lenders. The Credit Facility, as amended, consists of a $425.0 million secured facility for letters of credit (the “Secured Facility”) and a $500.0 million unsecured facility for revolving loans and letters of credit (the “Unsecured Facility”). Obligations of each borrower under the Secured Facility for letters of credit are secured by cash and eligible securities of such borrower held in collateral accounts. Commitments under the Credit Facility may be increased up to, but not exceeding, an aggregate of $1.25 billion. Arch Capital has a one-time option to convert any or all outstanding revolving loans of Arch Capital and/or Arch-U.S. to term loans with the same terms as the revolving loans except that any prepayments may not be re-borrowed. Arch-U.S. guarantees the obligations of Arch Capital, and Arch Capital guarantees the obligations of Arch-U.S. Borrowings of revolving loans may be made at a variable rate based on Secured Overnight Financing Rate (“SOFR”). Secured letters of credit are available for issuance on behalf of certain Arch Capital subsidiaries. At December 31, 2022,

the Secured Facility had $323.1 million of letters of credit outstanding and remaining capacity of $101.9 million, and the Unsecured Facility had no outstanding revolving loans or letters of credit, with remaining capacity of $500.0 million.

The Credit Facility contains certain restrictive covenants customary for facilities of this type, including restrictions on indebtedness, consolidated tangible net worth, minimum shareholders’ equity levels and minimum financial strength ratings. Arch Capital and its subsidiaries which are party to the agreement were in compliance with all covenants contained therein at December 31, 2022.

See note 19, “Debt and Financing Arrangements,” to our consolidated financial statements in Item 8 for additional disclosures concerning our senior notes and revolving credit agreement borrowings.

ARCH CAPITAL 88 2022 FORM 10-K

RATINGS

Our ability to underwrite business is affected by the quality of our claims paying ability and financial strength ratings as evaluated by independent agencies. Such ratings from third party internationally recognized statistical rating organizations or agencies are instrumental in establishing the financial security of companies in our industry. We believe that the primary users of such ratings include commercial and investment banks, policyholders, brokers, ceding companies and investors. Insurance ratings are also used by insurance and reinsurance intermediaries as an important means of assessing the financial strength and quality of insurers and reinsurers, and are often an important factor in the decision by an insured or intermediary of whether to place business with a particular insurance or reinsurance provider. Periodically, rating agencies evaluate us to confirm that we continue to meet their criteria for the ratings assigned to us by them. S&P, Moody’s, A.M. Best Company and Fitch Ratings are ratings agencies which have assigned financial strength ratings to one or more of Arch Capital’s subsidiaries.

If we are not able to obtain adequate capital, our business, results of operations and financial condition could be adversely affected, which could include, among other things, the following possible outcomes: (1) potential downgrades in the financial strength ratings assigned by ratings agencies to our operating subsidiaries, which could place those operating subsidiaries at a competitive disadvantage compared to higher-rated competitors; (2) reductions in the amount of business that our operating subsidiaries are able to write in order to meet capital adequacy-based tests enforced by statutory agencies; and (3) any resultant ratings downgrades could, among other things, affect our ability to write business and increase the cost of bank credit and letters of credit. In addition, under certain of the reinsurance agreements assumed by our reinsurance operations, upon the occurrence of a ratings downgrade or other specified triggering event with respect to our reinsurance operations, such as a reduction in surplus by specified amounts during specified periods, our ceding company clients may be provided with certain rights, including, among other things, the right to terminate the subject reinsurance agreement and/or to require that our reinsurance operations post additional collateral.

The ratings issued on our companies by these agencies are announced publicly and are available directly from the agencies. Our website www.archgroup.com (Investor Relations-Credit Ratings) contains information about our ratings, but such information on our website is not incorporated by reference into this report.

CATASTROPHIC EVENTS AND SEVERE ECONOMIC EVENTS

We have large aggregate exposures to natural and man-made catastrophic events, pandemic events like COVID-19 and severe economic events. Natural catastrophes can be caused by various events, including hurricanes, floods, windstorms, earthquakes, hailstorms, tornadoes, explosions, severe winter weather, fires, droughts and other natural disasters. Catastrophes can also cause losses in non-property business such as mortgage insurance, workers’ compensation or general liability. In addition to the nature of property business, we believe that economic and geographic trends affecting insured property, including inflation, property value appreciation and geographic concentration, tend to generally increase the size of losses from catastrophic events over time.

We have substantial exposure to unexpected, large losses resulting from future man-made catastrophic events, such as acts of war, acts of terrorism and political instability. These risks are inherently unpredictable. It is difficult to predict the timing of such events with statistical certainty or estimate the amount of loss any given occurrence will generate. It is not possible to completely eliminate our exposure to unforecasted or unpredictable events and, to the extent that losses from such risks occur, our financial condition and results of operations could be materially adversely affected. Therefore, claims for natural and man-made catastrophic events could expose us to large losses and cause substantial volatility in our results of operations, which could cause the value of our common shares to fluctuate widely. In certain instances, we specifically insure and reinsure risks resulting from terrorism. Even in cases where we attempt to exclude losses from terrorism and certain other similar risks from some coverages written by us, we may not be successful in doing so. Moreover, irrespective of the clarity and inclusiveness of policy language, there can be no assurance that a court or arbitration panel will limit enforceability of policy language or otherwise issue a ruling adverse to us.

We seek to limit our loss exposure by writing a number of our reinsurance contracts on an excess of loss basis, adhering to maximum limitations on reinsurance written in defined geographical zones, limiting program size for each client and prudent underwriting of each program written. In the case of proportional treaties, we may seek per occurrence limitations or loss ratio caps to limit the impact of losses from any one or series of events. In our insurance operations, we seek to limit our exposure through the purchase of reinsurance. We cannot be certain that any of these loss limitation methods will be effective. We also seek to limit our loss exposure by geographic diversification. Geographic zone limitations involve significant underwriting judgments, including the determination of the area of the zones and the inclusion of a particular policy within a particular zone's limits. There can

ARCH CAPITAL 89 2022 FORM 10-K

be no assurance that various provisions of our policies, such as limitations or exclusions from coverage or choice of forum, will be enforceable in the manner we intend. Disputes relating to coverage and choice of legal forum may also arise. Underwriting is inherently a matter of judgment, involving important assumptions about matters that are inherently unpredictable and beyond our control, and for which historical experience and probability analysis may not provide sufficient guidance. One or more catastrophic or other events could result in claims that substantially exceed our expectations, which could have a material adverse effect on our financial condition or our results of operations, possibly to the extent of eliminating our shareholders' equity.

For our natural catastrophe exposed business, we seek to limit the amount of exposure we will assume from any one insured or reinsured and the amount of the exposure to catastrophe losses from a single event in any geographic zone. We monitor our exposure to catastrophic events, including earthquake and wind and periodically reevaluate the estimated probable maximum pre-tax loss for such exposures. Our estimated probable maximum pre-tax loss is determined through the use of modeling techniques, but such estimate does not represent our total potential loss for such exposures.

Our models employ both proprietary and vendor-based systems and include cross-line correlations for property, marine, offshore energy, aviation, workers compensation and personal accident. We seek to limit the probable maximum pre-tax loss to a specific level for severe catastrophic events. Currently, we seek to limit our 1-in-250 year return period net probable maximum loss from a severe catastrophic event in any geographic zone to approximately 25% of tangible shareholders’ equity available to Arch (total shareholders’ equity available to Arch less goodwill and intangible assets). We reserve the right to change this threshold at any time.

Based on in-force exposure estimated as of January 1, 2023, our modeled peak zone catastrophe exposure is a windstorm affecting the Florida Tri-County, with a net probable maximum pre-tax loss of $970 million, followed by windstorms affecting the Northeast U.S., and the Gulf of Mexico with net probable maximum pre-tax losses of $908 million and $903 million, respectively. As of January 1, 2023, our modeled peak zone earthquake exposure (San Francisco area earthquake) represented approximately 60% of our peak zone catastrophe exposure, and our modeled peak zone international exposure (U.K. windstorm) was substantially less than both our peak zone windstorm and earthquake exposures.

We also have significant exposure to losses due to mortgage defaults resulting from severe economic events in the future. For our U.S. mortgage insurance business, we have developed a proprietary risk model (“Realistic Disaster

Scenario” or “RDS”) that simulates the maximum loss resulting from a severe economic downturn impacting the housing market. The RDS models the collective impact of adverse conditions for key economic indicators, the most significant of which is a decline in home prices. The RDS model projects paths of future home prices, unemployment rates, income levels and interest rates and assumes correlation across states and geographic regions. The resulting future performance of our in-force portfolio is then estimated under the economic stress scenario, reflecting loan and borrower information.

Currently, we seek to limit our modeled RDS loss from a severe economic event to approximately 25% of total tangible shareholders’ equity available to Arch. We reserve the right to change this threshold at any time. Based on in-force exposure estimated as of January 1, 2023, our modeled RDS loss was 12.3% of tangible shareholders’ equity available to Arch.

Net probable maximum loss estimates are net of expected reinsurance recoveries, before income tax and before excess reinsurance reinstatement premiums. RDS loss estimates are net of expected reinsurance recoveries and before income tax. Catastrophe loss estimates are reflective of the zone indicated and not the entire portfolio. Since hurricanes and windstorms can affect more than one zone and make multiple landfalls, our catastrophe loss estimates include clash estimates from other zones. Our catastrophe loss estimates and RDS loss estimates do not represent our maximum exposures and it is highly likely that our actual incurred losses would vary materially from the modeled estimates. There can be no assurances that we will not suffer pre-tax losses greater than 25% of our tangible shareholders’ equity from one or more catastrophic events or severe economic events due to several factors, including the inherent uncertainties in estimating the frequency and severity of such events and the margin of error in making such determinations resulting from potential inaccuracies and inadequacies in the data provided by clients and brokers, the modeling techniques and the application of such techniques or as a result of a decision to change the percentage of shareholders' equity exposed to a single catastrophic event or severe economic event. In addition, actual losses may increase if our reinsurers fail to meet their obligations to us or the reinsurance protections purchased by us are exhausted or are otherwise unavailable. See “Risk Factors—Risks Relating to Our Industry, Business and Operations” Depending on business opportunities and the mix of business that may comprise our insurance, reinsurance and mortgage portfolios, we may seek to adjust our self-imposed limitations on probable maximum pre-tax loss for catastrophe exposed business and mortgage default exposed business. See “—Summary of Critical Accounting Estimates—Ceded Reinsurance” for a discussion of our catastrophe reinsurance programs.

ARCH CAPITAL 90 2022 FORM 10-K

MARKET SENSITIVE INSTRUMENTS AND RISK MANAGEMENT

Our investment results are subject to a variety of risks, including risks related to changes in the business, financial condition or results of operations of the entities in which we invest, as well as changes in general economic conditions and overall market conditions. We are also exposed to potential loss from various market risks, including changes in equity prices, interest rates and foreign currency exchange rates.

In accordance with the SEC’s Financial Reporting Release No. 48, we performed a sensitivity analysis to determine the effects that market risk exposures could have on the future earnings, fair values or cash flows of our financial instruments as of December 31, 2022. Market risk represents the risk of changes in the fair value of a financial instrument and consists of several components, including liquidity, basis and price risks.

The sensitivity analysis performed as of December 31, 2022 presents hypothetical losses in cash flows, earnings and fair values of market sensitive instruments which were held by us on December 31, 2022 and are sensitive to changes in interest rates and equity security prices. This risk management discussion and the estimated amounts generated from the following sensitivity analysis represent forward-looking statements of market risk assuming certain adverse market conditions occur. Actual results in the future may differ materially from these projected results due to actual developments in the global financial markets. The analysis methods used by us to assess and mitigate risk should not be considered projections of future events of losses.

The focus of the SEC’s market risk rules is on price risk. For purposes of specific risk analysis, we employ sensitivity analysis to determine the effects that market risk exposures could have on the future earnings, fair values or cash flows of our financial instruments. The financial instruments included in the following sensitivity analysis consist of all of our investments and cash.

Investment Market Risk

Fixed Income Securities. We invest in interest rate sensitive securities, primarily debt securities. We consider the effect of interest rate movements on the fair value of our fixed maturities, short-term investments and certain of our other investments, equity securities and investment funds accounted for using the equity method which invest in fixed income securities (collectively, “Fixed Income Securities”) and the corresponding change in unrealized appreciation. As interest rates rise, the fair value of our Fixed Income Securities falls, and the converse is also true. Based on historical observations, there is a low probability that all

interest rate yield curves would shift in the same direction at the same time. Furthermore, at times interest rate movements in certain credit sectors exhibit a much lower correlation to changes in U.S. Treasury yields. Accordingly, the actual effect of interest rate movements may differ materially from the amounts set forth in the following tables.

The following table summarizes the effect that an immediate, parallel shift in the interest rate yield curve would have had on our investment portfolio at December 31, 2022 and 2021:

(U.S. dollars in billions)	Interest Rate Shift in Basis Points
	-100			-50			-		+50			+100
Dec. 31, 2022
Total fair value	$	27.19		$	26.79		$	26.42	$	26.05		$	25.71
Change from base	2.9		%	1.4		%			(1.4)		%	(2.7)		%
Change in unrealized value	$	0.77		$	0.37				$	(0.37)		$	(0.71)
Dec. 31, 2021
Total fair value	$	25.79		$	25.44		$	25.21	$	24.75		$	24.43
Change from base	2.3		%	0.9		%			(1.8)		%	(3.1)		%
Change in unrealized value	$	0.58		$	0.23				$	(0.45)		$	(0.78)

In addition, we consider the effect of credit spread movements on the market value of our Fixed Income Securities and the corresponding change in unrealized value. As credit spreads widen, the fair value of our Fixed Income Securities falls, and the converse is also true. In periods where the spreads on our Fixed Income Securities are much higher than their historical average due to short-term market dislocations, a parallel shift in credit spread levels would result in a much more pronounced change in unrealized value.

The following table summarizes the effect that an immediate, parallel shift in credit spreads in a static interest rate environment would have had on the portfolio at December 31, 2022 and 2021:

(U.S. dollars in billions)	Credit Spread Shift in Percentage
	-100			-50			-		+50			+100
Dec. 31, 2022
Total fair value	$	27.50		$	26.95		$	26.42	$	25.89		$	25.34
Change from base	4.1		%	2.0		%			(2.0)		%	(4.1)		%
Change in unrealized value	$	1.08		$	0.53				$	(0.53)		$	(1.08)
Dec. 31, 2021
Total fair value	$	26.17		$	25.69		$	25.21	$	24.72		$	24.24
Change from base	3.8		%	1.9		%			(1.9)		%	(3.8)		%
Change in unrealized value	$	0.97		$	0.48				$	(0.48)		$	(0.97)

Another method that attempts to measure portfolio risk is Value-at-Risk (“VaR”). VaR measures the worst expected loss under normal market conditions over a specific time interval at a given confidence level. The 1-year 95th

ARCH CAPITAL 91 2022 FORM 10-K

percentile parametric VaR reported herein estimates that 95% of the time, the portfolio loss in a one-year horizon would be less than or equal to the calculated number, stated as a percentage of the measured portfolio’s initial value. The VaR is a variance-covariance based estimate, based on linear sensitivities of a portfolio to a broad set of systematic market risk factors and idiosyncratic risk factors mapped to the portfolio exposures. The relationships between the risk factors are estimated using historical data, and the most recent data points are generally given more weight. As of December 31, 2022, our portfolio’s 95th percentile VaR was estimated to be 8.8%, compared to an estimated 4.8% at December 31, 2021. In periods where the volatility of the risk factors mapped to our portfolio’s exposures is higher due to market conditions, the resulting VaR is higher than in other periods.

Equity Securities. At December 31, 2022 and 2021, the fair value of our investments in equity securities and certain investments accounted for using the equity method with underlying equity strategies totaled $0.8 billion and $1.4 billion, respectively. These investments are exposed to price risk, which is the potential loss arising from decreases in fair value. An immediate hypothetical 10% decline in the value of each position would reduce the fair value of such investments by approximately $79.1 million and $137.5 million at December 31, 2022 and 2021, respectively, and would have decreased book value per share by approximately $0.21 and $0.36, respectively. An immediate hypothetical 10% increase in the value of each position would increase the fair value of such investments by approximately $79.1 million and $137.5 million at December 31, 2022 and 2021, respectively, and would have increased book value per share by approximately $0.21 and $0.36, respectively.

Investment-Related Derivatives. At December 31, 2022, the notional value of all derivative instruments (excluding foreign currency forward contracts which are included in the foreign currency exchange risk analysis below) was $6.6 billion, compared to $6.4 billion at December 31, 2021. If the underlying exposure of each investment-related derivative held at December 31, 2022 depreciated by 100 basis points, it would have resulted in a reduction in net income of approximately $66.3 million, and a decrease in book value per share of $0.18, compared to $63.8 million and $0.17, respectively, on investment-related derivatives held at December 31, 2021. If the underlying exposure of each investment-related derivative held at December 31, 2022 appreciated by 100 basis points, it would have resulted in an increase in net income of approximately $66.3 million, and an increase in book value per share of $0.18, compared to $63.8 million and $0.17, respectively, on investment-related derivatives held at December 31, 2021. See note 11, “Derivative Instruments,” to our consolidated financial statements in Item 8 for additional disclosures concerning derivatives.

For further discussion on investment activity, please refer to “—Financial Condition, Liquidity and Capital Resources—Financial Condition—Investable Assets.”

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Foreign Currency Exchange Risk

Foreign currency rate risk is the potential change in value, income and cash flow arising from adverse changes in foreign currency exchange rates. Through our subsidiaries and branches located in various foreign countries, we conduct our insurance and reinsurance operations in a variety of local currencies other than the U.S. Dollar. We generally hold investments in foreign currencies which are intended to mitigate our exposure to foreign currency fluctuations in our net insurance liabilities. We may also utilize foreign currency forward contracts and currency options as part of our investment strategy. See note 11, “Derivative Instruments,” to our consolidated financial statements in Item 8 for additional information.

The following table provides a summary of our net foreign currency exchange exposures, as well as foreign currency derivatives in place to manage these exposures:

(U.S. dollars in thousands, except  per share data)	December 31, 2022		December 31, 2021
Net assets (liabilities), denominated in foreign currencies, excluding shareholders’ equity and derivatives	$	(396,305)	$	(825,371)
Shareholders’ equity denominated in foreign currencies (1)	1,056,213		1,095,706
Net foreign currency forward contracts outstanding (2)	311,519		15,151
Net exposures denominated in foreign currencies	$	971,427	$	285,486
Pre-tax impact of a hypothetical 10% appreciation of the U.S. Dollar against foreign currencies:
Shareholders’ equity	$	(97,143)	$	(28,549)
Book value per share	$	(0.26)	$	(0.08)
Pre-tax impact of a hypothetical 10% decline of the U.S. Dollar against foreign currencies:
Shareholders’ equity	$	97,143	$	28,549
Book value per share	$	0.26	$	0.08

(1)    Represents capital contributions held in the foreign currencies of our operating units.

(2)    Represents the net notional value of outstanding foreign currency forward contracts.

Although the Company generally attempts to match the currency of its projected liabilities with investments in the same currencies, from time to time the Company may elect to over or underweight one or more currencies, which could increase the Company’s exposure to foreign currency fluctuations and increase the volatility of the Company’s shareholders’ equity. Historical observations indicate a low probability that all foreign currency exchange rates would shift against the U.S. Dollar in the same direction and at the same time and, accordingly, the actual effect of foreign currency rate movements may differ materially from the amounts set forth above. For further discussion on foreign exchange activity, please refer to “—Results of Operations.”

Effects of Inflation

General economic inflation has increased in recent quarters and may continue to remain at elevated levels for an extended period of time. The potential also exists, after a catastrophe loss or pandemic events like COVID-19, for the development of inflationary pressures in a local economy. This may have a material effect on the adequacy of our reserves for losses and loss adjustment expenses, especially in longer-tailed lines of business, and on the market value of our investment portfolio through rising interest rates. The anticipated effects of inflation are considered in our pricing models, reserving processes and exposure management, across all lines of business and types of loss including natural catastrophe events. The actual effects of inflation on our results cannot be accurately known until claims are ultimately settled and will vary by the specific type of inflation affecting each line of business.

ITEM 7A. QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK

Reference is made to the information appearing above under the subheading “Market Sensitive Instruments and Risk Management” under the caption “Management’s Discussion and Analysis of Financial Condition and Results of Operation,” which information is hereby incorporated by reference.

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ITEM 8.     FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA

Index to Financial Statements		Page No.
Report of Independent Registered Public Accounting Firm (PCAOB ID 238)		95
Consolidated Balance Sheets
	At December 31, 2022 and December 31, 2021	97
Consolidated Statements of Income
	For the years ended December 31, 2022, 2021 and 2020	98
Consolidated Statements of Comprehensive Income
	For the years ended December 31, 2022, 2021 and 2020	99
Consolidated Statements of Changes in Shareholders’ Equity
	For the years ended December 31, 2022, 2021 and 2020	100
Consolidated Statements of Cash Flows
	For the years ended December 31, 2022, 2021 and 2020	101
Notes to Consolidated Financial Statements
	Note 1 - General	102
	Note 2 - Acquisitions	102
	Note 3 - Significant Accounting Policies	102
	Note 4 - Segment Information	111
	Note 5 - Reserve for Losses and Loss Adjustment Expenses	118
	Note 6 - Short Duration Contracts	120
	Note 7 - Allowance for Expected Credit Losses	133
	Note 8 - Reinsurance	134
	Note 9 - Investment Information	136
	Note 10 - Fair Value	142
	Note 11 - Derivative Instruments	148
	Note 12 - VIE and Noncontrolling Interests	149
	Note 13 - Other Comprehensive Income (Loss)	151
	Note 14 - Earnings Per Common Share	153
	Note 15 - Income Taxes	153
	Note 16 - Transactions with Related Parties	156
	Note 17 - Leases	157
	Note 18 - Commitments and Contingencies	157
	Note 19 - Debt and Financing Arrangements	158
	Note 20 - Goodwill and Intangible Assets	160
	Note 21 - Shareholders’ Equity	161
	Note 22 - Share-Based Compensation	162
	Note 23 - Retirement Plans	165
	Note 24 - Legal Proceedings	165
	Note 25 - Statutory Information	165

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Report of Independent Registered Public Accounting Firm

To the Board of Directors and Shareholders of Arch Capital Group Ltd.

Opinions on the Financial Statements and Internal Control over Financial Reporting

We have audited the accompanying consolidated balance sheets of Arch Capital Group Ltd. and its subsidiaries (the “Company”) as of December 31, 2022 and 2021, and the related consolidated statements of income, of comprehensive income, of changes in shareholders’ equity and of cash flows for each of the three years in the period ended December 31, 2022, including the related notes and financial statement schedules listed in the index appearing under Item 15(a)(2) (collectively referred to as the “consolidated financial statements”). We also have audited the Company's internal control over financial reporting as of December 31, 2022, based on criteria established in Internal Control - Integrated Framework (2013) issued by the Committee of Sponsoring Organizations of the Treadway Commission (COSO).

In our opinion, the consolidated financial statements referred to above present fairly, in all material respects, the financial position of the Company as of December 31, 2022 and 2021, and the results of its operations and its cash flows for each of the three years in the period ended December 31, 2022, in conformity with accounting principles generally accepted in the United States of America. Also in our opinion, the Company maintained, in all material respects, effective internal control over financial reporting as of December 31, 2022, based on criteria established in Internal Control- Integrated Framework (2013) issued by the COSO.

Basis for Opinions

The Company's management is responsible for these consolidated financial statements, for maintaining effective internal control over financial reporting, and for its assessment of the effectiveness of internal control over financial reporting, included in Management's Annual Report on Internal Control Over Financial Reporting appearing under Item 9A. Our responsibility is to express opinions on the Company’s consolidated financial statements and on the Company's internal control over financial reporting based on our audits. We are a public accounting firm registered with the Public Company Accounting Oversight Board (United States)(PCAOB) and are required to be independent with respect to the Company in accordance with the U.S. federal securities laws and the applicable rules and regulations of the Securities and Exchange Commission and the PCAOB.

We conducted our audits in accordance with the standards of the PCAOB. Those standards require that we plan and perform the audits to obtain reasonable assurance about whether the consolidated financial statements are free of material misstatement, whether due to error or fraud, and whether effective internal control over financial reporting was maintained in all material respects.

Our audits of the consolidated financial statements included performing procedures to assess the risks of material misstatement of the consolidated financial statements, whether due to error or fraud, and performing procedures that respond to those risks. Such procedures included examining, on a test basis, evidence regarding the amounts and disclosures in the consolidated financial statements. Our audits also included evaluating the accounting principles used and significant estimates made by management, as well as evaluating the overall presentation of the consolidated financial statements. Our audit of internal control over financial reporting included obtaining an understanding of internal control over financial reporting, assessing the risk that a material weakness exists, and testing and evaluating the design and operating effectiveness of internal control based on the assessed risk. Our audits also included performing such other procedures as we considered necessary in the circumstances. We believe that our audits provide a reasonable basis for our opinions.

Definition and Limitations of Internal Control over Financial Reporting

A company’s internal control over financial reporting is a process designed to provide reasonable assurance regarding the reliability of financial reporting and the preparation of financial statements for external purposes in accordance with generally accepted accounting principles. A company’s internal control over financial reporting includes those policies and procedures that (i) pertain to the maintenance of records that, in reasonable detail, accurately and fairly reflect the transactions and dispositions of the assets of the company; (ii) provide reasonable assurance that transactions are recorded as necessary to permit preparation of financial statements in accordance with generally accepted accounting principles, and that receipts and expenditures of the company are being made only in accordance with authorizations of management and directors of the company; and (iii) provide reasonable assurance regarding prevention or timely detection of unauthorized acquisition, use, or disposition of the company’s assets that could have a material effect on the financial statements.

ARCH CAPITAL 95 2022 FORM 10-K

Because of its inherent limitations, internal control over financial reporting may not prevent or detect misstatements. Also, projections of any evaluation of effectiveness to future periods are subject to the risk that controls may become inadequate because of changes in conditions, or that the degree of compliance with the policies or procedures may deteriorate.

Critical Audit Matters

The critical audit matter communicated below is a matter arising from the current period audit of the consolidated financial statements that was communicated or required to be communicated to the audit committee and that (i) relates to accounts or disclosures that are material to the consolidated financial statements and (ii) involved our especially challenging, subjective, or complex judgments. The communication of critical audit matters does not alter in any way our opinion on the consolidated financial statements, taken as a whole, and we are not, by communicating the critical audit matter below, providing a separate opinion on the critical audit matter or on the accounts or disclosures to which it relates.

Valuation of Reserve for Losses and Loss Adjustment Expenses

As described in Notes 3, 5 and 6 to the consolidated financial statements, the reserve for losses and loss adjustment expenses represents estimates of future amounts required to pay losses and loss adjustment expenses for insured or reinsured events which have occurred at or before the balance sheet date. As of December 31, 2022, the Company’s total reserve for losses and loss adjustment expenses was $20.0 billion. For the insurance and reinsurance segments, management estimates ultimate losses and loss adjustment expenses using various generally accepted actuarial methods applied to known losses and other relevant information. Ultimate losses and loss adjustment expenses are generally determined by extrapolation of claim emergence and settlement patterns observed in the past that can reasonably be expected to persist into the future. Management makes a number of key assumptions in their reserving process, including estimating loss development patterns and expected loss ratios. For the mortgage segment, the lead actuarial methodology used by management is a frequency-severity method based on the inventory of pending delinquencies. The assumptions of frequency and severity reflect judgments based on historical data and experience.

The principal considerations for our determination that performing procedures relating to the valuation of the reserve for losses and loss adjustment expenses is a critical audit matter are (i) the significant judgment by management when developing their estimate, which in turn led to a high degree of auditor subjectivity and judgment in performing procedures related to the valuation of the reserve for losses and loss adjustment expenses, (ii) the significant auditor effort and judgment in evaluating audit evidence related to the aforementioned key actuarial methods and key assumptions, and (iii) the audit effort included the involvement of professionals with specialized skill and knowledge to assist in performing these procedures and evaluating the audit evidence obtained.

Addressing the matter involved performing procedures and evaluating audit evidence in connection with forming our overall opinion on the consolidated financial statements. These procedures included testing the effectiveness of controls relating to the valuation of the reserve for losses and loss adjustment expenses, including controls over the selection of key actuarial methods and development of key assumptions. These procedures also included, among others, the involvement of professionals with specialized skill and knowledge to assist in performing one or a combination of procedures, including (i) developing an independent estimate, on a test basis, of the reserve for losses and loss adjustment expenses, and comparing the independent estimate to management’s actuarially determined reserve for losses and loss adjustment expenses to evaluate the reasonableness of the reserve for losses and loss adjustment expenses and (ii) evaluating the appropriateness of the actuarial methods and reasonableness of the assumptions, related to loss development patterns, expected loss ratios, frequency, and severity used by management to determine the Company’s reserve for losses and loss adjustment expenses. Developing the independent estimate and evaluating the appropriateness of the key methods and reasonableness of the key assumptions related to loss development patterns, expected loss ratios, frequency and severity, as applicable, involved testing the completeness and accuracy of historical data provided by management.

/s/ PricewaterhouseCoopers LLP

New York, New York

February 24, 2023

We have served as the Company’s or its predecessor’s auditor since 1995.

ARCH CAPITAL 96 2022 FORM 10-K

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES CONSOLIDATED BALANCE SHEETS (U.S. dollars in thousands, except share data)
	December 31,
	2022		2021
Assets
Investments:
Fixed maturities available for sale, at fair value (amortized cost: $21,281,863 and $17,973,823; net of allowance for credit losses: $41,355 and $2,883)	$	19,682,789	$	17,998,109
Short-term investments available for sale, at fair value (amortized cost: $1,332,996 and $1,734,738; net of allowance for credit losses: $0 and $0 )	1,331,662		1,734,716
Equity securities, at fair value	859,969		1,804,170
Other investments (portion measured at fair value: $1,644,197 and $1,973,550)	1,644,197		1,973,550
Investments accounted for using the equity method	3,774,310		3,077,611
Total investments	27,292,927		26,588,156
Cash	855,118		858,668
Accrued investment income	158,680		85,453
Investment in operating affiliates	964,604		1,135,655
Premiums receivable (net of allowance for credit losses: $35,402 and $39,958)	3,624,777		2,633,280
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $21,544 and $13,230)	6,563,654		5,880,735
Contractholder receivables (net of allowance for credit losses: $2,691 and $3,437)	1,731,293		1,828,691
Ceded unearned premiums	1,799,197		1,729,455
Deferred acquisition costs	1,263,870		901,841
Receivable for securities sold	12,493		60,179
Goodwill and intangible assets	804,289		944,983
Other assets	2,919,605		2,453,849
Total assets	$	47,990,507	$	45,100,945
Liabilities
Reserve for losses and loss adjustment expenses	$	20,031,943	$	17,757,156
Unearned premiums	7,337,002		6,011,942
Reinsurance balances payable	1,529,919		1,583,253
Contractholder payables	1,733,984		1,832,127
Collateral held for insured obligations	249,238		242,352
Senior notes	2,725,410		2,724,394
Payable for securities purchased	95,041		64,850
Other liabilities	1,367,068		1,329,742
Total liabilities	35,069,605		31,545,816
Commitments and Contingencies
Redeemable noncontrolling interests	10,829		9,233
Shareholders’ Equity
Non-cumulative preferred shares	830,000		830,000
Common shares ($0.0011 par, shares issued: 588,250,762 and 583,289,850)	654		648
Additional paid-in capital	2,211,444		2,085,075
Retained earnings	15,892,065		14,455,868
Accumulated other comprehensive income (loss), net of deferred income tax	(1,646,170)		(64,600)
Common shares held in treasury, at cost (shares: 217,904,765 and 204,365,956)	(4,377,920)		(3,761,095)
Total shareholders' equity available to Arch	12,910,073		13,545,896
Non-redeemable noncontrolling interests	—		—
Total shareholders' equity	12,910,073		13,545,896
Total liabilities, noncontrolling interests and shareholders' equity	$	47,990,507	$	45,100,945

See Notes to Consolidated Financial Statements

ARCH CAPITAL 97 2022 FORM 10-K

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES CONSOLIDATED STATEMENTS OF INCOME (U.S. dollars in thousands, except share data)
	Year Ended December 31,
	2022		2021		2020
Revenues
Net premiums earned	$	9,678,077	$	8,082,298	$	6,991,935
Net investment income	496,547		389,118		519,608
Net realized gains (losses)	(662,734)		379,845		823,460
Other underwriting income	13,227		22,073		26,784
Equity in net income of investments accounted for using the equity method	115,856		366,402		146,693
Other income (loss)	(26,165)		10,244		29
Total revenues	9,614,808		9,249,980		8,508,509
Expenses
Losses and loss adjustment expenses	5,027,517		4,584,803		4,689,599
Acquisition expenses	1,739,580		1,303,178		1,004,842
Other operating expenses	1,128,175		998,595		875,176
Corporate expenses	95,482		79,157		81,988
Amortization of intangible assets	106,200		82,955		69,031
Interest expense	130,266		139,470		143,456
Net foreign exchange losses (gains)	(100,905)		(41,529)		83,634
Total expenses	8,126,315		7,146,629		6,947,726
Income before income taxes and income (loss) from operating affiliates	1,488,493		2,103,351		1,560,783
Income taxes:
Current tax expense (benefit)	201,216		295,533		197,662
Deferred tax expense (benefit)	(121,255)		(166,951)		(85,824)
Income tax expense	79,961		128,582		111,838
Income (loss) from operating affiliates	73,891		264,693		16,766
Net income	$	1,482,423	$	2,239,462	$	1,465,711
Net (income) loss attributable to noncontrolling interests	(5,490)		(82,613)		(60,190)
Net income available to Arch	1,476,933		2,156,849		1,405,521
Preferred dividends	(40,736)		(48,343)		(41,612)
Loss on redemption of preferred shares	—		(15,101)		—
Net income available to Arch common shareholders	$	1,436,197	$	2,093,405	$	1,363,909
Net income per common share and common share equivalent
Basic	$	3.90	$	5.34	$	3.38
Diluted	$	3.80	$	5.23	$	3.32
Weighted average common shares and common share equivalents outstanding
Basic	368,612,197		391,748,715		403,062,179
Diluted	377,609,767		400,345,936		410,259,455

See Notes to Consolidated Financial Statements

ARCH CAPITAL 98 2022 FORM 10-K

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME (U.S. dollars in thousands)
	Year Ended December 31,
	2022		2021		2020
Comprehensive Income
Net income	$	1,482,423	$	2,239,462	$	1,465,711
Other comprehensive income (loss), net of deferred income tax
Unrealized appreciation (decline) in value of available-for-sale investments:
Unrealized holding gains (losses) arising during year	(1,772,649)		(386,929)		678,717
Reclassification of net realized (gains) losses, included in net income	247,799		(116,068)		(426,187)
Foreign currency translation adjustments	(56,720)		(64,482)		33,336
Comprehensive income (loss)	(99,147)		1,671,983		1,751,577
Net (income) loss attributable to noncontrolling interests	(5,490)		(82,613)		(60,190)
Other comprehensive (income) loss attributable to noncontrolling interests	—		13,984		(9,062)
Comprehensive income available to Arch (loss)	$	(104,637)	$	1,603,354	$	1,682,325

See Notes to Consolidated Financial Statements

ARCH CAPITAL 99 2022 FORM 10-K

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES CONSOLIDATED STATEMENTS OF CHANGES IN SHAREHOLDERS' EQUITY (U.S. dollars in thousands)
	Year Ended December 31,
	2022		2021		2020
Non-cumulative preferred shares
Balance at beginning of year	$	830,000	$	780,000	$	780,000
Preferred shares issued	—		500,000		—
Preferred shares redeemed	—		(450,000)		—
Balance at end of year	830,000		830,000		780,000
Common shares
Balance at beginning of year	648		643		638
Common shares issued, net	6		5		5
Balance at end of year	654		648		643
Additional paid-in capital
Balance at beginning of year	2,085,075		1,977,794		1,889,683
Issue costs on preferred shares issued	—		(14,179)		—
Reversal of issue costs on preferred shares redeemed	—		15,101		—
Amortization of share-based compensation	87,620		86,053		70,535
Other changes	38,749		20,306		17,576
Balance at end of year	2,211,444		2,085,075		1,977,794
Retained earnings
Balance at beginning of year	14,455,868		12,362,463		11,021,006
Cumulative effect of an accounting change	—		—		(22,452)
Balance at beginning of year, as adjusted	14,455,868		12,362,463		10,998,554
Net income	1,482,423		2,239,462		1,465,711
Net (income) loss attributable to noncontrolling interests	(5,490)		(82,613)		(60,190)
Preferred share dividends	(40,736)		(48,343)		(41,612)
Loss on redemption of preferred shares	—		(15,101)		—
Balance at end of year	15,892,065		14,455,868		12,362,463
Accumulated other comprehensive income (loss)
Balance at beginning of year	(64,600)		488,895		212,091
Unrealized appreciation (decline) in value of available-for-sale investments, net of deferred income tax:
Balance at beginning of year	13,486		501,295		258,486
Unrealized holding gains (losses) during period, net of reclassification adjustment	(1,524,850)		(502,997)		252,530
Unrealized holding gains (losses) during period attributable to noncontrolling interests	—		15,188		(9,721)
Balance at end of year	(1,511,364)		13,486		501,295
Foreign currency translation adjustments, net of deferred income tax:
Balance at beginning of year	(78,086)		(12,400)		(46,395)
Foreign currency translation adjustments	(56,720)		(64,482)		33,336
Foreign currency translation adjustments attributable to noncontrolling interests	—		(1,204)		659
Balance at end of year	(134,806)		(78,086)		(12,400)
Balance at end of year	(1,646,170)		(64,600)		488,895
Common shares held in treasury, at cost
Balance at beginning of year	(3,761,095)		(2,503,909)		(2,406,047)
Shares repurchased for treasury	(616,825)		(1,257,186)		(97,862)
Balance at end of year	(4,377,920)		(3,761,095)		(2,503,909)
Total shareholders’ equity available to Arch	12,910,073		13,545,896		13,105,886
Non-redeemable noncontrolling interests	—		—		823,007
Total shareholders’ equity	$	12,910,073	$	13,545,896	$	13,928,893

See Notes to Consolidated Financial Statements

ARCH CAPITAL 100 2022 FORM 10-K

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES CONSOLIDATED STATEMENTS OF CASH FLOWS (U.S. dollars in thousands)
	Year Ended December 31,
	2022		2021		2020
Operating Activities
Net income	$	1,482,423	$	2,239,462	$	1,465,711
Adjustments to reconcile net income to net cash provided by operating activities:
Net realized (gains) losses	651,568		(427,367)		(844,625)
Equity in net (income) or loss of investments accounted for using the equity method and other income or loss	153,157		(464,050)		(47,951)
Amortization of intangible assets	106,200		82,955		69,031
Share-based compensation	87,628		87,094		71,262
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable	1,889,015		1,762,190		2,113,827
Unearned premiums, net of ceded unearned premiums	1,399,112		936,039		445,781
Premiums receivable	(1,109,229)		(685,214)		(318,643)
Deferred acquisition costs	(374,067)		(263,243)		(143,948)
Reinsurance balances payable	(35,509)		500,065		65,950
Other items, net	(435,071)		(340,376)		10,110
Net cash provided by operating activities	3,815,227		3,427,555		2,886,505
Investing Activities
Purchases of fixed maturity investments	(16,390,475)		(35,451,858)		(39,765,277)
Purchases of equity securities	(796,998)		(1,175,480)		(1,595,010)
Purchases of other investments	(1,720,457)		(1,859,096)		(1,808,727)
Proceeds from sales of fixed maturity investments	11,844,004		33,577,445		37,949,346
Proceeds from sales of equity securities	1,554,116		918,145		1,147,264
Proceeds from sales, redemptions and maturities of other investments	1,221,072		1,765,533		1,029,578
Proceeds from redemptions and maturities of fixed maturity investments	714,519		1,628,755		871,134
Net settlements of derivative instruments	(68,818)		(40,072)		179,006
Net (purchases) sales of short-term investments	467,249		165,272		(1,029,681)
Change in cash collateral related to securities lending	—		—		81,210
Purchase of operating affiliate	—		(753,916)		—
Impact of the deconsolidation of the variable interest entity	—		(349,202)		—
Purchases of fixed assets	(51,672)		(41,394)		(39,872)
Other	125,405		(523,864)		(62,197)
Net cash used for investing activities	(3,102,055)		(2,139,732)		(3,043,226)
Financing Activities
Proceeds from issuance of preferred shares, net	—		485,821		—
Redemption of preferred shares	—		(450,000)		—
Purchases of common shares under share repurchase program	(585,823)		(1,234,294)		(83,472)
Proceeds from common shares issued, net	6,660		6,418		1,876
Proceeds from borrowings	—		—		1,018,793
Repayments of borrowings	—		—		(359,000)
Change in cash collateral related to securities lending	—		—		(81,210)
Third party investment in non-redeemable noncontrolling interests	—		15,971		(2,867)
Dividends paid to redeemable noncontrolling interests	—		(1,907)		(4,945)
Other	(85,827)		(3,278)		73,715
Preferred dividends paid	(40,736)		(48,280)		(41,612)
Net cash provided by (used for) financing activities	(705,726)		(1,229,549)		521,278
Effects of exchange rate changes on foreign currency cash and restricted cash	(48,889)		(34,047)		22,289
Increase (decrease) in cash and restricted cash	(41,443)		24,227		386,846
Cash and restricted cash, beginning of year	1,314,771		1,290,544		903,698
Cash and restricted cash, end of year	$	1,273,328	$	1,314,771	$	1,290,544
Income taxes paid (received)	$	254,922	$	286,810	$	202,940
Interest paid	$	128,425	$	139,301	$	133,491

See Notes to Consolidated Financial Statements

ARCH CAPITAL 101 2022 FORM 10-K

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

1.    General

Arch Capital Group Ltd. (“Arch Capital” or “Arch”) is a publicly listed Bermuda exempted company which provides insurance, reinsurance and mortgage insurance on a worldwide basis through its wholly owned subsidiaries. As used herein, the “Company” means Arch Capital and its subsidiaries. Similarly, “Common Shares” means the common shares of Arch Capital.

The Company’s consolidated financial statements included the results of Somers Group Holdings Ltd. (formerly Watford Holdings Ltd.) and its wholly owned subsidiaries (“Somers”). Effective July 1, 2021, Somers is wholly owned by Greysbridge Holdings Ltd., (“Greysbridge”) and Greysbridge is owned 40% by the Company, 30% by certain investment funds managed by Kelso & Company (“Kelso”) and 30% by certain investment funds managed by Warburg Pincus LLC (“Warburg”). Based on the governing documents of Greysbridge, the Company concluded that, while it retains significant influence over Somers, Somers no longer constitutes a variable interest entity. Accordingly, effective July 1, 2021, Arch no longer consolidates the results of Somers in its consolidated financial statements and footnotes. See note 12, “Variable Interest Entity and Noncontrolling Interests”.

The Company has reclassified the presentation of certain prior year information to conform to the current presentation. Such reclassifications had no effect on the Company’s net income, shareholders’equity or cash flows. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.

2.    Acquisitions

Westpac Lenders Mortgage Insurance Limited (“WLMI”)

On August 31, 2021, the Company completed the acquisition of WLMI, an Australian Prudential Regulation Authority authorized captive lenders mortgage insurance (“LMI”) provider to the Westpac Banking Corporation (“Westpac”). As part of the acquisition, WLMI retained its existing risk in force and will remain Westpac’s exclusive provider of LMI on new mortgage originations for a period of 10 years from the acquisition date. The Company was renamed Arch Lenders Mortgage Indemnity Limited (“Arch Indemnity”) and will be the Company’s primary provider of LMI to the Australian market.

Somerset Bridge Group Limited, Southern Rock Holdings Limited and affiliates (“Somerset Group”)

On August 6, 2021, the Company completed the acquisition of Somerset Group. The acquisition includes Somerset Group’s motor insurance managing general agent, distribution capabilities through direct and aggregator channels, affiliated insurer and fully integrated claims operation.

In connection with the acquisitions noted above, the Company increased its goodwill and intangible assets by $350.1 million.

3.    Significant Accounting Policies

(a) Basis of Presentation

The consolidated financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America (“GAAP”) and include the accounts of Arch Capital and its subsidiaries, including Arch Reinsurance Ltd. (“Arch Re Bermuda”), Arch Reinsurance Company (“Arch Re U.S.”), Arch Capital Group (U.S.) Inc.(“Arch-U.S.”), Arch Insurance Company, Arch Specialty Insurance Company, Arch Property Casualty Insurance Company (“Arch P&C”), Arch Indemnity Insurance Company (“Arch Indemnity Insurance”), Arch Insurance Canada Ltd. (“Arch Insurance Canada”), Arch Reinsurance Europe Designated Activity Company (“Arch Re Europe”), Arch Mortgage Insurance Company (“AMIC”), Arch Mortgage Guaranty Company (“AMG”), United Guaranty Residential Insurance Company (“UGRIC”), Arch Indemnity, Arch Insurance (EU) Designated Activity Company (“Arch Insurance (EU)”), Arch Insurance (U.K.) Limited (“Arch Insurance (U.K.)”) and the Company’s participation on Lloyd’s of London syndicates: 2012 (“Arch Syndicate 2012”) and 1955 (“Arch Syndicate 1955” and together with Arch Syndicate 2012, the Company’s “Lloyd’s Syndicates”). All significant intercompany transactions and balances have been eliminated in consolidation.

The preparation of financial statements in conformity with GAAP requires management to make estimates and assumptions that affect the reported amounts of assets and liabilities and disclosure of contingent assets and liabilities at the date of the financial statements and the reported amounts of revenues and expenses during the reporting period. Actual results could differ materially from those estimates and assumptions. The Company’s principal estimates include:

•The reserve for losses and loss adjustment expenses;

•Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses, including the provision for uncollectible amounts;

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

•Estimates of written and earned premiums;

•The valuation of the investment portfolio and assessment of allowance for credit losses;

•The valuation of purchased intangible assets;

•The assessment of goodwill and intangible assets for impairment; and

•The valuation of deferred tax assets.

(b) Premium Revenues and Related Expenses

Insurance. Insurance premiums written are generally recorded at the policy inception and are primarily earned on a pro rata basis over the terms of the policies for all products, usually 12 months. Premiums written include estimates that are derived from multiple sources which include the historical experience of the underlying business, similar business and available industry information. Unearned premium reserves represent the portion of premiums written that relates to the unexpired terms of in-force insurance policies.

Reinsurance. Reinsurance premiums written include amounts reported by brokers and ceding companies, supplemented by the Company’s own estimates of premiums where reports have not been received. The determination of premium estimates requires a review of the Company’s experience with the ceding companies, familiarity with each market, the timing of the reported information, an analysis and understanding of the characteristics of each line of business, and management’s judgment of the impact of various factors, including premium or loss trends, on the volume of business written and ceded to the Company. On an ongoing basis, the Company’s underwriters review the amounts reported by these third parties for reasonableness based on their experience and knowledge of the subject class of business, taking into account the Company’s historical experience with the brokers or ceding companies. In addition, reinsurance contracts under which the Company assumes business generally contain specific provisions which allow the Company to perform audits of the ceding company to ensure compliance with the terms and conditions of the contract, including accurate and timely reporting of information. Based on a review of all available information, management establishes premium estimates where reports have not been received. Premium estimates are updated when new information is received and differences between such estimates and actual amounts are recorded in the period in which estimates are changed or the actual amounts are determined.

Reinsurance premiums written are recorded based on the type of contracts the Company writes. Premiums on the Company’s excess of loss and pro rata reinsurance contracts are estimated when the business is underwritten. For excess of loss contracts, premiums are recorded as written based on

the terms of the contract. Estimates of premiums written under pro rata contracts are recorded in the period in which the underlying risks are expected to incept and are based on information provided by the brokers and the ceding companies. For multi-year reinsurance treaties which are payable in annual installments, generally, only the initial annual installment is included as premiums written at policy inception due to the ability of the reinsured to commute or cancel coverage during the term of the policy. The remaining annual installments are included as premiums written at each successive anniversary date within the multi-year term.

Reinsurance premiums written, irrespective of the class of business, are generally earned on a pro rata basis over the terms of the underlying policies or reinsurance contracts. Contracts and policies written on a “losses occurring” basis cover claims that may occur during the term of the contract or policy, which is typically 12 months. Accordingly, the premium is earned evenly over the term. Contracts which are written on a “risks attaching” basis cover claims which attach to the underlying insurance policies written during the terms of such contracts. Premiums earned on such contracts usually extend beyond the original term of the reinsurance contract, typically resulting in recognition of premiums earned over a 24-month period. Certain of the Company’s reinsurance contracts include provisions that adjust premiums or acquisition expenses based upon the experience under the contracts. Premiums written and earned, as well as related acquisition expenses, are recorded based upon the projected experience under such contracts.

The Company also writes certain reinsurance business that is intended to provide insurers with risk management solutions that complement traditional reinsurance. Under these contracts, the Company assumes a measured amount of insurance risk in exchange for an anticipated margin, which is typically lower than on traditional reinsurance contracts. The terms and conditions of these contracts may include additional or return premiums based on loss experience, loss corridors, sublimits and caps. Examples of such business include aggregate stop-loss coverages, financial quota share coverages and multi-year retrospectively rated excess of loss coverages. If these contracts are deemed to transfer risk, they are accounted for as reinsurance. Otherwise, such contracts are accounted for under the deposit method.

Mortgage. Mortgage guaranty insurance policies are contracts that are generally non-cancelable by the insurer, are renewable at a fixed price, and provide for payment of premiums on a monthly, annual or single basis. Upon renewal, the Company is not able to re-underwrite or re-price its policies. Consistent with industry accounting practices, premiums written on a monthly basis are earned as coverage is provided. Premiums written on an annual basis are amortized on a monthly pro rata basis over the year of coverage. Primary mortgage insurance premiums written on

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

policies covering more than one year are referred to as single premiums. A portion of the revenue from single premiums is recognized in premiums earned in the current period, and the remaining portion is deferred as unearned premiums and earned over the estimated expiration of risk of the policy. If single premium policies related to insured loans are canceled due to repayment by the borrower and the policy is a non-refundable product, the remaining unearned premium related to each canceled policy is recognized as earned premium upon notification of the cancellation.

Reinstatement premiums for the Company’s insurance and reinsurance operations are recognized at the time a loss event occurs, where coverage limits for the remaining life of the contract are reinstated under pre-defined contract terms. Reinstatement premiums, if obligatory, are fully earned when recognized. The accrual of reinstatement premiums is based on an estimate of losses and loss adjustment expenses, which reflects management’s judgment.

Premium estimates are reviewed by management at least quarterly. Such review includes a comparison of actual reported premiums to expected ultimate premiums along with a review of the aging and collection of premium estimates. Based on management’s review, the appropriateness of the premium estimates is evaluated, and any adjustment to these estimates is recorded in the period in which it becomes known. Adjustments to premium estimates could be material and such adjustments could directly and significantly impact earnings favorably or unfavorably in the period they are determined because the estimated premium may be fully or substantially earned. A significant portion of amounts included as premiums receivable, which represent estimated premiums written, net of commissions, are not currently due based on the terms of the underlying contracts.

Unearned premiums represent the portion of premiums written that is applicable to the estimated unexpired risk of insured loans. A portion of premium payments may be refundable if the insured cancels coverage, which generally occurs when the loan is repaid, the loan amortizes to a sufficiently low amount to trigger a lender permitted or legally required cancellation, or the value of the property has increased sufficiently in accordance with the terms of the contract. Premium refunds reduce premiums earned in the consolidated statements of income. Generally, only unearned premiums are refundable.

Premiums receivable include amounts receivable from agents, brokers and insured that are both currently due and amounts not yet due on insurance, reinsurance and mortgage insurance policies. Premiums receivable balances are reported net of an allowance for expected credit losses. The Company monitors credit risk associated with premiums receivable through its ongoing review of amounts outstanding, aging of the receivable, historical loss data, and

counterparty financial strength measures. The allowance also includes estimated uncollectible amounts related to dispute risk. In certain instances, credit risk may be reduced by the Company’s right to offset loss obligations or unearned premiums against premiums receivable. Any allowance for credit losses is charged to net realized gains (losses) in the period the receivable is recorded and revised in subsequent periods to reflect changes in the Company’s estimate of expected credit losses. See note 7, “Allowance for Expected Credit Losses” for additional information.

Acquisition Costs. Acquisition costs that are directly related and incremental to the successful acquisition or renewal of business are deferred and amortized based on the type of contract. The Company’s insurance and reinsurance operations capitalize incremental direct external costs that result from acquiring a contract but do not capitalize salaries, benefits and other internal underwriting costs. For the Company’s mortgage insurance operations, which include a substantial direct sales force, both external and certain internal direct costs are deferred and amortized. For property and casualty insurance and reinsurance contracts, deferred acquisition costs are amortized over the period in which the related premiums are earned. Consistent with mortgage insurance industry accounting practice, amortization of acquisition costs related to the mortgage insurance contracts for each underwriting year’s book of business is recorded in proportion to estimated gross profits. Estimated gross profits are comprised of earned premiums and losses and loss adjustment expenses. For each underwriting year, the Company estimates the rate of amortization to reflect actual experience and any changes to persistency or loss development.

Deferred acquisition costs are carried at their estimated realizable value and take into account anticipated losses and loss adjustment expenses, based on historical and current experience, and anticipated investment income.

A premium deficiency occurs if the sum of anticipated losses and loss adjustment expenses, unamortized acquisition costs and maintenance costs exceed unearned premiums (including expected future premiums) and anticipated investment income. A premium deficiency reserve (“PDR”) is recorded by charging any unamortized acquisition costs to expense to the extent required in order to eliminate the deficiency. If the premium deficiency exceeds unamortized acquisition costs then a liability is accrued for the excess deficiency.

To assess the need for a PDR on mortgage exposures, the Company develops loss projections based on modeled loan defaults related to its current policies in force. This projection is based on recent trends in default experience, severity and rates of defaulted loans moving to claim, as well as recent trends in the rate at which loans are prepaid, and incorporates anticipated interest income. Evaluating the expected

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

profitability of the Company’s existing mortgage insurance business and the need for a PDR for its mortgage business involves significant reliance upon assumptions and estimates with regard to the likelihood, magnitude and timing of potential losses and premium revenues. No premium deficiency charges were recorded by the Company during 2022, 2021 or 2020.

(c) Deposit Accounting

Certain assumed reinsurance contracts that are deemed not to transfer insurance risk, are accounted for using the deposit method of accounting. However, it is possible that the Company could incur financial losses on such contracts. Management exercises significant judgment in the assumptions used in determining whether assumed contracts should be accounted for as reinsurance contracts or deposit contracts. For those contracts that contain only significant underwriting risk, the estimated profit margin is deferred and amortized over the contract period and such amount is included in the Company’s underwriting results. When the estimated profit margin is explicit, the margin is reflected as other underwriting income and any adverse financial results on such contracts are reflected as incurred losses. When the estimated profit margin is implicit, the margin is reflected as an offset to paid losses and any adverse financial results on such contracts are reflected as incurred losses. Additional judgments are required when applying the accounting guidance with respect to the revenue recognition criteria for contracts deemed to transfer only significant underwriting risk. For those contracts that contain only significant timing risk, an accretion rate is established at inception of the contract based on actuarial estimates whereby the deposit accounting liability is increased to the estimated amount payable over the contract term. The accretion on the deposit is based on the expected rate of return required to fund the expected future payment obligations. Periodically the Company reassesses the estimated ultimate liability and the related expected rate of return. The accretion of the deposit accounting liability as well as changes to the estimated ultimate liability and the accretion rate would be reflected as part of interest expense in the Company’s results of operations. Any negative accretion in a deposit accounting liability is shown in other underwriting income in the Company’s results of operations.

Under some of these contracts, the ceding company retains the related assets on a funds held basis. Such amounts are included in “Other assets” on the Company’s balance sheet. Interest income produced by those assets are recorded as part of net investment income in the Company's results of operations.

(d) Retroactive Reinsurance

Retroactive reinsurance reimburses a ceding company for liabilities incurred as a result of past insurable events covered by the underlying policies reinsured. In certain instances, reinsurance contracts cover losses both on a prospective basis and on a retroactive basis and, accordingly, the Company bifurcates the prospective and retrospective elements of these reinsurance contracts and accounts for each element separately where practical. Underwriting income generated in connection with retroactive reinsurance contracts is deferred and amortized into income over the settlement period while losses are charged to income immediately. Subsequent changes in estimated amount or timing of cash flows under such retroactive reinsurance contracts are accounted for by adjusting the previously deferred amount to the balance that would have existed had the revised estimate been available at the inception of the reinsurance transaction, with a corresponding charge or credit to income.

(e) Reinsurance Ceded

In the normal course of business, the Company purchases reinsurance to increase capacity and to limit the impact of individual losses and events on its underwriting results by reinsuring certain levels of risk with other insurance enterprises or reinsurers. The Company uses pro rata, excess of loss and facultative reinsurance contracts. Reinsurance ceding commissions that represent a recovery of acquisition costs are recognized as a reduction to acquisition costs while the remaining portion is deferred. The accompanying consolidated statement of income reflects premiums and losses and loss adjustment expenses and acquisition costs, net of reinsurance ceded. See note 8, “Reinsurance” for information on the Company's reinsurance usage. Reinsurance premiums ceded and unpaid losses and loss adjustment expenses recoverable are estimated in a manner consistent with that of the original policies issued and the terms of the reinsurance contracts. If the reinsurers are unable to satisfy their obligations under the agreements, the Company’s insurance or reinsurance subsidiaries would be liable for such defaulted amounts.

Reinsurance recoverables are recorded as assets, predicated on the reinsurers’ ability to meet their obligations under the reinsurance agreements. In certain instances, the Company obtains collateral, including letters of credit and trust accounts to further reduce the credit exposure on its reinsurance recoverables. The Company reports its reinsurance recoverables net of an allowance for expected credit loss. The allowance is based upon the Company’s ongoing review of amounts outstanding, the financial condition of its reinsurers, amounts and form of collateral obtained and other relevant factors. A ratings based probability-of-default and loss-given-default methodology is used to estimate the allowance for expected credit loss. Any

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allowance for credit losses is charged to net realized gains (losses) in the period the recoverable is recorded and revised in subsequent periods to reflect changes in the Company’s estimate of expected credit losses. See note 7, “Allowance for Expected Credit Losses” for additional information.

(f) Cash

Cash includes cash equivalents, which are investments with original maturities of three months or less which are not part of the investment portfolio.

(g) Restricted Cash

Restricted cash represents amounts held for the benefit of third parties or is legally or contractually restricted as to withdrawal or usage by the Company. Such amounts are included in “Other assets” on the Company’s balance sheet.

(h) Investments

The Company currently classifies substantially all of its fixed maturity investments and short-term investments as “available for sale” and, accordingly, they are carried at estimated fair value (also known as fair value) with the changes in fair value recorded as an unrealized gain or loss component of accumulated other comprehensive income in shareholders’ equity. The fair value of fixed maturity securities and equity securities is generally determined from quotations received from nationally recognized pricing services, or when such prices are not available, by reference to broker or underwriter bid indications. Short-term investments comprise securities due to mature within one year of the date of issue. Short-term investments include certain cash equivalents which are part of investment portfolios under the management of external and internal investment managers.

The Company’s investment portfolio includes certain funds that, due to their ownership structure, are accounted for by the Company using the equity method. In applying the equity method, these investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the fair value of the underlying securities in the funds). Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds. Changes in the carrying value of such investments are recorded in net income as “Equity in net income (loss) of investments accounted for using the equity method.” As such, fluctuations in the carrying value of the investments accounted for using the equity method may increase the volatility of the Company’s reported results of operations.

The Company’s investment portfolio includes equity securities that are accounted for at fair value. Such holdings primarily include publicly traded common stocks. Dividend income on equities is reflected in net investment income. Changes in fair value on equity securities are included in “Net realized gains (losses)” in the consolidated statement of income.

The Company elected to carry certain fixed maturity securities, equity securities, short-term investments and other investments at fair value under the fair value option afforded by accounting guidance regarding the fair value option for financial assets and liabilities. The fair value for certain of the Company’s other investments are determined using net asset values (“NAVs”) as advised by external fund managers. The NAV is based on the fund manager’s valuation of the underlying holdings in accordance with the fund’s governing documents.

Changes in fair value of investments accounted for using the fair value option are included in “Net realized gains (losses).” The primary reasons for electing the fair value option were to address simplification and cost-benefit considerations.

The Company invests in reverse repurchase agreements that are generally treated as collateralized receivables. Receivables for reverse repurchase agreements are reflected in “Other investments” or “Short-term investments” in the Company's consolidated balance sheet depending on their terms. These agreements are recorded at their contracted resale amount plus accrued interest, other than those that are accounted for at fair value. In reverse repurchase transactions, the Company obtains an interest in the purchased assets that are received as collateral.

The Company invests in limited partner interests and shares of limited liability companies. Such amounts are included in investments accounted for using the equity method and other investments. These investments can often have characteristics of a variable interest entity (“VIE”). A VIE refers to entities that have characteristics such as (i) insufficient equity at risk to allow the entity to finance its activities without additional financial support or (ii) instances where the equity investors, as a group, do not have the characteristic of a controlling financial interest. If the Company is determined to be the primary beneficiary, it is required to consolidate the VIE. The primary beneficiary is defined as the variable interest holder that is determined to have the controlling financial interest as a result of having both (i) the power to direct the activities of a VIE that most significantly impact the economic performance of the VIE and (ii) the obligation to absorb losses or right to receive benefits from the VIE that could potentially be significant to the VIE. At inception of the VIE as well as on an ongoing basis, the Company determines whether it is the primary beneficiary based on an analysis of the Company’s level of involvement in the VIE, the

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contractual terms, and the overall structure of the VIE. The Company's maximum exposure to loss with respect to these investments is limited to the investment carrying amounts reported in the Company's consolidated balance sheet and any unfunded commitment.

The Company conducts a periodic review to identify and evaluate credit based impairments related to the Company’s available for sale investments. The Company derives estimated credit losses by comparing expected future cash flows to be collected to the amortized cost of the security. Estimates of expected future cash flows consider among other things, macroeconomic conditions as well as the financial condition, near-term and long-term prospects for the issuer, and the likelihood of the recoverability of principal and interest. Effective January 1, 2020, credit losses are recognized through an allowance account subject to reversal, rather than a reduction in amortized cost. Declines in value attributable to factors other than credit are reported as an unrealized loss in other comprehensive income while the allowance for credit loss is charged to net realized gains (losses) in the consolidated statement of income.

For available for sale investments that the Company intends to sell or for which it is more likely than not that the Company would be required to sell before an anticipated recovery in value, the full amount of the impairment is included in net realized gains (losses). The new cost basis of the investment is the previous amortized cost basis reduced by the impairment recognized in net realized gains (losses). The new cost basis is not adjusted for any subsequent recoveries in fair value.

The Company reports accrued investment income separately from investment balances and has elected not to measure an allowance for credit losses for accrued investment income. Any uncollectible accrued interest income is written off in the period it is deemed uncollectible.

Net investment income includes interest and dividend income together with amortization of market premiums and discounts and is net of investment management and custody fees. Anticipated prepayments and expected maturities are used in applying the interest method for certain investments such as mortgage and other asset-backed securities. When actual prepayments differ significantly from anticipated prepayments, the effective yield is recalculated to reflect actual payments to date and anticipated future payments. The net investment in such securities is adjusted to the amount that would have existed had the new effective yield been applied since the acquisition of the security. Such adjustments, if any, are included in net investment income when determined.

Investment gains or losses realized on the sale of investments, except for certain fund investments, are determined on a first-in, first-out basis and are reflected in net income. Investment gains or losses realized on the sale of certain fund investments are determined on an average cost basis. Unrealized appreciation or decline in the value of available for sale securities, which are carried at fair value, is excluded from net income and recorded as a separate component of accumulated other comprehensive income, net of applicable deferred income tax.

(i) Derivative Instruments

The Company recognizes all derivative instruments, including embedded derivative instruments, at fair value in its consolidated balance sheets. The Company employs the use of derivative instruments within its operations to mitigate risks arising from assets and liabilities held in foreign currencies as well as part of its overall investment strategy. For such instruments, changes in assets and liabilities measured at fair value are recorded as “Net realized gains (losses)” in the consolidated statements of income. In addition, the Company’s derivative instruments include amounts related to underwriting activities where an insurance or reinsurance contract meets the accounting definition of a derivative instrument. For such contracts, changes in fair value are reflected in “Other underwriting income” in the consolidated statements of income as the underlying contract originates from the Company’s underwriting operations. For the periods ended 2022, 2021, and 2020, the Company did not designate any derivative instruments as hedges under the relevant accounting guidance. See note 11, “Derivative Instruments” for additional information.

(j) Reserves for Losses and Loss Adjustment Expenses

Insurance and Reinsurance. The reserve for losses and loss adjustment expenses consists of estimates of unpaid reported losses and loss adjustment expenses and estimates for losses incurred but not reported. The reserve for unpaid reported losses and loss adjustment expenses, established by management based on reports from ceding companies and claims from insureds, excludes estimates of amounts related to losses under high deductible policies, and represents the estimated ultimate cost of events or conditions that have been reported to or specifically identified by the Company. Such reserves are supplemented by management’s estimates of reserves for losses incurred for which reports or claims have not been received. The Company’s reserves are based on a combination of reserving methods, incorporating both Company and industry loss development patterns. The Company selects the initial expected loss and loss adjustment expense ratios based on information derived by its underwriters and actuaries during the initial pricing of the business, supplemented by industry data where appropriate. Such ratios consider, among other things, rate changes and

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changes in terms and conditions that have been observed in the market. These estimates are reviewed regularly and, as experience develops and new information becomes known, the reserves are adjusted as necessary. Such adjustments, if any, are reflected in income in the period in which they are determined. As actual loss information has been reported, the Company has developed its own loss experience and its reserving methods include other actuarial techniques. Over time, such techniques have been given further weight in its reserving process based on the continuing maturation of the Company’s reserves. Inherent in the estimates of ultimate losses and loss adjustment expenses are expected trends in claims severity and frequency and other factors which may vary significantly as claims are settled. Accordingly, ultimate losses and loss adjustment expenses may differ materially from the amounts recorded in the accompanying consolidated financial statements. Losses and loss adjustment expenses are recorded on an undiscounted basis, except for excess workers’ compensation and employers’ liability business written by the Company’s insurance operations.

Mortgage. The reserves for mortgage guaranty insurance losses and loss adjustment expenses are the estimated claim settlement costs on notices of delinquency that have been received by the Company, as well as loan delinquencies that have been incurred but have not been reported by the lenders. Consistent with primary mortgage insurance industry accounting practice, the Company does not establish loss reserves for future claims on insured loans that are not currently delinquent (defined as two or more payments in arrears). The Company establishes loss reserves on a case-by-case basis when insured loans are reported delinquent using estimated claim rates and average claim sizes for each cohort, net of any salvage recoverable. The Company also reserves for delinquencies that have occurred but have not yet been reported to the Company prior to the close of an accounting period. To determine this reserve, the Company estimates the number of delinquencies not yet reported using historical information regarding late reported delinquencies and applies estimated claim rates and claim sizes for the estimated delinquencies not yet reported.

The establishment of reserves across the Company’s segments is an inherently uncertain process, are necessarily based on estimates, and the ultimate net cost may vary from such estimates. The methods for making such estimates and for establishing the resulting liability are reviewed and updated using the most current information available. Any resulting adjustments, which may be material, are reflected in current operations.

(k) Contractholder Receivables and Payables and Collateral Held for Insured Obligations

Certain insurance policies written by the Company’s U.S. insurance operations feature large deductibles, primarily in its construction and national accounts line of business. Under such contracts, the Company is obligated to pay the claimant for the full amount of the claim. The Company is subsequently reimbursed by the policy holder for the deductible amount. These amounts are included on a gross basis in the consolidated balance sheet as contractholder payables and contractholder receivables. In the event that the Company is unable to collect from the policyholder, the Company would be liable for such defaulted amounts. Collateral, primarily in the form of letters of credit, cash and trusts, is obtained from the policyholder to mitigate the Company’s credit risk. In the instances where the Company receives collateral in the form of cash, the Company reflects it in “Collateral held for insured obligations.”

Contractholder receivables are reported net of an allowance for expected credit losses. The allowance is based upon the Company’s ongoing review of amounts outstanding, changes in policyholder credit standing, amounts and form of collateral obtained, and other relevant factors. A ratings based probability-of-default and loss-given-default methodology is used to estimate the allowance for expected credit losses. Any allowance for credit losses is charged to net realized gains (losses) in the period the receivable is recorded and revised in subsequent periods to reflect changes in the Company’s estimate of expected credit losses. See note 7, “Allowance for Expected Credit Losses” for additional information.

(l) Foreign Exchange

Assets and liabilities of foreign operations whose functional currency is not the U.S. Dollar are translated at the prevailing exchange rates at each balance sheet date. Revenues and expenses of such foreign operations are translated at average exchange rates during the year. The net effect of the translation adjustments for foreign operations is included in accumulated other comprehensive income, net of applicable deferred income tax. Monetary assets and liabilities, such as premiums receivable and the reserve for losses and loss adjustment expenses, denominated in foreign currencies are revalued at the exchange rate in effect at the balance sheet date with the resulting foreign exchange gains and losses included in net income. Accounts that are classified as non-monetary, such as deferred acquisition costs and the unearned premium reserves, are not revalued. In the case of foreign currency denominated fixed maturity securities which are classified as “available for sale,” the change in exchange rates between the local currency in which the investments are denominated and the Company’s functional currency at each balance sheet date is included in unrealized appreciation or

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decline in value of securities, a component of accumulated other comprehensive income, net of applicable deferred income tax.

(m) Income Taxes

Deferred income taxes reflect the expected future tax consequences of temporary differences between the carrying amounts of assets and liabilities for financial reporting purposes and amounts used for income tax purposes. A valuation allowance is recorded if it is more likely than not that some or all of a deferred tax asset may not be realized. The Company considers future taxable income and feasible tax planning strategies in assessing the need for a valuation allowance. In the event the Company determines that it will not be able to realize all or part of its deferred income tax assets in the future, an adjustment to the deferred income tax assets would be charged to income in the period in which such determination is made. In addition, if the Company subsequently assesses that the valuation allowance is no longer needed, a benefit would be recorded to income in the period in which such determination is made. See note 15, “Income Taxes” for additional information.

The Company recognizes a tax benefit where it concludes that it is more likely than not that the tax benefit will be sustained on audit by the taxing authority based solely on the technical merits of the associated tax position. If the recognition threshold is met, the Company recognizes a tax benefit measured at the largest amount of the tax benefit that, in the Company’s judgment, is greater than 50% likely to be realized. The Company records interest and penalties related to unrecognized tax benefits in the provision for income taxes.

(n) Share-Based Payment Arrangements

The Company applies a fair value based measurement method in accounting for its share-based payment arrangements with eligible employees and directors. Compensation expense is estimated based on the fair value of the award at the grant date and is recognized in net income over the requisite service period with a corresponding increase in shareholders’ equity. No value is attributed to awards that employees forfeit because they fail to satisfy vesting conditions. The Company’s (i) time-based awards generally vest over a three year period with one-third vesting on the first, second and third anniversaries of the grant date and (ii) performance-based awards cliff vest after each three year performance period based on achievement of the specified performance criteria. The share-based compensation expense associated with awards that have graded vesting features and vest based on service conditions only is calculated on a straight-line basis over the requisite service period for the entire award. Compensation expense recognized in connection with performance awards is based

on the achievement of the specified performance and service conditions. The final measure of compensation expense recognized over the requisite service period reflects the final performance outcome. During the recognition period compensation expense is accrued based on the performance condition that is probable of achievement. For awards granted to retirement-eligible employees where no service is required for the employee to retain the award, the grant date fair value is immediately recognized as compensation expense at the grant date because the employee is able to retain the award without continuing to provide service. For employees near retirement eligibility, attribution of compensation cost is over the period from the grant date to the retirement eligibility date. These charges had no impact on the Company’s cash flows or total shareholders’ equity. See note 22, “Share-Based Compensation” for information relating to the Company’s share-based payment awards.

(o) Guaranty Fund and Other Related Assessments

Liabilities for guaranty fund and other related assessments in the Company’s insurance and reinsurance operations are accrued when the Company receives notice that an amount is payable, or earlier if a reasonable estimate of the assessment can be made.

(p) Treasury Shares

Treasury shares are common shares purchased by the Company and not subsequently canceled. These shares are recorded at cost and result in a reduction of the Company’s shareholders’ equity in its Consolidated Balance Sheets.

(q) Goodwill and Intangible Assets

Goodwill represents the excess of the purchase price of business combination over the fair value of the net assets acquired and is assigned to the applicable reporting unit at acquisition. Goodwill is evaluated for impairment on an annual basis. Impairment tests may be performed more frequently if the facts and circumstances indicate a possible impairment. In performing impairment tests, the Company may first assess qualitative factors to determine whether it is more likely than not (that is, more than a 50% probability) that the fair value of a reporting unit exceeds its carrying amount as a basis for determining whether it is necessary to perform goodwill impairment test described in the accounting guidance.

Indefinite-lived intangible assets, such as insurance licenses are evaluated for impairment similar to goodwill. Finite-lived intangible assets and liabilities include the value of acquired insurance and reinsurance contracts, which are estimated based on the present value of future expected cash flows and amortized in proportion to the estimated profits expected to be realized. Other finite-lived intangible assets, including

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customer lists, trade name and IT platforms, are amortized over their useful lives. Finite-lived intangible assets and liabilities are periodically reviewed for indicators of impairment. An impairment is recognized when the carrying amount is not recoverable from its undiscounted cash flows and is measured as the difference between the carrying amount and fair value.

If goodwill or intangible assets are impaired, such assets are written down to their fair values with the related expense recorded in the Company’s results of operations.

(r) Investment in Operating Affiliates

Investment in operating affiliates primarily represent the Company’s investments in which it has significant influence and which are accounted for under the equity method of accounting. In applying the equity method of accounting, investments in operating affiliates are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of net income or loss of the operating affiliate. The Company records its proportionate share of other comprehensive income or loss of the operating affiliate as a component of other comprehensive income. Adjustments are based on the most recently available financial information from the operating affiliate. Changes in the carrying value of these investments are recorded in income (loss) from operating affiliates.

(s) Funds Held Arrangements

Funds held arrangements are agreements with a third party reinsurance company, where the reinsured retains the related assets on a funds held basis. Such amounts are included in “Other assets” on the Company’s balance sheet. Investment returns produced by those assets are recorded as part of net investment income and net realized gains (losses) in the Company's consolidated results of operations. Funds held as collateral by the Company are included in “Other liabilities” and changes to the funds held liability are reflected as part of interest expense in the Company’s consolidated results of operations.

(t) Recent Accounting Pronouncements

Recently Issued Accounting Standards Adopted

The Company adopted ASU 2019-12, “Simplifying the Accounting for Income Taxes.” This ASU eliminates certain exceptions for recognizing deferred taxes for investments, performing intraperiod tax allocations and calculating income taxes in interim periods. The ASU also clarifies the accounting for transactions that result in a step-up in the tax basis of goodwill. The adoption of this guidance did not have a material effect on the Company’s consolidated financial statements.

Recently Issued Accounting Standards Not Yet Adopted

ASU 2020-04, “Facilitation of the Effects of Reference Rate Reform on Financial Reporting,” was issued in March 2020 and amended in December 2022 with ASU 2022-06, “Reference Rate Reform (Topic 848)”. This ASU provides optional expedients and exceptions for applying GAAP to investments, derivatives, or other transactions that reference the London Interbank Offered Rate (“LIBOR”) or another reference rate expected to be discontinued because of reference rate reform. Along with the optional expedients, the amendments include a general principle that permits an entity to consider contract modifications due to reference reform to be an event that does not require contract re-measurement at the modification date or reassessment of a previous accounting determination. The amendment deferred the sunset date from December 31, 2022 to December 31, 2024. As a result, this standard can be adopted no later than December 31, 2024, with early adoption permitted. Based on its current analysis, the Company does not expect that the new guidance will have a material effect on the Company’s consolidated financial statements.

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4.    Segment Information

The Company classifies its businesses into three underwriting segments – insurance, reinsurance and mortgage – and two operating segments – corporate and ‘other.’ The Company determined its reportable segments using the management approach described in accounting guidance regarding disclosures about segments of an enterprise and related information. The accounting policies of the segments are the same as those used for the preparation of the Company’s consolidated financial statements. Intersegment business is allocated to the segment accountable for the underwriting results.

The Company’s insurance, reinsurance and mortgage segments each have managers who are responsible for the overall profitability of their respective segments and who are directly accountable to the Company’s chief operating decision makers, the Chief Executive Officer of Arch Capital, Chief Financial Officer and Treasurer of Arch Capital and the President and Chief Underwriting Officer of Arch Capital. The chief operating decision makers do not assess performance, measure return on equity or make resource allocation decisions on a line of business basis. Management measures segment performance for its three underwriting segments based on underwriting income or loss. The Company does not manage its assets by underwriting segment, with the exception of goodwill and intangible assets, and, accordingly, investment income is not allocated to each underwriting segment.

The insurance segment consists of the Company’s insurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include:

•    Construction and national accounts: primary and excess casualty coverages for middle market and large construction accounts, a comprehensive range of products for middle market accounts in specialty industries and casualty solutions for large national accounts, including loss sensitive primary insurance programs (large deductible, self-insured retention and retrospectively rated programs).

•    Excess and surplus casualty: primary and excess casualty insurance coverages written on a non-admitted basis.

•    Professional lines: directors’ and officers’ liability, errors and omissions liability, employment practices liability, fiduciary liability, crime, professional indemnity and other financial related coverages for corporate, private equity, venture capital, real estate investment trust, limited partnership, financial institution and not-for-profit clients of all sizes, cyber insurance, and medical professional and general liability

insurance coverages for the healthcare industry. The business is predominately written on a claims-made basis.

•    Programs: primarily targeting program managers with unique expertise and niche products offering some combination of general liability, commercial automobile, property, inland marine, umbrella and workers’ compensation.

•    Property, energy, marine and aviation: primary and excess general property insurance coverages, including catastrophe-exposed property coverage, for commercial clients. Coverages for marine include hull, cargo, war, specie and liability. Aviation, stand-alone terrorism and political risks are also offered. Coverage may be provided for operational and construction risk.

•    Travel, accident and health: specialty travel and accident and related insurance products for individual, group travelers, travel agents and suppliers, as well as accident and health, which provides accident, disability and medical plan insurance coverages for employer groups, medical plan members, students and other participant groups.

•    Warranty and lenders solutions: collateral protection, debt cancellation and service contract reimbursement products to banks, credit unions, automotive dealerships and original equipment manufacturers and other specialty programs that pertain to automotive lending and leasing.

•    Other: includes alternative market risks (including captive insurance programs), excess workers’ compensation and employer’s liability insurance coverages for qualified self-insured groups, associations and trusts, and contract, commercial and transactional surety coverages.

The reinsurance segment consists of the Company’s reinsurance underwriting units which offer specialty product lines on a worldwide basis. Reinsurance agreements are typically offered on a proportional and/or excess of loss basis and provide coverage to ceding company clients for specific underlying written policies. Product lines include:

•Casualty: provides coverage on third party liability exposures including, among others, executive assurance, professional liability, excess and umbrella liability, excess motor and healthcare business, and workers’ compensation. Business is assumed primarily on a treaty basis, with some facultative coverages also offered.

•Marine and aviation: provides coverage for energy, hull, cargo, specie, liability and transit, and aviation business, including airline and general aviation risks. Business written may also include space business, which

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includes coverages for satellite assembly, launch and operation for commercial space programs.

•Other specialty: provides coverage for proportional motor reinsurance, whole account multi-line treaties, cyber, trade credit and surety, accident and health, workers’ compensation catastrophe, agriculture and political risk, among others.

•Property catastrophe: provides protection for most types of catastrophic losses, including hurricane, earthquake, flood, tornado, hail and fire, and for other perils on a case-by-case basis. Excess of loss coverages are triggered when aggregate losses and loss adjustment expense from a single occurrence of a covered peril exceed the retention specified in the contract.

•Property excluding property catastrophe: provides coverage for personal lines and/or commercial property exposures and principally covers buildings, structures, equipment and contents. The primary perils in this business include fire, explosion, collapse, riot, vandalism, wind, tornado, flood and earthquake. Business is assumed on either a treaty or facultative basis.

•Other: includes life reinsurance business, casualty clash business and, in limited instances, non-traditional business which is intended to provide insurers with risk management solutions that complement traditional reinsurance.

The mortgage segment includes the Company’s underwriting units which offer mortgage insurance and reinsurance products on a worldwide basis. Underwriting units include:

•U.S. primary mortgage insurance: offers private mortgage insurance through Arch Mortgage Insurance Company and United Guaranty Residential Insurance Company (combined “Arch MI U.S.”), both approved eligible mortgage insurers by Fannie Mae and Freddie Mac. Arch MI U.S. also includes AMG, which is not a government sponsored enterprise (“GSE”) approved entity.

•U.S. credit risk transfer (“CRT”) and other: underwrites CRT transactions, which are predominantly with GSEs, and other U.S. reinsurance transactions.

•International mortgage insurance/reinsurance: underwrites mortgage insurance and reinsurance outside of the U.S.

The corporate segment results include net investment income, net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings), equity in net income or loss of investments accounted for using the equity method, other income (loss), corporate expenses, transaction costs and other, amortization of intangible assets, interest expense, net foreign exchange gains or losses, income taxes, income or loss from operating affiliates and items related to the Company’s non-cumulative preferred shares. Such amounts exclude the results of the ‘other’ segment.

Through June 30, 2021, the ‘other’ segment included the results of Somers. In July 2021, the Company announced the completion of the previously disclosed acquisition of Somers by Greysbridge. Based on the governing documents of Greysbridge, the Company has concluded that, while it retains significant influence over Somers, Somers no longer constitutes a variable interest entity. Accordingly, effective July 1, 2021, Arch no longer consolidates the results of Somers in its consolidated financial statements. See note 12, “Variable Interest Entity and Noncontrolling Interests.”

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The following tables summarize the Company’s underwriting income or loss by segment, together with a reconciliation of underwriting income or loss to net income available to Arch common shareholders, summary information regarding net premiums written and earned by major line of business and net premiums written by location:

	Year Ended December 31, 2022
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	6,930,864		$	6,948,438		$	1,454,971		$	15,326,447		$	—		$	15,326,447
Premiums ceded	(1,910,222)			(2,024,462)			(322,400)			(4,249,258)			—			(4,249,258)
Net premiums written	5,020,642			4,923,976			1,132,571			11,077,189			—			11,077,189
Change in unearned premiums	(461,307)			(964,595)			26,790			(1,399,112)			—			(1,399,112)
Net premiums earned	4,559,335			3,959,381			1,159,361			9,678,077			—			9,678,077
Other underwriting income	—			4,871			8,356			13,227			—			13,227
Losses and loss adjustment expenses	(2,782,945)			(2,568,843)			324,271			(5,027,517)			—			(5,027,517)
Acquisition expenses	(885,866)			(813,555)			(40,159)			(1,739,580)			—			(1,739,580)
Other operating expenses	(665,472)			(267,531)			(195,172)			(1,128,175)			—			(1,128,175)
Underwriting income	$	225,052		$	314,323		$	1,256,657		1,796,032			—			1,796,032
Net investment income										496,547			—			496,547
Net realized gains (losses)										(662,734)			—			(662,734)
Equity in net income (loss) of investments accounted for using the equity method										115,856			—			115,856
Other income (loss)										(26,165)			—			(26,165)
Corporate expenses										(94,390)			—			(94,390)
Transaction costs and other										(1,092)			—			(1,092)
Amortization of intangible assets										(106,200)			—			(106,200)
Interest expense										(130,266)			—			(130,266)
Net foreign exchange gains (losses)										100,905			—			100,905
Income (loss) before income taxes and income (loss) from operating affiliates										1,488,493			—			1,488,493
Income tax expense										(79,961)			—			(79,961)
Income (loss) from operating affiliates										73,891			—			73,891
Net income (loss)										1,482,423			—			1,482,423
Amounts attributable to redeemable noncontrolling interests										(5,490)			—			(5,490)
Net income (loss) available to Arch										1,476,933			—			1,476,933
Preferred dividends										(40,736)			—			(40,736)
Net income (loss) available to Arch common shareholders										$	1,436,197		$	—		$	1,436,197
Underwriting Ratios
Loss ratio	61.0		%	64.9		%	-28.0		%	51.9		%	—		%	51.9		%
Acquisition expense ratio	19.4		%	20.5		%	3.5		%	18.0		%	—		%	18.0		%
Other operating expense ratio	14.6		%	6.8		%	16.8		%	11.7		%	—		%	11.7		%
Combined ratio	95.0		%	92.2		%	-7.7		%	81.6		%	—		%	81.6		%
Goodwill and intangible assets	$	228,532		$	144,846		$	430,911		$	804,289		$	—		$	804,289
Total investable assets										$	28,065,497		$	—		$	28,065,497
Total assets										47,990,507			—			47,990,507
Total liabilities										35,069,605			—			35,069,605

(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

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	Year Ended December 31, 2021
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	5,867,734		$	5,093,930		$	1,507,825		$	12,463,788		$	457,465		$	12,752,487
Premiums ceded	(1,719,541)			(1,839,556)			(246,757)			(3,800,153)			(102,763)			(3,734,150)
Net premiums written	4,148,193			3,254,374			1,261,068			8,663,635			354,702			9,018,337
Change in unearned premiums	(521,725)			(413,931)			22,351			(913,305)			(22,734)			(936,039)
Net premiums earned	3,626,468			2,840,443			1,283,419			7,750,330			331,968			8,082,298
Other underwriting income	—			3,669			17,665			21,334			739			22,073
Losses and loss adjustment expenses	(2,344,365)			(1,924,719)			(56,677)			(4,325,761)			(259,042)			(4,584,803)
Acquisition expenses, net	(606,265)			(536,754)			(97,418)			(1,240,437)			(62,741)			(1,303,178)
Other operating expenses	(558,906)			(212,810)			(194,010)			(965,726)			(32,869)			(998,595)
Underwriting income (loss)	$	116,932		$	169,829		$	952,979		1,239,740			(21,945)			1,217,795
Net investment income										346,808			42,310			389,118
Net realized gains (losses)										299,207			80,638			379,845
Equity in net income (loss) of investments accounted for using the equity method										366,402			—			366,402
Other income (loss)										10,244			—			10,244
Corporate expenses										(77,119)			—			(77,119)
Transaction costs and other										(1,103)			(935)			(2,038)
Amortization of intangible assets										(82,057)			(898)			(82,955)
Interest expense										(131,060)			(8,410)			(139,470)
Net foreign exchange gains (losses)										42,854			(1,325)			41,529
Income (loss) before income taxes and income (loss) from operating affiliates										2,013,916			89,435			2,103,351
Income tax expense										(128,348)			(234)			(128,582)
Income (loss) from operating affiliates										264,693			—			264,693
Net income (loss)										2,150,261			89,201			2,239,462
Amounts attributable to redeemable noncontrolling interests										(2,346)			(1,953)			(4,299)
Amounts attributable to nonredeemable noncontrolling interests										—			(78,314)			(78,314)
Net income (loss) available to Arch										2,147,915			8,934			2,156,849
Preferred dividends										(48,343)			—			(48,343)
Loss on redemption of preferred shares										(15,101)			—			(15,101)
Net income (loss) available to Arch common shareholders										$	2,084,471		$	8,934		$	2,093,405
Underwriting Ratios
Loss ratio	64.6		%	67.8		%	4.4		%	55.8		%	78.0		%	56.7		%
Acquisition expense ratio	16.7		%	18.9		%	7.6		%	16.0		%	18.9		%	16.1		%
Other operating expense ratio	15.4		%	7.5		%	15.1		%	12.5		%	9.9		%	12.4		%
Combined ratio	96.7		%	94.2		%	27.1		%	84.3		%	106.8		%	85.2		%
Goodwill and intangible assets	$	256,434		$	183,523		$	505,026		$	944,983		$	—		$	944,983
Total investable assets										$	27,442,153		$	—		$	27,442,153
Total assets										45,100,945			—			45,100,945
Total liabilities										31,545,816			—			31,545,816

(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

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	Year Ended December 31, 2020
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	4,688,562		$	3,472,086		$	1,473,999		$	9,632,691		$	728,546		$	10,088,068
Premiums ceded	(1,525,655)			(1,014,716)			(194,149)			(2,732,564)			(190,957)			(2,650,352)
Net premiums written	3,162,907			2,457,370			1,279,850			6,900,127			537,589			7,437,716
Change in unearned premiums	(291,487)			(295,141)			118,085			(468,543)			22,762			(445,781)
Net premiums earned	2,871,420			2,162,229			1,397,935			6,431,584			560,351			6,991,935
Other underwriting income	(31)			4,454			20,316			24,739			2,045			26,784
Losses and loss adjustment expenses	(2,092,453)			(1,628,320)			(528,344)			(4,249,117)			(440,482)			(4,689,599)
Acquisition expenses, net	(418,483)			(354,048)			(134,240)			(906,771)			(98,071)			(1,004,842)
Other operating expenses	(489,153)			(168,011)			(162,202)			(819,366)			(55,810)			(875,176)
Underwriting income (loss)	$	(128,700)		$	16,304		$	593,465		481,069			(31,967)			449,102
Net investment income										401,908			117,700			519,608
Net realized gains (losses)										813,781			9,679			823,460
Equity in net income (loss) of investments accounted for using the equity method										146,693			—			146,693
Other income (loss)										29			—			29
Corporate expenses										(68,492)			—			(68,492)
Transaction costs and other										(9,456)			(4,040)			(13,496)
Amortization of intangible assets										(69,031)			—			(69,031)
Interest expense										(120,214)			(23,242)			(143,456)
Net foreign exchange gains (losses)										(80,161)			(3,473)			(83,634)
Income (loss) before income taxes and income (loss) from operating affiliates										1,496,126			64,657			1,560,783
Income tax expense										(111,812)			(26)			(111,838)
Income (loss) from operating affiliates										16,766			—			16,766
Net income										1,401,080			64,631			1,465,711
Amounts attributable to redeemable noncontrolling interests										(2,997)			(4,117)			(7,114)
Amounts attributable to nonredeemable noncontrolling interests										—			(53,076)			(53,076)
Net income (loss) available to Arch										1,398,083			7,438			1,405,521
Preferred dividends										(41,612)			—			(41,612)
Net income (loss) available to Arch common shareholders										$	1,356,471		$	7,438		$	1,363,909
Underwriting Ratios
Loss ratio	72.9		%	75.3		%	37.8		%	66.1		%	78.6		%	67.1		%
Acquisition expense ratio	14.6		%	16.4		%	9.6		%	14.1		%	17.5		%	14.4		%
Other operating expense ratio	17.0		%	7.8		%	11.6		%	12.7		%	10.0		%	12.5		%
Combined ratio	104.5		%	99.5		%	59.0		%	92.9		%	106.1		%	94.0		%
Goodwill and intangible assets	$	280,978		$	18,963		$	385,272		$	685,213		$	7,650		$	692,863
Total investable assets										$	26,856,295		$	2,657,612		$	29,513,907
Total assets										39,791,983			3,490,314			43,282,297
Total liabilities										26,789,149			2,505,707			29,294,856

(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

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The following tables provide summary information regarding net premiums earned by major line of business and net premiums written by underwriting location:

INSURANCE SEGMENT	Year Ended December 31,
	2022		2021		2020
Net premiums earned (1)
Professional lines	$	1,314,236	$	942,817	$	655,872
Property, energy, marine and aviation	772,388		667,892		506,182
Programs	589,860		506,867		432,854
Travel, accident and health	491,847		255,590		190,944
Construction and national accounts	432,020		416,107		398,999
Excess and surplus casualty	393,353		318,027		270,620
Warranty and lenders solutions	127,222		153,958		114,687
Other	438,409		365,210		301,262
Total	$	4,559,335	$	3,626,468	$	2,871,420
Net premiums written by underwriting location (1)
United States	$	3,340,038	$	2,813,039	$	2,158,415
Europe	1,405,719		1,125,192		856,572
Other	274,885		209,962		147,920
Total	$	5,020,642	$	4,148,193	$	3,162,907

REINSURANCE SEGMENT	Year Ended December 31,
	2022		2021		2020
Net premiums earned (1)
Other specialty	$	1,377,880	$	818,801	$	626,409
Property excluding property catastrophe	1,091,440		836,573		562,208
Casualty	854,543		666,754		549,056
Property catastrophe	366,991		280,738		237,736
Marine and aviation	159,401		152,955		109,624
Other	109,126		84,622		77,196
Total	$	3,959,381	$	2,840,443	$	2,162,229
Net premiums written by underwriting location (1)
United States	$	1,246,507	$	828,504	$	687,622
Bermuda	2,561,771		1,557,294		1,001,990
Europe and other	1,115,698		868,576		767,758
Total	$	4,923,976	$	3,254,374	$	2,457,370

MORTGAGE SEGMENT	Year Ended December 31,
	2022		2021		2020
Net premiums earned by underwriting location
United States	$	815,519	$	970,507	$	1,158,563
Other	343,842		312,912		239,372
Total	$	1,159,361	$	1,283,419	$	1,397,935
Net premiums written by underwriting location
United States	$	780,256	$	914,477	$	1,021,950
Other	352,315		346,591		257,900
Total	$	1,132,571	$	1,261,068	$	1,279,850

(1)    Segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions.

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OTHER SEGMENT	Year Ended December 31,
	2022		2021		2020
Net premiums earned (1)
Casualty	$	—	$	138,551	$	245,272
Other specialty	—		118,356		186,717
Property catastrophe	—		15,235		23,037
Property excluding property catastrophe	—		6,578		1,130
Marine and aviation	—		190		429
Other	—		53,058		103,766
Total	$	—	$	331,968	$	560,351
Net premiums written by underwriting location (1)
United States	$	—	$	63,403	$	115,471
Europe	—		91,499		97,753
Bermuda	—		199,800		324,365
Total	$	—	$	354,702	$	537,589

(1)    Segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions.

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5.    Reserve for Losses and Loss Adjustment Expenses

The following table represents an analysis of losses and loss adjustment expenses and a reconciliation of the beginning and ending reserve for losses and loss adjustment expenses:

	Year Ended December 31,
	2022		2021		2020
Reserve for losses and loss adjustment expenses at beginning of year	$	17,757,156	$	16,513,929	$	13,891,842
Unpaid losses and loss adjustment expenses recoverable	5,599,231		4,314,855		4,082,650
Net reserve for losses and loss adjustment expenses at beginning of year	12,157,925		12,199,074		9,809,192
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year	5,798,528		4,940,987		4,851,051
Prior years	(771,011)		(356,184)		(161,452)
Total net incurred losses and loss adjustment expenses	5,027,517		4,584,803		4,689,599
Net losses and loss adjustment expense reserves of acquired business (1)	—		104,176		—
Retroactive reinsurance transactions (2)	—		(444,147)		182,210
Impact of deconsolidation of Somers (3)	—		(1,460,611)		—
Foreign exchange (gains) losses and other	(290,376)		1,181		179,190
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year	(887,464)		(734,846)		(661,529)
Prior years	(2,254,484)		(2,091,705)		(1,999,588)
Total net paid losses and loss adjustment expenses	(3,141,948)		(2,826,551)		(2,661,117)
Net reserve for losses and loss adjustment expenses at end of year	13,753,118		12,157,925		12,199,074
Unpaid losses and loss adjustment expenses recoverable	6,278,825		5,599,231		4,314,855
Reserve for losses and loss adjustment expenses at end of year	$	20,031,943	$	17,757,156	$	16,513,929

(1)    Represents activity related to the Company’s acquisitions in the 2021 period. See note 2, “Acquisitions.”

(2)    See ‘Retroactive Reinsurance Transactions’ section.

(3)    See note 12, “Variable Interest Entity and Noncontrolling Interests.”

Development on Prior Year Loss Reserves

Year Ended December 31, 2022

During 2022, the Company recorded estimated net favorable development on prior year loss reserves of $771.0 million, which consisted of net favorable development of $25.3 million from the insurance segment, $191.6 million from the reinsurance segment and $554.1 million from the mortgage segment.

The insurance segment’s net favorable development of $25.3 million, or 0.6 points of net earned premium, consisted of $55.3 million of net favorable development in short-tailed lines partially offset by $29.9 million of net adverse development from medium-tailed and long-tailed lines. Net favorable development in short-tailed lines reflected $37.4 million of favorable development in warranty and lenders solutions, primarily from the 2021 accident year (i.e., the year in which a loss occurred), and $14.8 million of favorable development related to travel and accident

business, primarily from the 2020 and 2021 accident years. Net adverse development in medium-tailed lines reflected $24.7 million of adverse development in professional liability business, primarily from the 2013 to 2015 and 2018 to 2020 accident years, and $6.4 million of adverse development in contract binding business, across most accident years, partially offset by $12.9 million of favorable development in marine business, across most accident years. Net adverse development in long-tail lines reflected $18.5 million of adverse development related to casualty business, primarily from the 2020 and 2021 accident years, and $7.3 million of adverse development on construction and national accounts, primarily from the 2017, 2020 and 2021 accident years. This is partially offset by $21.5 million of favorable development in other business, including alternative markets and excess workers’ compensation, primarily from the 2019 and prior accident years.

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The reinsurance segment’s net favorable development of $191.6 million, or 4.8 points of net earned premium, consisted of $196.2 million of net favorable development from short-tailed and medium-tailed lines, partially offset by $4.6 million of net adverse development from long-tailed lines. Net favorable development in short-tailed lines reflected $109.4 million of favorable development from property other than property catastrophe business, primarily from the 2018 to 2021 underwriting years (i.e., all premiums and losses attributable to contracts having an inception or renewal date within the given twelve-month period), $24.0 million of favorable development from property catastrophe business, primarily from the 2018 to 2020 underwriting years, and $35.0 million from other specialty business, primarily from the 2016 and 2021 underwriting years. Net favorable development in medium-tailed lines reflected $28.0 million in marine and aviation lines, across most underwriting years. Net adverse development in long-tailed lines primarily reflected $4.6 million in casualty, spread across many prior underwriting years.

The mortgage segment experienced net favorable development of $554.1 million, or 47.8 points of net earned premium, with the majority of reserve releases being on COVID-related delinquencies associated with the U.S. first lien portfolio from the 2020 and 2021 accident years. The Company’s credit risk transfer, international, second lien and student loan businesses also contributed to the favorable development.

Year Ended December 31, 2021

During 2021, the Company recorded estimated net favorable development on prior year loss reserves of $356.2 million, which consisted of net favorable development of $16.2 million from the insurance segment, $178.8 million from the reinsurance segment, $169.6 million from the mortgage segment, partially offset by $8.4 million of adverse development from the ‘other’ segment (activity prior to the deconsolidation of Somers).

The insurance segment’s net favorable development of $16.2 million, or 0.4 points of net earned premium, consisted of $109.8 million of net favorable development in short-tailed and long-tailed lines mostly offset by $93.5 million of net adverse development from medium-tailed lines. Net favorable development of $81.7 million in short-tailed lines reflected $38.9 million of favorable development from property (excluding marine), primarily from the 2018 to 2020 accident years, $26.7 million of favorable development in warranty and lenders solutions, primarily from the 2020 accident year, and $16.2 million of favorable development on travel and accident, primarily from the 2016 to 2020 accident years. Net favorable development of $28.1 million in long-tailed lines reflected favorable development in construction, national accounts and alternative markets, primarily from the

2016 to 2019 accident years, partially offset by adverse development in executive assurance, primarily from the 2015, 2017 and 2018 accident years. Net adverse development in medium-tailed lines reflected $57.6 million of adverse development in contract binding, primarily from the 2013 to 2019 accident years and $30.8 million of adverse development in professional liability, primarily from the 2018 to 2020 accident years.

The reinsurance segment’s net favorable development of $178.8 million, or 6.3 points of net earned premium, consisted of $184.1 million of net favorable development from short-tailed and medium-tailed lines, partially offset by $5.3 million of net adverse development from long-tailed lines. Net favorable development of $175.5 million in short-tailed lines reflected $123.3 million from other specialty lines, primarily from the 2014 to 2019 underwriting years, and $88.6 million of favorable development from property other than property catastrophe business, primarily from the 2015 to 2020 underwriting years. Such amounts were partially offset by adverse development of $36.4 million from property catastrophe, primarily from the 2020 underwriting year. Adverse development in long-tailed lines reflected an increase in casualty, primarily from the 2018 underwriting year.

The mortgage segment experienced net favorable development of $169.6 million, or 13.2 points of net earned premium. Approximately a third of this development came from the U.S. first lien portfolio, which benefited from improving economic conditions and rising home prices, resulting in reduced claim rate assumptions primarily associated with pre-pandemic delinquencies. Various vintage CRT contracts also experienced similar effects and contributed to the favorable development, including the effect of contracts called by the GSEs. Subrogation recoveries on second lien and student loan business and international business also contributed to the favorable development.

Year Ended December 31, 2020

During 2020, the Company recorded estimated net favorable development on prior year loss reserves of $161.5 million, which consisted of net favorable development of $7.8 million from the insurance segment, $134.0 million from the reinsurance segment, $19.0 million from the mortgage segment, and $0.7 million from the ‘other’ segment.

The insurance segment’s net favorable development of $7.8 million, or 0.3 points of net earned premium, consisted of $83.0 million of net favorable development in short-tailed and long-tailed lines partially offset by $75.2 million of net adverse development from medium-tailed lines. Net favorable development of $33.6 million in short-tailed lines reflected $21.6 million of favorable development from property (excluding marine), primarily from the 2015 to 2018

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accident years, and $8.4 million of favorable development on travel and accident, primarily from the 2019 accident year. Net favorable development of $49.4 million in long-tailed lines included $38.8 million of favorable development related to other business, including alternative markets and excess workers’ compensation, across all accident years, and $9.3 million of favorable development related to construction business. Net adverse development in medium-tailed lines reflected $37.9 million of adverse development in surety business, primarily from the 2019 accident year, $23.1 million in contract binding business, primarily from the 2016 to 2019 accident years, and $16.0 million in program business, primarily from the 2016 to 2019 accident years.

The reinsurance segment’s net favorable development of $134.0 million, or 6.2 points of net earned premium, consisted of $155.9 million of net favorable development from short-tailed and medium-tailed lines, partially offset by $21.9 million of net adverse development from long-tailed lines. Net favorable development of $144.0 million in short-tailed lines reflected $87.7 million related to property catastrophe and property other than property catastrophe business, primarily from the 2015 to 2019 underwriting years, and $53.6 million from other specialty lines, across most underwriting years. The net reduction of loss estimates for the reinsurance segment’s short-tailed lines primarily resulted from varying levels of reported and paid claims activity than previously anticipated which led to decreases in

certain loss ratio selections during 2020. Adverse development in long-tailed lines reflected an increase in casualty, primarily from the 2012 to 2015 underwriting years.

The mortgage segment’s net favorable development of $19.0 million, or 1.4 points of net earned premium, included $16.2 million of favorable development on U.S. primary mortgage insurance business. Such development was primarily driven by subrogation recoveries on second lien business and student loan business.

Retroactive Reinsurance Transactions

In 2021, the Company entered into a retroactive reinsurance transaction with third party reinsurer to reinsure run-off liabilities associated with certain U.S. insurance exposures.

In 2021, the Company entered into a reinsurance to close with the related party, in connection with the 2018 and prior years of account for certain London syndicate business. See note 16, “Transactions with Related Parties”.

In 2020, the Company entered into a reinsurance-to-close agreement related to a third party arrangement covering the 2017 and prior years of account for certain London syndicate business.

6.    Short Duration Contracts

The Company’s reserves for losses and loss adjustment expenses primarily relate to short-duration contracts with various characteristics (e.g., type of coverage, geography, claims duration). The Company considered such information in determining the level of disaggregation for disclosures related to its short-duration contracts, as detailed in the table below:

Reportable segment	Level of disaggregation	Included lines of business
Insurance	Property energy, marine and aviation	Property energy, marine and aviation
	Third party occurrence business	Excess and surplus casualty (excluding contract binding); construction and national accounts; and other (including alternative market risks, excess workers’ compensation and employer’s liability insurance coverages)
	Third party claims-made business	Professional lines
	Multi-line and other specialty	Programs; contract binding (part of excess and surplus casualty); travel, accident and health; warranty and lenders solutions; and other (contract and commercial surety coverages)
Reinsurance	Casualty	Casualty
	Property catastrophe	Property catastrophe
	Property excluding property catastrophe	Property excluding property catastrophe
	Marine and aviation	Marine and aviation
	Other specialty	Other specialty
Mortgage	Direct mortgage insurance in the U.S.	Mortgage insurance on U.S. primary exposures

The Company determined the following to be insignificant for disclosure purposes: (i) certain mortgage business, including non-U.S. primary business, second lien and student loan exposures, global mortgage reinsurance and participation in various GSE credit risk-sharing products and (ii) certain reinsurance business, including casualty clash and non-traditional lines. Such amounts are included as reconciling items.

The Company is required to establish reserves for losses and loss adjustment expenses (“Loss Reserves”) that arise from the business the Company underwrites. Loss Reserves for the insurance, reinsurance and mortgage segments represent estimates of future amounts required to pay losses and loss adjustment expenses for insured or reinsured events which have occurred at or before the balance sheet date. Loss Reserves do not reflect contingency reserve allowances to account for future loss occurrences. Losses arising from future events will be estimated and recognized at the time the losses are incurred and could be substantial.

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Insurance Segment

Loss Reserves for the insurance segment are comprised of estimated amounts for (1) reported losses (“case reserves”) and (2) incurred but not reported losses (“IBNR reserves”). Generally, claims personnel determine whether to establish a case reserve for the estimated amount of the ultimate settlement of individual claims. The estimate reflects the judgment of claims personnel based on general corporate reserving practices, the experience and knowledge of such personnel regarding the nature and value of the specific type of claim and, where appropriate, advice of counsel. The Company also contracts with a number of outside third party administrators in the claims process who, in certain cases, have limited authority to establish case reserves. The work of such administrators is reviewed and monitored by our claims personnel. Loss Reserves are also established to provide for loss adjustment expenses and represent the estimated expense of settling claims, including legal and other fees and the general expenses of administering the claims adjustment process. Periodically, adjustments to the case reserves may be made as additional information is reported or payments are made. IBNR reserves are established to provide for incurred claims which have not yet been reported at the balance sheet date as well as to adjust for any projected variance in case reserving. Actuaries estimate ultimate losses and loss adjustment expenses using various generally accepted actuarial methods applied to known losses and other relevant information. Like case reserves, IBNR reserves are adjusted as additional information becomes known or payments are made. The process of estimating reserves involves a considerable degree of judgment by management and, as of any given date, is inherently uncertain.

Ultimate losses and loss adjustment expenses are generally determined by projection of claim emergence and settlement patterns observed in the past that can reasonably be expected to persist into the future. In forecasting ultimate losses and loss adjustment expenses with respect to any line of business, past experience with respect to that line of business is the primary resource, developed through both industry and company experience, but cannot be relied upon in isolation. Uncertainties in estimating ultimate losses and loss adjustment expenses are magnified by the length of the time lag between when a claim actually occurs and when it is reported and settled. This time lag is sometimes referred to as the “claim-tail.” During this period additional facts regarding coverages written in prior accident years, as well as about actual claims and trends, may become known and, as a result, may lead to adjustments of the related Loss Reserves. If the Company determines that an adjustment is appropriate, the adjustment is recorded in the accounting period in which such determination is made. Accordingly, should Loss Reserves need to be increased or decreased in the future from amounts currently established, future results of operations would be negatively or positively impacted respectively. The

Company authorizes managing general agents, general agents and other producers to write program business on the Company’s behalf within prescribed underwriting authorities. This delegated authority process introduces additional complexity to the actuarial determination of unpaid future losses and loss adjustment expenses. In order to monitor adherence to the underwriting guidelines given to such parties, the Company periodically performs underwriting and claims due diligence reviews.

In determining ultimate losses and loss adjustment expenses, the cost to indemnify claimants, provide needed legal defense and other services for insureds and administer the investigation and adjustment of claims are considered. These claim costs are influenced by many factors that change over time, such as expanded coverage definitions as a result of new court decisions, inflation in costs to repair or replace damaged property, inflation in the cost of medical services and legislated changes in statutory benefits, as well as by the particular, unique facts that pertain to each claim. As a result, the rate at which claims arose in the past and the costs to settle them may not always be representative of what will occur in the future. The factors influencing changes in claim costs are often difficult to isolate or quantify and developments in paid and incurred losses from historical trends are frequently subject to multiple and conflicting interpretations. Changes in coverage terms or claims handling practices may also cause future experience and/or development patterns to vary from the past. A key objective of actuaries in developing estimates of ultimate losses and loss adjustment expenses, and resulting IBNR reserves, is to identify aberrations and systemic changes occurring within historical experience and adjust for them so that the future can be projected more reliably. Because of the factors previously discussed, this process requires the substantial use of informed judgment and is inherently uncertain.

Although Loss Reserves are initially determined based on underwriting and pricing analyses, the Company’s insurance segment applies several generally accepted actuarial methods, as discussed below, on a quarterly basis to evaluate the Loss Reserves, in addition to the expected loss method, in particular for Loss Reserves from more mature accident years (the year in which a loss occurred). Each quarter, as part of the reserving process, the segments’ actuaries reaffirm that the assumptions used in the reserving process continue to form a sound basis for the projection of liabilities. If actual loss activity differs substantially from expectations based on historical information, an adjustment to Loss Reserves may be supported. The Company places more or less reliance on a particular actuarial method based on the facts and circumstances at the time the estimates of Loss Reserves are made.

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These methods generally fall into one of the following categories or are hybrids of one or more of the following categories:

•Expected loss methods - these methods are based on the assumption that ultimate losses vary proportionately with premiums. Expected loss and loss adjustment expense ratios are typically developed based upon the information derived by underwriters and actuaries during the initial pricing of the business, supplemented by industry data available from organizations, such as statistical bureaus and consulting firms, where appropriate. These ratios consider, among other things, rate increases and changes in terms and conditions that have been observed in the market. Expected loss methods are useful for estimating ultimate losses and loss adjustment expenses in the early years of long-tailed lines of business, when little or no paid or incurred loss information is available, and is commonly applied when limited loss experience exists for a company.

•Historical incurred loss development methods - these methods assume that the ratio of losses in one period to losses in an earlier period will remain constant in the future. These methods use incurred losses (i.e., the sum of cumulative historical loss payments plus outstanding case reserves) over discrete periods of time to estimate future losses. Historical incurred loss development methods may be preferable to historical paid loss development methods because they explicitly take into account open cases and the claims adjusters’ evaluations of the cost to settle all known claims. However, historical incurred loss development methods necessarily assume that case reserving practices are consistently applied over time. Therefore, when there have been significant changes in how case reserves are established, using incurred loss data to project ultimate losses may be less reliable than other methods.

•Historical paid loss development methods - these methods, like historical incurred loss development methods, assume that the ratio of losses in one period to losses in an earlier period will remain constant. These methods use historical loss payments over discrete periods of time to estimate future losses and necessarily assume that factors that have affected paid losses in the past, such as inflation or the effects of litigation, will remain constant in the future. Because historical paid loss development methods do not use incurred losses to estimate ultimate losses, they may be more reliable than the other methods that use incurred losses in situations where there are significant changes in how incurred losses are established by a company’s claims adjusters. However, historical paid loss development methods are more leveraged (meaning that small changes in payments have a larger impact on estimates of ultimate losses) than

actuarial methods that use incurred losses because cumulative loss payments take much longer to equal the expected ultimate losses than cumulative incurred amounts. In addition, and for similar reasons, historical paid loss development methods are often slow to react to situations when new or different factors arise than those that have affected paid losses in the past.

•Adjusted historical paid and incurred loss development methods - these methods take traditional historical paid and incurred loss development methods and adjust them for the estimated impact of changes from the past in factors such as inflation, the speed of claim payments or the adequacy of case reserves. Adjusted historical paid and incurred loss development methods are often more reliable methods of predicting ultimate losses in periods of significant change, provided the actuaries can develop methods to reasonably quantify the impact of changes. As such, these methods utilize more judgment than historical paid and incurred loss development methods.

•Bornhuetter-Ferguson (“B-F”) paid and incurred loss methods - these methods utilize actual paid and incurred losses and expected patterns of paid and incurred losses, taking the initial expected ultimate losses into account to determine an estimate of expected ultimate losses. The B-F paid and incurred loss methods are useful when there are few reported claims and a relatively less stable pattern of reported losses.

•Frequency-Severity methods - These methods utilize actual paid and incurred claim experience, but break the data down into its component pieces: claim counts, often expressed as a ratio to exposure or premium (frequency), and average claim size (severity). The component pieces are projected to an ultimate level and multiplied together to result in an estimate of ultimate loss. These methods are especially useful when the severity of claims can be confined to a relatively stable range of estimated ultimate average claim value.

•Additional analyses - other methodologies are often used in the reserving process for specific types of claims or events, such as catastrophic or other specific major events. These include vendor catastrophe models, which are typically used in the estimation of Loss Reserves at the early stage of known catastrophic events before information has been reported to an insurer or reinsurer.

In the initial reserving process for short-tail insurance lines (consisting of property, energy, marine and aviation and other exposures including travel, accident and health, and warranty and lenders solutions), the Company relies on a combination of the reserving methods discussed above. For catastrophe-exposed business, the reserving process also includes the usage of catastrophe models for known events

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and a heavy reliance on analysis of individual catastrophic events and management judgment. The development of losses on short-tail business can be unstable, especially for policies characterized by high severity, low frequency losses. As time passes, for a given accident year, additional weight is given to the paid and incurred B-F loss development methods and eventually to the historical paid and incurred loss development methods in the reserving process. The Company makes a number of key assumptions in their reserving process, including that historical paid and reported development patterns are stable, catastrophe models provide useful information about our exposure to catastrophic events that have occurred and underwriters’ judgment as to potential loss exposures can be relied on. The expected loss ratios used in the initial reserving process for short-tail business have varied over time due to changes in pricing, reinsurance structure, estimates of catastrophe losses, policy changes (such as attachment points, class and limits) and geographical distribution. As losses in short-tail lines are reported relatively quickly, expected loss ratios are selected for the current accident year based upon actual attritional loss ratios for earlier accident years, adjusted for rate changes, inflation, changes in reinsurance programs and expected attritional losses based on modeling. Furthermore, ultimate losses for short-tail business are known in a reasonably short period of time.

In the initial reserving process for medium-tail and long-tail insurance lines (consisting of third party occurrence business, third party claims made business, and other exposures including surety, programs and contract binding exposures), the Company primarily relies on the expected loss method. The development of the Company’s medium-tail and long-tail business may be unstable, especially if there are high severity major events, as a portion of the Company’s casualty business is in high excess layers. As time passes, for a given accident year, additional weight is given to the paid and incurred B-F loss development methods and historical paid and incurred loss development methods in the reserving process. The Company makes a number of key assumptions

in reserving for medium-tail and long-tail lines, including that the pricing loss ratio is the best estimate of the ultimate loss ratio at the time the policy is entered into, that the loss development patterns, which are based on a combination of company and industry loss development patterns and adjusted to reflect differences in the insurance segment’s mix of business, are reasonable and that claims personnel and underwriters analyses of our exposure to major events are assumed to be the best estimate of exposure to the known claims on those events. The expected loss ratios used in the initial reserving process for medium-tail and long-tail business for recent accident years have varied over time, in some cases significantly, from earlier accident years. As the credibility of historical experience for earlier accident years increases, the experience from these accident years will be given a greater weighting in the actuarial analysis to determine future accident year expected loss ratios, adjusted for changes in pricing, loss trends, terms and conditions and reinsurance structure.

From time to time, the Company enters into loss portfolio transfer and adverse development cover reinsurance agreements accounted for as retroactive reinsurance. These agreements transfer Loss Reserves and future favorable or adverse development on certain runoff programs and certain third party occurrence business, within multi-line and other specialty business (the “Covered Lines”). As incurred losses and allocated loss adjustment expenses for the Covered Lines are ceded to the reinsurer, the Company is not exposed to changes in the amount, timing and uncertainty of cash flows arising from the Covered Lines. To avoid distortion, the incurred losses and allocated loss adjustment expenses and cumulative paid losses and loss adjustment expenses for the Covered Lines are excluded entirely from the tables below. Unpaid loss and loss adjustment expenses recoverable at December 31, 2022 included $280.2 million related to such reinsurance agreements.

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The following tables present information on the insurance segment’s short-duration insurance contracts:

Property, energy, marine and aviation ($000’s except claim count)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	158,548	$	156,147	$	148,622	$	142,889	$	134,473	$	133,400	$	128,157	$	126,825	$	125,813	$	124,868	$	27	3,982
2014			148,104		145,679		147,248		136,050		132,166		134,192		134,895		134,803		133,605		1,674		3,557
2015					112,299		109,769		103,921		102,449		97,789		91,770		91,833		90,816		2,654		4,244
2016							104,002		100,843		105,184		100,003		95,989		92,108		87,618		61		5,704
2017									280,686		246,264		235,924		230,413		231,199		225,298		3,268		6,287
2018											180,981		186,030		173,693		170,057		170,411		7,177		5,048
2019													179,056		178,564		165,477		161,156		4,162		5,942
2020															359,394		329,362		335,747		28,330		8,546
2021																	426,870		428,719		54,746		7,566
2022																			521,750		208,080		8,965
																	Total		$	2,279,988
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	32,216	$	84,680	$	110,432	$	119,649	$	121,779	$	125,014	$	122,894	$	124,227	$	124,381	$	124,402
2014			25,849		53,632		77,764		84,061		87,681		98,423		115,253		122,165		122,792
2015					23,561		64,900		76,282		86,196		87,870		86,190		87,260		87,564
2016							24,684		83,218		98,303		97,089		94,570		90,808		87,232
2017									30,215		139,849		195,512		211,688		215,874		217,764
2018											30,026		102,285		134,858		142,838		149,663
2019													26,130		105,380		133,911		139,141
2020															55,619		194,487		251,055
2021																	90,423		267,677
2022																			100,476
									Total										1,547,766
									All outstanding liabilities before 2013, net of reinsurance										18,239
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	750,461

Third party occurrence business ($000’s except claim count)
	Incurred losses and allocated loss adjustment expenses, net of reinsurance																				December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	282,852	$	296,668	$	306,572	$	301,622	$	281,637	$	274,246	$	272,385	$	269,297	$	270,110	$	263,430	$	43,148	66,118
2014			329,718		335,587		338,505		342,759		339,403		343,904		342,641		343,286		345,024		60,263		75,557
2015					358,769		391,570		398,565		391,797		391,132		382,427		386,465		379,226		75,540		78,507
2016							389,530		394,190		405,803		399,315		374,654		367,586		363,453		93,800		78,576
2017									417,097		417,662		422,360		412,231		406,857		406,165		114,603		84,418
2018											430,128		452,879		450,647		451,164		458,050		156,700		77,685
2019													455,928		487,080		480,535		471,279		195,283		84,985
2020															606,640		616,314		640,231		309,019		90,795
2021																	621,972		662,716		431,302		89,718
2022																			688,082		614,366		70,380
																	Total		$	4,677,656
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	6,840	$	29,215	$	71,335	$	101,153	$	122,045	$	149,012	$	164,090	$	174,591	$	184,444	$	192,159
2014			9,200		40,226		71,473		112,541		161,935		191,108		211,440		223,895		237,135
2015					11,110		44,514		88,411		139,364		181,505		211,510		227,439		249,399
2016							11,679		41,920		87,543		136,759		164,534		194,637		215,481
2017									13,391		52,309		99,806		134,988		165,468		220,660
2018											16,991		63,776		115,049		154,138		198,502
2019													18,375		73,075		121,646		172,948
2020															24,407		76,567		154,902
2021																	26,235		90,791
2022																			23,981
									Total										1,755,958
									All outstanding liabilities before 2013, net of reinsurance										263,297
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	3,184,995

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Third party claims-made business ($000’s except claim count)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	301,608	$	320,266	$	324,044	$	320,177	$	294,372	$	290,852	$	281,642	$	271,156	$	273,607	$	281,584	$	14,639	14,953
2014			264,273		279,410		298,541		278,556		281,271		297,248		291,498		287,573		296,153		21,206		15,482
2015					258,740		277,358		276,256		259,830		255,207		252,263		267,725		266,758		18,198		14,392
2016							274,996		291,258		308,080		314,412		321,764		326,960		329,534		29,356		15,083
2017									270,272		285,738		311,724		308,172		323,128		316,673		45,042		15,198
2018											272,543		314,112		319,646		336,106		347,449		61,612		15,934
2019													289,128		317,312		317,363		322,178		93,422		15,858
2020															383,497		413,156		423,375		187,245		15,438
2021																	514,676		517,975		351,736		15,751
2022																			657,664		575,484		18,190
																	Total		$	3,759,343
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	19,007	$	87,386	$	137,857	$	179,261	$	197,861	$	216,984	$	238,730	$	245,423	$	246,813	$	253,570
2014			13,814		63,288		129,409		172,722		207,447		229,314		243,137		249,307		260,333
2015					9,059		52,007		100,030		126,431		174,084		193,105		216,892		220,871
2016							10,537		68,157		127,203		158,127		205,478		242,300		256,705
2017									9,281		67,529		112,975		143,064		195,788		232,508
2018											12,241		68,244		118,105		158,389		208,063
2019													12,373		65,286		122,046		154,630
2020															17,070		87,248		151,750
2021																	23,253		90,487
2022																			25,244
									Total										1,854,161
									All outstanding liabilities before 2013, net of reinsurance										86,120
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	1,991,302

Multi-line and other specialty ($000’s except claim count)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	264,243	$	272,335	$	263,631	$	263,928	$	251,894	$	253,271	$	248,634	$	245,825	$	245,069	$	244,191	$	2,761	86,371
2014			301,548		325,705		318,453		318,268		317,197		313,221		310,051		309,061		310,977		3,968		130,844
2015					334,684		357,939		356,777		364,815		356,657		349,432		347,206		344,974		5,632		170,579
2016							408,686		430,976		427,829		416,108		409,987		408,004		408,716		8,616		189,406
2017									482,436		501,026		491,347		500,947		504,322		512,717		12,776		229,570
2018											512,406		564,563		562,848		565,116		564,693		21,722		256,621
2019													566,864		612,179		640,262		651,004		38,672		250,441
2020															618,340		569,123		515,016		87,261		162,214
2021																	635,186		618,581		153,336		113,165
2022																			678,479		425,107		89,859
																	Total		$	4,849,348
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	86,680	$	150,925	$	180,428	$	213,461	$	225,324	$	234,330	$	236,375	$	237,293	$	238,321	$	238,257
2014			107,726		196,899		234,267		267,079		281,195		291,727		293,131		294,630		295,896
2015					138,153		236,108		277,850		305,895		320,971		326,652		330,431		331,320
2016							175,948		304,743		341,789		362,823		379,305		385,314		390,350
2017									181,102		342,385		380,696		423,480		446,002		471,978
2018											211,711		389,047		442,643		479,824		508,649
2019													211,970		385,794		486,882		548,844
2020															171,994		309,106		358,967
2021																	156,992		334,549
2022																			177,092
									Total										3,655,902
									All outstanding liabilities before 2013, net of reinsurance										22,275
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	1,215,721

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The following table presents the average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance, as of December 31, 2022:

	Average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance
	Year 1		Year 2		Year 3		Year 4		Year 5		Year 6		Year 7		Year 8		Year 9		Year 10
Property, energy, marine and aviation	20.3	%	44.2	%	18.4	%	5.2	%	1.5	%	1.1	%	2.0	%	2.2	%	0.3	%	—	%
Third party occurrence business	3.4	%	9.3	%	11.8	%	11.2	%	9.7	%	9.7	%	5.4	%	4.5	%	3.8	%	2.9	%
Third party claims-made business	4.1	%	17.2	%	17.2	%	11.4	%	13.6	%	8.8	%	6.4	%	2.0	%	2.1	%	2.4	%
Multi-line and other specialty	34.3	%	28.9	%	10.9	%	8.8	%	4.5	%	3.1	%	0.9	%	0.4	%	0.4	%	—	%

Reinsurance Segment

Loss Reserves for the Company’s reinsurance segment are comprised of (1) case reserves, (2) additional case reserves (“ACRs”) and (3) IBNR reserves. The Company receives reports of claims notices from ceding companies and records case reserves based upon the amount of reserves recommended by the ceding company. Case reserves may be supplemented by ACRs, which may be estimated by the Company’s claims personnel ahead of official notification from the ceding company, or when judgment regarding the size or severity of the known event differs from the ceding company. In certain instances, the Company establishes ACRs even when the ceding company does not report any liability on a known event. In addition, specific claim information reported by ceding companies or obtained through claim audits can alert the Company to emerging trends such as changing legal interpretations of coverage and liability, claims from unexpected sources or classes of business, and significant changes in the frequency or severity of individual claims. Such information is often used in the process of estimating IBNR reserves. IBNR reserves are established to provide for incurred claims which have not yet been reported at the balance sheet date as well as to adjust for any projected variance in case reserving. Actuaries estimate ultimate losses and loss adjustment expenses using various generally accepted actuarial methods applied to known losses and other relevant information. Like case reserves, IBNR reserves are adjusted as additional information becomes known or payments are made. The process of estimating Loss Reserves involves a considerable degree of judgment by management and, as of any given date, is inherently uncertain.

The estimation of Loss Reserves for the reinsurance segment is subject to the same risk factors as the estimation of Loss Reserves for the insurance segment. In addition, the inherent uncertainties of estimating such reserves are even greater for reinsurers, due primarily to the following factors: (1) the claim-tail for reinsurers is generally longer because claims are first reported to the ceding company and then to the reinsurer through one or more intermediaries, (2) the reliance on premium estimates, where reports have not been received from the ceding company, in the reserving process, (3) the potential for writing a number of reinsurance contracts with different ceding companies with the same exposure to a single loss event, (4) the diversity of loss development

patterns among different types of reinsurance contracts, (5) the necessary reliance on the ceding companies for information regarding reported claims and (6) the differing reserving practices among ceding companies.

Ultimate losses and loss adjustment expenses are generally determined by projection of claim emergence and settlement patterns observed in the past that can reasonably be expected to persist into the future. As with the insurance segment, the process of estimating Loss Reserves for the reinsurance segment involves a considerable degree of judgment by management and, as of any given date, is inherently uncertain. As discussed above, such uncertainty is greater for reinsurers compared to insurers. As a result, our reinsurance operations obtain information from numerous sources to assist in the process. Pricing actuaries from the reinsurance segment devote considerable effort to understanding and analyzing a ceding company’s operations and loss history during the underwriting of the business, using a combination of ceding company and industry statistics. Such statistics normally include historical premium and loss data by class of business, individual claim information for larger claims, distributions of insurance limits provided, loss reporting and payment patterns, and rate change history. This analysis is used to project expected loss ratios for each treaty during the upcoming contract period.

As mentioned above, there can be a considerable time lag from the time a claim is reported to a ceding company to the time it is reported to the reinsurer. The lag can be several years in some cases and may be attributed to a number of reasons, including the time it takes to investigate a claim, delays associated with the litigation process, the deterioration in a claimant’s physical condition many years after an accident occurs, the case reserving approach of the ceding company, etc. In the reserving process, the Company assumes that such lags are predictable, on average, over time and therefore the lags are contemplated in the loss reporting patterns used in their actuarial methods. This means that the reinsurance segment must rely on estimates for a longer period of time than does an insurance company. Backlogs in the recording of assumed reinsurance can also complicate the accuracy of loss reserve estimation. As of December 31, 2022 there were no significant backlogs related to the processing of assumed reinsurance information at our reinsurance operations.

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The reinsurance segment relies heavily on information reported by ceding companies, as discussed above. In order to determine the accuracy and completeness of such information, underwriters, actuaries, and claims personnel often perform audits of ceding companies and regularly review information received from ceding companies for unusual or unexpected results. Material findings are usually discussed with the ceding companies. The Company sometimes encounters situations where they determine that a claim presentation from a ceding company is not in accordance with contract terms. In these situations, the Company attempts to resolve the dispute with the ceding company. Most situations are resolved amicably and without the need for litigation or arbitration. However, in the infrequent situations where a resolution is not possible, the Company will vigorously defend its position in such disputes.

Although Loss Reserves are initially determined based on underwriting and pricing analysis, the Company applies several generally accepted actuarial methods, as discussed above, on a quarterly basis to evaluate its Loss Reserves in addition to the expected loss method, in particular for reserves from more mature underwriting years (the year in which business is underwritten). Each quarter, as part of the reserving process, the Company’s actuaries reaffirm that the assumptions used in the reserving process continue to form a sound basis for projection of liabilities. If actual loss activity differs substantially from expectations based on historical information, an adjustment to Loss Reserves may be supported. Estimated Loss Reserves for more mature underwriting years are now based more on actual loss activity and historical patterns than on the initial assumptions based on pricing indications. More recent underwriting years rely more heavily on internal pricing assumptions. The Company places more or less reliance on a particular actuarial method based on the facts and circumstances at the time the estimates of Loss Reserves are made.

In the initial reserving process for short-tail reinsurance lines (consisting of property excluding property catastrophe and property catastrophe exposures), the Company relies on a combination of the reserving methods discussed above. For known catastrophic events, the reserving process also includes the usage of catastrophe models and a heavy reliance on analysis which includes ceding company inquiries and management judgment. The development of property losses may be unstable, especially where there is high catastrophic exposure, may be characterized by high severity, low frequency losses for excess and catastrophe-exposed business and may be highly correlated across contracts. As time passes, for a given underwriting year, additional weight is given to the paid and incurred B-F loss development methods and historical paid and incurred loss development

methods in the reserving process. The Company makes a number of key assumptions in reserving for short-tail lines, including that historical paid and reported development patterns are stable, catastrophe models provide useful information about our exposure to catastrophic events that have occurred and our underwriters’ judgment and guidance received from ceding companies as to potential loss exposures may be relied on. The expected loss ratios used in the initial reserving process for property exposures have varied over time due to changes in pricing, reinsurance structure, estimates of catastrophe losses, terms and conditions and geographical distribution. As losses in property lines are reported relatively quickly, expected loss ratios are selected for the current underwriting year incorporating the experience for earlier underwriting years, adjusted for rate changes, inflation, changes in reinsurance programs, expectations about present and future market conditions and expected attritional losses based on modeling. Due to the short-tail nature of property business, reported loss experience emerges quickly and ultimate losses are known in a reasonably short period of time.

In the initial reserving process for medium-tail and long-tail reinsurance lines (consisting of casualty, other specialty, marine and aviation and other exposures), the Company primarily relies on the expected loss method. The development of medium-tail and long-tail business may be unstable, especially if there are high severity major events, with business written on an excess of loss basis typically having a longer tail than business written on a pro rata basis. As time passes, for a given underwriting year, additional weight is given to the paid and incurred B-F loss development methods and eventually to the historical paid and incurred loss development methods in the reserving process. Our reinsurance operations make a number of key assumptions in reserving for medium-tail and long-tail lines, including that the pricing loss ratio is the best estimate of the ultimate loss ratio at the time the contract is entered into, historical paid and reported development patterns are stable and claims personnel and underwriters’ analyses of our exposure to major events are our best estimate of our exposure to the known claims on those events. The expected loss ratios used in our reinsurance operations’ initial reserving process for medium-tail and long-tail contracts have varied over time due to changes in pricing, terms and conditions and reinsurance structure. As the credibility of historical experience for earlier underwriting years increases, the experience from these underwriting years is used in the actuarial analysis to determine future underwriting year expected loss ratios, adjusted for changes in pricing, loss trends, terms and conditions and reinsurance structure.

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The following tables present information on the reinsurance segment’s short-duration insurance contracts:

Casualty ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	163,425	$	156,619	$	152,392	$	146,230	$	134,204	$	132,701	$	129,120	$	133,401	$	133,687	$	133,094	$	26,542	N/A
2014			212,923		217,991		214,724		227,485		224,105		233,922		234,293		230,944		231,175		33,255		N/A
2015					217,343		216,759		224,385		231,473		235,637		242,554		245,756		247,419		44,753		N/A
2016							208,192		221,004		242,089		257,214		264,573		264,475		268,079		46,122		N/A
2017									262,894		251,827		267,173		293,381		304,194		310,858		52,415		N/A
2018											270,621		284,405		276,802		281,852		293,320		56,325		N/A
2019													325,359		334,755		361,549		372,669		93,310		N/A
2020															378,668		367,595		349,831		169,909		N/A
2021																	434,187		431,165		292,696		N/A
2022																			541,941		482,552		N/A
																	Total		$	3,179,551
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	2,421	$	9,822	$	22,886	$	42,861	$	54,323	$	62,751	$	70,289	$	76,141	$	81,167	$	87,485
2014			3,885		15,973		40,651		63,214		90,530		113,596		133,263		143,929		152,586
2015					4,440		20,208		46,933		70,523		95,988		119,096		136,138		151,119
2016							5,720		25,626		51,494		86,362		112,818		131,341		155,584
2017									6,417		30,316		63,922		112,474		136,489		163,243
2018											7,576		31,240		106,443		128,728		154,173
2019													15,798		57,568		96,593		129,766
2020															17,646		50,383		90,156
2021																	14,633		53,264
2022																			17,638
									Total										1,155,014
									All outstanding liabilities before 2013, net of reinsurance										299,288
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	2,323,825

Property catastrophe ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	65,372	$	45,962	$	34,959	$	30,518	$	27,974	$	27,248	$	26,415	$	26,543	$	26,344	$	26,221	$	(138)	N/A
2014			43,800		29,801		24,500		21,764		20,026		19,326		19,229		19,004		19,045		(10)		N/A
2015					32,748		17,558		11,425		5,531		3,779		3,133		2,932		2,569		68		N/A
2016							23,224		16,582		12,749		9,190		6,886		5,987		5,181		877		N/A
2017									86,410		53,699		49,507		35,893		24,239		21,026		(803)		N/A
2018											73,041		52,001		33,425		19,831		10,722		3,039		N/A
2019													25,526		14,252		13,093		4,590		4,576		N/A
2020															260,244		322,680		326,262		33,413		N/A
2021																	308,014		302,124		29,963		N/A
2022																			299,636		73,474		N/A
																	Total		$	1,017,376
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	12,035	$	18,496	$	23,001	$	24,697	$	26,329	$	26,549	$	26,549	$	27,233	$	26,998	$	27,023
2014			13,619		19,544		17,902		18,679		18,244		18,421		18,550		18,629		18,592
2015					(3,141)		(2,109)		1,843		2,103		1,659		1,745		1,817		1,874
2016							(7,039)		1,759		1,870		2,932		2,086		2,433		2,594
2017									30,625		31,621		37,084		27,060		14,215		16,034
2018											27,424		7,344		18,253		(10,934)		(8,100)
2019													4,374		8,845		12,895		(11,472)
2020															52,592		152,075		200,510
2021																	64,408		167,806
2022																			69,969
									Total										484,830
									All outstanding liabilities before 2013, net of reinsurance										2,612
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	535,158

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Property excluding property catastrophe ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	114,775	$	76,290	$	69,981	$	65,734	$	64,013	$	63,247	$	62,070	$	62,774	$	62,288	$	63,390	$	29	N/A
2014			142,092		116,331		98,263		90,031		87,768		83,476		81,812		80,348		79,307		443		N/A
2015					213,681		187,932		183,709		187,569		186,861		175,812		172,189		166,580		3,909		N/A
2016							174,506		144,323		136,367		134,362		138,216		135,116		128,941		6,208		N/A
2017									266,628		247,462		235,310		227,891		212,133		204,128		8,794		N/A
2018											222,932		238,876		234,794		211,852		201,429		7,370		N/A
2019													214,513		204,620		194,164		189,456		8,407		N/A
2020															366,726		338,712		319,097		36,912		N/A
2021																	545,101		497,059		83,934		N/A
2022																			742,703		360,528		N/A
																	Total		$	2,592,090
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	25,943	$	42,418	$	49,433	$	52,614	$	53,400	$	55,272	$	60,777	$	61,640	$	61,665	$	63,228
2014			23,342		62,414		71,144		76,060		77,687		78,067		78,029		77,728		77,894
2015					75,458		118,396		148,887		159,482		164,637		158,293		158,537		159,054
2016							33,236		94,121		97,918		103,202		111,039		113,300		114,432
2017									27,456		124,220		155,139		162,933		177,737		181,029
2018											29,654		107,172		151,632		166,598		174,778
2019													42,919		123,293		149,377		161,573
2020															100,927		207,061		242,844
2021																	135,815		269,481
2022																			142,938
									Total										1,587,251
									All outstanding liabilities before 2013, net of reinsurance										5,765
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	1,010,604

Marine and aviation ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	38,167	$	36,765	$	35,669	$	34,293	$	34,207	$	33,453	$	33,001	$	29,434	$	26,728	$	25,695	$	1,012	N/A
2014			30,566		28,757		26,995		25,297		23,302		22,919		21,698		21,651		18,511		800		N/A
2015					33,134		37,019		31,499		31,373		30,423		28,120		27,299		25,008		1,514		N/A
2016							27,258		22,625		23,448		19,122		16,834		14,896		11,952		4,080		N/A
2017									28,590		26,165		23,613		20,749		19,842		17,329		4,178		N/A
2018											27,613		25,680		24,058		24,192		21,052		3,738		N/A
2019													48,383		54,684		60,321		60,635		5,574		N/A
2020															82,716		75,695		79,338		28,621		N/A
2021																	110,129		95,586		51,391		N/A
2022																			125,685		99,917		N/A
																	Total		$	480,791
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	4,751	$	13,054	$	17,678	$	20,580	$	21,557	$	22,803	$	23,176	$	22,941	$	22,912	$	23,648
2014			4,005		7,795		11,335		12,209		14,368		14,794		15,650		15,729		17,084
2015					(6)		13,321		18,852		20,623		22,318		21,971		22,114		22,297
2016							(7,371)		(1,739)		445		3,169		5,764		6,656		7,028
2017									1,650		6,433		9,249		10,897		11,488		11,817
2018											1,993		6,817		11,021		13,332		13,923
2019													10,537		21,261		28,680		34,637
2020															9,096		26,129		42,203
2021																	8,407		24,108
2022																			12,101
									Total										208,846
									All outstanding liabilities before 2013, net of reinsurance										17,999
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	289,944

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Other specialty ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	304,905	$	280,398	$	269,105	$	267,106	$	266,970	$	264,418	$	263,713	$	257,960	$	255,453	$	254,380	$	4,327	N/A
2014			328,056		308,074		310,153		303,589		298,357		299,789		295,270		289,460		287,941		6,034		N/A
2015					271,235		269,237		267,079		263,826		263,985		261,158		250,103		248,848		6,340		N/A
2016							313,982		310,907		303,432		295,116		301,277		296,251		293,571		8,371		N/A
2017									382,884		375,347		357,762		357,212		355,763		351,478		22,234		N/A
2018											402,372		395,484		390,135		413,116		408,905		32,668		N/A
2019													414,049		393,864		387,810		383,491		38,889		N/A
2020															579,367		511,136		506,164		57,946		N/A
2021																	589,452		590,091		148,264		N/A
2022																			924,130		601,334		N/A
																	Total		$	4,248,999
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	81,609	$	155,936	$	188,651	$	209,775	$	222,292	$	229,228	$	237,023	$	237,559	$	240,669	$	243,881
2014			92,743		181,222		223,243		240,680		250,427		263,123		266,898		270,529		271,712
2015					80,453		157,176		190,699		204,444		216,683		227,879		230,640		231,384
2016							103,649		196,496		231,761		249,699		265,763		271,609		277,028
2017									130,150		245,165		285,299		299,405		312,273		322,863
2018											124,996		265,000		303,141		323,868		340,061
2019													116,762		204,625		267,972		293,260
2020															129,621		285,729		361,031
2021																	146,503		300,025
2022																			175,834
									Total										2,817,079
									All outstanding liabilities before 2013, net of reinsurance										13,001
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	1,444,921

The following table presents the average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance, as of December 31, 2022:

	Average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance
	Year 1		Year 2		Year 3		Year 4		Year 5		Year 6		Year 7		Year 8		Year 9		Year 10
Casualty	2.8	%	7.8	%	12.4	%	11.3	%	9.5	%	8.2	%	7.5	%	5.0	%	3.8	%	4.7	%
Property catastrophe	41.7	%	27.3	%	49.4	%	(115.6)	%	(10.7)	%	4.1	%	1.7	%	1.7	%	(0.5)	%	0.1	%
Property excluding property catastrophe	27.0	%	37.4	%	13.2	%	5.6	%	4.0	%	0.6	%	2.4	%	0.4	%	0.1	%	2.5	%
Marine and aviation	4.5	%	28.8	%	18.3	%	10.9	%	8.4	%	3.0	%	2.4	%	0.1	%	3.6	%	2.9	%
Other specialty	29.9	%	29.9	%	13.1	%	6.0	%	4.4	%	3.3	%	1.8	%	0.6	%	0.8	%	1.3	%

Mortgage Segment

The Company’s mortgage segment includes (1) U.S. primary mortgage insurance (2) U.S. credit risk transfer and other, and (3) international mortgage insurance and reinsurance. The latter two categories along with second lien and student loan exposures are excluded on the basis of insignificance for the purposes of presenting disclosures related to short duration contracts.

For primary mortgage insurance business, the Company establishes case reserves for loans that have been reported as delinquent by loan servicers as well as those that are delinquent but not reported (IBNR reserves). The Company also reserves for the expenses of adjusting claims related to these delinquencies. The trigger that creates a case reserve estimate is that an insured loan is reported to us as being two payments in arrears. The actuarial reviews and documentation created in the reserving process are completed in accordance with generally accepted actuarial standards.

The selected assumptions reflect actuarial judgment based on the analysis of historical data and experience combined with information concerning current underwriting, economic, judicial, regulatory and other influences on ultimate claim settlements.

Because the reserving process requires the Company to forecast future conditions, it is inherently uncertain and requires significant judgment and estimation. The use of different estimates would result in the establishment of different reserve levels. Additionally, changes in estimates are likely to occur from period to period as economic conditions change, and the ultimate liability may vary significantly from the estimates used. Major risk factors include (but are not limited to) changes in home prices and borrower equity, which can limit the borrower’s ability to sell the property and satisfy the outstanding loan balance, and changes in unemployment, which can affect the borrower’s income and ability to make mortgage payments. The unique nature of the COVID-19 pandemic, with no historical

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precedent, adds further uncertainty to current reserve estimates.

The lead actuarial methodology used by the Company is a frequency-severity method based on the inventory of pending delinquencies. Each month the loan servicers report the delinquency status of each insured loan. Using the frequency-severity method allows the Company to take advantage of its knowledge of the number of delinquent loans and the coverage provided (“risk size”) on those loans by directly relating the reserves to these amounts. The delinquencies are grouped into homogeneous cohorts for analysis, reflecting the age of delinquency. A claim rate is then developed for each cohort which represents the frequency with which the delinquencies become claims. The claim frequency rates are based on an analysis of the patterns of emerging cure counts and claim counts, the foreclosure status of the pending delinquencies, the product and geographical mix of the delinquencies and our view of future economic and claim conditions, which include trends in home prices and unemployment. Claim rates can vary materially by age of delinquency, depending on the mix of delinquencies and economic conditions.

Claim size severity estimates are determined by examining the risk sizes on the delinquent loans and estimating the portion of risk that will be paid, as well as any expenses. This is done based on a review of historical development patterns, an assessment of economic conditions and the level of equity the borrowers may have in their homes, as well as considering economic conditions and loss mitigation opportunities. Mortgage insurance is generally not subject to large claim sizes, as with some other lines of insurance. A claim size over $250,000 is rare, and this helps reduce the volatility of claim size estimates.

The claim rate and claim size assumptions generate case reserves for the population of reported delinquencies. The reserve for unreported delinquencies (included in IBNR reserves) is estimated by looking at historical patterns of reporting. Claim rates and claim sizes can then be assigned to estimated unreported delinquencies using assumptions made in the establishment of case reserves.

Mortgage insurance Loss Reserves are short-tail, in the sense that the vast majority of delinquencies are resolved within two years of being reported. Due to the forbearances and foreclosure moratoriums associated with COVID-19, settlement timelines have been extended. While reserves are initially analyzed by reserve cohort, as described above, they are also rolled up by underwriting year to ensure that reserve assumptions are consistent with the performance of the underwriting year. The accuracy of prior reserve assumptions is also checked in hindsight to determine if adjustments to the assumptions are needed.

Loss Reserves for the Company’s mortgage reinsurance business and GSE credit risk sharing transactions are comprised of case reserves and IBNR reserves. The Company’s mortgage reinsurance operations receive reports of delinquent loans and claims notices from ceding companies and record case reserves based upon the amount of reserves recommended by the ceding company. In addition, specific claim and delinquency information reported by ceding companies is used in the process of estimating IBNR reserves.

ARCH CAPITAL 131 2022 FORM 10-K

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

The following table presents information on the mortgage segment’s short-duration insurance contracts:

U.S. primary mortgage insurance ($000’s except claim count)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims	Cumulative number of paid claims
Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	469,311	$	419,668	$	411,793	$	405,809	$	395,693	$	393,149	$	390,987	$	391,062	$	391,324	$	390,299	2	9,474
2014			316,095		297,151		279,434		266,027		265,992		261,091		262,682		262,829		260,554		4	6,311
2015					222,790		197,238		198,001		194,677		189,235		190,913		190,560		188,649		1	4,573
2016							183,556		170,532		148,715		140,608		142,392		141,657		137,415		—	3,445
2017									179,376		132,220		107,255		108,181		109,242		102,005		(1)	2,516
2018											132,318		96,357		89,120		87,962		71,976		(4)	1,718
2019													108,424		119,253		110,362		63,485		74	1,002
2020															420,003		373,533		78,334		476	299
2021																	144,375		77,212		379	72
2022																			173,327		2,147	7
															Total				$	1,543,256
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	41,447		203,957		308,956		353,189		373,909		382,200		386,853		387,894		387,879		388,036
2014			20,099		129,159		201,925		233,879		247,038		254,175		256,285		256,875		257,232
2015					16,159		92,431		151,222		171,337		180,321		183,472		184,025		184,955
2016							11,462		72,201		113,357		127,286		131,161		131,717		132,387
2017									8,622		48,112		78,650		87,317		89,756		91,645
2018											3,966		31,478		50,135		55,853		58,687
2019													2,899		20,105		29,102		34,178
2020															1,040		4,144		7,740
2021																	469		1,687
2022																			176
																			1,156,723
									All outstanding liabilities before 2013, net of reinsurance										10,585
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	397,118

The following table presents the average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance, as of December 31, 2022:

Average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance
	Year 1		Year 2		Year 3		Year 4		Year 5		Year 6		Year 7		Year 8		Year 9		Year 10
U.S. Primary	5.6	%	30.9	%	23.8	%	9.8	%	4.0	%	1.8	%	0.7	%	0.3	%	0.1	%	—	%

ARCH CAPITAL 132 2022 FORM 10-K

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

The following table represents a reconciliation of the disclosures of net incurred and paid loss development tables to the reserve for losses and loss adjustment expenses at December 31, 2022:

	December 31, 2022
Net outstanding liabilities
Insurance
Property, energy, marine and aviation	$	750,461
Third party occurrence business	3,184,995
Third party claims-made business	1,991,302
Multi-line and other specialty	1,215,721
Reinsurance
Casualty	2,323,825
Property catastrophe	535,158
Property excluding property catastrophe	1,010,604
Marine and aviation	289,944
Other specialty	1,444,921
Mortgage
U.S. primary	397,118
Other short duration lines not included in disclosures	301,222
Total for short duration lines	13,445,271
Unpaid losses and loss adjustment expenses recoverable
Insurance
Property, energy, marine and aviation	423,740
Third party occurrence business	1,761,871
Third party claims-made business	995,921
Multi-line and other specialty	173,051
Reinsurance
Casualty	684,663
Property catastrophe	595,740
Property excluding property catastrophe	206,867
Marine and aviation	186,416
Other specialty	656,130
Mortgage
U.S. primary	37,531
Other short duration lines not included in disclosures (1)	560,642
Intercompany eliminations	(3,747)
Total for short duration lines	6,278,825
Lines other than short duration	102,283
Discounting	(60,536)
Unallocated claims adjustment expenses	266,100
	307,847
Total gross reserves for losses and loss adjustment expenses	$	20,031,943

(1)    Includes unpaid loss and loss adjustment expenses recoverable of $280.2 million related to the loss portfolio transfer reinsurance agreements.

7.    Allowance for Expected Credit Losses

Premiums Receivable

The following table provides a roll forward of the allowance for expected credit losses of the Company’s premium receivables:

Year Ended December 31, 2022	Premium Receivables, Net of Allowance		Allowance for Expected Credit Losses
Balance at beginning of period	$	2,633,280	$	39,958
Change for provision of expected credit losses (1)			(4,556)
Balance at end of period	$	3,624,777	$	35,402
Year Ended December 31, 2021
Balance at beginning of period	$	2,064,586	$	37,781
Change for provision of expected credit losses (1)			2,177
Balance at end of period	$	2,633,280	$	39,958

(1) Amounts deemed uncollectible are written-off in operating expenses. For the 2022 and 2021 periods, amounts written off totaled $11.4 million and $3.8 million, respectively.

Reinsurance Recoverables

The Company monitors the financial condition of its reinsurers and attempts to place coverages only with substantial, financially sound carriers. Although the Company has not experienced any material credit losses to date, an inability of its reinsurers or retrocessionaires to meet their obligations to it over the relevant exposure periods for any reason could have a material adverse effect on its financial condition and results of operations.

The following table provides a roll forward of the allowance for expected credit losses of the Company’s reinsurance recoverables:

Year Ended December 31, 2022	Reinsurance Recoverables, Net of Allowance		Allowance for Expected Credit Losses
Balance at beginning of period	$	5,880,735	$	13,230
Change for provision of expected credit losses			8,314
Balance at end of period	$	6,563,654	$	21,544
Year Ended December 31, 2021
Balance at beginning of period	$	4,500,802	$	11,636
Change for provision of expected credit losses			1,594
Balance at end of period	5,880,735		$	13,230

ARCH CAPITAL 133 2022 FORM 10-K

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums) at December 31, 2022 and 2021:

	December 31,
	2022			2021
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	$	6,563,654		$	5,880,735
% due from carriers with A.M. Best rating of “A-” or better	68.8		%	69.7		%
% due from all other rated carriers	0.1		%	0.1		%
% due from all other carriers with no A.M. Best rating (1)	31.1		%	30.2		%
Largest balance due from any one carrier as % of total shareholders’ equity	9.0		%	6.7		%

(1)    At December 31, 2022 and 2021 period, over 95% and 91% of such amount is collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other, respectively.

Contractholder Receivables

The following table provides a roll forward of the allowance for expected credit losses of the Company’s contractholder receivables:

Year Ended December 31, 2022	Contractholder Receivables, Net of Allowance		Allowance for Expected Credit Losses
Balance at beginning of period	$	1,828,691	$	3,437
Change for provision of expected credit losses			(746)
Balance at end of period	$	1,731,293	$	2,691
Year Ended December 31, 2021
Balance at beginning of period	$	1,986,924	$	8,638
Change for provision of expected credit losses			(5,201)
Balance at end of period	1,828,691		$	3,437

8.    Reinsurance

In the normal course of business, the Company’s insurance subsidiaries cede a portion of their premium through pro rata and excess of loss reinsurance agreements on a treaty or facultative basis to third parties. The Company’s reinsurance subsidiaries participate in “common account” retrocessional arrangements for certain pro rata treaties. Such arrangements reduce the effect of individual or aggregate losses to all companies participating on such treaties, including the reinsurers, such as the Company’s reinsurance subsidiaries, and the ceding company. In addition, the Company’s reinsurance subsidiaries may purchase retrocessional coverage as part of their risk management program. The Company’s mortgage subsidiaries cede a portion of their premium through quota share arrangements and enter into various aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies. Reinsurance recoverables are recorded as assets, predicated on the reinsurers’ ability to meet their obligations under the reinsurance agreements. If the reinsurers are unable to satisfy their obligations under the agreements, the Company’s insurance or reinsurance subsidiaries would be liable for such defaulted amounts.

The effects of reinsurance on the Company’s written and earned premiums and losses and loss adjustment expenses with unaffiliated reinsurers were as follows:

	Year Ended December 31,
	2022		2021		2020
Premiums Written
Direct	$	8,540,787	$	7,706,832	$	6,553,910
Assumed	6,785,660		5,045,655		3,534,158
Ceded	(4,249,258)		(3,734,150)		(2,650,352)
Net	$	11,077,189	$	9,018,337	$	7,437,716
Premiums Earned
Direct	$	8,057,635	$	7,149,794	$	6,361,451
Assumed	5,767,738		4,333,873		3,213,873
Ceded	(4,147,296)		(3,401,369)		(2,583,389)
Net	$	9,678,077	$	8,082,298	$	6,991,935
Losses and Loss Adjustment Expenses
Direct	$	3,990,768	$	4,266,758	$	4,392,392
Assumed	3,559,133		2,826,820		2,204,323
Ceded	(2,522,384)		(2,508,775)		(1,907,116)
Net	$	5,027,517	$	4,584,803	$	4,689,599

ARCH CAPITAL 134 2022 FORM 10-K

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

Bellemeade Re

The Company has entered into various aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda (the “Bellemeade Agreements”). For the respective coverage periods, the Company will retain the first layer of the respective aggregate losses and the special purpose reinsurance companies will provide second layer coverage up to the outstanding coverage amount. The Company will then retain losses in excess of the outstanding coverage limit. The aggregate excess of loss reinsurance coverage decreases over a ten-year period as the underlying covered mortgages amortize. See note 12, “Variable Interest Entity and Noncontrolling Interests.”

The following table summarizes the respective coverages and retentions at December 31, 2022:

			December 31, 2022
Bellemeade Entities (Issue Date)	Initial Coverage at Issuance		Current Coverage		Remaining Retention, Net
2017-1 Ltd. (1)	$	368,114	$	36,679	$	142,461
2018-1 Ltd. (2)	374,460		89,698		143,592
2018-3 Ltd. (3)	506,110		199,237		152,861
2019-1 Ltd. (4)	341,790		107,880		118,908
2019-2 Ltd. (5)	621,022		325,462		191,550
2019-3 Ltd. (6)	700,920		222,977		208,931
2019-4 Ltd. (7)	577,267		266,124		142,564
2020-2 Ltd. (8)	449,167		105,110		237,709
2020-3 Ltd. (9)	451,816		250,971		161,544
2020-4 Ltd. (10)	337,013		101,729		138,131
2021-1 Ltd. (11)	643,577		503,267		153,525
2021-2 Ltd. (12)	616,017		535,461		138,524
2021-3 Ltd. (13)	639,391		616,959		132,492
2022-1 Ltd. (14)	316,760		316,760		143,577
2022-2 Ltd. (15)	327,165		327,165		217,436
Total	$	7,270,589	$	4,005,479	$	2,423,805

(1)    Issued in October 2017, covering in-force policies issued between January 1, 2017 and June 30, 2017.

(2)    Issued in April 2018, covering in-force policies issued between July 1, 2017 and December 31, 2017.

(3)    Issued in October 2018, covering in-force policies issued between January 1, 2018 and June 30, 2018.

(4)    Issued in March 2019, covering in-force policies primarily issued between 2005 to 2008 under United Guaranty Residential Insurance Company (“UGRIC”); as well as policies issued through 2015 under both UGRIC and Arch Mortgage Insurance Company.

(5)    Issued in April 2019, covering in-force policies issued between July 1, 2018 and December 31, 2018.

(6)    Issued in July 2019, covering in-force policies issued in 2016.

(7)    Issued in October 2019, covering in-force policies issued between January 1, 2019 and June 30, 2019.

(8)    Issued in September 2020, covering in-force policies issued between January 1, 2020 and May 31, 2020. $423 million was directly funded by Bellemeade 2020-2 Ltd. with an additional $26 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(9)    Issued in November 2020, covering in-force policies issued between June 1, 2020 and August 31, 2020. $418 million was directly funded by Bellemeade 2020-3 Ltd. with an additional $34 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(10)    Issued in December 2020, covering in-force policies issued between July 1, 2019 and December 31, 2019. $321 million was directly funded by Bellemeade 2020-4 Ltd. with an additional $16 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(11) Issued in March 2021, covering in-force policies issued between September 1, 2020 and November 30, 2020. $580 million was directly funded by Bellemeade Re 2021-1 Ltd. with an additional $64 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(12) Issued in June 2021, covering in-force policies issued between December 1, 2020 and March 31, 2021. $523 million was directly funded by Bellemeade Re 2021-2 Ltd. via insurance-linked notes, with an additional $93 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(13) Issued in September 2021, covering in-force policies issued between April 1, 2021 and June 30, 2021. $508 million was directly funded by Bellemeade Re 2021-3 Ltd. via insurance-linked notes, with an additional $131 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(14) Issued in January 2022, covering in-force policies issued between July 1, 2021 and November 30, 2021. $284 million was directly funded by Bellemeade Re 2022-1 Ltd. via insurance-linked notes, with an additional $33 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(15) Issued in September 2022, covering in-force policies issued between November 1, 2021 and June 30, 2022. $201 million was directly funded by Bellemeade Re 2022-2 Ltd. via insurance-linked notes, with an additional $126 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

ARCH CAPITAL 135 2022 FORM 10-K

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

9.    Investment Information

Available For Sale Investments

The following table summarizes the fair value and cost or amortized cost of the Company’s securities classified as available for sale:

	Estimated Fair Value		Gross Unrealized Gains		Gross Unrealized Losses		Allowance for Expected Credit Losses		Cost or Amortized Cost
December 31, 2022
Fixed maturities:
Corporate bonds	$	8,020,128	$	55,468	$	(781,353)	$	(29,950)	$	8,775,963
Mortgage backed securities	795,391		4,933		(86,587)		2		877,043
Municipal bonds	419,166		3,149		(33,360)		(100)		449,477
Commercial mortgage backed securities	1,047,275		608		(57,667)		(3,415)		1,107,749
U.S. government and government agencies	5,161,193		14,891		(342,963)		—		5,489,265
Non-U.S. government securities	2,312,819		8,870		(237,846)		(1,882)		2,543,677
Asset backed securities	1,926,817		761		(106,623)		(6,010)		2,038,689
Total	19,682,789		88,680		(1,646,399)		(41,355)		21,281,863
Short-term investments	1,331,662		554		(1,888)		—		1,332,996
Total	$	21,014,451	$	89,234	$	(1,648,287)	$	(41,355)	$	22,614,859
December 31, 2021
Fixed maturities:
Corporate bonds	$	6,553,333	$	104,170	$	(69,194)	$	(2,037)	$	6,520,394
Mortgage backed securities	408,477		2,825		(5,410)		(48)		411,110
Municipal bonds	404,666		18,724		(1,409)		(2)		387,353
Commercial mortgage backed securities	1,046,484		1,740		(3,117)		(6)		1,047,867
U.S. government and government agencies	4,772,764		10,076		(45,967)		—		4,808,655
Non-U.S. government securities	2,120,294		54,048		(34,749)		(82)		2,101,077
Asset backed securities	2,692,091		6,540		(11,108)		(708)		2,697,367
Total	17,998,109		198,123		(170,954)		(2,883)		17,973,823
Short-term investments	1,734,716		568		(590)		—		1,734,738
Total	$	19,732,825	$	198,691	$	(171,544)	$	(2,883)	$	19,708,561

ARCH CAPITAL 136 2022 FORM 10-K

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

The following table summarizes, for all available for sale securities in an unrealized loss position, the fair value and gross unrealized loss by length of time the security has been in a continual unrealized loss position:

	Less than 12 Months				12 Months or More				Total
	Estimated Fair Value		Gross Unrealized Losses		Estimated Fair Value		Gross Unrealized Losses		Estimated Fair Value		Gross Unrealized Losses
December 31, 2022
Fixed maturities:
Corporate bonds	$	4,822,624	$	(393,112)	$	2,559,399	$	(388,241)	$	7,382,023	$	(781,353)
Mortgage backed securities	545,844		(51,673)		154,154		(34,914)		699,998		(86,587)
Municipal bonds	363,936		(29,924)		16,282		(3,436)		380,218		(33,360)
Commercial mortgage backed securities	598,392		(34,899)		445,175		(22,768)		1,043,567		(57,667)
U.S. government and government agencies	3,556,676		(197,259)		1,442,542		(145,704)		4,999,218		(342,963)
Non-U.S. government securities	1,702,973		(153,587)		541,652		(84,259)		2,244,625		(237,846)
Asset backed securities	1,148,220		(65,189)		512,376		(41,434)		1,660,596		(106,623)
Total	12,738,665		(925,643)		5,671,580		(720,756)		18,410,245		(1,646,399)
Short-term investments	236,735		(1,888)		—		—		236,735		(1,888)
Total	$	12,975,400	$	(927,531)	$	5,671,580	$	(720,756)	$	18,646,980	$	(1,648,287)
December 31, 2021
Fixed maturities:
Corporate bonds	$	3,639,582	$	(63,938)	$	98,867	$	(5,256)	$	3,738,449	$	(69,194)
Mortgage backed securities	222,176		(3,545)		46,809		(1,865)		268,985		(5,410)
Municipal bonds	26,665		(385)		16,361		(1,024)		43,026		(1,409)
Commercial mortgage backed securities	675,603		(2,805)		5,908		(312)		681,511		(3,117)
U.S. government and government agencies	4,211,621		(44,180)		33,373		(1,787)		4,244,994		(45,967)
Non-U.S. government securities	1,511,301		(31,983)		62,957		(2,766)		1,574,258		(34,749)
Asset backed securities	1,667,002		(9,853)		33,082		(1,255)		1,700,084		(11,108)
Total	11,953,950		(156,689)		297,357		(14,265)		12,251,307		(170,954)
Short-term investments	284,733		(590)		—		—		284,733		(590)
Total	$	12,238,683	$	(157,279)	$	297,357	$	(14,265)	$	12,536,040	$	(171,544)

At December 31, 2022, on a lot level basis, approximately 9,810 security lots out of a total of approximately 12,590 security lots were in an unrealized loss position and the largest single unrealized loss from a single lot in the Company’s fixed maturity portfolio was $7.2 million. The Company believes that such securities were temporarily impaired at December 31, 2022. At December 31, 2021, on a lot level basis, approximately 4,700 security lots out of a total of approximately 10,240 security lots were in an unrealized loss position and the largest single unrealized loss from a single lot in the Company’s fixed maturity portfolio was $1.1 million.

ARCH CAPITAL 137 2022 FORM 10-K

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

The contractual maturities of the Company’s fixed maturities are shown in the following table. Expected maturities, which are management’s best estimates, will differ from contractual maturities because borrowers may have the right to call or prepay obligations with or without call or prepayment penalties.

	December 31, 2022				December 31, 2021
Maturity	Estimated Fair Value		Amortized Cost		Estimated Fair Value		Amortized Cost
Due in one year or less	$	510,669	$	536,962	$	300,889	$	299,772
Due after one year through five years	11,014,753		11,714,427		8,355,255		8,339,387
Due after five years through 10 years	3,984,497		4,527,447		4,689,155		4,684,393
Due after 10 years	403,387		479,546		505,758		493,927
	15,913,306		17,258,382		13,851,057		13,817,479
Mortgage backed securities	795,391		877,043		408,477		411,110
Commercial mortgage backed securities	1,047,275		1,107,749		1,046,484		1,047,867
Asset backed securities	1,926,817		2,038,689		2,692,091		2,697,367
Total	$	19,682,789	$	21,281,863	$	17,998,109	$	17,973,823

Equity Securities, at Fair Value

At December 31, 2022, the Company held $860.0 million of equity securities, at fair value, compared to $1.8 billion at December 31, 2021.

Net Investment Income

The components of net investment income were derived from the following sources:

	Year Ended December 31,
	2022		2021		2020
Fixed maturities	$	468,659	$	330,061	$	412,481
Term loans	2,038		34,843		84,149
Equity securities	22,497		42,396		28,958
Short-term investments	29,519		6,928		10,840
Other (1)	44,609		62,895		72,395
Gross investment income	567,322		477,123		608,823
Investment expenses	(70,775)		(88,005)		(89,215)
Net investment income	$	496,547	$	389,118	$	519,608

(1)    Includes income distributions from investment funds and other items

Net Realized Gains (Losses)

Net realized gains (losses) were as follows:

	Year Ended December 31,
	2022		2021		2020
Available for sale securities:
Gross gains on investment sales	$	81,161	$	313,886	$	595,941
Gross losses on investment sales	(317,150)		(156,791)		(117,282)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	(70,951)		7,953		15,881
Other investments	(19,498)		116,781		13,656
Equity securities	(4,520)		13,028		14,629
Short-term investments	(3,012)		601		2,279
Equity securities, at fair value :
Net realized gains (losses) on securities sold	74,922		122,606		26,849
Net unrealized gains (losses) on equity securities still held at reporting date	(267,927)		48,746		102,394
Allowance for credit losses:
Investments related	(43,909)		(2,100)		(3,597)
Underwriting related	(13,274)		1,062		(10,007)
Net impairment losses	—		—		(533)
Derivative instruments (1)	(75,023)		(32,390)		179,675
Other (2)	(3,553)		(53,537)		3,575
Net realized gains (losses)	$	(662,734)	$	379,845	$	823,460

(1)    See note 11, “Derivative Instruments” for information on the Company’s derivative instruments.

(2)    2021 period reflected $33.1 million of losses related to the Company’s

deconsolidation of Somers.

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

Other Investments

The following table summarizes the Company’s other investments and other investable assets:

	December 31,
	2022		2021
Fixed maturities	$	554,120	$	416,698
Other investments	1,043,184		1,432,553
Short-term investments	33,101		97,806
Equity securities	13,792		26,493
Total other investments	$	1,644,197	$	1,973,550

The following table summarizes the Company’s other investments, as detailed in the previous table, by strategy:

	December 31,
	2022		2021
Lending	405,871		536,345
Investment grade fixed income	271,143		147,810
Term loan investments	163,941		484,950
Private equity	123,266		91,126
Energy	22,627		81,692
Credit related funds	56,336		70,278
Infrastructure	—		20,352
Total	$	1,043,184	$	1,432,553

Investments Accounted For Using the Equity Method

The following table summarizes the Company’s investments accounted for using the equity method, by strategy:

	December 31,
	2022		2021
Credit related funds	$	1,135,818	$	1,022,334
Private equity	916,534		436,042
Real estate	535,238		396,395
Lending	531,339		376,649
Infrastructure	245,246		230,070
Equities	169,156		395,090
Fixed income	130,062		101,890
Energy	110,917		119,141
Total	$	3,774,310	$	3,077,611

In applying the equity method, investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the fair value of the underlying securities in the funds). Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds.

Equity in Net Income (Loss) of Investments Accounted For Using the Equity Method

The Company recorded equity in net income related to investments accounted for using the equity method of $115.9 million for 2022, compared to $366.4 million for 2021 and $146.7 million for 2020. In applying the equity method, investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the market value of the underlying securities in the funds).

A summary of financial information for the Company’s investment funds and operating affiliates accounted for using the equity method is as follows:

	December 31,
	2022		2021
Invested assets	$	74,960,738	$	58,508,009
Total assets	88,062,991		69,648,905
Total liabilities	27,553,307		17,944,325
Net assets	$	60,509,684	$	51,704,580

	Year Ended December 31,
	2022		2021		2020
Total revenues	$	12,305,082	$	11,785,949	$	5,762,098
Total expenses	5,374,047		3,238,606		1,656,029
Net income (loss)	$	6,931,035	$	8,547,343	$	4,106,069

Certain of the Company’s other investments and investments accounted for using the equity method are in investment funds for which the Company has the option to redeem at agreed upon values as described in each investment fund’s subscription agreement. Depending on the terms of the various subscription agreements, investments in investment funds may be redeemed daily, monthly, quarterly or on other terms. Two common redemption restrictions which may impact the Company’s ability to redeem these investment funds are gates and lockups. A gate is a suspension of redemptions which may be implemented by the general partner or investment manager of the fund in order to defer, in whole or in part, the redemption request in the event the aggregate amount of redemption requests exceeds a predetermined percentage of the investment fund's net assets which may otherwise hinder the general partner or investment manager's ability to liquidate holdings in an orderly fashion in order to generate the cash necessary to fund extraordinarily large redemption payouts. A lockup period is the initial amount of time an investor is contractually required to hold the security before having the ability to redeem. If the investment funds are eligible to be redeemed, the time to redeem such fund can take weeks or months following the notification.

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Limited Partnership Interests

In the normal course of its activities, the Company invests in limited partnerships as part of its overall investment strategy. Such amounts are included in ‘investments accounted for using the equity method’ and ‘investments accounted for using the fair value option.’ The Company determined that these limited partnership interests represented variable interests in the funds. The Company’s maximum exposure to loss with respect to these investments is limited to the investment carrying amounts reported in the Company’s consolidated balance sheet and any unfunded commitment.

The following table summarizes investments in limited partnership interests where the Company has a variable interest by balance sheet item:

	December 31,
	2022		2021
Investments accounted for using the equity method (1)	$	3,774,310	$	3,077,611
Investments accounted for using the fair value option (2)	130,466		170,595
Total	$	3,904,776	$	3,248,206

(1)     Aggregate unfunded commitments were $2.6 billion at December 31, 2022, consistent with $2.6 billion at December 31, 2021.

(2)    Aggregate unfunded commitments were $16.7 million at December 31, 2022, compared to $18.8 million at December 31, 2021.

Investments in Operating Affiliates

Investments in which the Company has significant influence over the operating and financial policies are classified as ‘investments in operating affiliates’ on the Company’s balance sheets and are accounted for under the equity method. Such investments primarily include the Company’s investment in Coface SA (“Coface”), Greysbridge and Premia. Investments in Coface and Premia are generally recorded on a three month lag, while the Company’s investment in Greysbridge is not recorded on a lag.

In 2021, the Company completed the share purchase agreement with Natixis to purchase 29.5% of the common

equity of Coface, a France-based leader in the global trade credit insurance market. The consideration paid was €9.95 per share, or an aggregate €453 million (approximately $546 million) including related fees. Income (loss) from operating affiliates reflected a one-time gain of $74.5 million realized from the acquisition. As a result of equity method accounting rules, approximately $36 million of additional gain was deferred and will generally be recognized over the next five years. As of December 31, 2022, the Company owned approximately 29.9% of the issued shares of Coface, or 30.1% excluding treasury shares, with a carrying value of $562.9 million, compared to $630.5 million at December 31, 2021.

In July 2021, the Company announced the completion of the previously disclosed acquisition of Somers by Greysbridge for a cash purchase price of $35.00 per common share.

Effective July 1, 2021, Somers is wholly owned by Greysbridge, and Greysbridge is owned 40% by the Company, 30% by certain investment funds managed by Kelso and 30% by certain investment funds managed by Warburg. At December 31, 2022 the Company’s carrying value in Greysbridge was $305.6 million, compared to $375.7 million at December 31, 2021. The Company’s carrying value in Greysbridge at December 31, 2021 reflected aggregate purchase price of $278.9 million along with income (loss) from operating affiliates, which included a one-time gain of $95.7 million recognized from the acquisition. In addition, the ‘net realized gains (losses)’ line on the Company’s consolidated statements of income included a $33.1 million loss as a result of deconsolidation of Somers in the Company’s financial statements following the close of the transaction. See note 12, “Variable Interest Entity and Noncontrolling Interests.”

The Company recorded income from operating affiliates of $73.9 million for 2022, compared to income of $264.7 million for 2021 and $16.8 million for 2020.

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Allowance for Expected Credit Losses

The following table provides a roll forward of the allowance for expected credit losses of the Company’s securities classified as available for sale:

Year Ended December 31, 2022	Structured Securities (1)		Municipal Bonds		Non-U.S. Government Securities		Corporate Bonds		Total
Balance at beginning of period	$	802	$	2	$	82	$	1,997	$	2,883
Additions for current-period provision for expected credit losses	14,184		359		1,616		39,477		55,636
Additions (reductions) for previously recognized expected credit losses	(3,184)		(261)		275		(8,619)		(11,789)
Reductions due to disposals	(2,379)		—		(91)		(2,905)		(5,375)
Balance at end of period	$	9,423	$	100	$	1,882	$	29,950	$	41,355
Year Ended December 31, 2021
Balance at beginning of period	$	1,490	$	11	$	—	$	896	$	2,397
Additions for current-period provision for expected credit losses	602		—		82		2,858		3,542
Additions (reductions) for previously recognized expected credit losses	(847)		(9)		—		(402)		(1,258)
Reductions due to disposals (2)	(443)		—		—		(1,355)		(1,798)
Balance at end of period	$	802	$	2	$	82	$	1,997	$	2,883

(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed

(2)    Reduction for the 2021 periods primarily related to the Company’s deconsolidation of Somers.

Restricted Assets

The Company is required to maintain assets on deposit, which primarily consist of fixed maturities, with various regulatory authorities to support its underwriting operations. The Company’s subsidiaries maintain assets in trust accounts as collateral for transactions with affiliated companies and also have investments in segregated portfolios primarily to provide collateral or guarantees for letters of credit to third parties

The following table details the value of the Company’s restricted assets:

	December 31,
	2022		2021
Assets used for collateral or guarantees:
Affiliated transactions	$	4,254,398	$	4,223,955
Third party agreements	2,632,892		2,289,631
Deposits with U.S. regulatory authorities	776,342		798,100
Other (1)	1,037,848		938,046
Total restricted assets	$	8,701,480	$	8,249,732

(1) Primarily includes Funds at Lloyds, deposits with non-U.S. regulatory authorities and other restricted assets.

Reconciliation of Cash and Restricted Cash

The following table details reconciliation of cash and restricted cash within the Consolidated Balance Sheets:

	December 31,
	2022		2021		2020
Cash	$	855,118	$	858,668	$	906,448
Restricted cash (included in ‘other assets’)	418,210		456,103		384,096
Cash and restricted cash	$	1,273,328	$	1,314,771	$	1,290,544

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10.    Fair Value

Accounting guidance regarding fair value measurements addresses how companies should measure fair value when they are required to use a fair value measure for recognition or disclosure purposes under GAAP and provides a common definition of fair value to be used throughout GAAP. It defines fair value as the price that would be received to sell an asset or paid to transfer a liability in an orderly fashion between market participants at the measurement date. In addition, it establishes a three-level valuation hierarchy for the disclosure of fair value measurements. The valuation hierarchy is based upon the transparency of inputs to the valuation of an asset or liability as of the measurement date. The level in the hierarchy within which a given fair value measurement falls is determined based on the lowest level input that is significant to the measurement (Level 1 being the highest priority and Level 3 being the lowest priority).

The levels in the hierarchy are defined as follows:

Level 1:	Inputs to the valuation methodology are observable inputs that reflect quoted prices (unadjusted) for identical assets or liabilities in active markets
Level 2:	Inputs to the valuation methodology include quoted prices for similar assets and liabilities in active markets, and inputs that are observable for the asset or liability, either directly or indirectly, for substantially the full term of the financial instrument
Level 3:	Inputs to the valuation methodology are unobservable and significant to the fair value measurement

Following is a description of the valuation methodologies used for securities measured at fair value, as well as the general classification of such securities pursuant to the valuation hierarchy. The Company reviews its securities measured at fair value and discusses the proper classification of such investments with investment advisers and others.

The Company determines the existence of an active market based on its judgment as to whether transactions for the financial instrument occur in such market with sufficient frequency and volume to provide reliable pricing information. The independent pricing sources obtain market quotations and actual transaction prices for securities that have quoted prices in active markets. The Company uses quoted values and other data provided by nationally recognized independent pricing sources as inputs into its process for determining fair values of its fixed maturity investments. To validate the techniques or models used by pricing sources, the Company's review process includes, but is not limited to: (i) quantitative analysis (e.g., comparing the quarterly return for each managed portfolio to its target

benchmark, with significant differences identified and investigated); (ii) a review of the prices obtained in the pricing process and the range of resulting fair values; (iii) initial and ongoing evaluation of methodologies used by outside parties to calculate fair value; (iv) a comparison of the fair value estimates to the Company’s knowledge of the current market; (v) a comparison of the pricing services' fair values to other pricing services' fair values for the same investments; and (vi) periodic back-testing, which includes randomly selecting purchased or sold securities and comparing the executed prices to the fair value estimates from the pricing service. A price source hierarchy was maintained in order to determine which price source would be used (i.e., a price obtained from a pricing service with more seniority in the hierarchy will be used over a less senior one in all cases). The hierarchy prioritizes pricing services based on availability and reliability and assigns the highest priority to index providers. Based on the above review, the Company will challenge any prices for a security or portfolio which are considered not to be representative of fair value.

In certain circumstances, when fair values are unavailable from these independent pricing sources, quotes are obtained directly from broker-dealers who are active in the corresponding markets. Such quotes are subject to the validation procedures noted above. Of the $23.8 billion of financial assets and liabilities measured at fair value at December 31, 2022, approximately $12.6 million, or 0.1%, were priced using non-binding broker-dealer quotes. Of the $23.8 billion of financial assets and liabilities measured at fair value at December 31, 2021, approximately $7.7 million, or 0.0%, were priced using non-binding broker-dealer quotes.

Fixed maturities

The Company uses the market approach valuation technique to estimate the fair value of its fixed maturity securities, when possible. The market approach includes obtaining prices from independent pricing services, such as index providers and pricing vendors, as well as to a lesser extent quotes from broker-dealers. The independent pricing sources obtain market quotations and actual transaction prices for securities that have quoted prices in active markets. Each source has its own proprietary method for determining the fair value of securities that are not actively traded. In general, these methods involve the use of “matrix pricing” in which the independent pricing source uses observable market inputs including, but not limited to, investment yields, credit risks and spreads, benchmarking of like securities, broker-dealer quotes, reported trades and sector groupings to determine a reasonable fair value. The following describes the significant inputs generally used to determine the fair value of the Company’s fixed maturity securities by asset class:

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U.S. government and government agencies – valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The Company determined that all U.S. Treasuries would be classified as Level 1 securities due to observed levels of trading activity, the high number of strongly correlated pricing quotes received on U.S. Treasuries and other factors. The fair values of U.S. government agency securities are generally determined using the spread above the risk-free yield curve. As the yields for the risk-free yield curve and the spreads for these securities are observable market inputs, the fair values of U.S. government agency securities are classified within Level 2.

Corporate bonds – valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined using the spread above the risk-free yield curve. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. As the significant inputs used in the pricing process for corporate bonds are observable market inputs, the fair value of these securities are classified within Level 2. A small number of securities are included in Level 3 due to the lack of an available independent price source for such securities. As the significant inputs used to price these securities are unobservable, the fair value of such securities are classified as Level 3.

Mortgage-backed securities – valuations provided by independent pricing services, substantially all through pricing vendors and index providers with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models (including Option Adjusted Spread) which use spreads to determine the expected average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. The pricing services also review prepayment speeds and other indicators, when applicable. As the significant inputs used in the pricing process for mortgage-backed securities are observable market inputs, the fair value of these securities are classified within Level 2.

Municipal bonds – valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The fair values of these securities are generally determined using spreads obtained from broker-dealers who trade in the relevant security market, trade prices and the new issue market. As the significant inputs used in the pricing process for municipal bonds are observable market inputs, the fair value of these securities are classified within Level 2.

Commercial mortgage-backed securities – valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models which use spreads to determine the appropriate average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. As the significant inputs used in the pricing process for commercial mortgage-backed securities are observable market inputs, the fair value of these securities are classified within Level 2.

Non-U.S. government securities – valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The fair values of these securities are generally based on international indices or valuation models which include daily observed yield curves, cross-currency basis index spreads and country credit spreads. As the significant inputs used in the pricing process for non-U.S. government securities are observable market inputs, the fair value of these securities are classified within Level 2.

Asset-backed securities – valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models (including Option Adjusted Spread) which use spreads to determine the appropriate average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. As the significant inputs used in the pricing process for asset-backed securities are observable market inputs, the fair value of these securities are classified within Level 2. A small number of securities are included in Level 3 due to a low level of transparency on the inputs used in the pricing process.

Equity securities

The Company determined that exchange-traded equity securities would be included in Level 1 as their fair values are based on quoted market prices in active markets. Other equity securities are included in Level 2 of the valuation hierarchy. A small number of securities are included in Level 3 due to the lack of an available independent price source for such securities. As the significant inputs used to price these securities are unobservable, the fair value of such securities are classified as Level 3.

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Other investments

The Company determined that exchange-traded investments would be included in Level 1 as their fair values are based on quoted market prices in active markets. Other investments also include term loan investments for which fair values are estimated by using quoted prices of term loan investments with similar characteristics, pricing models or matrix pricing. Such investments are generally classified within Level 2. A small number of securities are included in Level 3 due to the lack of an available independent price source for such securities.

Derivative instruments

The Company’s futures contracts, foreign currency forward contracts, interest rate swaps and other derivatives trade in the over-the-counter derivative market. The Company uses the market approach valuation technique to estimate the fair value for these derivatives based on significant observable market inputs from third party pricing vendors, non-binding broker-dealer quotes and/or recent trading activity. As the significant inputs used in the pricing process for these derivative instruments are observable market inputs, the fair value of these securities are classified within Level 2.

Short-term investments

The Company determined that certain of its short-term investments held in highly liquid money market-type funds, Treasury bills and commercial paper would be included in Level 1 as their fair values are based on quoted market prices in active markets. The fair values of other short-term investments are generally determined using the spread above the risk-free yield curve and are classified within Level 2.

Residential mortgage loans

The Company’s residential mortgage loans (included in ‘other assets’ in the consolidated balance sheets) include amounts related to the Company’s whole mortgage loan purchase and sell program. Fair values of residential mortgage loans are generally determined based on market prices. As significant inputs used in pricing process for these residential mortgage loans are observable market inputs, the fair value of these securities are classified within Level 2.

Other liabilities

The Company’s other liabilities include contingent and deferred consideration liabilities related to the Company’s acquisitions. Contingent consideration liabilities are remeasured at fair value at each balance sheet date with changes in fair value recognized in ‘net realized gains (losses)’. To determine the fair value of contingent consideration liabilities, the Company estimates the future payments using an income approach based on modeled inputs which include a weighted average cost of capital. Deferred consideration liabilities are measured at fair value on the transaction date. The Company determined that contingent and deferred consideration liabilities would be included within Level 3.

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The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2022:

			Fair Value Measurement Using:
	Estimated Fair Value		Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Assets measured at fair value:
Available for sale securities:
Fixed maturities:
Corporate bonds	$	8,020,128	$	—	$	7,898,901	$	121,227
Mortgage backed securities	795,391		—		795,391		—
Municipal bonds	419,166		—		419,166		—
Commercial mortgage backed securities	1,047,275		—		1,047,275		—
U.S. government and government agencies	5,161,193		5,144,467		16,726		—
Non-U.S. government securities	2,312,819		—		2,312,819		—
Asset backed securities	1,926,817		—		1,926,817		—
Total	19,682,789		5,144,467		14,417,095		121,227
Short-term investments	1,331,662		1,197,304		134,358		—
Equity securities, at fair value	859,969		828,513		28,042		3,414
Derivative instruments (2)	148,301		—		148,301		—
Residential mortgage loans	2,283		—		2,283		—
Fair value option:
Corporate bonds	542,755		—		542,755		—
Non-U.S. government bonds	4,315		—		4,315		—
Asset backed securities	1,652		—		1,652		—
U.S. government and government agencies	5,398		5,398		—		—
Short-term investments	33,101		699		32,402		—
Equity securities	13,792		9,619		—		4,173
Other investments	196,215		—		162,956		33,259
Other investments measured at net asset value (1)	846,969
Total	1,644,197		15,716		744,080		37,432
Total assets measured at fair value	$	23,669,201	$	7,186,000	$	15,474,159	$	162,073
Liabilities measured at fair value:
Contingent consideration liabilities	$	(14,246)	$	—	$	—	$	(14,246)
Derivative instruments (2)	(75,961)		—		(75,961)		—
Total liabilities measured at fair value	$	(90,207)	$	—	$	(75,961)	$	(14,246)

(1)    In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.

(2)    See note 11, “Derivative Instruments.”

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The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2021:

			Fair Value Measurement Using:
	Estimated Fair Value		Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Assets measured at fair value:
Available for sale securities:
Fixed maturities:
Corporate bonds	$	6,553,333	$	—	$	6,553,320	$	13
Mortgage backed securities	408,477		—		408,477		—
Municipal bonds	404,666		—		404,666		—
Commercial mortgage backed securities	1,046,484		—		1,046,484		—
U.S. government and government agencies	4,772,764		4,744,517		28,247		—
Non-U.S. government securities	2,120,294		—		2,120,294		—
Asset backed securities	2,692,091		—		2,688,744		3,347
Total	17,998,109		4,744,517		13,250,232		3,360
Equity securities, at fair value	1,804,170		1,762,864		38,388		2,918
Short-term investments	1,734,716		1,052,822		681,894		—
Derivative instruments (2)	127,121		—		127,121		—
Residential mortgage loans	49,847		—		49,847		—
Fair value option:
Corporate bonds	388,546		—		388,546		—
Non-U.S. government bonds	23,785		—		23,785		—
Asset backed securities	4,367		—		4,367		—
U.S. government and government agencies	—		—		—		—
Short-term investments	97,806		528		97,278		—
Equity securities	26,493		21,745		—		4,748
Other investments	310,798		20,352		262,465		27,981
Other investments measured at net asset value (1)	1,121,755
Total	1,973,550		42,625		776,441		32,729
Total assets measured at fair value	$	23,687,513	$	7,602,828	$	14,923,923	$	39,007
Liabilities measured at fair value:
Contingent consideration liabilities	$	(16,960)	$	—	$	—	$	(16,960)
Derivative instruments (2)	(54,224)		—		(54,224)		—
Total liabilities measured at fair value	$	(71,184)	$	—	$	(54,224)	$	(16,960)

(1)    In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.

(2)    See note 11, “Derivative Instruments.”

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The following table presents a reconciliation of the beginning and ending balances for all financial assets and liabilities measured at fair value on a recurring basis using Level 3 inputs for 2022 and 2021:

			Assets										Liabilities
	Available For Sale				Fair Value Option						Fair Value
	Structured Securities (1)		Corporate Bonds		Corporate Bonds		Other Investments		Equity Securities		Equity Securities		Other Liabilities
Year Ended December 31, 2022
Balance at beginning of year	$	3,347	$	13	$	—	$	27,981	$	4,748	$	2,918	$	(16,960)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	(592)		352		—		(781)		(575)		(470)		(364)
Included in other comprehensive income	(1)		(1,095)		—		—		—		—		1,170
Purchases, issuances, sales and settlements
Purchases	—		150,013		—		12,381		—		969		—
Issuances	—		—		—		—		—		—		—
Sales	(2,051)		(5,363)		—		(3,339)		—		(3)		—
Settlements	(703)		(26,250)		—		(2,983)		—		—		1,908
Transfers in and/or out of Level 3	—		3,557		—		—		—		—		—
Balance at end of year	$	—	$	121,227	$	—	$	33,259	$	4,173	$	3,414	$	(14,246)
Year Ended December 31, 2021
Balance at beginning of year	$	3,426	$	13	$	985	$	67,103	$	68,988	$	42,015	$	(461)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	(135)		—		13		868		4,941		1,958		—
Included in other comprehensive income	133		—		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		—		13,213		—		5,718		(16,494)
Issuances	—		—		—		—		—		—		—
Sales (3)	—		—		(998)		(53,203)		(69,181)		(46,773)		—
Settlements	(77)		—		—		—		—		—		(5)
Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of year	$	3,347	$	13	$	—	$	27,981	$	4,748	$	2,918	$	(16,960)

(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

(2)    Gains or losses were included in net realized gains (losses).

(3)     Sales for the 2021 period primarily relates to the Company’s deconsolidation of Somers.

Financial Instruments Disclosed, But Not Carried, At Fair Value

The Company uses various financial instruments in the normal course of its business. The carrying values of cash, accrued investment income, receivable for securities sold, certain other assets, payable for securities purchased and certain other liabilities approximated their fair values at December 31, 2022, due to their respective short maturities. As these financial instruments are not actively traded, their respective fair values are classified within Level 2.

At December 31, 2022, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.7 billion and had a fair value of $2.4 billion. At December 31, 2021, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.7 billion and had a fair value of $3.3 billion. The fair values of the senior notes were obtained

from a third party pricing service and are based on observable market inputs. As such, the fair value of the senior notes is classified within Level 2.

Fair Value Measurements on a Non-Recurring Basis

The Company measures the fair value of certain assets on a non-recurring basis, generally quarterly, annually, or when events or changes in circumstances indicate that the carrying amount of the assets may not be recoverable. These assets include investments accounted for using the equity method, certain other investments, goodwill and intangible assets, and long-lived assets. The Company uses a variety of techniques to measure the fair value of these assets when appropriate, as described below:

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Investments accounted for using the equity method. When the Company determines that the carrying value of these assets may not be recoverable, the Company records the assets at fair value with the loss recognized in income. In such cases, the Company measures the fair value of these assets using the techniques discussed above in “—Fair Value Measurements on a Recurring Basis.”

Goodwill and Intangible Assets. The Company tests goodwill and intangible assets annually for impairment whenever events or changes in circumstances indicate the carrying amount may not be recoverable. When the Company determines goodwill and intangible assets may be impaired, the Company uses techniques including discounted expected future cash flows, to measure fair value.

Long-Lived Assets. The Company tests its long-lived assets for impairment whenever events or changes in circumstances indicate the carrying amount of a long-lived asset may not be recoverable.

11.    Derivative Instruments

The Company’s investment strategy allows for the use of derivative instruments. The Company’s derivative instruments are recorded on its consolidated balance sheets at fair value. The Company utilizes exchange traded U.S. Treasury note, Eurodollar and other futures contracts and commodity futures to manage portfolio duration or replicate investment positions in its portfolios and the Company routinely utilizes foreign currency forward contracts, currency options, index futures contracts and other derivatives as part of its total return objective. In addition, certain of the Company’s investments are managed in portfolios which incorporate the use of foreign currency forward contracts which are intended to provide an economic hedge against foreign currency movements.

In addition, the Company purchases to-be-announced mortgage backed securities (“TBAs”) as part of its investment strategy. TBAs represent commitments to purchase a future issuance of agency mortgage backed securities. For the period between purchase of a TBA and issuance of the underlying security, the Company’s position is accounted for as a derivative. The Company purchases TBAs in both long and short positions to enhance investment performance and as part of its overall investment strategy.

The following table summarizes information on the fair values and notional values of the Company’s derivative instruments:

	Estimated Fair Value
	Asset Derivatives (1)		Liability Derivatives (1)		Notional Value (2)
December 31, 2022
Futures contracts	$	50,629	$	(16,963)	$	3,138,446
Foreign currency forward contracts	38,891		(35,446)		1,136,126
Other	58,781		(23,552)		3,591,793
Total	$	148,301	$	(75,961)
December 31, 2021
Futures contracts	$	34,999	$	(9,808)	$	2,826,564
Foreign currency forward contracts	7,734		(11,390)		915,962
TBAs	11,227		—		11,227
Other	73,161		(33,026)		3,736,773
Total	$	127,121	$	(54,224)

(1)    The fair value of asset derivatives are included in ‘other assets’ and the fair value of liability derivatives are included in ‘other liabilities.’

(2)    Represents the absolute notional value of all outstanding contracts, consisting of long and short positions.

The Company did not hold any derivatives which were designated as hedging instruments at December 31, 2022 or 2021.

The Company’s derivative instruments can be traded under master netting agreements, which establish terms that apply to all derivative transactions with a counterparty. In the event of a bankruptcy or other stipulated event of default, such agreements provide that the non-defaulting party may elect to terminate all outstanding derivative transactions, in which case all individual derivative positions (loss or gain) with a counterparty are closed out and netted and replaced with a single amount, usually referred to as the termination amount, which is expressed in a single currency. The resulting single net amount, where positive, is payable to the party “in-the-money” regardless of whether or not it is the defaulting party, unless the parties have agreed that only the non-defaulting party is entitled to receive a termination payment where the net amount is positive and is in its favor.

At December 31, 2022, $147.4 million and $73.2 million, respectively, of asset derivatives and liability derivatives were subject to a master netting agreement compared to $122.3 million and $53.9 million, respectively, at December 31, 2021. The remaining derivatives included in the table above were not subject to a master netting agreement.

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Realized and unrealized contract gains and losses on the Company’s derivative instruments are reflected in ‘net realized gains (losses)’ in the consolidated statements of income, as summarized in the following table:

Derivatives not designated as hedging instruments	Year Ended December 31,
	2022		2021		2020
Net realized gains (losses):
Futures contracts	$	(86,634)	$	(15,262)	$	114,987
Foreign currency forward contracts	6,144		(39,755)		49,974
TBAs	(51)		(233)		1,129
Other	5,518		22,860		13,585
Total	$	(75,023)	$	(32,390)	$	179,675

12. Variable Interest Entity and Noncontrolling Interests

Somers Holdings Ltd.

In March 2014, the Company invested $100.0 million and acquired 2,500,000 common shares of Somers. Somers was considered a VIE and the Company concluded that it was the primary beneficiary of Somers. In the 2020 fourth quarter, Arch Capital, Somers and Greysbridge, a wholly-owned subsidiary of Arch Capital, entered into an Agreement and Plan of Merger (as amended, the “Merger Agreement”). The merger and the related Greysbridge equity financing closed on July 1, 2021. Effective July 1, 2021, Somers is wholly owned by Greysbridge, and Greysbridge is owned 40% by the Company, 30% by certain investment funds managed by Kelso and 30% by certain investment funds managed by Warburg. Based on the governing documents of Greysbridge, the Company concluded that, while it retains significant influence over Somers, Somers no longer constitutes a variable interest entity. Accordingly, effective July 1, 2021, the Company no longer consolidates the results of Somers in its consolidated financial statements and footnotes. The Company classifies its investment as ‘investments in operating affiliates’ on the Company’s balance sheets and is accounted for under the equity method.

The following table summarizes Somers’ cash flow from operating, investing and financing activities.

	Year Ended December 31,
	2022	2021	2020
Total cash provided by (used for):
Operating activities	—	46,991	181,736
Investing activities	—	96,325	258,589
Financing activities	—	(2,042)	(335,776)

Non-redeemable noncontrolling interests

The following table sets forth activity in the non-redeemable noncontrolling interests:

	December 31,
	2022		2021
Balance, beginning of year	$	—	$	823,007
Impact of deconsolidation of Somers	—		(918,874)
Additional paid in capital attributable to noncontrolling interests	—		22,113
Amounts attributable to noncontrolling interests	—		78,314
Other comprehensive (income) loss attributable to noncontrolling interests	—		(4,560)
Balance, end of year	$	—	$	—

Redeemable noncontrolling interests

The following table sets forth activity in the redeemable noncontrolling interests:

	December 31,
	2022		2021		2020
Balance, beginning of year	$	9,233	$	58,548	$	55,404
Impact of deconsolidation of Somers	—		(48,919)		—
Other	1,596		(396)		3,144
Balance, end of year	$	10,829	$	9,233	$	58,548

The portion of income or loss attributable to third party investors is recorded in the consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests’ as summarized in the table below:

	December 31,
	2022		2021		2020
Amounts attributable to non-redeemable noncontrolling interests	$	—	$	(78,314)	$	(53,076)
Amounts attributable to redeemable noncontrolling interests	(5,490)		(4,299)		(7,114)
Net (income) loss attributable to noncontrolling interests	$	(5,490)	$	(82,613)	$	(60,190)

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Bellemeade Re

The Company has entered into aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda (the “Bellemeade Agreements”). At the time the Bellemeade Agreements were entered into, the applicability of the accounting guidance that addresses VIEs was evaluated. As a result of the evaluation of the Bellemeade Agreements, the Company concluded that these entities are VIEs. However, given that the ceding insurers do not have the unilateral power to direct those activities that are significant to their economic performance, the Company does not consolidate such entities in its consolidated financial statements.

The following table presents the total assets of the Bellemeade entities, as well as the Company’s maximum exposure to loss associated with these VIEs, calculated as the maximum historical observable spread between the benchmark index for each respective transaction and short term invested trust asset yields. The benchmark index for agreements effective prior to 2021 is based on one-month LIBOR, while the 2021 and later agreements benchmark index is based on the Secured Overnight Financing Rate (“SOFR”). SOFR is a measure of the cost of borrowing cash overnight, collateralized by U.S. Treasury securities, and is based on directly observable U.S. Treasury-backed repurchase transactions.

			December 31, 2022										December 31, 2021
			Maximum Exposure to Loss										Maximum Exposure to Loss
Bellemeade Entities (Issue Date)	Total VIE Assets		On-Balance Sheet (Asset) Liability		Off-Balance Sheet		Total		Coverage Remaining from Reinsurers (1)		Total VIE Assets		On-Balance Sheet (Asset) Liability		Off-Balance Sheet		Total
2017-1 Ltd. (Oct-17)	$	36,679	$	(6)	$	14	$	8	$	—	$	108,368	$	(159)	$	424	$	265
2018-1 Ltd. (Apr-18)	89,698		(153)		508		355		—		181,136		(528)		1,268		740
2018-3 Ltd. (Oct-18)	199,237		(250)		771		521		—		302,563		(1,018)		2,496		1,478
2019-1 Ltd. (Mar-19)	107,880		(48)		593		545		—		181,324		(380)		5,807		5,427
2019-2 Ltd. (Apr-19)	325,462		(206)		4,356		4,150		—		398,316		(515)		3,998		3,483
2019-3 Ltd. (Jul-19)	222,977		(104)		1,229		1,125		—		409,859		(584)		3,190		2,606
2019-4 Ltd. (Oct-19)	266,124		(142)		3,640		3,498		—		411,954		(462)		4,759		4,297
2020-2 Ltd. (Sep-20)	105,110		(8)		492		484		—		217,766		(177)		1,984		1,807
2020-3 Ltd. (Nov-20)	243,891		53		2,872		2,925		7,079		348,818		(128)		5,793		5,665
2020-4 Ltd. (Dec-20)	97,563		32		642		674		4,165		176,826		(50)		1,630		1,580
2021-1 Ltd. (Mar-21)	467,469		239		2,743		2,982		35,798		568,986		(303)		3,283		2,980
2021-2 Ltd. (Jun-21)	458,362		581		2,855		3,436		77,099		522,807		281		4,124		4,405
2021-3 Ltd. (Sep-21)	489,927		217		2,704		2,921		127,032		507,873		(411)		3,446		3,035
2022-1 Ltd. (Jan-22)	283,500		399		1,765		2,164		33,260
2022-2 Ltd. (Sep-22)	201,005		1,172		1,616		2,788		126,160
Total	$	3,594,884	$	1,776	$	26,800	$	28,576	$	410,593	$	4,336,596	$	(4,434)	$	42,202	$	37,768

(1) Coverage from a separate panel of reinsurers remaining at December 31, 2022.

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13.     Other Comprehensive Income (Loss)

The following table presents the changes in each component of AOCI, net of noncontrolling interests:

	Unrealized Appreciation on Available-For-Sale Investments		Foreign Currency Translation Adjustments		Total
Year Ended December 31, 2022
Beginning balance	$	13,486	$	(78,086)	$	(64,600)
Other comprehensive income (loss) before reclassifications	(1,772,649)		(56,720)		(1,829,369)
Amounts reclassified from accumulated other comprehensive income	247,799		—		247,799
Net current period other comprehensive income (loss)	(1,524,850)		(56,720)		(1,581,570)
Ending balance	$	(1,511,364)	$	(134,806)	$	(1,646,170)
Year Ended December 31, 2021
Beginning balance	$	501,295	$	(12,400)	$	488,895
Other comprehensive income (loss) before reclassifications	(371,741)		(65,686)		(437,427)
Amounts reclassified from accumulated other comprehensive income	(116,068)		—		(116,068)
Net current period other comprehensive income (loss)	(487,809)		(65,686)		(553,495)
Ending balance	$	13,486	$	(78,086)	$	(64,600)
Year Ended December 31, 2020
Beginning balance	$	258,486	$	(46,395)	$	212,091
Other comprehensive income (loss) before reclassifications	668,996		33,995		702,991
Amounts reclassified from accumulated other comprehensive income	(426,187)		—		(426,187)
Net current period other comprehensive income (loss)	242,809		33,995		276,804
Ending balance	$	501,295	$	(12,400)	$	488,895

The following tables present details about amounts reclassified from accumulated other comprehensive income and the tax effects allocated to each component of other comprehensive income (loss):

	Consolidated Statement of Income	Amounts Reclassified from AOCI
Details About	Line Item That Includes	Year Ended December 31,
AOCI Components	Reclassification	2022		2021		2020
Unrealized appreciation on available-for-sale investments
	Net realized gains (losses)	$	(235,989)	$	157,095	$	478,659
	Provision for credit losses	(43,909)		(2,099)		(3,597)
	Other-than-temporary impairment losses	—		—		(533)
	Total before tax	(279,898)		154,996		474,529
	Income tax (expense) benefit	32,099		(38,928)		(48,342)
	Net of tax	$	(247,799)	$	116,068	$	426,187

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Following are the related tax effects allocated to each component of other comprehensive income (loss):

	Before Tax		Tax Expense		Net of Tax
	Amount		(Benefit)		Amount
Year Ended December 31, 2022
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(2,010,443)	$	(237,794)	$	(1,772,649)
Less reclassification of net realized gains (losses) included in net income	(279,898)		(32,099)		(247,799)
Foreign currency translation adjustments	(56,554)		166		(56,720)
Other comprehensive income (loss)	$	(1,787,099)	$	(205,529)	$	(1,581,570)
Year Ended December 31, 2021
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(406,774)	$	(19,845)	$	(386,929)
Less reclassification of net realized gains (losses) included in net income	154,996		38,928		116,068
Foreign currency translation adjustments	(64,423)		59		(64,482)
Other comprehensive income (loss)	$	(626,193)	$	(58,714)	$	(567,479)
Year Ended December 31, 2020
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	754,572	$	75,855	$	678,717
Less reclassification of net realized gains (losses) included in net income	474,529		48,342		426,187
Foreign currency translation adjustments	33,706		370		33,336
Other comprehensive income (loss)	$	313,749	$	27,883	$	285,866

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14.    Earnings Per Common Share

The calculation of basic earnings per common share is computed by dividing income available to Arch common shareholders by the weighted average number of Common Shares and common share equivalents outstanding. The following table sets forth the computation of basic and diluted earnings per common share:

	Year Ended December 31,
	2022		2021		2020
Numerator:
Net income	$	1,482,423	$	2,239,462	$	1,465,711
Amounts attributable to noncontrolling interests	(5,490)		(82,613)		(60,190)
Net income available to Arch	1,476,933		2,156,849		1,405,521
Preferred dividends	(40,736)		(48,343)		(41,612)
Loss on redemption of preferred shares	—		(15,101)		—
Net income available to Arch common shareholders	$	1,436,197	$	2,093,405	$	1,363,909
Denominator:
Weighted average common shares outstanding	368,612,197		391,748,715		403,062,179
Effect of dilutive common share equivalents:
Nonvested restricted shares	2,103,036		1,996,524		1,682,309
Stock options (1)	6,894,534		6,600,697		5,514,967
Weighted average common shares and common share equivalents outstanding – diluted	377,609,767		400,345,936		410,259,455
Earnings per common share:
Basic	$	3.90	$	5.34	$	3.38
Diluted	$	3.80	$	5.23	$	3.32

(1)    Certain stock options were not included in the computation of diluted earnings per share where the exercise price of the stock options exceeded the average market price and would have been anti-dilutive or where, when applying the treasury stock method to in-the-money options, the sum of the proceeds, including unrecognized compensation, exceeded the average market price and would have been anti-dilutive. For 2022, 2021 and 2020, the number of stock options excluded were 798,053, 2,398,608 and 2,249,821, respectively.

15.     Income Taxes

Arch Capital is incorporated under the laws of Bermuda and, under current Bermuda law, is not obligated to pay any taxes in Bermuda based upon income or capital gains. The Company has received a written undertaking from the Minister of Finance in Bermuda under the Exempted Undertakings Tax Protection Act 1966 that, in the event that any legislation is enacted in Bermuda imposing any tax computed on profits, income, gain or appreciation on any capital asset, or any tax in the nature of estate duty or inheritance tax, such tax will not be applicable to Arch Capital or any of its operations until March 31, 2035. This undertaking does not, however, prevent the imposition of taxes on any person ordinarily resident in Bermuda or any company in respect of its ownership of real property or leasehold interests in Bermuda.

Arch Capital and its non-U.S. subsidiaries will be subject to U.S. federal income tax only to the extent that they derive U.S. source income that is subject to U.S. withholding tax, or income that is effectively connected with the conduct of a trade or business within the U.S. and is not exempt from U.S.

tax under an applicable income tax treaty with the U.S., or because a non-U.S. subsidiary has elected to be treated as a U.S. taxpayer. Arch Capital and its non-U.S. subsidiaries will be subject to a withholding tax on dividends from U.S. investments and interest from certain U.S. payors (subject to reduction by any applicable income tax treaty). Arch Capital and its non-U.S. subsidiaries intend to conduct their operations in a manner that will not cause them to be treated as engaged in a trade or business in the United States and, therefore, will not be required to pay U.S. federal income taxes (other than U.S. excise taxes on insurance and reinsurance premium and withholding taxes on dividends and certain other U.S. source investment income). However, because there is uncertainty as to the activities which constitute being engaged in a trade or business within the United States, there can be no assurances that the U.S. Internal Revenue Service will not contend successfully that Arch Capital, or its non-U.S. subsidiaries that do not elect to become U.S. taxpayers, are engaged in a trade or business in the United States. If Arch Capital or any of its non-U.S. subsidiaries were subject to U.S. income tax, Arch Capital’s shareholders’ equity and earnings could be materially adversely affected. Arch Capital has subsidiaries and branches that operate in various jurisdictions around the world that are subject to tax in the jurisdictions in which they

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operate. The significant jurisdictions in which Arch Capital’s subsidiaries and branches are subject to tax are the United States, United Kingdom, Ireland, Canada, Switzerland, Australia and Denmark.

The components of income taxes attributable to operations were as follows:

	Year Ended December 31,
	2022		2021		2020
Current expense (benefit):
United States	$	195,588	$	284,274	$	181,571
Non-U.S.	5,628		11,259		16,091
	201,216		295,533		197,662
Deferred expense (benefit):
United States	(96,599)		(123,261)		(89,170)
Non-U.S.	(24,656)		(43,690)		3,346
	(121,255)		(166,951)		(85,824)
Income tax expense	$	79,961	$	128,582	$	111,838

The Company’s income or loss before income taxes was earned in the following jurisdictions:

	Year Ended December 31,
	2022		2021		2020
Income (Loss) Before Income Taxes:
Bermuda	$	985,828	$	1,518,616	$	1,114,117
United States	400,865		643,239		409,893
Other	175,691		206,187		53,539
Total	$	1,562,384	$	2,368,042	$	1,577,549

The expected tax provision computed on pre-tax income or loss at the weighted average tax rate has been calculated as the sum of the pre-tax income in each jurisdiction multiplied by that jurisdiction’s applicable statutory tax rate. The 2022 applicable statutory tax rates by jurisdiction were as follows: Bermuda (0.0%), United States (21.0%), United Kingdom (19.0%), Ireland (12.5%), Denmark (22.0%), Canada (26.5%), Gibraltar (12.5%), Australia (30.0%), Hong Kong (16.5%) and the Netherlands (25.8%).

A reconciliation of the difference between the provision for income taxes and the expected tax provision at the weighted average tax rate follows:

	Year Ended December 31,
	2022		2021		2020
Expected income tax expense (benefit) computed on pre-tax income at weighted average income tax rate	$	110,337	$	158,269	$	111,947
Addition (reduction) in income tax expense (benefit) resulting from:
Investment income	(12,762)		(23,572)		(1,824)
State taxes, net of U.S. federal tax benefit	10,650		20,978		5,027
Dividend withholding taxes	10,559		12,211		7,105
Change in valuation allowance	(22,726)		(40,425)		13,190
Base eroding tax	7,694		—		—
Share based compensation	(9,159)		(5,339)		(2,533)
Tax credits	(9,736)		—		—
Intercompany loan write-off	(3,544)		—		(22,083)
Other	(1,352)		6,460		1,009
Income tax expense (benefit)	$	79,961	$	128,582	$	111,838

The effect of a change in tax laws or rates on deferred tax assets and liabilities is recognized in income in the period in which such change is enacted.

Deferred income tax assets and liabilities reflect temporary differences based on enacted tax rates between the carrying amounts of assets and liabilities for financial reporting and income tax purposes.

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Significant components of the Company’s deferred income tax assets and liabilities were as follows:

	December 31,
	2022		2021
Deferred income tax assets:
Net operating loss	$	76,665	$	87,960
Discounting of net loss reserves	77,556		72,001
Net unearned premium reserve	96,581		75,483
Compensation liabilities	55,269		28,062
Foreign tax credit carryforward	16,738		20,058
Bad debt reserves	17,365		10,252
Depreciation and amortization	141,409		115,041
Lease liability	26,681		21,453
Net unrealized decline of investments	192,949		—
Lloyds year of account deferral	1,385		—
Other, net	14,450		703
Deferred tax assets before valuation allowance	717,048		431,013
Valuation allowance	(6,968)		(43,953)
Deferred tax assets net of valuation allowance	710,080		387,060
Deferred income tax liabilities:
Deposit accounting liability	(2,658)		(1,578)
Goodwill and intangibles	(38,905)		(70,549)
Lloyds year of account deferral	—		(12,514)
Contingency reserve	(43,870)		(49,486)
Deferred policy acquisition costs	(63,708)		(25,612)
Investment related	(9,225)		(7,492)
Net unrealized appreciation of investments	—		(8,377)
Right-of-use asset	(20,781)		(17,406)
Total deferred tax liabilities	(179,147)		(193,014)
Net deferred income tax assets	$	530,933	$	194,046

The Company provides a valuation allowance to reduce the net value of certain deferred tax assets to an amount which management expects to more likely than not be realized. As of December 31, 2022, the Company’s valuation allowance was $7.0 million, compared to $44.0 million at December 31, 2021. The valuation allowance at December 31, 2022, was primarily attributable to valuation allowances on the Company’s Ireland and Hong Kong operations and certain other deferred tax assets relating to tax attributes that have a limited use.

At December 31, 2022, the Company’s net operating loss carryforwards and tax credits were as follows:

	Year Ended December 31,
	2022		Expiration
Operating Loss Carryforwards
United Kingdom	$	198,571	No expiration
Ireland	61,685		No expiration
Australia	32,333		No expiration
Hong Kong	28,080		No expiration
Netherlands	60		No expiration
United States (1)	23,766		2029 - 2038
Tax Credits
U.K. foreign tax credits	13,907		No expiration
U.S. foreign tax credits	2,830		2029 - 2032

(1) On January 30, 2014, the Company’s U.S. mortgage operations underwent an ownership change for U.S. federal income tax purposes as a result of the Company’s acquisition of the CMG Entities. As a result of this ownership change, a limitation has been imposed upon the utilization of approximately $7.0 million of the Company’s existing U.S. net operating loss carryforwards. Utilization is limited to approximately $0.6 million per year in accordance with Section 382 of the Internal Revenue Code of 1986 as amended (“the Code”).

The Company’s U.S. mortgage operations are eligible for a tax deduction, subject to certain limitations, under Section 832(e) of the Code for amounts required by state law or regulation to be set aside in statutory contingency reserves. The deduction is allowed only to the extent that the Company purchases non-interest bearing U.S. Mortgage Guaranty Tax and Loss Bonds (“T&L Bonds”) issued by the U.S. Treasury Department in an amount equal to the tax benefit derived from deducting any portion of the statutory contingency reserves. T&L Bonds are reflected in ‘other assets’ on the Company’s balance sheet and totaled approximately $12.4 million at December 31, 2022, compared to $31.6 million at December 31, 2021.

Deferred income tax liabilities have not been accrued with respect to the undistributed earnings of the Company's U.S., U.K. and Ireland subsidiaries as it is the Company’s intention that all such earnings will be indefinitely reinvested. If the earnings were to be distributed, as dividends or otherwise, such amounts may be subject to withholding tax in the jurisdiction of the paying entity. The Company no longer intends to indefinitely reinvest earnings from the Company's Canada subsidiary, however, no income or withholding taxes have been accrued as the Canada subsidiary does not have positive cumulative earnings and profits and therefore a distribution from this particular subsidiary would not be subject to income taxes or withholding taxes. Potential tax implications of repatriation from the Company’s unremitted earnings that are indefinitely reinvested are driven by facts at the time of distribution. Therefore, it is not practicable to estimate the income tax liabilities that might be incurred if

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such earnings were remitted. Distributions from the U.K. or Ireland would not be subject to withholding tax and no deferred income tax liability would need to be accrued.

The Company recognizes interest and penalties relating to unrecognized tax benefits in the provision for income taxes. As of December 31, 2022, the Company’s total unrecognized tax benefits, including interest and penalties, were $2.0 million. If recognized, the full amount of the unrecognized tax benefit would impact the consolidated effective tax rate. A reconciliation of the beginning and ending amount of unrecognized tax benefits is as follows:

	December 31,
	2022		2021
Balance at beginning of year	$	2,008	$	2,008
Additions based on tax positions related to the current year	—		—
Additions for tax positions of prior years	—		—
Reductions for tax positions of prior years	—		—
Settlements	—		—
Balance at end of year	$	2,008	$	2,008

The Company, its subsidiaries and branches file income tax returns in various federal, state and local jurisdictions. The following table details open tax years that are potentially subject to examination by local tax authorities, in the following major jurisdictions:

Jurisdiction	Tax Years
United States	2015-2022
United Kingdom	2020-2022
Ireland	2018-2022
Canada	2018-2022
Switzerland	2018-2022
Denmark	2018-2022
Australia	2018-2022

As of December 31, 2022, the Company’s current income tax payable (included in “Other liabilities”) was $40.6 million.

Inflation Reduction Act of 2022.

On August 16, 2022, the U.S. government enacted the Inflation Reduction Act of 2022, which among other things implements a 15% minimum tax on book income of certain large corporations, a 1% excise tax on net stock repurchases and several tax incentives to promote clean energy. The effective date of these provisions is January 1, 2023. Based on its current analysis of the provisions, the Company does not expect that this legislation will have a material effect on the Company’s consolidated financial statements.

16.    Transactions with Related Parties

In 2017, the Company acquired approximately 25% of Premia Holdings Ltd. Premia Holdings Ltd. is the parent of Premia Reinsurance Ltd., a multi-line Bermuda reinsurance company (together with Premia Holdings Ltd., “Premia”). Premia’s strategy is to reinsure or acquire companies or reserve portfolios in the non-life property and casualty insurance and reinsurance run-off market. Arch Re Bermuda and certain Arch co-investors invested $100.0 million and acquired approximately 25% of Premia as well as warrants to purchase additional common equity. Arch has appointed two directors to serve on the seven person board of directors of Premia. Arch Re Bermuda is providing a 25% quota share reinsurance treaty on certain business written by Premia. During 2022, Arch Re Bermuda entered into certain reinsurance transactions with Premia which generated net premiums written and earned of $121.1 million and $119.9 million, respectively, compared to $40.4 million of net premiums written and earned in 2021. At December 31, 2022, Arch Re Bermuda recorded a funds held asset from Premia of $118.7 million, compared to $53.5 million at December 31, 2021.

In the 2021 first quarter, as part of the Company’s acquisition of Barbican, the Company entered into an agreement with Premia Managing Agency Limited for the reinsurance to close of Syndicate 1955’s 2018 underwriting year of account into Premia Syndicate 1884’s 2021 underwriting year of account. The reinsurance to close covers legacy business underwritten by Syndicate 1955 on the underwriting 2018 and prior years of account and under the agreement, approximately $380 million of net liabilities was transferred to Syndicate 1884, with an effective date of January 1, 2021. The Company had no reinsurance recoverable on unpaid and paid losses or funds held liability at December 31, 2022 and December 31, 2021.

In July 2021, following consummation of the Merger Agreement and the related Greysbridge equity financing, pursuant to which Somers became wholly owned by Greysbridge, and Greysbridge is owned 40% by the Company, 30% by certain funds managed by Kelso and 30% by certain funds managed by Warburg. During the 2022 and 2021 period, the Company entered into certain reinsurance transactions with Somers. The Company’s net premiums written was reduced by $519.4 million and $379.1 million, for the 2022 and 2021 periods, respectively (which included reinsurance transactions as well as those entered into in conjunction with the Merger Agreement). In addition, Somers paid certain acquisition costs and administrative fees to the Company. At December 31, 2022, the Company recorded a reinsurance recoverable on unpaid and paid losses from Somers of $1.2 billion and a reinsurance balance payable to Somers of $413.8 million. At December 31, 2021,

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reinsurance recoverable on unpaid and paid losses from Somers was $902.8 million, with a reinsurance balance payable to Somers of $258.4 million. See note 12, “Variable Interest Entity and Noncontrolling Interests.”

The Company has a put/call option that was entered into in connection with the Greysbridge equity financing, whereby beginning January 1, 2024 the Company will have a call right (but not the obligation) and Warburg and Kelso will each have a put right (but not the obligation) to buy/sell one third of their initial shares annually at the tangible book value per share of Greysbridge for the most recently ended fiscal quarter.

As of December 31, 2022, the Company owns $35.0 million in aggregate principal amount of Somers 6.5% senior notes, due July 2, 2029.

17.    Leases

In the ordinary course of business, the Company renews and enters into new leases for office property and equipment. At the lease inception date, the Company determines whether a contract contains a lease and its classification as a finance or operating lease. Primarily all of the Company’s leases are classified as operating leases. The Company’s operating leases have remaining lease terms of up to 10 years, some of which include options to extend the lease term. The Company considers these options when determining the lease term and measuring its lease liability and right-of-use asset. In addition, the Company’s lease agreements do not contain any material residual value guarantees or material restrictive covenants.

Short-term operating leases with an initial term of twelve months or less were excluded on the Company's consolidated balance sheet and represent an inconsequential amount of operating lease expense.

As most leases do not provide an implicit rate, the Company uses its incremental borrowing rate based on the information available at the lease commencement date in determining the present value of lease payments.

Additional information regarding the Company’s operating leases is as follows:

	December 31,
	2022			2021
Operating lease costs	$	33,571		$	31,691
Sublease income (1)	$	(988)		$	—
Cash payments included in the measurement of lease liabilities reported in operating cash flows	$	26,051		$	32,094
Right-of-use assets obtained in exchange for new lease liabilities	$	42,841		$	22,686
Right-of-use assets (2)	$	123,083		$	106,836
Operating lease liability (2)	$	151,890		$	126,711
Weighted average discount rate	4.2		%	3.9		%
Weighted average remaining lease term	6.6 years			5.9 years

(1)    The sublease income primarily relates to office property in Raleigh, North Carolina.

(2)    The right-of-use assets are included in ‘other assets’ while the operating lease liability is included in ‘other liabilities.’

The following table presents the contractual maturities of the Company's operating lease liabilities at December 31, 2022:

Years Ending December 31,
2023	$	31,861
2024	30,091
2025	24,651
2026	21,939
2027	17,859
2028 and thereafter	48,522
Total undiscounted lease liability	$	174,923
Less: present value adjustment	(23,033)
Operating lease liability	$	151,890

Rental expense was approximately $38.9 million, $39.1 million and $37.4 million for 2022, 2021 and 2020, respectively.

18.    Commitments and Contingencies

Concentrations of Credit Risk

The creditworthiness of a counterparty is evaluated by the Company, taking into account credit ratings assigned by independent agencies. The credit approval process involves an assessment of factors, including, among others, the counterparty, country and industry credit exposure limits. Collateral may be required, at the discretion of the Company, on certain transactions based on the creditworthiness of the counterparty.

The areas where significant concentrations of credit risk may exist include unpaid losses and loss adjustment expenses recoverable, contractholder receivables, ceded unearned premiums, paid losses and loss adjustment expenses recoverable net of reinsurance balances payable, investments and cash and cash equivalent balances. A credit exposure exists with respect to reinsurance recoverables as they may

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become uncollectible. The Company manages its credit risk in its reinsurance relationships by transacting with reinsurers that it considers financially sound and, if necessary, the Company may hold collateral in the form of funds, trust accounts and/or irrevocable letters of credit. This collateral can be drawn on for amounts that remain unpaid beyond specified time periods on an individual reinsurer basis. In addition, certain insurance policies written by the Company’s insurance operations feature large deductibles, primarily in its construction and national accounts lines of business. Under such contracts, the Company is obligated to pay the claimant for the full amount of the claim. The Company is subsequently reimbursed by the policyholder for the deductible amount. These amounts are included on a gross basis in the consolidated balance sheet in contractholder payables and contractholder receivables, respectively. In the event that the Company is unable to collect from the policyholder, the Company would be liable for such defaulted amounts. Collateral, primarily in the form of letters of credit, cash and trusts, is obtained from the policyholder to mitigate the Company’s credit risk. In the instances where the company receives collateral in the form of cash, the Company records a related liability in “Collateral held for insured obligations.”

In addition, the Company underwrites a significant amount of its business through brokers and a credit risk exists should any of these brokers be unable to fulfill their contractual obligations with respect to the payments of insurance and reinsurance balances owed to the Company. The following table summarizes the percentage of the Company’s gross premiums written generated from or placed by the largest brokers:

Broker	Year Ended December 31,
	2022		2021		2020
Marsh & McLennan Companies and its subsidiaries	17.3	%	18.3	%	13.3	%
Aon Corporation and its subsidiaries	13.8	%	12.2	%	12.0	%

No other broker and no one insured or reinsured accounted for more than 10% of gross premiums written for 2022, 2021 and 2020.

The Company’s available for sale investment portfolio is managed in accordance with guidelines that have been tailored to meet specific investment strategies, including standards of diversification, which limit the allowable holdings of any single issue. There were no investments in any entity in excess of 10% of the Company’s shareholders’ equity at December 31, 2022 other than investments issued or guaranteed by the United States government or its agencies.

Investment Commitments

The Company’s investment commitments, which are primarily related to agreements entered into by the Company to invest in funds and separately managed accounts when called upon, were approximately $2.9 billion and $3.0 billion at December 31, 2022 and 2021, respectively.

Purchase Obligations

The Company has also entered into certain agreements which commit the Company to purchase goods or services, primarily related to software and computerized systems. Such purchase obligations were approximately $150.1 million and $114.1 million at December 31, 2022 and 2021, respectively.

Employment and Other Arrangements

At December 31, 2022, the Company has entered into employment agreements with certain of its executive officers. Such employment arrangements provide for compensation in the form of base salary, annual bonus, share-based awards, participation in the Company’s employee benefit programs and the reimbursements of expenses.

19.    Debt and Financing Arrangements

The Company’s senior notes payable at December 31, 2022 and 2021 were as follows:

					Carrying Amount at
	Interest		Principal		December 31,
	(Fixed)		Amount		2022		2021
2034 notes (1)	7.350	%	300,000		297,618		297,488
2043 notes (2)	5.144	%	500,000		495,188		495,063
2026 notes (3)	4.011	%	500,000		498,073		497,633
2046 notes (4)	5.031	%	450,000		445,582		445,490
2050 notes (5)	3.635	%	1,000,000		988,949		988,720
			$	2,750,000	$	2,725,410	$	2,724,394

(1) Senior notes of Arch Capital issued on May 4, 2004 and due May 1, 2034 (“2034 notes”).

(2) Senior notes of Arch-U.S., a wholly-owned subsidiary of Arch Capital, issued on December 13, 2013 and due November 1, 2043 (“2043 notes”), fully and unconditionally guaranteed by Arch Capital.

(3) Senior notes of Arch Capital Finance LLC (“Arch Finance”), a wholly-owned finance subsidiary of Arch Capital, issued on December 8, 2016 and due December 15, 2026 (“2026 notes”), fully and unconditionally guaranteed by Arch Capital.

(4) Senior notes of Arch Finance issued on December 8, 2016 and due December 15, 2046 (“2046 notes”), fully and unconditionally guaranteed by Arch Capital

(5) Senior notes of Arch Capital issued on June 30, 2020 and due June 30, 2050 (“2050 notes”).

The 2034 notes are Arch Capital’s senior unsecured obligations and rank equally with all of its existing and future senior unsecured indebtedness. Interest payments on the 2034 notes are due on May 1st and November 1st of each year.

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Arch Capital may redeem the 2034 notes at any time and from time to time, in whole or in part, at a “make-whole” redemption price.

The 2043 notes are unsecured and unsubordinated obligations of Arch-U.S. and Arch Capital, respectively, and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch-U.S. and Arch Capital, respectively. Interest payments on the 2043 notes are due on May 1st and November 1st of each year. Arch-U.S. may redeem the 2043 notes at any time and from time to time, in whole or in part, at a “make-whole” redemption price.

The 2026 notes are unsecured and unsubordinated obligations of Arch Finance and Arch Capital, respectively, and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch Finance and Arch Capital, respectively. Interest payments on the 2026 notes are due on June 15th and December 15th of each year. Arch Finance may redeem the 2026 notes at any time and from time to time, in whole or in part, at a “make-whole” redemption price.

The 2046 notes are unsecured and unsubordinated obligations of Arch Finance and Arch Capital, respectively, and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch Finance and Arch Capital, respectively. Interest payments on the 2046 notes are due on June 15th and December 15th of each year. Arch Finance may redeem the 2046 notes at any time and from time to time, in whole or in part, at a “make-whole” redemption price.

The 2050 notes are Arch Capital’s senior unsecured obligations and rank equally with all of its existing and future senior unsecured indebtedness. Interest payments on the 2050 notes are due on June 30 and December 30 of each year. Arch Capital may redeem the 2050 notes at any time and from time to time, in whole or in part, at a “make-whole” redemption price.

Letter of Credit and Revolving Credit Facilities

In the normal course of its operations, the Company enters into agreements with financial institutions to obtain secured and unsecured credit facilities. On April 7, 2022, Arch Capital and certain of its subsidiaries amended its existing credit agreement into a $925.0 million facility (the “Credit Facility”) with a syndication of lenders. The Credit Facility, as amended, consists of a $425.0 million secured facility for letters of credit (the “Secured Facility”) and a $500.0 million unsecured facility for revolving loans and letters of credit (the “Unsecured Facility”). Obligations of each borrower under the Secured Facility for letters of credit are secured by cash and eligible securities of such borrower held in collateral accounts. Commitments under the Credit Facility may be increased up to, but not exceeding, an aggregate of $1.25 billion. Arch Capital has a one-time option to convert

any or all outstanding revolving loans of Arch Capital and/or Arch-U.S. to term loans with the same terms as the revolving loans except that any prepayments may not be re-borrowed. Arch-U.S. guarantees the obligations of Arch Capital, and Arch Capital guarantees the obligations of Arch-U.S. Borrowings of revolving loans may be made at a variable rate based on SOFR. Secured letters of credit are available for issuance on behalf of certain Arch Capital subsidiaries. At December 31, 2022, the Secured Facility had $323.1 million of letters of credit outstanding and remaining capacity of $101.9 million, and the Unsecured Facility had no outstanding revolving loans or letters of credit, with remaining capacity of $500.0 million.

The Credit Facility contains certain restrictive and maintenance covenants customary for facilities of this type, including restrictions on indebtedness, minimum consolidated tangible net worth, maximum leverage levels and minimum financial strength ratings. Arch Capital and its subsidiaries which are party to the agreement were in compliance with all covenants contained therein at December 31, 2022.

Commitments under the Credit Facility will expire on December 17, 2024, and all loans then outstanding must be repaid. Letters of credit issued under the Unsecured Facility will not have an expiration date later than December 17, 2025.

In addition, certain of Arch Capital’s subsidiaries had outstanding secured and unsecured letters of credit through other facilities of $24.6 million and $400.0 million respectively, which were issued in the normal course of business (“LOC Facilities”). The principal purpose of the LOC Facilities is to issue, as required, evergreen standby letters of credit in favor of primary insurance or reinsurance counterparties with which certain of Arch Capital’s subsidiaries has entered into reinsurance arrangements. This is required to ensure that such counterparties are permitted to take credit for reinsurance obtained in United States jurisdictions where such subsidiaries are not licensed or otherwise admitted as an insurer, as required under insurance regulations in the United States, and to comply with requirements of Lloyd’s of London in connection with qualifying quota share and other arrangements. The amount of letters of credit issued is driven by, among other things, the timing and payment of catastrophe losses, loss development of existing reserves, the payment pattern of such reserves, the further expansion of business and the loss experience of such business.

When issued, all secured letters of credit are secured by a portion of the investment portfolio. At December 31, 2022, these letters of credit were secured by investments with a fair value of $465.2 million. The Company had no outstanding revolving credit agreement borrowings at December 31, 2022 and 2021.

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Federal Home Loan Bank Membership

Certain subsidiaries of the Company are members of Federal Home Loan Banks (“FHLBs”). Members may borrow from the FHLBs at competitive rates subject to certain conditions. Conditions include maintaining sufficient collateral deposits for funding and a requirement to hold stock in the FHLBs related to both membership and outstanding advances. At December 31, 2022 the Company had no advances outstanding under the FHLB program, compared to $80.0 million of advances outstanding under the FHLB program, which was secured by investments with a fair value of $80.2 million at December 31, 2021. Advances outstanding under the FHLB program are included in ‘other liabilities’ on the Company’s balance sheet.

20.    Goodwill and Intangible Assets

The following table shows an analysis of goodwill and intangible assets:

	Goodwill		Intangible assets (indefinite life)		Intangible assets (finite life)		Total
Net balance at Dec. 31, 2020	$	314,629	$	79,219	$	299,015	$	692,863
Acquisitions (1)	31,677		—		318,459		350,136
Amortization	—		—		(82,955)		(82,955)
Impact of deconsolidation of Somers (2)	—		(7,650)		—		(7,650)
Foreign currency movements and other adjustments	(1,441)		(212)		(5,758)		(7,411)
Net balance at Dec. 31, 2021	344,865		71,357		528,761		944,983
Acquisitions (1)	8,389		—		—		8,389
Amortization	—		—		(106,200)		(106,200)
Foreign currency movements and other adjustments	(11,181)		(2,576)		(29,126)		(42,883)
Net balance at Dec. 31, 2022	$	342,073	$	68,781	$	393,435	$	804,289
Gross balance at Dec. 31, 2022	$	351,231	$	70,246	$	1,102,298	$	1,523,775
Accumulated amortization	—		—		(678,020)		(678,020)
Foreign currency movements and other adjustments	(9,158)		(1,465)		(30,843)		(41,466)
Net balance at Dec. 31, 2022	$	342,073	$	68,781	$	393,435	$	804,289

(1)    See note 2, “Acquisitions.”

(2)    See note 12, “Variable Interest Entity and Noncontrolling Interests.”

The following table presents the components of goodwill and intangible assets:

	Gross Balance		Accumulated Amortization		Foreign Currency Translation Adjustment and Other		Net Balance
Dec. 31, 2022
Acquired insurance contracts	$	451,505	$	(426,202)	$	339	$	25,642
Operating platform	52,674		(50,302)		2		2,374
Distribution relationships	602,518		(207,908)		(31,110)		363,500
Goodwill	351,231		—		(9,158)		342,073
Insurance licenses	48,331		—		—		48,331
Syndicate capacity	21,915		—		(1,465)		20,450
Unfavorable service contract	(9,533)		9,533		—		—
Other	5,134		(3,141)		(74)		1,919
Total	$	1,523,775	$	(678,020)	$	(41,466)	$	804,289
Dec. 31, 2021
Acquired insurance contracts	$	451,505	$	(409,592)	$	339	$	42,252
Operating platform	52,674		(48,838)		56		3,892
Distribution relationships	602,518		(120,302)		(2,207)		480,009
Goodwill	342,842		—		2,023		344,865
Insurance licenses	48,331		—		—		48,331
Syndicate capacity	21,915		—		1,111		23,026
Unfavorable service contract	(9,533)		9,435		—		(98)
Other	5,134		(2,542)		114		2,706
Total	$	1,515,386	$	(571,839)	$	1,436	$	944,983

The estimated remaining amortization expense for the Company’s intangible assets with finite lives is as follows:

2023	$	91,605
2024	73,366
2025	41,060
2026	32,091
2027	29,268
2028 and thereafter	126,045
Total	$	393,435

The estimated remaining useful lives of these assets range from one to fourteen years at December 31, 2022.

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21.    Shareholders’ Equity

Authorized and Issued

The authorized share capital of Arch Capital consists of 1.8 billion Common Shares, par value of $0.0011 per share, and 50 million Preferred Shares, par value of $0.01 per share.

Common Shares

The following table presents a roll-forward of changes in Arch Capital’s issued and outstanding Common Shares:

	Year Ended December 31,
	2022	2021	2020
Common Shares:
Shares issued and outstanding, beginning of year	583,289,850	579,000,841	574,617,195
Shares issued (1)	3,517,399	2,669,229	2,646,164
Restricted shares issued, net of cancellations	1,443,513	1,619,780	1,737,482
Shares issued and outstanding, end of year	588,250,762	583,289,850	579,000,841
Common shares in treasury, end of year	(217,904,765)	(204,365,956)	(172,280,199)
Shares issued and outstanding, end of year	370,345,997	378,923,894	406,720,642

(1)    Includes shares issued from the exercise of stock options and stock appreciation rights, the vesting of restricted share units and shares issued from the employee share purchase plan.

Share Repurchase Program

The Board of Directors of Arch Capital (the “Board”) has authorized the investment in Arch Capital’s common shares through a share repurchase program. At December 31, 2022, $1.0 billion of share repurchases were available under the program. Repurchases under the program may be effected from time to time in open market or privately negotiated transactions through December 31, 2024. The timing and amount of the repurchase transactions under this program will depend on a variety of factors, including market conditions and corporate and regulatory considerations.

Repurchases of Arch Capital’s common shares in connection with the share repurchase plan and other share-based transactions were held in the treasury under the cost method, and the cost of the common shares acquired is included in ‘Common shares held in treasury, at cost.’ At December 31, 2022, Arch Capital held 217.9 million shares for an aggregate cost of $4.4 billion in treasury, at cost.

The Company’s repurchases under the share repurchase program were as follows:

	Year Ended December 31,
	2022		2021		2020
Aggregate cost of shares repurchased	$	585,823	$	1,234,294	$	83,472
Shares repurchased	12,891,405		31,486,830		2,850,102
Average price per share repurchased	$	45.44	$	39.20	$	29.29

Since the inception of the share repurchase program through December 31, 2022, Arch Capital has repurchased approximately 433.6 million common shares for an aggregate purchase price of $5.9 billion.

Series G Preferred Shares

In June 2021, Arch Capital completed a $500 million underwritten public offering of 20.0 million depositary shares

(the “Depositary Shares”), each of which represents a 1/1,000th interest in a share of its 4.55% Non-Cumulative Preferred Shares, Series G, $0.01 par value and $25,000 liquidation preference per share (equivalent to $25 liquidation preference per Depositary Share) (the “Series G Preferred Shares”). Each Depositary Share, evidenced by a depositary receipt, entitles the holder, through the depositary,

to a proportional fractional interest in all rights and preferences of the Series G Preferred Shares represented thereby (including any dividend, liquidation, redemption and voting rights).

Holders of Series G Preferred Shares will be entitled to receive dividend payments only when, as and if declared by the Board or a duly authorized committee of the Board. Any such dividends will be payable from, and including, the date of original issue on a noncumulative basis, quarterly in arrears on the last day of March, June, September and December of each year, at an annual rate of 4.55%. Dividends on the Series G Preferred Shares are not cumulative. The Company will be restricted from paying dividends on or repurchasing its common shares unless certain dividend payments are made on the Series G Preferred Shares. The Company may not declare or pay a dividend on the Series G Preferred Shares under certain circumstances, including if the Company is or, after giving effect to such payment, would be in breach of applicable individual or group solvency and liquidity requirements or applicable individual or group enhanced capital requirements (“ECR”). The Series G Preferred Shares may not be redeemed at any time if the ECR would be breached immediately before or after giving effect to such redemption, unless the Company replaces the capital represented by preference shares to be redeemed with capital having equal or better capital treatment.

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Except in specified circumstances relating to certain tax or corporate events, the Series G Preferred Shares are not redeemable prior to June 11, 2026. On and after that date, the

Series G Preferred Shares will be redeemable at the Company’s option, in whole or in part, at a redemption price of $25,000 per share of the Series G Preferred Shares (equivalent to $25 per depositary share), plus any declared and unpaid dividends, without accumulation of any undeclared dividends to, but excluding, the redemption date. The Depositary Shares will be redeemed if and to the extent the related Series G Preferred Shares are redeemed by the Company. Neither the Depositary Shares nor the Series G Preferred Shares have a stated maturity, nor will they be subject to any sinking fund or mandatory redemption. The Series G Preferred Shares are not convertible into any other securities. The Series G Preferred Shares do not have voting rights, except under limited circumstances. The net proceeds from the Series G Preferred Share offerings were used to redeem the Company’s outstanding 5.25% Series E Non-Cumulative Preferred Shares.

Series F Preferred Shares

In August 2017 and November 2017, Arch Capital completed combined $330 million of underwritten public offerings ($230 million in August 2017 and $100 million in November 2017) of 13.2 million depositary shares (the “Series F Depositary Shares”), each of which represents a 1/1,000th interest in a share of its 5.45% Non-Cumulative Preferred Shares, Series F, with a $0.01 par value and $25,000 liquidation preference per share (equivalent to $25 liquidation preference per Series F Depositary Share) (the “Series F Preferred Shares”). Each Series F Depositary Share, evidenced by a depositary receipt, entitles the holder, through the depositary, to a proportional fractional interest in all rights and preferences of the Series F Preferred Shares represented thereby (including any dividend, liquidation, redemption and voting rights).

Holders of Series F Preferred Shares will be entitled to receive dividend payments only when, as and if declared by the Board or a duly authorized committee of the board. Any such dividends will be payable from, and including, the date of original issue on a noncumulative basis, quarterly in arrears on the last day of March, June, September and December of each year, at an annual rate of 5.45%. Dividends on the Series F Preferred Shares are not cumulative. The Company will be restricted from paying dividends on or repurchasing its common shares unless certain dividend payments are made on the Series F Preferred Shares.

Except in specified circumstances relating to certain tax or corporate events, the Series F Preferred Shares are not redeemable prior to August 17, 2022 (the fifth anniversary of the issue date). On and after that date, the Series F Preferred

Shares will be redeemable at the Company’s option, in whole or in part, at a redemption price of $25,000 per share of the Series F Preferred Shares (equivalent to $25 per depositary share), plus any declared and unpaid dividends, without accumulation of any undeclared dividends to, but excluding, the redemption date. The Series F Depositary Shares will be redeemed if and to the extent the related Series F Preferred Shares are redeemed by the Company. Neither the Series F Depositary Shares nor the Series F Preferred Shares have a stated maturity, nor will they be subject to any sinking fund or mandatory redemption. The Series F Preferred Shares are not convertible into any other securities. The Series F Preferred Shares will not have voting rights, except under limited circumstances. The net proceeds from the Series F Preferred Share offerings were used to redeem the Company’s outstanding 6.75% Series C Non-Cumulative Preferred Shares.

Series E Preferred Shares

In September, 2021, Arch Capital redeemed all outstanding 5.25% Series E non-cumulative preferred shares. The preferred shares were redeemed at a redemption price equal to $25 per share, plus all declared and unpaid dividends to (but excluding) the redemption date. In accordance with GAAP, following the redemption, original issuance costs related to such shares have been removed from additional paid-in capital and recorded as a “loss on redemption of preferred shares.” Such adjustment had no impact on total shareholders’ equity or cash flows.

22.    Share-Based Compensation

Long Term Incentive and Share Award Plans

The Company utilizes share-based compensation plans for officers, other employees and directors of Arch Capital and its subsidiaries to provide competitive compensation opportunities, to encourage long-term service, to recognize individual contributions and reward achievement of performance goals and to promote the creation of long-term value for shareholders by aligning the interests of such persons with those of shareholders.

The 2022 Long-Term Incentive and Share Award Plan (“the 2022 Plan”) became effective as of May 4, 2022 following approval by shareholders of the Company. The 2022 Plan provides for the issuance of stock options, stock appreciation rights, restricted shares, restricted share units payable in common shares or cash, dividend equivalents, performance shares and performance units and other share-based awards to Arch Capital’s eligible employees and directors. The number of common shares reserved for grants under the 2022 Plan, subject to anti-dilution adjustments in the event of certain changes in Arch Capital’s capital structure, is 9,000,000; provided that no more than 6,000,000 common

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shares may be issued as incentive stock options under Section 422 of the Code. The 2022 Plan will terminate as to future awards on February 25, 2032. At December 31, 2022, 9,000,000 shares are available for future issuance.

The 2018 Long-Term Incentive and Share Award Plan (the “2018 Plan”) became effective as of May 9, 2018 following approval by shareholders of the Company. The 2018 Plan provides for the issuance of restricted stock units, performance units, restricted shares, performance shares, stock options and stock appreciation rights and other equity-based awards to our employees and directors. The 2018 Plan authorizes the issuance of 34,500,000 common shares and will terminate as to future awards on February 28, 2028. At December 31, 2022, 4,577,991 shares are available for future issuance.

The 2015 Long Term Incentive and Share Award Plan (the (“2015 Plan”) authorizes the issuance of 12,900,000 common shares and became effective as of May 7, 2015 following approval by shareholders of the Company. The 2015 Plan provides for the issuance of share-based awards to our employees and directors and will terminate as to future awards on February 26, 2025. At December 31, 2022, 504,872 shares are available for future issuance.

Upon shareholder approval on May 6, 2016, the Amended and Restated Arch Capital Group Ltd. 2007 Employee Share Purchase Plan (the “ESPP”) became effective and a total of 4,689,777 common shares were reserved for issuance. The purpose of the ESPP is to give employees of Arch Capital and its subsidiaries an opportunity to purchase common shares through payroll deductions, thereby encouraging employees to share in the economic growth and success of Arch Capital and its subsidiaries. The ESPP is designed to qualify as an “employee share purchase plan” under Section 423 of the Code. At December 31, 2022, 1,041,837 shares remain available for issuance.

Stock Options and Stock Appreciation Rights

The Company generally issues stock options and SARs to eligible employees, with exercise prices equal to the fair market values of the Company’s Common Shares on the grant dates. Such grants generally vest over a three year period with one-third vesting on the first, second and third anniversaries of the grant date.

The grant date fair value is determined using the Black-Scholes option valuation model. The expected life assumption is based on an expected term analysis, which incorporates the Company’s historical exercise experience. Expected volatility is based on the Company’s daily historical trading data of its common shares. The table below summarizes the assumptions used.

	Year Ended December 31,
	2022		2021		2020
Dividend yield	—	%	—	%	—	%
Expected volatility	24.0	%	24.2	%	16.6	%
Risk free interest rate	2.0	%	1.0	%	1.2	%
Expected option life	6.0 years		6.0 years		6.0 years

A summary of stock option and SAR activity under the Company’s Long Term Incentive and Share Award Plans during 2022 is presented below:

	Year Ended December 31, 2022
	Number of Options / SARs	Weighted Average Exercise Price		Weighted Average Contractual Term	Aggregate Intrinsic Value
Outstanding, beginning of year	17,083,160	$	25.06
Granted	784,963	$	47.46
Exercised	(3,412,371)	$	16.91
Forfeited or expired	(34,851)	$	39.96
Outstanding, end of year	14,420,901	$	28.17	4.37	$	499,051
Exercisable, end of year	12,433,470	$	26.20	3.77	$	454,769

The aggregate intrinsic value of stock options and SARs exercised represents the difference between the exercise price of the stock options and SARs and the closing market price of the Company’s common shares on the exercise dates. During 2022, the Company received proceeds of $17.2 million from the exercise of stock options and recognized a tax benefit of $8.7 million from the exercise of stock options and SARs.

	Year Ended December 31,
	2022		2021		2020
Weighted average grant date fair value	$	13.26	$	9.22	$	8.14
Aggregate intrinsic value of Options/SARs exercised	$	113,409	$	47,074	$	59,723

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Restricted Common Shares and Restricted Units

The Company also issues restricted share and unit awards to eligible employees and directors, for which the fair value is equal to the fair market values of the Company’s Common Shares on the grant dates. Restricted share and unit awards generally vest over a three year period with one-third vesting on the first, second and third anniversaries of the grant date.

A summary of restricted share and restricted unit activity under the Company’s Long Term Incentive and Share Award Plans for 2022 is presented below:

	Restricted Common Shares		Restricted Unit Awards
Unvested Shares:
Unvested balance, beginning of year	2,070,837		699,866
Granted	914,694		174,699
Vested	(744,096)		(330,144)
Forfeited	(75,881)		(27,128)
Unvested balance, end of year	2,165,554		517,293
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year	$	36.35	$	33.29
Granted	$	47.45	$	47.50
Vested	$	38.21	$	34.38
Forfeited	$	41.13	$	37.51
Unvested balance, end of year	$	40.23	$	37.17

The following table presents the weighted average grant date fair value of restricted shares and restricted unit awards granted and the aggregate fair value of restricted shares and unit awards vesting in each year.

	Year Ended December 31,
	2022		2021		2020
Restricted shares and restricted unit awards granted	1,089,393		1,261,773		1,535,330
Weighted average grant date fair value	$	47.45	$	36.12	$	37.55
Aggregate fair value of vested restricted share and unit awards	$	78,129	$	65,477	$	39,703

The aggregate intrinsic value of restricted units outstanding at December 31, 2022 was $32.5 million.

Performance Awards

The Company also issues performance share and unit awards (“performance awards”) to eligible employees, which are earned based on the achievement of pre-established threshold, target and maximum goals over three-year performance periods. Final payouts depend on the level of achievement along with each employees continued service through the vest date, and can vary between 0% and 200%. The grant date fair value of the performance awards is measured using a Monte Carlo simulation model, which incorporated the assumptions summarized in the table below. Expected volatility is based on the Company’s daily historical trading data of its common shares. The cumulative compensation expense recognized and unrecognized as of any reporting period date represents the adjusted estimate of performance shares and units that will ultimately be awarded, valued at their original grant date fair values.

	Year Ended December 31,
	2022		2021		2020
Expected volatility	38.1	%	37.5	%	18.1	%
Risk free interest rate	1.7	%	0.3	%	1.1	%

	Performance Shares		Performance Units
Unvested Shares:
Unvested balance, beginning of year	1,861,760		29,770
Granted	669,742		21,030
Performance adjustment (1) (2)	(54,904)		8,921
Vested	(583,544)		(19,695)
Forfeited	(10,138)		(316)
Unvested balance, end of year	1,882,916		39,710
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year	$	38.93	$	38.71
Granted	$	49.91	$	49.91
Performance adjustment (1) (2)	$	36.07	$	35.83
Vested	$	36.07	$	35.83
Forfeited	$	49.91	$	49.91
Unvested balance, end of year	$	43.75	$	45.33

(1)    The performance adjustment represents the difference between the number of performance shares granted and earned, which vested following the end of the performance period. The performance shares were granted at the maximum level of achievement.

(2)    The performance adjustment represents the change in PSUs, which vested following the end of the performance period. The performance units were granted at the target level of achievement.

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The following table presents the weighted average grant date fair values of performance awards granted.

	Year Ended December 31,
	2022		2021		2020
Performance awards	690,772		685,104		557,204
Weighted average grant date fair value	$	49.91	$	37.38	$	44.17

The issuance of share-based awards and amortization thereon has no effect on the Company’s consolidated shareholders’ equity.

Share-Based Compensation Expense

The following tables present pre-tax and after-tax share-based compensation expense recognized as well as the unrecognized compensation cost associated with unvested awards and the weighted average period over which it is expected to be recognized.

	Year Ended December 31,
	2022		2021		2020
Pre-Tax
Stock options and SARs	$	11,891	$	12,316	$	11,744
Restricted share and unit awards	50,278		46,817		41,284
Performance awards	21,510		23,696		14,729
ESPP	3,993		3,751		2,135
Total	$	87,672	$	86,580	$	69,892
After-Tax
Stock options and SARs	$	10,726	$	10,927	$	10,388
Restricted share and unit awards	42,346		39,349		34,599
Performance awards	19,794		21,920		13,380
ESPP	3,660		3,471		1,978
Total	$	76,526	$	75,667	$	60,345

	December 31, 2022
	Stock Options and SARs		Restricted Common Shares and Units		Performance Common Shares and Units
Unrecognized compensation cost related to unvested awards	$	6,357	$	42,096	$	7,520
Weighted average recognition period (years)	0.75		1.00		0.48

23.    Retirement Plans

For purposes of providing employees with retirement benefits, the Company maintains defined contribution retirement plans. Contributions are based on the participants’ eligible compensation. For 2022, 2021 and 2020, the Company expensed $67.0 million, $60.4 million and $52.0 million, respectively, related to these retirement plans.

24.    Legal Proceedings

The Company, in common with the insurance industry in general, is subject to litigation and arbitration in the normal course of its business. As of December 31, 2022, the Company was not a party to any litigation or arbitration which is expected by management to have a material adverse effect on the Company’s results of operations and financial condition and liquidity.

25.    Statutory Information

The Company’s insurance and reinsurance subsidiaries are subject to insurance and/or reinsurance laws and regulations in the jurisdictions in which they operate. These regulations include certain restrictions on the amount of dividends or other distributions available to shareholders without prior approval of the insurance regulatory authorities.

The actual and required statutory capital and surplus for the Company’s principal operating subsidiaries at December 31, 2022 and 2021:

	December 31,
	2022		2021
Actual capital and surplus (1):
Bermuda	$	19,546,128	$	17,528,510
Ireland	968,443		958,200
United States	6,194,954		5,600,652
United Kingdom	1,018,092		902,002
Canada	68,637		70,063
Australia	284,998		283,693
Required capital and surplus:
Bermuda	$	6,449,878	$	5,661,301
Ireland	815,194		794,933
United States	1,748,543		1,717,646
United Kingdom	543,104		563,164
Canada	47,825		42,513
Australia	175,885		214,022

(1)Such amounts include ownership interests in affiliated insurance and reinsurance subsidiaries.

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There were no state-prescribed or permitted regulatory accounting practices for any of the Company’s insurance or reinsurance entities that resulted in reported statutory surplus that differed from that which would have been reported under the prescribed practices of the respective regulatory authorities, including the National Association of Insurance Commissioners. The differences between statutory financial statements and statements prepared in accordance with GAAP vary by jurisdiction, however, with the primary differences being that statutory financial statements may not reflect deferred acquisition costs, certain net deferred tax assets, goodwill and intangible assets, unrealized appreciation or depreciation on debt securities and certain unauthorized reinsurance recoverables and include contingency reserves.

The statutory net income (loss) for the Company’s principal operating subsidiaries for 2022, 2021 and 2020 was as follows:

	Year Ended December 31,
	2022		2021		2020
Statutory net income (loss):
Bermuda	$	1,729,925	$	2,370,746	$	1,579,889
Ireland	(52,757)		25,191		18,397
United States	219,524		345,790		143,271
United Kingdom	56,818		35,286		4,078
Canada	9,215		6,985		(1,049)
Australia	38,538		11,874		(8,601)

Bermuda

The Company’s Bermuda insurance and reinsurance subsidiaries are subject to the Bermuda Insurance Act 1978 and related regulations, each as amended (the “Insurance Act”). Arch Re Bermuda, the Company’s principal reinsurance and insurance subsidiary, is registered as a Class 4 insurer and long-term insurer while Arch Group Reinsurance Ltd. (“AGRL”) is registered as a Class 3A general business insurer and provides affiliated quota share reinsurance covering certain U.S. business. The Insurance Act requires that both entities maintain minimum statutory capital and surplus equal to the greater of a minimum solvency margin and the enhanced capital requirement (“ECR”) as determined by the Bermuda Monetary Authority (“BMA”). The ECR is calculated based on the Bermuda Solvency Capital Requirement model, a risk-based model that takes into account the risk characteristics of different aspects of the company’s business. At December 31, 2022 and 2021, the actual and required capital and surplus were based on the economic balance sheet requirements.

Under the Insurance Act, Arch Re Bermuda and AGRL are restricted with respect to the payment of dividends. Each entity is prohibited from declaring or paying in any financial year dividends of more than 25% of its total statutory capital and surplus (as shown on its previous financial year’s

statutory balance sheet) unless it files, at least seven days before payment of such dividends, with the BMA an affidavit stating that it will continue to meet the required margins following the declaration of those dividends. Accordingly, Arch Re Bermuda can pay approximately $3.7 billion to Arch Capital during 2023 without providing an affidavit to the BMA. Dividends or distributions, if any, made by AGRL would result in an increase in available capital at Arch-U.S.

Ireland

The Company has three Irish subsidiaries: Arch Re Europe, an authorized life and non-life reinsurer, Arch Insurance (EU), an authorized non-life insurer and Arch Underwriting Europe, a registered insurance and reinsurance intermediary. Irish authorized reinsurers and insurers, such as Arch Re Europe, Arch Insurance (EU) and Irish intermediaries, such as Arch Underwriters Europe, are also subject to the general body of Irish laws and regulations including the provisions of the Companies Act 2014. As part of the Company’s Brexit plan, Arch Insurance (EU) received approval from the Central Bank of Ireland (“CBI”) to expand the nature of its business in 2019 commenced writing insurance lines in the European Economic Area in 2020, and the Part VII Transfer was completed at the end of December 2020. Arch Re Europe, Arch Insurance (EU) and Arch Underwriters Europe are subject to the supervision of the CBI and must comply with Irish insurance acts and regulations as well as with directions and guidance issued by the CBI. Arch Re Europe and Arch Insurance (EU) are required to maintain a minimum level of capital. At December 31, 2022 and 2021, these requirements were met.

The amount of dividends these subsidiaries are permitted to declare is limited to accumulated, realized profits, so far as not previously utilized by distribution or capitalization, less its accumulated, realized losses, so far as not previously written off in a reduction or reorganization of capital duly made. The solvency and capital requirements must still be met following any distribution. Dividends or distributions, if any, made by Arch Re Europe would result in an increase in available capital at Arch Re Bermuda.

United States

The Company’s U.S. insurance and reinsurance subsidiaries are subject to insurance laws and regulations in the jurisdictions in which they operate. The ability of the Company’s regulated insurance subsidiaries to pay dividends or make distributions is dependent on their ability to meet applicable regulatory standards. These regulations include restrictions that limit the amount of dividends or other distributions, such as loans or cash advances, available to shareholders without prior approval of the insurance regulatory authorities.

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Dividends or distributions, if any, made by Arch Re U.S. would result in an increase in available capital at Arch-U.S., the Company’s U.S. holding company. Arch Re U.S. can declare a maximum of approximately $255.4 million of dividends during 2023 subject to the approval of the Commissioner of the Delaware Department of Insurance.

AMIC and UGRIC are approved as eligible mortgage insurers by Fannie Mae and Freddie Mac, subject to maintaining certain requirements (“eligible mortgage insurers”). In April 2015, the GSEs published their original comprehensive, requirements, known as the Private Mortgage Insurer Eligibility Requirements or “PMIERs.” Revised and restated in September 2018, and clarified thereafter by the Guidance Letters 2020-1 and 2021-1 issued by the GSEs in 2020 and 2021, respectively, the PMIERs apply to the Company’s eligible mortgage insurers, but do not apply to AMG, which is not GSE-approved.

The amount of assets required to satisfy the revised financial requirements of the PMIERs may be affected by many factors, including macro-economic conditions, the size and composition of our mortgage insurance portfolio, and the amount of risk ceded to reinsurers that may be deducted in our calculation of “minimum required assets.”

The Company’s U.S. mortgage insurance subsidiaries are subject to regulation by their domiciliary and primary regulators, the Wisconsin Office of the Commissioner of Insurance (“Wisconsin OCI”) for AMIC and AMG, the North Carolina Department of Insurance (“NC DOI”) for UGRIC, and by state insurance departments in each state in which they are licensed. As mandated by state insurance laws, mortgage insurers are generally mono-line companies. Each company is subject to the statutory requirements of their domiciliary regulator as to payment of dividends and return of capital; the GSEs may also impart limitations on the Company’s eligible mortgage insurers, such as required minimum assets. Under respective state law, the Company’s U.S. mortgage subsidiaries can declare a maximum of approximately $156.5 million of ordinary dividends in 2023, however, dividend capacity is limited by the respective companies unassigned surplus amounts. Such dividends would increase the available capital at Arch U.S. MI Holdings Inc., a subsidiary of Arch-U.S.

Mortgage insurance companies licensed in Wisconsin or North Carolina are required to establish contingency loss reserves for purposes of statutory accounting in an amount equal to at least 50% of net earned premiums. These amounts generally cannot be withdrawn for a period of 10 years and are separate liabilities for statutory accounting purposes, which affects the ability to pay dividends. However, with prior regulatory approval, a mortgage insurance company may make early withdrawals from the contingency reserve

when incurred losses exceed 35% of net premiums earned in a calendar year.

Under Wisconsin and North Carolina law, as well as that of 14 other states, a mortgage insurer must maintain a minimum amount of statutory capital relative to its risk in force in order for the mortgage insurer to continue to write new business. While formulations of minimum capital vary in certain jurisdictions, the most common measure applied allows for a maximum risk-to-capital ratio of 25 to 1. Wisconsin and North Carolina require mortgage insurers to maintain a “minimum policyholder position” calculated in accordance with their respective regulations. Policyholders' position consists primarily of statutory policyholders' surplus plus the contingency loss reserves.

United Kingdom

The Prudential Regulation Authority (“PRA”) and the Financial Conduct Authority (“FCA”) regulate insurance and reinsurance companies and the FCA regulates firms carrying on insurance mediation activities operating in the U.K., both under the Financial Services and Markets Act 2000. In May 2004, Arch Insurance (U.K.) was granted the relevant permissions for the classes of insurance business which it underwrites in the U.K. AMAL currently manages Arch Syndicate 2012 and Arch Syndicate 1955 pursuant to its authorizations by the U.K. regulators and Lloyd’s. All U.K. companies are also subject to a range of statutory provisions, including the laws and regulations of the Companies Act 2006 (as amended) (the “U.K. Companies Act”).

Arch Insurance (U.K.) and AMAL must maintain a margin of solvency at all times under the Solvency II Directive from the European Insurance and Occupational Pensions Authority. The regulations stipulate that insurers are required to maintain the minimum capital requirement and solvency capital requirement at all times. At December 31, 2022 and 2021, these requirements were met.

As corporate members of Lloyd’s, AMAL (as managing agent of the Company’s Lloyd’s Syndicates) and each syndicate’s respective corporate members are subject to the oversight of the Council of Lloyd’s. The capital required to support a Syndicate’s underwriting capacity, or funds at Lloyd’s, is assessed annually and is determined by Lloyd’s in accordance with the capital adequacy rules established by the PRA. The Company has provided capital to support the underwriting of Arch Syndicate 2012 and Arch Syndicate 1955 in the form of pledged assets and letters of credit provided by Arch Re Bermuda. The amount which the Company provides as funds at Lloyd’s is not available for distribution to the Company for the payment of dividends. Lloyd’s is supervised by the PRA and required to implement certain rules prescribed by the PRA under the Lloyd’s Act of 1982 regarding the operation of the Lloyd’s market. With

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respect to managing agents and corporate members, Lloyd’s prescribes certain minimum standards relating to management and control, solvency and other requirements and monitors managing agents’ compliance with such standards.

Under U.K. law, all U.K. companies are restricted from declaring a dividend to their shareholders unless they have “profits available for distribution.” The calculation as to whether a company has sufficient profits is based on its accumulated realized profits minus its accumulated realized losses. U.K. insurance regulatory laws do not prohibit the payment of dividends, but the PRA or FCA, as applicable, requires that insurance companies and insurance intermediaries maintain certain solvency margins and may restrict the payment of a dividend by Arch Insurance (U.K.) and AMAL.

Canada

Arch Insurance Canada and the Canadian branch of Arch Re U.S. (“Arch Re Canada”) are subject to federal, as well as provincial and territorial, regulation in Canada. The Office of the Superintendent of Financial Institutions (“OSFI”) is the federal regulatory body that, under the Insurance Companies Act (Canada), regulates federal Canadian and non-Canadian insurance companies operating in Canada. Arch Insurance Canada and Arch Re Canada are subject to regulation in the provinces and territories in which they underwrite insurance/reinsurance, and the primary goal of insurance/reinsurance regulation at the provincial and territorial levels is to govern the market conduct of insurance/reinsurance companies. Arch Insurance Canada is licensed to carry on insurance business by OSFI and in each province and territory. Arch Re Canada is licensed to carry-on reinsurance business by OSFI and in the provinces of Ontario and Quebec.

Under the Insurance Companies Act (Canada), Arch Insurance Canada is required to maintain an adequate amount of capital in Canada, calculated in accordance with a test promulgated by OSFI called the Minimum Capital Test (“MCT”), and Arch Re Canada is required to maintain an adequate margin of assets over liabilities in Canada, calculated in accordance with a test promulgated by OSFI called the Branch Adequacy of Assets Test. Under the Insurance Companies Act (Canada), approval of the Minister of Finance (Canada) is required in connection with certain acquisitions of shares of, or control of, Canadian insurance companies such as Arch Insurance Canada, and notice to and/or approval of OSFI is required in connection with the payment of dividends by or redemption of shares by Canadian insurance companies such as Arch Insurance Canada.

Australia

The Australian Prudential Regulation Authority (“APRA”) is an independent statutory authority responsible for prudential supervision of institutions across banking, insurance and superannuation and promotes financial stability in Australia. Arch Indemnity has been authorized to conduct monoline lenders’ mortgage insurance business in Australia since June 2002 and was acquired by Arch Capital on August 30, 2021 and since that date is the primary provider of lenders’ mortgage insurance for the group. Arch Indemnity has also been licensed by the Australian Securities and Investments Commission (“ASIC”) since March 2011 to engage in credit activities in Australia. Arch LMI Pty Ltd. (“Arch LMI”) was formerly authorized by APRA in January 2019 to conduct monoline lenders’ mortgage insurance business in Australia; however, in December 2022, we converted Arch LMI to a services company for our Australian lenders mortgage insurance operations and the company relinquished its APRA authorization. Major regulatory requirements that are applicable to Arch Indemnity in general as an insurance provider and financial institution in Australia include requirements and compliance with minimum capital levels; risk management strategy; corporate governance standards, privacy legislation on the collection, use and storage of personal information; cyber security obligations imposed by APRA and ASIC; modern slavery legislation; anti-money laundering and counter-terrorism legislation. At December 31, 2022 and 2021, these requirements were met.

Arch Capital also conducts property and casualty insurance business in Australia through the Company’s Lloyd’s platform. This insurance business is managed by and distributed through local coverholders and is subject to Lloyd’s Supervision. In addition, the business is subject to local Australian prudential regulatory oversight by APRA, and additional separate financial services market conduct regulation by the Australian Securities and Investments Commission.

ARCH CAPITAL 168 2022 FORM 10-K

ITEM 9. CHANGES IN AND DISAGREEMENTS WITH ACCOUNTANTS ON ACCOUNTING AND FINANCIAL DISCLOSURE

None.

ITEM 9A. CONTROLS AND PROCEDURES

Evaluation of Disclosure Controls and Procedures

In connection with the filing of this Form 10-K, our management, including the Chief Executive Officer and Chief Financial Officer, conducted an evaluation, as of December 31, 2022, for the purposes set forth in the applicable rules under the Securities and Exchange Act of 1934, as amended (the “Exchange Act”). Based on that evaluation, the Chief Executive Officer and Chief Financial Officer concluded that the disclosure controls and procedures are effective.

We continue to enhance our operating procedures and internal controls (including information technology initiatives and controls over financial reporting) to effectively support our business and our regulatory and reporting requirements. Our management does not expect that our disclosure controls or our internal controls will prevent all errors and all fraud. A control system, no matter how well conceived and operated, can provide only reasonable, not absolute, assurance that the objectives of the control system are met. Further, the design of a control system must reflect the fact that there are resource constraints, and the benefits of controls must be considered relative to their costs. As a result of the inherent limitations in all control systems, no evaluation of controls can provide absolute assurance that all control issues and instances of fraud, if any, within the company have been detected. These inherent limitations include the realities that judgments in decision making can be faulty, and that breakdowns can occur because of simple error or mistake. Additionally, controls can be circumvented by the individual acts of some persons or by collusion of two or more people.

The design of any system of controls also is based in part upon certain assumptions about the likelihood of future events, and there can be no assurance that any design will succeed in achieving its stated goals under all potential future conditions; over time, controls may become inadequate because of changes in conditions, or the degree of

compliance with the policies or procedures may deteriorate. As a result of the inherent limitations in a cost-effective control system, misstatement due to error or fraud may occur and not be detected. Accordingly, our disclosure controls and procedures are designed to provide reasonable, not absolute, assurance that the disclosure controls and procedures are met.

Management’s Annual Report on Internal Control Over Financial Reporting

Our management is responsible for establishing and maintaining adequate internal control over financial reporting, as defined in Rules 13a-15(f) and 15d-15(f) under the Exchange Act. Our management assessed the effectiveness of our internal control over financial reporting as of December 31, 2022. In making this assessment, management used the criteria set forth by the Committee of Sponsoring Organizations (COSO) of the Treadway Commission in Internal Control-Integrated Framework (2013).

Based on our assessment, management determined that, as of December 31, 2022, our internal control over financial reporting was effective. The effectiveness of our internal control over financial reporting as of December 31, 2022 has been audited by PricewaterhouseCoopers LLP, an independent registered public accounting firm, as stated in their report included in Item 8.

Changes in Internal Control Over Financial Reporting

There have been no changes in internal control over financial reporting that occurred in connection with our evaluation required pursuant to Rules 13a-15 and 15d-15 under the Exchange Act during the fiscal quarter ended December 31, 2022 that have materially affected, or are reasonably likely to materially affect, internal control over financial reporting.

ARCH CAPITAL 169 2022 FORM 10-K

ITEM 9B. OTHER INFORMATION

None.

ITEM 9C. DISCLOSURE REGARDING FOREIGN JURISDICTIONS THAT PREVENT INSPECTIONS

Not applicable.

PART III

ITEM 10. DIRECTORS, EXECUTIVE OFFICERS AND CORPORATE GOVERNANCE

The information required by this item is incorporated by reference from the information to be included in our definitive proxy statement (“Proxy Statement”) for our annual meeting of shareholders to be held in 2023, which we intend to file with the SEC pursuant to Regulation 14A no later than 120 days after the end of the Company’s fiscal year which ended on December 31, 2022. Copies of our code of ethics applicable to our chief executive officer, chief financial officer and principal accounting officer or controller are available free of charge to investors upon written request addressed to the attention of Arch Capital’s corporate secretary, Waterloo House, 100 Pitts Bay Road, Pembroke HM 08, Bermuda. In addition, our code of ethics and certain other basic corporate documents, including the charters of our audit committee, compensation committee and nominating committee are posted on our website located at www.archgroup.com.

If any substantive amendments are made to the code of ethics or if there is a grant of a waiver, including any implicit waiver, we will disclose the nature of such amendment or waiver on our website or in a report on Form 8-K, to the extent required by applicable law or the rules and regulations of any exchange applicable to us. Our website address is intended to be an inactive, textual reference only and none of the material on our website is incorporated by reference into this report.

ITEM 11. EXECUTIVE COMPENSATION

The information required by this item is incorporated by reference from the information to be included in the Proxy Statement which we intend to file pursuant to Regulation 14A with the SEC no later than 120 days after the end of the Company’s fiscal year ended on December 31, 2022, which Proxy Statement is incorporated by reference.

ARCH CAPITAL 170 2022 FORM 10-K

ITEM 12. SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND MANAGEMENT AND RELATED STOCKHOLDER MATTERS

Other than the information set forth below, the information required by this item is incorporated by reference from the information to be included in the Proxy Statement which we intend to file pursuant to Regulation 14A with the SEC no later than 120 days after the end of the Company’s fiscal year ended on December 31, 2022, which Proxy Statement is incorporated by reference.

The following information is as of December 31, 2022:

	Column A	Column B		Column C
Plan Category	Number of Securities to be Issued Upon Exercise of Outstanding Stock Options(1), Warrants and Rights	Weighted-Average Exercise Price of Outstanding Stock Options(1), Warrants and Rights ($)		Number of Securities Remaining Available for Future Issuance Under Equity Compensation Plans (Excluding Securities Reflected in Column A)
Equity compensation plans approved by security holders	14,977,904	$	28.17	15,124,700
Equity compensation plans not approved by security holders	—	—		—
Total	14,977,904	$	28.17	15,124,700	(2)

________________________

(1)    Includes all vested and unvested stock options outstanding of 14,420,901 and restricted stock and performance units outstanding of 557,003. The weighted average exercise price does not take into account restricted stock units. In addition, the weighted average remaining contractual life of the Company's outstanding exercisable stock options and SARs at December 31, 2022 was 4.4 years.

(2)    Includes 1,041,837 common shares remaining available for future issuance under our Employee Share Purchase Plan and 14,082,863 common shares remaining available for future issuance under our equity compensation plans. Shares available for future issuance under our equity compensation plans may be issued in the form of stock options, SARs, restricted shares, restricted share units payable in common shares or cash, share awards in lieu of cash awards, dividend equivalents, performance shares and performance units and other share-based awards. In addition, 10,476,836 common shares, or 69.3% of the 15,124,700 common shares remaining available for future issuance may be issued in connection with full value awards (i.e., awards other than stock options or SARs).

ITEM 13. CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS, AND DIRECTOR INDEPENDENCE

The information required by this item is incorporated by reference from the information to be included in the Proxy Statement which we intend to file pursuant to Regulation 14A with the SEC no later than 120 days after the end of the Company’s fiscal year ended on December 31, 2022, which Proxy Statement is incorporated by reference.

ITEM 14. PRINCIPAL ACCOUNTANT FEES AND SERVICES

The information required by this item is incorporated by reference from the information to be included in our Proxy Statement which we intend to file pursuant to Regulation 14A with the SEC no later than 120 days after the end of the Company’s fiscal year ended on December 31, 2022, which Proxy Statement is incorporated by reference.

ARCH CAPITAL 171 2022 FORM 10-K

PART IV

ITEM 15. EXHIBITS AND FINANCIAL STATEMENT SCHEDULES

(a) Financial Statements, Financial Statement Schedules and Exhibits.
1. Financial Statements
	Included in Part II – see Item 8 of this report.
2. Financial Statement Schedules
		Page No.
II. Condensed Financial Information of Registrant
	As of December 31, 2022 and 2021, and for the years ended December 31, 2022, 2021 and 2020	178
III. Supplementary Insurance Information
	For the years ended December 31, 2022, 2021 and 2020	181
IV. Reinsurance
	For the years ended December 31, 2022, 2021 and 2020	182
VI. Supplementary Information for Property and Casualty Insurance Underwriters
	For the years ended December 31, 2022, 2021 and 2020	183

Schedules other than those listed above are omitted for the reason that they are not applicable or the information is provided in Item 8 of this report.

ARCH CAPITAL 172 2022 FORM 10-K

3. Exhibits

		Incorporated by Reference
Exhibit Number	Exhibit Description	Form	Original Number	Date Filed	Filed Herewith
2.1	Memorandum of Association of ACGL	S-4	3.1	September 8, 2000
2.2	Bye-Laws of ACGL	10-Q	3	August 5, 2016
2.3	ACGL Certificate of Deposit of Memorandum of Increase of Share Capital	10-K	3.3	February 28, 2011
3.1	Certificate of Designations of Series F Non-Cumulative Preferred Shares	8-K	4.1	August 17, 2017
3.2	Certificate of Designations of Series G Non-Cumulative Preferred Shares	8-K	4.1	June 11, 2021
3.3	Specimen Common Share Certificate	10-K	4.1	April 2, 2001
3.4	Specimen Series F Non-Cumulative Preferred Share Certificate	8-K	4.2	August 17, 2017
3.5	Specimen Series G Non-Cumulative Preferred Share Certificate	8-K	4.2	June 11, 2021
4.1	Indenture, dated as of May 4, 2004, between ACGL, as issuer, and The Bank of New York Mellon, as successor trustee to JPMorgan Chase Bank, N.A. (formerly JPMorgan Chase Bank) (“JPMCB”), as trustee	8-K	4.1	June 30, 2020
4.2	First Supplemental Indenture, dated as of May 4, 2004, between ACGL, as issuer, and JPMCB, as trustee	8-K	99.3	May 7, 2004
4.3	Second Supplemental Indenture, dated as of June 30, 2020, by and between Arch Capital Group Ltd. and The Bank of New York Mellon (including the form of Global Notes for the Notes).	8-K	4.2	June 30, 2020
4.4.1	Indenture, dated as of December 13, 2013, among Arch Capital Group (U.S.) Inc. (“Arch U.S.”), as issuer, ACGL, as guarantor, and The Bank of New York Mellon (“BNYM”), as trustee	8-K	4.1	December 13, 2013
4.4.2	First Supplemental Indenture, dated as of December 13, 2013, among Arch U.S., as issuer, ACGL, as guarantor, and BNYM, as trustee	8-K	4.2	December 13, 2013
4.4.3	Second Supplemental Indenture, dated as of May 10, 2018, among Arch Capital Finance LLC, as issuer, ACGL, as guarantor, and BNYM, as trustee	8-K	4.1	May 15, 2018
4.5.1	Deposit Agreement, dated August 17, 2017, between ACGL, as issuer, and AST, as depositary, registrar and transfer agent and as dividend disbursing agent and redemption agent, and the holders from time to time of the depositary receipts	8-K	4.3	August 17, 2017
4.5.2	Deposit Agreement, dated June 11, 2021, between ACGL, as issuer, and AST, as depositary, registrar and transfer agent and as dividend disbursing agent and redemption agent, and the holders from time to time of the depositary receipts	8-K	4.3	June 11, 2021
4.6.1	Form of Depositary Receipt, dated August 17, 2017	8-K	4.4	August 17, 2017
4.6.2	Form of Depositary Receipt, dated June 11, 2021	8-K	4.4	June 11, 2021
4.7.1	Indenture, dated as of December 8, 2016, among Arch Capital Finance LLC, as issuer, ACGL, as guarantor, and BNYM, as trustee	8-K	4.1	December 9, 2016
4.7.2	First Supplemental Indenture, dated as of December 8, 2016, among Arch Capital Finance LLC, as issuer, ACGL, as guarantor, and BNYM, as trustee	8-K	4.2	December 9, 2016
4.8	Description of Securities	10-K	4.8	February 25, 2022
10.2.1	Third Amended and Restated ACGL Incentive Compensation Plan†	10-Q	10.7	August 5, 2016
10.2.2	First Amendment to Third Amended and Restated ACGL Incentive Compensation Plan†	10-Q	10.1	May 5, 2017
10.2.3	Second Amendment to Third Amended and Restated ACGL Incentive Compensation Plan	10-K	4.8	February 25, 2022
10.3.1	ACGL 2007 Long Term Incentive and Share Award Plan†	DEF 14A		April 3, 2007
10.3.2	ACGL 2012 Long Term Incentive and Share Award Plan†	DEF 14A		March 27, 2012
10.3.3	ACGL 2015 Long Term Incentive and Share Award Plan†	DEF 14A		March 26, 2015
10.3.4	ACGL 2018 Long Term Incentive and Share Award Plan†	DEF 14A		March 28, 2018
10.3.5	ACGL Amended and Restated 2007 Employee Share Purchase Plan†	DEF 14A		March 23, 2016
10.3.6	ACGL 2022 Long Term Incentive and Share Award Plan†	8-K	10.1	May 4, 2022
10.4.1	Form of Restricted Share Agreement, dated as of May 13, 2015, between ACGL and each of, Marc Grandisson, Nicolas Papadopoulo, Maamoun Rajeh and Louis T. Petrillo†	10-Q	10.2	August 7, 2015
10.4.2	Form of Restricted Share Agreement, dated as of May 13, 2016, between ACGL and each of Marc Grandisson, Nicolas Papadopoulo, Maamoun Rajeh and Louis T. Petrillo†	10-Q	10.2	August 5, 2016
10.4.3	Form of Restricted Share Agreement, dated as of May 4, 2017, between ACGL and each of the Non-Employee Directors of ACGL†	10-Q	10.3	August 4, 2017

ARCH CAPITAL 173 2022 FORM 10-K

10.4.4	Form of Restricted Share Agreement, dated as of May 8, 2017, between ACGL and each of Marc Grandisson, Nicolas Papadopoulo, Maamoun Rajeh and Louis T. Petrillo†	10-Q	10.4	August 4, 2017
10.4.5	Form of Restricted Share Agreement, dated as of September 19, 2017, between ACGL and each of Nicolas Papadopoulo and Maamoun Rajeh†	10-K	10.4.13	February 28, 2018
10.4.6	Form of Restricted Share Agreement for Named Executive Officers and certain Executive Officers of ACGL and subsidiaries†	10-Q	10.3	August 8, 2018
10.4.7	Form of Restricted Share Agreement between ACGL and each of the Non-Employee Directors of ACGL†	10-Q	10.6	August 8, 2018
10.5	Form of Performance Restricted Share Agreement for Named Executive Officers and certain Executive Officers of ACGL and subsidiaries†	10-Q	10.5	August 8, 2018
10.6.1	Form of Non-Qualified Stock Option Agreement, dated as of May 13, 2015, between ACGL and each of Marc Grandisson†	10-Q	10.3	August 7, 2015
10.6.2	Form of Non-Qualified Stock Option Agreement, dated as of May 13, 2016, between ACGL and each of Marc Grandisson, Nicolas Papadopoulo, Maamoun Rajeh and Louis T. Petrillo†	10-Q	10.3	August 5, 2016
10.6.3	Form of Non-Qualified Stock Option Agreement, dated as of May 8, 2017, between ACGL and each of Marc Grandisson, Nicolas Papadopoulo, Maamoun Rajeh and Louis T. Petrillo†	10-Q	10.5	August 4, 2017
10.6.4	Non-Qualified Stock Option Agreement, dated as of September 19, 2017, between ACGL and Maamoun Rajeh†	10-K	10.5.6	February 28, 2018
10.6.5	Non-Qualified Stock Option Agreement, dated as of September 19, 2017, between ACGL and Nicolas Papadopoulo†	10-K	10.5.7	February 28, 2018
10.6.6	Form of Non-Qualified Stock Option Agreement for Named Executive Officers and certain Executive Officers of ACGL and subsidiaries†	10-Q	10.4	August 8, 2018
10.6.7	Non-Qualified Stock Option Agreement, dated as of April 9, 2018, between ACGL and Marc Grandisson†	10-Q	10.5	May 9, 2018
10.7.1	Form of Share Appreciation Right Agreement, dated as of May 9, 2013, between ACGL and each of Marc Grandisson, Maamoun Rajeh and Louis T. Petrillo†	10-Q	10.2	November 8, 2013
10.7.2	Form of Share Appreciation Right Agreement, dated as of May 13, 2014, between ACGL and each of Marc Grandisson, Maamoun Rajeh and Louis T. Petrillo†	10-Q	10.3	August 8, 2014
10.7.3	Share Appreciation Right Agreement, dated as of July 1, 2014, between ACGL and Maamoun Rajeh†	10-Q	10.15	November 3, 2017
10.7.4	Share Appreciation Right Agreement, dated as of November 6, 2014, between ACGL and Marc Grandisson†	10-Q	10.2	May 8, 2015
10.8.1	Employment Agreement, dated as of October 27, 2008, between ACGL and John D. Vollaro†	8-K	10.1	October 28, 2008
10.8.2	Amendment to Employment Agreement, dated February 27, 2015, between ACGL and John D. Vollaro†	10-Q	10.1	May 8, 2015
10.8.3	Second Amendment to Employment Agreement, dated as of January 1, 2018, between ACGL and John D. Vollaro†	10-Q	10.1	May 9, 2018
10.10	Employment Agreement, dated as of September 19, 2017 between ACGL and Maamoun Rajeh†	10-Q	10.26	November 3, 2017
10.11	Employment Agreement, dated as of September 19, 2017 between ACGL and Nicholas Papadopoulo†	10-Q	10.27	November 3, 2017
10.12	Employment Agreement, dated as of May 25, 2018, between ACGL and François Morin†	8-K/A	10.1	July 26, 2018
10.13	Employment Agreement, dated as of April 9, 2018, between ACGL and Marc Grandisson†	8-K/A	10.1	April 11, 2018
10.14	Employment Agreement, dated as of November 13, 2018, between Arch Capital Services Inc. and Louis Petrillo†	10-K	10.16	February 28, 2019
10.15	Employment Agreement dated as of October 1,2019 between Arch Capital Group Ltd. and David Gansberg †	10-K	10.16	February 28, 2020
10.16	Employment Agreement dated as of May 7, 2021 between Arch Capital Group Ltd. and Christine Todd †	10-Q	10.1	August 5, 2021
10.17	Arch U.S. Executive Supplemental Non-Qualified Savings and Retirement Plan†	10-K	10.24	March 2, 2009
10.18.1	Third Amended and Restated Credit Agreement, dated as of December 17, 2019, by and among ACGL, certain of its subsidiaries as subsidiary borrowers, Bank of America, N.A., as Administrative Agent, Fronting Bank and L/C Administrator, and the lenders party thereto	8-K	10.1	December 18, 2019
10.18.2	First Amendment to Third Amended and Restated Credit Agreement, dated as of August 12, 2020 by and among Arch Capital Group Ltd., the other Loan Parties party hereto, the Lenders party hereto, and Bank of America, N.A., as Administrative Agent.	10-Q	10.1	November 4, 2021

ARCH CAPITAL 174 2022 FORM 10-K

10.18.3	The LIBOR Transition Amendment to the Third Amended and Restated Credit Agreement, dated as of September 29, 2021.	10-Q	10.2	November 4, 2021
10.18.4	Second Amendment to Third Amended and Restated Credit Agreement, effective as of April 7, 2022, by and among Arch Capital Group Ltd., certain of its subsidiaries, Bank of America, N.A., as Administrative Agent, and the lenders party thereto	8-K	10.1	April 12, 2022
21	Subsidiaries of Registrant				X
23	Consent of PricewaterhouseCoopers LLP				X
24	Power of Attorney				X
31.1	Certification of Chief Executive Officer pursuant to Section 302 of the Sarbanes-Oxley Act of 2002				X
31.2	Certification of Chief Financial Officer pursuant to Section 302 of the Sarbanes-Oxley Act of 2002				X
32.1	Certification of Chief Executive Officer pursuant to Section 906 of the Sarbanes-Oxley Act of 2002				X
32.2	Certification of Chief Financial Officer pursuant to Section 906 of the Sarbanes-Oxley Act of 2002				X
101	The following financial information from ACGL’s Annual Report on Form 10-K for the year ended December 31, 2022 formatted in Inline XBRL: (i) Consolidated Balance Sheets at December 31, 2022 and 2021; (ii) Consolidated Statements of Income for the years ended December 31, 2022, 2021 and 2020; (iii) Consolidated Statements of Comprehensive Income for the years ended December 31, 2022, 2021 and 2020; (iv) Consolidated Statements of Changes in Shareholders’ Equity for the years ended December 31, 2022, 2021 and 2020; (v) Consolidated Statements of Cash Flows for the years ended December 31, 2022, 2021 and 2020; and (vi) Notes to Consolidated Financial Statements				X
104	Cove Page Interactive Data File (embedded within the Inline XBRL document)

†    Management contract or compensatory plan or arrangement.

ARCH CAPITAL 175 2022 FORM 10-K

SIGNATURES

Pursuant to the requirements of Section 13 or 15(d) of the Securities Exchange Act of 1934, the Registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

ARCH CAPITAL GROUP LTD. (Registrant)
By:	/s/ Marc Grandisson
	Name:	Marc Grandisson
	Title:	Chief Executive Officer (Principal Executive Officer)

February 24, 2023

Pursuant to the requirements of the Securities Exchange Act of 1934, this report has been signed below by the following persons on behalf of the Registrant and in the capacities and on the dates indicated.

Name	Title	Date
/s/ Marc Grandisson
Marc Grandisson	Chief Executive Officer (Principal Executive Officer)	February 24, 2023
/s/ François Morin
François Morin	Executive Vice President and Chief Financial Officer (Principal Financial Officer and Principal Accounting Officer) and Treasurer	February 24, 2023
*
John M. Pasquesi	Chairman of the Board	February 24, 2023
*
John L. Bunce, Jr.	Director	February 24, 2023
*
Eric W. Doppstadt	Director	February 24, 2023
*
Francis Ebong	Director	February 24, 2023
*
Laurie S. Goodman	Director	February 24, 2023

ARCH CAPITAL 176 2022 FORM 10-K

Name	Title	Date
*
Moira Kilcoyne	Director	February 24, 2023
*
Eileen Mallesch	Director	February 24, 2023
*
Louis J. Paglia	Director	February 24, 2023
*
Brian S. Posner	Director	February 24, 2023
*
Eugene S. Sunshine	Director	February 24, 2023
*
John D. Vollaro	Director	February 24, 2023
*
Thomas R. Watjen	Director	February 24, 2023

___________________

*    By François Morin, as attorney-in-fact and agent, pursuant to a power of attorney, a copy of which has been filed with the Securities and Exchange Commission as Exhibit 24 to this report.

/s/ François Morin
Name:	François Morin Attorney-in-Fact

ARCH CAPITAL 177 2022 FORM 10-K

SCHEDULE II

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONDENSED FINANCIAL INFORMATION OF REGISTRANT

(U.S. dollars in thousands)

Balance Sheet

(Parent Company Only)

	December 31,
	2022		2021
Assets
Total investments	$	7,282	$	2,038
Cash	11,393		16,317
Investments in subsidiaries	14,191,188		14,822,024
Investment in operating affiliates	5,259		6,877
Due from subsidiaries and affiliates	1,554		11
Other assets	17,203		9,604
Total assets	$	14,233,879	$	14,856,871
Liabilities
Senior notes	$	1,286,567	$	1,286,208
Other liabilities	37,239		24,767
Total liabilities	1,323,806		1,310,975
Shareholders' Equity
Non-cumulative preferred shares	830,000		830,000
Common shares ($0.0011 par, shares issued: 588,250,762 and 583,289,850)	654		648
Additional paid-in capital	2,211,444		2,085,075
Retained earnings	15,892,065		14,455,868
Accumulated other comprehensive income (loss), net of deferred income tax	(1,646,170)		(64,600)
Common shares held in treasury, at cost (shares: 217,904,765 and 204,365,956)	(4,377,920)		(3,761,095)
Total shareholders' equity	$	12,910,073	$	13,545,896
Total liabilities and shareholders' equity	$	14,233,879	$	14,856,871

The financial information for the parent company (Arch Capital Group Ltd.) should be read in conjunction with the Consolidated Financial Statements and Notes thereto.

ARCH CAPITAL 178 2022 FORM 10-K

SCHEDULE II

(continued)

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONDENSED FINANCIAL INFORMATION OF REGISTRANT

(U.S. dollars in thousands)

Statement of Income

(Parent Company Only)

	Year Ended
	December 31,
	2022		2021		2020
Revenues
Net investment income	$	2,058	$	1,524	$	53
Net realized gains (losses)	29		—		(2,110)
Total revenues	2,087		1,524		(2,057)
Expenses
Corporate expenses	85,997		71,818		65,566
Interest expense	58,759		58,741		40,445
Net foreign exchange (gains) losses	(1)		7		3
Total expenses	144,755		130,566		106,014
Income (loss) before income taxes and income (loss) from operating affiliates	(142,668)		(129,042)		(108,071)
Income (loss) from operating affiliates	(1,047)		(590)		(437)
Income (loss) before equity in net income of subsidiaries	(143,715)		(129,632)		(108,508)
Equity in net income of subsidiaries	1,592,929		2,286,481		1,514,029
Net income available to Arch	1,449,214		2,156,849		1,405,521
Preferred dividends	(40,736)		(48,343)		(41,612)
Loss on redemption of preferred shares	—		(15,101)		—
Net income available to Arch common shareholders	$	1,408,478	$	2,093,405	$	1,363,909

The financial information for the parent company (Arch Capital Group Ltd.) should be read in conjunction with the Consolidated Financial Statements and Notes thereto.

ARCH CAPITAL 179 2022 FORM 10-K

SCHEDULE II

(continued)

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONDENSED FINANCIAL INFORMATION OF REGISTRANT

(U.S. dollars in thousands)

Statement of Cash Flows

(Parent Company Only)

	Year Ended
	December 31,
	2022		2021		2020
Operating Activities:
Net Cash Provided By Operating Activities	$	621,307	$	1,727,529	$	124,751
Investing Activities:
Net (purchases) sales of short-term investments	(4,838)		(1,866)		(130)
Capital contributed to subsidiaries	—		(487,161)		(988,975)
Purchase of fixed assets	(22)		(783)		(15)
Other	(1,462)		—		—
Net Cash Used For Investing Activities	(6,322)		(489,810)		(989,120)
Financing Activities:
Purchases of common shares under share repurchase program	(585,823)		(1,234,294)		(83,472)
Proceeds from common shares issued, net	6,660		6,418		1,876
Proceeds from issuance of preferred shares, net	—		485,821		—
Redemption of preferred shares	—		(450,000)		—
Proceeds from borrowings	—		—		988,393
Preferred dividends paid	(40,736)		(48,280)		(41,612)
Net Cash Used For Financing Activities	(619,899)		(1,240,335)		865,185
Increase (decrease) in cash and restricted cash	(4,914)		(2,616)		816
Cash and restricted cash, beginning of year	16,344		18,960		18,144
Cash and restricted cash, end of period	$	11,430	$	16,344	$	18,960

The financial information for the parent company (Arch Capital Group Ltd.) should be read in conjunction with the Consolidated Financial Statements and Notes thereto.

ARCH CAPITAL 180 2022 FORM 10-K

SCHEDULE III

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

SUPPLEMENTARY INSURANCE INFORMATION

(U.S. dollars in thousands)

	Deferred Acquisition Costs	Reserves for Losses and Loss Adjustment Expenses	Unearned Premiums	Net Premiums Earned	Net Investment Income (1)	Net Losses and Loss Adjustment Expenses Incurred	Amortization of Deferred Acquisition Costs	Other Operating Expenses (2)	Net Premiums Written
December 31, 2022
Insurance	$301,398	$11,017,327	$3,381,810	$4,559,335	NM	$2,782,945	$885,866	$665,472	$5,020,642
Reinsurance	992,339	8,305,854	3,206,284	3,959,381	NM	2,568,843	813,555	267,531	4,923,976
Mortgage	(29,867)	708,762	748,908	1,159,361	NM	(324,271)	40,159	195,172	1,132,571
Other
Total	$1,263,870	$20,031,943	$7,337,002	$9,678,077	NM	$5,027,517	$1,739,580	$1,128,175	$11,077,189
December 31, 2021
Insurance	$378,265	$9,810,622	$2,937,664	$3,626,468	NM	$2,344,365	$606,265	$558,906	$4,148,193
Reinsurance	424,390	6,878,721	2,263,264	2,840,443	NM	1,924,719	536,754	212,810	3,254,374
Mortgage	99,186	1,067,813	811,014	1,283,419	NM	56,677	97,418	194,010	1,261,068
Other				331,968	NM	259,042	62,741	32,869	354,702
Total	$901,841	$17,757,156	$6,011,942	$8,082,298	NM	$4,584,803	$1,303,178	$998,595	$9,018,337
December 31, 2020
Insurance	$254,833	$8,989,930	$2,334,225	$2,871,420	NM	$2,092,453	$418,483	$489,153	$3,162,907
Reinsurance	278,422	5,027,742	1,356,983	2,162,229	NM	1,628,320	354,048	168,011	2,457,370
Mortgage	203,748	976,673	740,043	1,397,935	NM	528,344	134,240	162,202	1,279,850
Other	53,705	1,519,583	407,714	560,351	NM	440,482	98,071	55,810	537,589
Total	$790,708	$16,513,928	$4,838,965	$6,991,935	NM	$4,689,599	$1,004,842	$875,176	$7,437,716

(1)    The Company does not manage its assets by segment and, accordingly, net investment income is not allocated to each underwriting segment. See note 4, “Segment Information,” to our consolidated financial statements in Item 8 for information related to the ‘other’ segment.

(2)    Certain other operating expenses relate to the Company’s corporate segment. Such amounts are not reflected in the table above. See note 4, “Segment Information,” to our consolidated financial statements in Item 8 for information related to the corporate segment.

ARCH CAPITAL 181 2022 FORM 10-K

SCHEDULE IV

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

REINSURANCE

(U.S. dollars in thousands)

	Gross Amount		Ceded to Other Companies (1)		Assumed From Other Companies (1)		Net Amount		Percentage of Amount Assumed to Net
Year Ended December 31, 2022
Premiums Written:
Insurance	$	6,889,358	$	(1,910,222)	$	41,506	$	5,020,642	0.8	%
Reinsurance	395,063		(2,024,462)		6,553,375		4,923,976		133.1	%
Mortgage	1,256,366		(322,400)		198,605		1,132,571		17.5	%
Total	$	8,540,787	$	(4,249,258)	$	6,785,660	$	11,077,189	61.3	%
Year Ended December 31, 2021
Premiums Written:
Insurance	$	5,833,873	$	(1,719,541)	$	33,861	$	4,148,193	0.8	%
Reinsurance	408,520		(1,839,556)		4,685,410		3,254,374		144.0	%
Mortgage	1,213,333		(246,757)		294,492		1,261,068		23.4	%
Other	251,106		(102,763)		206,359		354,702		58.2	%
Total	$	7,706,832	$	(3,734,150)	$	5,045,655	$	9,018,337	55.9	%
Year Ended December 31, 2020
Premiums Written:
Insurance	$	4,659,416	$	(1,525,655)	$	29,146	$	3,162,907	0.9	%
Reinsurance	305,435		(1,014,716)		3,166,651		2,457,370		128.9	%
Mortgage	1,192,316		(194,149)		281,683		1,279,850		22.0	%
Other	396,743		(190,957)		331,803		537,589		61.7	%
Total	$	6,553,910	$	(2,650,352)	$	3,534,158	$	7,437,716	47.5	%

(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions and are included in the gross premiums written of each segment. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

ARCH CAPITAL 182 2022 FORM 10-K

SCHEDULE VI

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

SUPPLEMENTARY INFORMATION FOR PROPERTY AND CASUALTY INSURANCE UNDERWRITERS

(U.S. dollars in thousands)

Column A	Column B		Column C		Column D		Column E		Column F		Column G		Column H				Column I		Column J		Column K
Affiliation with Registrant	Deferred Acquisition Costs		Reserves for Losses and Loss Adjustment Expenses		Discount, if any, deducted in Column C		Unearned Premiums		Net Premiums Earned		Net Investment Income		Net Losses and Loss Adjustment Expenses Incurred Related to				Amortization of Deferred Acquisition Costs		Net Paid Losses and Loss Adjustment Expenses		Net Premiums Written
													(a) Current Year		(b) Prior Years
Consolidated Subsidiaries
2022	$	1,263,870	$	20,031,943	$	60,536	$	7,337,002	$	9,678,077	$	496,547	$	5,798,528	$	(771,011)	$	1,739,580	$	3,141,948	$	11,077,189
2021	901,841		17,757,156		55,575		6,011,942		8,082,298		389,118		4,940,987		(356,184)		1,303,178		2,826,551		9,018,337
2020	790,708		16,513,929		23,326		4,838,965		6,991,935		519,608		4,851,051		(161,452)		1,004,842		2,661,117		7,437,716

ITEM 16.     FORM 10-K SUMMARY

Not applicable.

ARCH CAPITAL 183 2022 FORM 10-K

EX-21

Exhibit 21

SUBSIDIARIES OF REGISTRANT

Name	Jurisdiction of Incorporation
Alternative Re Holdings Limited	Bermuda
Alternative Re Limited	Bermuda
Alwyn Insurance Company Limited	Gibraltar
Arch Capital Finance (Ireland) Limited	Ireland
Arch Capital Finance LLC	Delaware
Arch Capital Group (U.S.) Inc.	Delaware
Arch Capital Holdings Ltd.	Bermuda
Arch Capital Services LLC	Delaware
Arch Credit Risk Services (Bermuda) Ltd.	Bermuda
Arch Europe Insurance Services Ltd	United Kingdom
Arch Financial Holdings Australia Pty Ltd	Australia
Arch Financial Holdings B.V.	Netherlands
Arch Financial Holdings Canada Ltd.	Canada
Arch Financial Holdings Europe I Limited	Ireland
Arch Financial Holdings Europe II Limited	Ireland
Arch Financial Holdings Europe III Limited	Ireland
Arch Financial Holdings Europe IV Limited	Ireland
Arch Fund Management Ltd.	Bermuda
Arch Global Services (Cyprus) Ltd.	Cyprus
Arch Global Services (Philippines) Inc.	Philippines
Arch Global Services Holdings Ltd.	Philippines
Arch Group Foundation	Delaware
Arch Group Reinsurance Limited	Bermuda
Arch Indemnity Insurance Company	Missouri
Arch Insurance (EU) Designated Activity Company	Ireland

Arch Insurance (UK) Limited	United Kingdom
Arch Insurance Canada Ltd.	Canada
Arch Insurance Company	Missouri
Arch Insurance Group Inc.	Delaware
Arch Insurance Solutions Inc.	Delaware
Arch Intermediaries Group Limited	United Kingdom
Arch Investment Holdings (Cyprus) Ltd	Cyprus
Arch Investment Holdings I Ltd.	Bermuda
Arch Investment Holdings II Ltd.	Bermuda
Arch Investment Holdings III Ltd.	Bermuda
Arch Investment Holdings IV Ltd.	Bermuda
Arch Investment ICAV	Ireland
Arch Investments II LLC	Delaware
Arch Investment Management Ltd.	Bermuda
Arch Investment Property Holdings Ltd.	Bermuda
Arch Lenders Mortgage Indemnity Limited	Australia
Arch Life Insurance Company of America	Kansas
Arch LMI Pty Ltd	Australia
Arch Managing Agency Limited	United Kingdom
Arch MI Asia Limited	Hong Kong
Arch Mortgage Assurance Company	Wisconsin
Arch Mortgage Funding, Inc.	Delaware
Arch Mortgage Guaranty Company	Wisconsin
Arch Mortgage Insurance Company	Wisconsin
Arch Mortgage Risk Transfer Holdings Inc.	Delaware
Arch Mortgage Risk Transfer PCC Inc.	District of Columbia
Arch Property Casualty Insurance Company	Missouri
Arch Re Underwriting ApS	Denmark
Arch Reinsurance Company	Delaware

Arch Reinsurance Europe Underwriting Designated Activity Company	Ireland
Arch Reinsurance Ltd.	Bermuda
Arch Services Holdings Inc.	Delaware
Arch Specialty Insurance Agency Inc.	Missouri
Arch Specialty Insurance Company	Missouri
Arch Syndicate Investments Ltd	United Kingdom
Arch Underwriters Ltd.	Bermuda
Arch Underwriters Europe Limited	Ireland
Arch Underwriters (Gulf) Limited	Dubai International Financial Centre
Arch Underwriting Agency (Australia) Pty. Ltd.	Australia
Arch Underwriting Agency LLC	Delaware
Arch Underwriting at Lloyd’s Ltd	United Kingdom
Arch Underwriting at Lloyd’s (Australia) Pty Ltd	Australia
Arch Underwriters Inc.	Delaware
Arch U.S. MI Holdings Inc.	Delaware
Arch U.S. MI Services Inc.	Delaware
Axiom Underwriting Agency Limited	United Kingdom
Barbican Group Holdings Limited	Guernsey
Barbican Holdings (UK) Limited	United Kingdom
Barbican Reinsurance Company Limited	Guernsey
Barbican Specialty Reinsurance Company Limited	Guernsey
Barbican Underwriting Limited	United Kingdom
First American Service Corporation	Missouri
First Shield Consumer Service Corporation	Missouri
First Shield Consumer Service Corporation of Florida	Missouri
First Shield Service Corporation	Missouri
First Shield Service Corporation of Florida	Missouri
Gulf Re Holdings Limited	Jersey (Channel Islands)

Gulf Reinsurance Limited	Dubai International Financial Centre
Idlemear Holdings Limited	United Kingdom
McNeil & Company, Inc.	New York
Obelisk Underwriting Limited	United Kingdom
Out of Towne, LLC	Virginia
Panacea Limited	Gibraltar
Penflex Actuarial Services LLC	New York
SALT Insurance Services Limited	United Kingdom
Somerset Bridge Group Limited	United Kingdom
Somerset Bridge Insurance Services Limited	United Kingdom
Somerset Bridge Ltd	United Kingdom
Somerset Bridge Shared Services Limited	United Kingdom
Soundview Claims Solutions Inc.	Delaware
Southern Rock Holdings Limited	Gibraltar
Southern Rock Insurance Company Limited	Gibraltar
Thomas Underwriting Agency Ltd	United Kingdom
United Guaranty Residential Insurance Company	North Carolina
United Guaranty Residential Insurance Company of North Carolina	North Carolina
United Guaranty Services, Inc.	North Carolina
Ventus Risk Management, Inc.	Delaware

EX-23

Exhibit 23

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We hereby consent to the incorporation by reference in the Registration Statements on Form S-3 (No. 333-250869) and Form S-8 (Nos. 333-224783, 333-211193, 333-142835, 333-181308, 333- 203993 and 333-265285) of Arch Capital Group Ltd. of our report dated February 24, 2023 relating to the financial statements, financial statement schedules and the effectiveness of internal control over financial reporting, which appears in this Form 10-K.

/s/ PricewaterhouseCoopers LLP

New York, New York

February 24, 2023

EX-24

Exhibit 24

Power of Attorney

KNOW ALL PERSONS BY THESE PRESENTS, that each person whose signature appears below constitutes and appoints Marc Grandisson and François Morin as his or her true and lawful attorney-in-fact and agent, with full power of substitution and resubstitution, for him and in his name, place and stead, in any and all capacities, to sign Arch Capital Group Ltd.’s Annual Report on Form 10-K for the year ended December 31, 2022 and any and all amendments and supplements thereto, and to file the same with the Commission, granting unto said attorney-in-fact and agent full power and authority to do and perform each and every act and thing requisite and necessary to be done in connection therewith, as fully to all intents and purposes as he or she might or could do in person, hereby ratifying and confirming all that said attorney-in-fact and agent, or his substitute or substitutes, may lawfully do or cause to be done by virtue hereof.

Signature	Title	Date
/s/ Marc Grandisson	Chief Executive Officer (Principal Executive Officer)	February 24, 2023
Marc Grandisson
/s/ François Morin	Executive Vice President and Chief Financial Officer (Principal Financial Officer and Principal Accounting Officer) and Treasurer	February 24, 2023
François Morin
/s/ John M. Pasquesi	Chairman of the Board	February 24, 2023
John M. Pasquesi
/s/ John L. Bunce, Jr.	Director	February 24, 2023
John L. Bunce, Jr.
/s/ Eric W. Doppstadt	Director	February 24, 2023
Eric W. Doppstadt
/s/Francis Ebong	Director	February 24, 2023
Francis Ebong
/s/ Laurie S. Goodman	Director	February 24, 2023
Laurie S. Goodman
/s/ Moira Kilcoyne	Director	February 24, 2023
Moira Kilcoyne
/s/ Eileen Mallesch	Director	February 24, 2023
Eileen Mallesch
/s/ Louis J. Paglia	Director	February 24, 2023
Louis J. Paglia
/s/ Brian S. Posner	Director	February 24, 2023
Brian S. Posner
/s/ Eugene S. Sunshine	Director	February 24, 2023
Eugene S. Sunshine
/s/ John D. Vollaro	Director	February 24, 2023
John D. Vollaro
/s/ Thomas R. Watjen	Director	February 24, 2023
Thomas R. Watjen

EX-31.1

Exhibit 31.1

Certification
of Chief Executive Officer

Pursuant to Section 302 of the

Sarbanes-Oxley Act of 2002

I, Marc Grandisson, certify that:

1.I have reviewed this annual report on Form 10-K of Arch Capital Group Ltd.;

2.Based on my knowledge, this report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by this report;

3.Based on my knowledge, the financial statements, and other financial information included in this report, fairly present in all material respects the financial condition, results of operations and cash flows of the registrant as of, and for, the periods presented in the report;

4.The registrant’s other certifying officer and I are responsible for establishing and maintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and internal control over financial reporting (as defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) for the registrant and have:

a.Designed such disclosure controls and procedures, or caused such disclosure controls and procedures to be designed under our supervision, to ensure that material information relating to the registrant, including its consolidated subsidiaries, is made known to us by others within those entities, particularly during the period in which this report is being prepared;

b.Designed such internal control over financial reporting, or caused such internal control over financial reporting to be designed under our supervision, to provide reasonable assurance regarding the reliability of financial reporting and the preparation of financial statements for external purposes in accordance with generally accepted accounting principles;

c.Evaluated the effectiveness of the registrant’s disclosure controls and procedures and presented in this report our conclusions about the effectiveness of the disclosure controls and procedures, as of the end of the period covered by this report based on such evaluation; and

d.Disclosed in this report any change in the registrant’s internal control over financial reporting that occurred during the registrant’s most recent fiscal quarter (the registrant’s fourth fiscal quarter in the case of an annual report) that has materially affected, or is reasonably likely to materially affect, the registrant’s internal control over financial reporting; and

5.The registrant’s other certifying officer and I have disclosed, based on our most recent evaluation of internal control over financial reporting, to the registrant’s auditors and to the audit committee of registrant’s board of directors (or persons performing the equivalent functions):

a.    All significant deficiencies and material weaknesses in the design or operation of internal control over financial reporting which are reasonably likely to adversely affect the registrant’s ability to record, process, summarize and report financial information; and

b.    Any fraud, whether or not material, that involves management or other employees who have a significant role in the registrant’s internal control over financial reporting.

Date:	February 24, 2023
By:	/s/ Marc Grandisson
Name:	Marc Grandisson
Title:	Chief Executive Officer

EX-31.2

Exhibit 31.2

Certification
of Chief Financial Officer

Pursuant to Section 302 of the

Sarbanes-Oxley Act of 2002

I, François Morin, certify that:

1.I have reviewed this annual report on Form 10-K of Arch Capital Group Ltd.;

2.Based on my knowledge, this report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by this report;

3.Based on my knowledge, the financial statements, and other financial information included in this report, fairly present in all material respects the financial condition, results of operations and cash flows of the registrant as of, and for, the periods presented in the report;

4.The registrant’s other certifying officer and I are responsible for establishing and maintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and internal control over financial reporting (as defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) for the registrant and have:

a.Designed such disclosure controls and procedures, or caused such disclosure controls and procedures to be designed under our supervision, to ensure that material information relating to the registrant, including its consolidated subsidiaries, is made known to us by others within those entities, particularly during the period in which this report is being prepared;

b.Designed such internal control over financial reporting, or caused such internal control over financial reporting to be designed under our supervision, to provide reasonable assurance regarding the reliability of financial reporting and the preparation of financial statements for external purposes in accordance with generally accepted accounting principles;

c.Evaluated the effectiveness of the registrant’s disclosure controls and procedures and presented in this report our conclusions about the effectiveness of the disclosure controls and procedures, as of the end of the period covered by this report based on such evaluation; and

d.Disclosed in this report any change in the registrant’s internal control over financial reporting that occurred during the registrant’s most recent fiscal quarter (the registrant’s fourth fiscal quarter in the case of an annual report) that has materially affected, or is reasonably likely to materially affect, the registrant’s internal control over financial reporting; and

5.The registrant’s other certifying officer and I have disclosed, based on our most recent evaluation of internal control over financial reporting, to the registrant’s auditors and to the audit committee of registrant’s board of directors (or persons performing the equivalent functions):

a.    All significant deficiencies and material weaknesses in the design or operation of internal control over financial reporting which are reasonably likely to adversely affect the registrant’s ability to record, process, summarize and report financial information; and

b.    Any fraud, whether or not material, that involves management or other employees who have a significant role in the registrant’s internal control over financial reporting.

Date:	February 24, 2023
By:	/s/ François Morin
Name:	François Morin
Title:	Executive Vice President, Chief Financial Officer and Treasurer

EX-32.1

Exhibit 32.1

Certification Pursuant to Chapter 63, Title 18 United States Code §1350
As Adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

In connection with the Annual Report of Arch Capital Group Ltd. (the “Company”) on Form 10-K for the period ending December 31, 2022 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), Marc Grandisson, as Chief Executive Officer of the Company, certifies pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1)the Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2)the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date:	February 24, 2023
By:	/s/ Marc Grandisson
Name:	Marc Grandisson
Title:	Chief Executive Officer

A signed original of this written statement required by Section 906 or other document authenticating, acknowledging or otherwise adopting the signature that appears in typed form within the electronic version of this written statement required by Section 906, has been provided to Arch Capital Group Ltd. and will be retained by Arch Capital Group Ltd. and furnished to the Securities and Exchange Commission or its staff upon request.

EX-32.2

Exhibit 32.2

Certification Pursuant to Chapter 63, Title 18 United States Code §1350
As Adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

In connection with the Annual Report of Arch Capital Group Ltd. (the “Company”) on Form 10-K for the period ending December 31, 2022 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), François Morin, as Executive Vice President, Chief Financial Officer and Treasurer of the Company, certifies pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1)the Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2)the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date:	February 24, 2023
By:	/s/ François Morin
Name:	François Morin
Title:	Executive Vice President, Chief Financial Officer and Treasurer

A signed original of this written statement required by Section 906 or other document authenticating, acknowledging or otherwise adopting the signature that appears in typed form within the electronic version of this written statement required by Section 906, has been provided to Arch Capital Group Ltd. and will be retained by Arch Capital Group Ltd. and furnished to the Securities and Exchange Commission or its staff upon request.

XML

Document and Entity Information - USD ($) $ in Billions	12 Months Ended
	Dec. 31, 2022	Feb. 17, 2023	Jun. 30, 2022
Document and Entity Information [Abstract]
Document Type	10-K
Document Annual Report	true
Amendment Flag	false
Document Transition Report	false
Document Period End Date	Dec. 31, 2022
Entity File Number	001-16209
Entity Registrant Name	ARCH CAPITAL GROUP LTD.
Entity Incorporation, State or Country Code	D0
Entity Tax Identification Number	98-0374481
Entity Address, Address Line One	Waterloo House, Ground Floor
Entity Address, Address Line Two	100 Pitts Bay Road,
Entity Address, City or Town	Pembroke
Entity Address, Postal Zip Code	HM 08,
Entity Address, Country	BM
City Area Code	(441)
Local Phone Number	278-9250
Entity Listings [Line Items]
Entity Well-known Seasoned Issuer	Yes
Entity Voluntary Filers	No
Entity Current Reporting Status	Yes
Entity Interactive Data Current	Yes
Entity Filer Category	Large Accelerated Filer
Entity Small Business	false
Entity Emerging Growth Company	false
ICFR Auditor Attestation Flag	true
Entity Shell Company	false
Entity Public Float			$ 16.3
Entity Common Stock, Shares Outstanding		371,196,508
Documents Incorporated by Reference	Portions of Part III and Part IV incorporate by reference our definitive proxy statement for the 2023 annual meeting of shareholders to be filed with the Securities and Exchange Commission pursuant to Regulation 14A within 120 days after December 31, 2022.
Entity Central Index Key	0000947484
Current Fiscal Year End Date	--12-31
Document Fiscal Year Focus	2022
Document Fiscal Period Focus	FY
Common shares
Entity Listings [Line Items]
Title of 12(b) Security	Common Shares, $0.0011 par value per share
Trading Symbol	ACGL
Security Exchange Name	NASDAQ
Series F depositary share equivalent
Entity Listings [Line Items]
Title of 12(b) Security	Depositary shares, each representing a 1/1,000th interest in a 5.45% Series F preferred share
Trading Symbol	ACGLO
Security Exchange Name	NASDAQ
Series G depositary share equivalent
Entity Listings [Line Items]
Title of 12(b) Security	Depositary shares, each representing a 1/1,000th interest in a 4.55% Series G preferred share
Trading Symbol	ACGLN
Security Exchange Name	NASDAQ

XML

Audit Information	12 Months Ended
	Dec. 31, 2022
Audit Information [Abstract]
Auditor Name	PricewaterhouseCoopers LLP
Auditor Location	New York, New York
Auditor Firm ID	238

XML

Consolidated Balance Sheets - USD ($) $ in Thousands	Dec. 31, 2022	Dec. 31, 2021
Investments:
Debt securities available for sale, at fair value	$ 21,014,451	$ 19,732,825
Equity securities, at fair value	859,969	1,804,170
Other investments (portion measured at fair value: $1,644,197 and $1,973,550)	1,644,197	1,973,550
Investments accounted for using the equity method	3,774,310	3,077,611
Total investments	27,292,927	26,588,156
Cash	855,118	858,668
Accrued investment income	158,680	85,453
Investment in operating affiliates	964,604	1,135,655
Premiums receivable (net of allowance for credit losses: $35,402 and $39,958)	3,624,777	2,633,280
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $21,544 and $13,230)	6,563,654	5,880,735
Contractholder receivables (net of allowance for credit losses: $2,691 and $3,437)	1,731,293	1,828,691
Ceded unearned premiums	1,799,197	1,729,455
Deferred acquisition costs	1,263,870	901,841
Receivable for securities sold	12,493	60,179
Goodwill and intangible assets	804,289	944,983
Other assets	2,919,605	2,453,849
Total assets	47,990,507	45,100,945
Liabilities
Reserve for losses and loss adjustment expenses	20,031,943	17,757,156
Unearned premiums	7,337,002	6,011,942
Reinsurance balances payable	1,529,919	1,583,253
Contractholder payables	1,733,984	1,832,127
Collateral held for insured obligations	249,238	242,352
Senior notes	2,725,410	2,724,394
Payable for securities purchased	95,041	64,850
Other liabilities	1,367,068	1,329,742
Total liabilities	35,069,605	31,545,816
Commitments and Contingencies
Redeemable noncontrolling interests	10,829	9,233
Shareholders’ Equity
Non-cumulative preferred shares	830,000	830,000
Common shares ($0.0011 par, shares issued: 588,250,762 and 583,289,850)	654	648
Additional paid-in capital	2,211,444	2,085,075
Retained earnings	15,892,065	14,455,868
Accumulated other comprehensive income (loss), net of deferred income tax	(1,646,170)	(64,600)
Common shares held in treasury, at cost (shares: 217,904,765 and 204,365,956)	(4,377,920)	(3,761,095)
Total shareholders' equity available to Arch	12,910,073	13,545,896
Total liabilities, noncontrolling interests and shareholders' equity	47,990,507	45,100,945
Fixed maturities available for sale, at fair value (amortized cost: $21,281,863 and $17,973,823; net of allowance for credit losses: $41,355 and $2,883)
Investments:
Debt securities available for sale, at fair value	19,682,789	17,998,109
Short-term investments available for sale, at fair value (amortized cost: $1,332,996 and $1,734,738; net of allowance for credit losses: $0 and $0 )
Investments:
Debt securities available for sale, at fair value	$ 1,331,662	$ 1,734,716

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Consolidated Balance Sheets (Parentheticals) - USD ($) $ in Thousands	Dec. 31, 2022	Dec. 31, 2021
Fixed maturities available for sale, at amortized cost	$ 22,614,859	$ 19,708,561
Allowance for credit losses on investments	41,355	2,883
Investments accounted for using the fair value option	1,644,197	1,973,550
Allowance for credit losses on premiums receivable	35,402	39,958
Allowance for credit losses on reinsurance recoverable	21,544	13,230
Allowance for credit loss on contractholder receivable	$ 2,691	$ 3,437
Common shares, par value per share	$ 0.0011	$ 0.0011
Common shares issued (shares)	588,250,762	583,289,850
Common shares held in treasury (shares)	217,904,765	204,365,956
Fixed maturities available for sale, at fair value (amortized cost: $21,281,863 and $17,973,823; net of allowance for credit losses: $41,355 and $2,883)
Fixed maturities available for sale, at amortized cost	$ 21,281,863	$ 17,973,823
Allowance for credit losses on investments	41,355	2,883
Short-term investments available for sale, at fair value (amortized cost: $1,332,996 and $1,734,738; net of allowance for credit losses: $0 and $0 )
Fixed maturities available for sale, at amortized cost	1,332,996	1,734,738
Allowance for credit losses on investments	$ 0	$ 0

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Consolidated Statements of Income - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Revenues
Net premiums earned	$ 9,678,077	$ 8,082,298	$ 6,991,935
Net investment income	496,547	389,118	519,608
Net realized gains (losses)	(662,734)	379,845	823,460
Other underwriting income	13,227	22,073	26,784
Equity in net income of investments accounted for using the equity method	115,856	366,402	146,693
Other income (loss)	(26,165)	10,244	29
Total revenues	9,614,808	9,249,980	8,508,509
Expenses
Losses and loss adjustment expenses	5,027,517	4,584,803	4,689,599
Acquisition expenses	1,739,580	1,303,178	1,004,842
Other operating expenses	1,128,175	998,595	875,176
Corporate expenses	95,482	79,157	81,988
Amortization of intangible assets	106,200	82,955	69,031
Interest expense	130,266	139,470	143,456
Net foreign exchange losses (gains)	(100,905)	(41,529)	83,634
Total expenses	8,126,315	7,146,629	6,947,726
Income before income taxes and income (loss) from operating affiliates	1,488,493	2,103,351	1,560,783
Income taxes:
Current tax expense (benefit)	201,216	295,533	197,662
Deferred tax expense (benefit)	(121,255)	(166,951)	(85,824)
Income tax expense	79,961	128,582	111,838
Income (loss) from operating affiliates	73,891	264,693	16,766
Net income	1,482,423	2,239,462	1,465,711
Net (income) loss attributable to noncontrolling interests	(5,490)	(82,613)	(60,190)
Net income available to Arch	1,476,933	2,156,849	1,405,521
Preferred share dividends	(40,736)	(48,343)	(41,612)
Loss on redemption of preferred shares	0	(15,101)	0
Net income available to Arch common shareholders	$ 1,436,197	$ 2,093,405	$ 1,363,909
Net income per common share and common share equivalent
Basic (per share)	$ 3.90	$ 5.34	$ 3.38
Diluted (per share)	$ 3.80	$ 5.23	$ 3.32
Weighted average common shares and common share equivalents outstanding
Basic (shares)	368,612,197	391,748,715	403,062,179
Diluted (shares)	377,609,767	400,345,936	410,259,455

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Consolidated Statements of Comprehensive Income - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Comprehensive Income
Net income	$ 1,482,423	$ 2,239,462	$ 1,465,711
Unrealized appreciation (decline) in value of available-for-sale investments:
Unrealized holding gains (losses) arising during year	(1,772,649)	(386,929)	678,717
Reclassification of net realized (gains) losses, included in net income	247,799	(116,068)	(426,187)
Foreign currency translation adjustments	(56,720)	(64,482)	33,336
Comprehensive income (loss)	(99,147)	1,671,983	1,751,577
Net (income) loss attributable to noncontrolling interests	(5,490)	(82,613)	(60,190)
Other comprehensive (income) loss attributable to noncontrolling interests	0	13,984	(9,062)
Comprehensive income available to Arch (loss)	$ (104,637)	$ 1,603,354	$ 1,682,325

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Consolidated Statements of Changes in Shareholders' Equity - USD ($) $ in Thousands	Total	Non-cumulative preferred shares	Common shares	Additional paid-in capital	Retained earnings	Retained earnings Cumulative Effect, Period of Adoption, Adjustment	Retained earnings Cumulative Effect, Period of Adoption, Adjusted Balance	Accumulated other comprehensive income (loss)	Unrealized appreciation (decline) in value of available-for-sale investments, net of deferred income tax	Foreign currency translation adjustments, net of deferred income tax	Common shares held in treasury, at cost
Balance at beginning of year at Dec. 31, 2019		$ 780,000	$ 638	$ 1,889,683	$ 11,021,006	$ (22,452)	$ 10,998,554	$ 212,091	$ 258,486	$ (46,395)	$ (2,406,047)
Preferred shares issued		0
Preferred shares redeemed		0
Common shares issued, net			5
Issue costs on preferred shares issued				0
Loss on redemption of preferred shares	$ 0			0	0
Amortization of share-based compensation				70,535
Other changes				17,576
Net income	1,465,711				1,465,711
Net (income) loss attributable to noncontrolling interests	(60,190)				(60,190)
Preferred share dividends	(41,612)				(41,612)
Unrealized holding gains (losses) during period, net of reclassification adjustment									252,530
Unrealized holding gains (losses) during period attributable to noncontrolling interests									(9,721)
Foreign currency translation adjustments	33,336									33,336
Foreign currency translation adjustments attributable to noncontrolling interests										659
Shares repurchased for treasury	(83,472)										(97,862)
Balance at end of year at Dec. 31, 2020	$ 13,105,886	780,000	643	1,977,794	12,362,463	0	12,362,463	488,895	501,295	(12,400)	(2,503,909)
Accounting Standards Update [Extensible Enumeration]	Accounting Standards Update 2016-13 [Member]
Non-redeemable noncontrolling interests	$ 823,007
Total shareholders' equity	13,928,893
Preferred shares issued		500,000
Preferred shares redeemed		(450,000)
Common shares issued, net			5
Issue costs on preferred shares issued				(14,179)
Loss on redemption of preferred shares	(15,101)			15,101	(15,101)
Amortization of share-based compensation				86,053
Other changes				20,306
Net income	2,239,462				2,239,462
Net (income) loss attributable to noncontrolling interests	(82,613)				(82,613)
Preferred share dividends	(48,343)				(48,343)
Unrealized holding gains (losses) during period, net of reclassification adjustment									(502,997)
Unrealized holding gains (losses) during period attributable to noncontrolling interests									15,188
Foreign currency translation adjustments	(64,482)									(64,482)
Foreign currency translation adjustments attributable to noncontrolling interests										(1,204)
Shares repurchased for treasury	(1,234,294)										(1,257,186)
Balance at end of year at Dec. 31, 2021	13,545,896	830,000	648	2,085,075	14,455,868	$ 0	$ 14,455,868	(64,600)	13,486	(78,086)	(3,761,095)
Non-redeemable noncontrolling interests	0
Total shareholders' equity	13,545,896
Preferred shares issued		0
Preferred shares redeemed		0
Common shares issued, net			6
Issue costs on preferred shares issued				0
Loss on redemption of preferred shares	0			0	0
Amortization of share-based compensation				87,620
Other changes				38,749
Net income	1,482,423				1,482,423
Net (income) loss attributable to noncontrolling interests	(5,490)				(5,490)
Preferred share dividends	(40,736)				(40,736)
Unrealized holding gains (losses) during period, net of reclassification adjustment									(1,524,850)
Unrealized holding gains (losses) during period attributable to noncontrolling interests									0
Foreign currency translation adjustments	(56,720)									(56,720)
Foreign currency translation adjustments attributable to noncontrolling interests										0
Shares repurchased for treasury	(585,823)										(616,825)
Balance at end of year at Dec. 31, 2022	12,910,073	$ 830,000	$ 654	$ 2,211,444	$ 15,892,065			$ (1,646,170)	$ (1,511,364)	$ (134,806)	$ (4,377,920)
Non-redeemable noncontrolling interests	0
Total shareholders' equity	$ 12,910,073

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Consolidated Statements of Cash Flows - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Operating Activities
Net income	$ 1,482,423	$ 2,239,462	$ 1,465,711
Adjustments to reconcile net income to net cash provided by operating activities:
Net realized (gains) losses	651,568	(427,367)	(844,625)
Equity in net (income) or loss of investments accounted for using the equity method and other income or loss	153,157	(464,050)	(47,951)
Amortization of intangible assets	106,200	82,955	69,031
Share-based compensation	87,628	87,094	71,262
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable	1,889,015	1,762,190	2,113,827
Unearned premiums, net of ceded unearned premiums	1,399,112	936,039	445,781
Premiums receivable	(1,109,229)	(685,214)	(318,643)
Deferred acquisition costs	(374,067)	(263,243)	(143,948)
Reinsurance balances payable	(35,509)	500,065	65,950
Other items, net	(435,071)	(340,376)	10,110
Net cash provided by operating activities	3,815,227	3,427,555	2,886,505
Investing Activities:
Purchases of fixed maturity investments	(16,390,475)	(35,451,858)	(39,765,277)
Purchases of equity securities	(796,998)	(1,175,480)	(1,595,010)
Purchases of other investments	(1,720,457)	(1,859,096)	(1,808,727)
Proceeds from sales of fixed maturity investments	11,844,004	33,577,445	37,949,346
Proceeds from sales of equity securities	1,554,116	918,145	1,147,264
Proceeds from sales, redemptions and maturities of other investments	1,221,072	1,765,533	1,029,578
Proceeds from redemptions and maturities of fixed maturity investments	714,519	1,628,755	871,134
Net settlements of derivative instruments	(68,818)	(40,072)	179,006
Net (purchases) sales of short-term investments	467,249	165,272	(1,029,681)
Change in cash collateral related to securities lending	0	0	81,210
Purchase of operating affiliate	0	(753,916)	0
Impact of the deconsolidation of the variable interest entity	0	(349,202)	0
Purchases of fixed assets	(51,672)	(41,394)	(39,872)
Other	125,405	(523,864)	(62,197)
Net cash used for investing activities	(3,102,055)	(2,139,732)	(3,043,226)
Financing Activities:
Proceeds from issuance of preferred shares, net	0	485,821	0
Redemption of preferred shares	0	(450,000)	0
Purchases of common shares under share repurchase program	(585,823)	(1,234,294)	(83,472)
Proceeds from common shares issued, net	6,660	6,418	1,876
Proceeds from borrowings	0	0	1,018,793
Repayments of borrowings	0	0	(359,000)
Change in cash collateral related to securities lending	0	0	(81,210)
Third party investment in non-redeemable noncontrolling interests	0	15,971	(2,867)
Dividends paid to redeemable noncontrolling interests	0	(1,907)	(4,945)
Other	(85,827)	(3,278)	73,715
Preferred dividends paid	(40,736)	(48,280)	(41,612)
Net Cash Provided by (Used in) Financing Activities	(705,726)	(1,229,549)	521,278
Effects of exchange rate changes on foreign currency cash and restricted cash	(48,889)	(34,047)	22,289
Increase (decrease) in cash and restricted cash	(41,443)	24,227	386,846
Cash and restricted cash, beginning of year	1,314,771	1,290,544	903,698
Cash and restricted cash, end of year	1,273,328	1,314,771	1,290,544
Supplemental cash flow information
Income taxes paid (received)	254,922	286,810	202,940
Interest paid	$ 128,425	$ 139,301	$ 133,491

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General

12 Months Ended

Dec. 31, 2022

Organization, Consolidation and Presentation of Financial Statements [Abstract]

General

Arch Capital Group Ltd. (“Arch Capital” or “Arch”) is a publicly listed Bermuda exempted company which provides insurance, reinsurance and mortgage insurance on a worldwide basis through its wholly owned subsidiaries. As used herein, the “Company” means Arch Capital and its subsidiaries. Similarly, “Common Shares” means the common shares of Arch Capital.

The Company’s consolidated financial statements included the results of Somers Group Holdings Ltd. (formerly Watford Holdings Ltd.) and its wholly owned subsidiaries (“Somers”). Effective July 1, 2021, Somers is wholly owned by Greysbridge Holdings Ltd., (“Greysbridge”) and Greysbridge is owned 40% by the Company, 30% by certain investment funds managed by Kelso & Company (“Kelso”) and 30% by certain investment funds managed by Warburg Pincus LLC (“Warburg”). Based on the governing documents of Greysbridge, the Company concluded that, while it retains significant influence over Somers, Somers no longer constitutes a variable interest entity. Accordingly, effective July 1, 2021, Arch no longer consolidates the results of Somers in its consolidated financial statements and footnotes. See note 12, “Variable Interest Entity and Noncontrolling Interests”.

The Company has reclassified the presentation of certain prior year information to conform to the current presentation. Such reclassifications had no effect on the Company’s net income, shareholders’equity or cash flows. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.

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Acquisitions

12 Months Ended

Dec. 31, 2022

Business Combinations [Abstract]

Business Acquired

Westpac Lenders Mortgage Insurance Limited (“WLMI”)

On August 31, 2021, the Company completed the acquisition of WLMI, an Australian Prudential Regulation Authority authorized captive lenders mortgage insurance (“LMI”) provider to the Westpac Banking Corporation (“Westpac”). As part of the acquisition, WLMI retained its existing risk in force and will remain Westpac’s exclusive provider of LMI on new mortgage originations for a period of 10 years from the acquisition date. The Company was renamed Arch Lenders Mortgage Indemnity Limited (“Arch Indemnity”) and will be the Company’s primary provider of LMI to the Australian market.

Somerset Bridge Group Limited, Southern Rock Holdings Limited and affiliates (“Somerset Group”)

On August 6, 2021, the Company completed the acquisition of Somerset Group. The acquisition includes Somerset Group’s motor insurance managing general agent, distribution capabilities through direct and aggregator channels, affiliated insurer and fully integrated claims operation.

In connection with the acquisitions noted above, the Company increased its goodwill and intangible assets by $350.1 million.

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Significant Accounting Policies

12 Months Ended

Dec. 31, 2022

Accounting Policies [Abstract]

Significant accounting policies

(a) Basis of Presentation

The consolidated financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America (“GAAP”) and include the accounts of Arch Capital and its subsidiaries, including Arch Reinsurance Ltd. (“Arch Re Bermuda”), Arch Reinsurance Company (“Arch Re U.S.”), Arch Capital Group (U.S.) Inc.(“Arch-U.S.”), Arch Insurance Company, Arch Specialty Insurance Company, Arch Property Casualty Insurance Company (“Arch P&C”), Arch Indemnity Insurance Company (“Arch Indemnity Insurance”), Arch Insurance Canada Ltd. (“Arch Insurance Canada”), Arch Reinsurance Europe Designated Activity Company (“Arch Re Europe”), Arch Mortgage Insurance Company (“AMIC”), Arch Mortgage Guaranty Company (“AMG”), United Guaranty Residential Insurance Company (“UGRIC”), Arch Indemnity, Arch Insurance (EU) Designated Activity Company (“Arch Insurance (EU)”), Arch Insurance (U.K.) Limited (“Arch Insurance (U.K.)”) and the Company’s participation on Lloyd’s of London syndicates: 2012 (“Arch Syndicate 2012”) and 1955 (“Arch Syndicate 1955” and together with Arch Syndicate 2012, the Company’s “Lloyd’s Syndicates”). All significant intercompany transactions and balances have been eliminated in consolidation.

The preparation of financial statements in conformity with GAAP requires management to make estimates and assumptions that affect the reported amounts of assets and liabilities and disclosure of contingent assets and liabilities at the date of the financial statements and the reported amounts of revenues and expenses during the reporting period. Actual results could differ materially from those estimates and assumptions. The Company’s principal estimates include:

•The reserve for losses and loss adjustment expenses;

•Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses, including the provision for uncollectible amounts;

•Estimates of written and earned premiums;

•The valuation of the investment portfolio and assessment of allowance for credit losses;

•The valuation of purchased intangible assets;

•The assessment of goodwill and intangible assets for impairment; and

•The valuation of deferred tax assets.

(b) Premium Revenues and Related Expenses

Insurance. Insurance premiums written are generally recorded at the policy inception and are primarily earned on a pro rata basis over the terms of the policies for all products, usually 12 months. Premiums written include estimates that are derived from multiple sources which include the historical experience of the underlying business, similar business and available industry information. Unearned premium reserves represent the portion of premiums written that relates to the unexpired terms of in-force insurance policies.

Reinsurance. Reinsurance premiums written include amounts reported by brokers and ceding companies, supplemented by the Company’s own estimates of premiums where reports have not been received. The determination of premium estimates requires a review of the Company’s experience with the ceding companies, familiarity with each market, the timing of the reported information, an analysis and understanding of the characteristics of each line of business, and management’s judgment of the impact of various factors, including premium or loss trends, on the volume of business written and ceded to the Company. On an ongoing basis, the Company’s underwriters review the amounts reported by these third parties for reasonableness based on their experience and knowledge of the subject class of business, taking into account the Company’s historical experience with the brokers or ceding companies. In addition, reinsurance contracts under which the Company assumes business generally contain specific provisions which allow the Company to perform audits of the ceding company to ensure compliance with the terms and conditions of the contract, including accurate and timely reporting of information. Based on a review of all available information, management establishes premium estimates where reports have not been received. Premium estimates are updated when new information is received and differences between such estimates and actual amounts are recorded in the period in which estimates are changed or the actual amounts are determined.

Reinsurance premiums written are recorded based on the type of contracts the Company writes. Premiums on the Company’s excess of loss and pro rata reinsurance contracts are estimated when the business is underwritten. For excess of loss contracts, premiums are recorded as written based on

the terms of the contract. Estimates of premiums written under pro rata contracts are recorded in the period in which the underlying risks are expected to incept and are based on information provided by the brokers and the ceding companies. For multi-year reinsurance treaties which are payable in annual installments, generally, only the initial annual installment is included as premiums written at policy inception due to the ability of the reinsured to commute or cancel coverage during the term of the policy. The remaining annual installments are included as premiums written at each successive anniversary date within the multi-year term.

Reinsurance premiums written, irrespective of the class of business, are generally earned on a pro rata basis over the terms of the underlying policies or reinsurance contracts. Contracts and policies written on a “losses occurring” basis cover claims that may occur during the term of the contract or policy, which is typically 12 months. Accordingly, the premium is earned evenly over the term. Contracts which are written on a “risks attaching” basis cover claims which attach to the underlying insurance policies written during the terms of such contracts. Premiums earned on such contracts usually extend beyond the original term of the reinsurance contract, typically resulting in recognition of premiums earned over a 24-month period. Certain of the Company’s reinsurance contracts include provisions that adjust premiums or acquisition expenses based upon the experience under the contracts. Premiums written and earned, as well as related acquisition expenses, are recorded based upon the projected experience under such contracts.

The Company also writes certain reinsurance business that is intended to provide insurers with risk management solutions that complement traditional reinsurance. Under these contracts, the Company assumes a measured amount of insurance risk in exchange for an anticipated margin, which is typically lower than on traditional reinsurance contracts. The terms and conditions of these contracts may include additional or return premiums based on loss experience, loss corridors, sublimits and caps. Examples of such business include aggregate stop-loss coverages, financial quota share coverages and multi-year retrospectively rated excess of loss coverages. If these contracts are deemed to transfer risk, they are accounted for as reinsurance. Otherwise, such contracts are accounted for under the deposit method.

Mortgage. Mortgage guaranty insurance policies are contracts that are generally non-cancelable by the insurer, are renewable at a fixed price, and provide for payment of premiums on a monthly, annual or single basis. Upon renewal, the Company is not able to re-underwrite or re-price its policies. Consistent with industry accounting practices, premiums written on a monthly basis are earned as coverage is provided. Premiums written on an annual basis are amortized on a monthly pro rata basis over the year of coverage. Primary mortgage insurance premiums written on

policies covering more than one year are referred to as single premiums. A portion of the revenue from single premiums is recognized in premiums earned in the current period, and the remaining portion is deferred as unearned premiums and earned over the estimated expiration of risk of the policy. If single premium policies related to insured loans are canceled due to repayment by the borrower and the policy is a non-refundable product, the remaining unearned premium related to each canceled policy is recognized as earned premium upon notification of the cancellation.

Reinstatement premiums for the Company’s insurance and reinsurance operations are recognized at the time a loss event occurs, where coverage limits for the remaining life of the contract are reinstated under pre-defined contract terms. Reinstatement premiums, if obligatory, are fully earned when recognized. The accrual of reinstatement premiums is based on an estimate of losses and loss adjustment expenses, which reflects management’s judgment.

Premium estimates are reviewed by management at least quarterly. Such review includes a comparison of actual reported premiums to expected ultimate premiums along with a review of the aging and collection of premium estimates. Based on management’s review, the appropriateness of the premium estimates is evaluated, and any adjustment to these estimates is recorded in the period in which it becomes known. Adjustments to premium estimates could be material and such adjustments could directly and significantly impact earnings favorably or unfavorably in the period they are determined because the estimated premium may be fully or substantially earned. A significant portion of amounts included as premiums receivable, which represent estimated premiums written, net of commissions, are not currently due based on the terms of the underlying contracts.

Unearned premiums represent the portion of premiums written that is applicable to the estimated unexpired risk of insured loans. A portion of premium payments may be refundable if the insured cancels coverage, which generally occurs when the loan is repaid, the loan amortizes to a sufficiently low amount to trigger a lender permitted or legally required cancellation, or the value of the property has increased sufficiently in accordance with the terms of the contract. Premium refunds reduce premiums earned in the consolidated statements of income. Generally, only unearned premiums are refundable.

Premiums receivable include amounts receivable from agents, brokers and insured that are both currently due and amounts not yet due on insurance, reinsurance and mortgage insurance policies. Premiums receivable balances are reported net of an allowance for expected credit losses. The Company monitors credit risk associated with premiums receivable through its ongoing review of amounts outstanding, aging of the receivable, historical loss data, and

counterparty financial strength measures. The allowance also includes estimated uncollectible amounts related to dispute risk. In certain instances, credit risk may be reduced by the Company’s right to offset loss obligations or unearned premiums against premiums receivable. Any allowance for credit losses is charged to net realized gains (losses) in the period the receivable is recorded and revised in subsequent periods to reflect changes in the Company’s estimate of expected credit losses. See note 7, “Allowance for Expected Credit Losses” for additional information.

Acquisition Costs. Acquisition costs that are directly related and incremental to the successful acquisition or renewal of business are deferred and amortized based on the type of contract. The Company’s insurance and reinsurance operations capitalize incremental direct external costs that result from acquiring a contract but do not capitalize salaries, benefits and other internal underwriting costs. For the Company’s mortgage insurance operations, which include a substantial direct sales force, both external and certain internal direct costs are deferred and amortized. For property and casualty insurance and reinsurance contracts, deferred acquisition costs are amortized over the period in which the related premiums are earned. Consistent with mortgage insurance industry accounting practice, amortization of acquisition costs related to the mortgage insurance contracts for each underwriting year’s book of business is recorded in proportion to estimated gross profits. Estimated gross profits are comprised of earned premiums and losses and loss adjustment expenses. For each underwriting year, the Company estimates the rate of amortization to reflect actual experience and any changes to persistency or loss development.

Deferred acquisition costs are carried at their estimated realizable value and take into account anticipated losses and loss adjustment expenses, based on historical and current experience, and anticipated investment income.

A premium deficiency occurs if the sum of anticipated losses and loss adjustment expenses, unamortized acquisition costs and maintenance costs exceed unearned premiums (including expected future premiums) and anticipated investment income. A premium deficiency reserve (“PDR”) is recorded by charging any unamortized acquisition costs to expense to the extent required in order to eliminate the deficiency. If the premium deficiency exceeds unamortized acquisition costs then a liability is accrued for the excess deficiency.

To assess the need for a PDR on mortgage exposures, the Company develops loss projections based on modeled loan defaults related to its current policies in force. This projection is based on recent trends in default experience, severity and rates of defaulted loans moving to claim, as well as recent trends in the rate at which loans are prepaid, and incorporates anticipated interest income. Evaluating the expected

profitability of the Company’s existing mortgage insurance business and the need for a PDR for its mortgage business involves significant reliance upon assumptions and estimates with regard to the likelihood, magnitude and timing of potential losses and premium revenues. No premium deficiency charges were recorded by the Company during 2022, 2021 or 2020.

(c) Deposit Accounting

Certain assumed reinsurance contracts that are deemed not to transfer insurance risk, are accounted for using the deposit method of accounting. However, it is possible that the Company could incur financial losses on such contracts. Management exercises significant judgment in the assumptions used in determining whether assumed contracts should be accounted for as reinsurance contracts or deposit contracts. For those contracts that contain only significant underwriting risk, the estimated profit margin is deferred and amortized over the contract period and such amount is included in the Company’s underwriting results. When the estimated profit margin is explicit, the margin is reflected as other underwriting income and any adverse financial results on such contracts are reflected as incurred losses. When the estimated profit margin is implicit, the margin is reflected as an offset to paid losses and any adverse financial results on such contracts are reflected as incurred losses. Additional judgments are required when applying the accounting guidance with respect to the revenue recognition criteria for contracts deemed to transfer only significant underwriting risk. For those contracts that contain only significant timing risk, an accretion rate is established at inception of the contract based on actuarial estimates whereby the deposit accounting liability is increased to the estimated amount payable over the contract term. The accretion on the deposit is based on the expected rate of return required to fund the expected future payment obligations. Periodically the Company reassesses the estimated ultimate liability and the related expected rate of return. The accretion of the deposit accounting liability as well as changes to the estimated ultimate liability and the accretion rate would be reflected as part of interest expense in the Company’s results of operations. Any negative accretion in a deposit accounting liability is shown in other underwriting income in the Company’s results of operations.

Under some of these contracts, the ceding company retains the related assets on a funds held basis. Such amounts are included in “Other assets” on the Company’s balance sheet. Interest income produced by those assets are recorded as part of net investment income in the Company's results of operations.

(d) Retroactive Reinsurance

Retroactive reinsurance reimburses a ceding company for liabilities incurred as a result of past insurable events covered by the underlying policies reinsured. In certain instances, reinsurance contracts cover losses both on a prospective basis and on a retroactive basis and, accordingly, the Company bifurcates the prospective and retrospective elements of these reinsurance contracts and accounts for each element separately where practical. Underwriting income generated in connection with retroactive reinsurance contracts is deferred and amortized into income over the settlement period while losses are charged to income immediately. Subsequent changes in estimated amount or timing of cash flows under such retroactive reinsurance contracts are accounted for by adjusting the previously deferred amount to the balance that would have existed had the revised estimate been available at the inception of the reinsurance transaction, with a corresponding charge or credit to income.

(e) Reinsurance Ceded

In the normal course of business, the Company purchases reinsurance to increase capacity and to limit the impact of individual losses and events on its underwriting results by reinsuring certain levels of risk with other insurance enterprises or reinsurers. The Company uses pro rata, excess of loss and facultative reinsurance contracts. Reinsurance ceding commissions that represent a recovery of acquisition costs are recognized as a reduction to acquisition costs while the remaining portion is deferred. The accompanying consolidated statement of income reflects premiums and losses and loss adjustment expenses and acquisition costs, net of reinsurance ceded. See note 8, “Reinsurance” for information on the Company's reinsurance usage. Reinsurance premiums ceded and unpaid losses and loss adjustment expenses recoverable are estimated in a manner consistent with that of the original policies issued and the terms of the reinsurance contracts. If the reinsurers are unable to satisfy their obligations under the agreements, the Company’s insurance or reinsurance subsidiaries would be liable for such defaulted amounts.

Reinsurance recoverables are recorded as assets, predicated on the reinsurers’ ability to meet their obligations under the reinsurance agreements. In certain instances, the Company obtains collateral, including letters of credit and trust accounts to further reduce the credit exposure on its reinsurance recoverables. The Company reports its reinsurance recoverables net of an allowance for expected credit loss. The allowance is based upon the Company’s ongoing review of amounts outstanding, the financial condition of its reinsurers, amounts and form of collateral obtained and other relevant factors. A ratings based probability-of-default and loss-given-default methodology is used to estimate the allowance for expected credit loss. Any

allowance for credit losses is charged to net realized gains (losses) in the period the recoverable is recorded and revised in subsequent periods to reflect changes in the Company’s estimate of expected credit losses. See note 7, “Allowance for Expected Credit Losses” for additional information.

(f) Cash

Cash includes cash equivalents, which are investments with original maturities of three months or less which are not part of the investment portfolio.

(g) Restricted Cash

Restricted cash represents amounts held for the benefit of third parties or is legally or contractually restricted as to withdrawal or usage by the Company. Such amounts are included in “Other assets” on the Company’s balance sheet.

(h) Investments

The Company currently classifies substantially all of its fixed maturity investments and short-term investments as “available for sale” and, accordingly, they are carried at estimated fair value (also known as fair value) with the changes in fair value recorded as an unrealized gain or loss component of accumulated other comprehensive income in shareholders’ equity. The fair value of fixed maturity securities and equity securities is generally determined from quotations received from nationally recognized pricing services, or when such prices are not available, by reference to broker or underwriter bid indications. Short-term investments comprise securities due to mature within one year of the date of issue. Short-term investments include certain cash equivalents which are part of investment portfolios under the management of external and internal investment managers.

The Company’s investment portfolio includes certain funds that, due to their ownership structure, are accounted for by the Company using the equity method. In applying the equity method, these investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the fair value of the underlying securities in the funds). Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds. Changes in the carrying value of such investments are recorded in net income as “Equity in net income (loss) of investments accounted for using the equity method.” As such, fluctuations in the carrying value of the investments accounted for using the equity method may increase the volatility of the Company’s reported results of operations.

The Company’s investment portfolio includes equity securities that are accounted for at fair value. Such holdings primarily include publicly traded common stocks. Dividend income on equities is reflected in net investment income. Changes in fair value on equity securities are included in “Net realized gains (losses)” in the consolidated statement of income.

The Company elected to carry certain fixed maturity securities, equity securities, short-term investments and other investments at fair value under the fair value option afforded by accounting guidance regarding the fair value option for financial assets and liabilities. The fair value for certain of the Company’s other investments are determined using net asset values (“NAVs”) as advised by external fund managers. The NAV is based on the fund manager’s valuation of the underlying holdings in accordance with the fund’s governing documents.

Changes in fair value of investments accounted for using the fair value option are included in “Net realized gains (losses).” The primary reasons for electing the fair value option were to address simplification and cost-benefit considerations.

The Company invests in reverse repurchase agreements that are generally treated as collateralized receivables. Receivables for reverse repurchase agreements are reflected in “Other investments” or “Short-term investments” in the Company's consolidated balance sheet depending on their terms. These agreements are recorded at their contracted resale amount plus accrued interest, other than those that are accounted for at fair value. In reverse repurchase transactions, the Company obtains an interest in the purchased assets that are received as collateral.

The Company invests in limited partner interests and shares of limited liability companies. Such amounts are included in investments accounted for using the equity method and other investments. These investments can often have characteristics of a variable interest entity (“VIE”). A VIE refers to entities that have characteristics such as (i) insufficient equity at risk to allow the entity to finance its activities without additional financial support or (ii) instances where the equity investors, as a group, do not have the characteristic of a controlling financial interest. If the Company is determined to be the primary beneficiary, it is required to consolidate the VIE. The primary beneficiary is defined as the variable interest holder that is determined to have the controlling financial interest as a result of having both (i) the power to direct the activities of a VIE that most significantly impact the economic performance of the VIE and (ii) the obligation to absorb losses or right to receive benefits from the VIE that could potentially be significant to the VIE. At inception of the VIE as well as on an ongoing basis, the Company determines whether it is the primary beneficiary based on an analysis of the Company’s level of involvement in the VIE, the

contractual terms, and the overall structure of the VIE. The Company's maximum exposure to loss with respect to these investments is limited to the investment carrying amounts reported in the Company's consolidated balance sheet and any unfunded commitment.

The Company conducts a periodic review to identify and evaluate credit based impairments related to the Company’s available for sale investments. The Company derives estimated credit losses by comparing expected future cash flows to be collected to the amortized cost of the security. Estimates of expected future cash flows consider among other things, macroeconomic conditions as well as the financial condition, near-term and long-term prospects for the issuer, and the likelihood of the recoverability of principal and interest. Effective January 1, 2020, credit losses are recognized through an allowance account subject to reversal, rather than a reduction in amortized cost. Declines in value attributable to factors other than credit are reported as an unrealized loss in other comprehensive income while the allowance for credit loss is charged to net realized gains (losses) in the consolidated statement of income.

For available for sale investments that the Company intends to sell or for which it is more likely than not that the Company would be required to sell before an anticipated recovery in value, the full amount of the impairment is included in net realized gains (losses). The new cost basis of the investment is the previous amortized cost basis reduced by the impairment recognized in net realized gains (losses). The new cost basis is not adjusted for any subsequent recoveries in fair value.

The Company reports accrued investment income separately from investment balances and has elected not to measure an allowance for credit losses for accrued investment income. Any uncollectible accrued interest income is written off in the period it is deemed uncollectible.

Net investment income includes interest and dividend income together with amortization of market premiums and discounts and is net of investment management and custody fees. Anticipated prepayments and expected maturities are used in applying the interest method for certain investments such as mortgage and other asset-backed securities. When actual prepayments differ significantly from anticipated prepayments, the effective yield is recalculated to reflect actual payments to date and anticipated future payments. The net investment in such securities is adjusted to the amount that would have existed had the new effective yield been applied since the acquisition of the security. Such adjustments, if any, are included in net investment income when determined.

Investment gains or losses realized on the sale of investments, except for certain fund investments, are determined on a first-in, first-out basis and are reflected in net income. Investment gains or losses realized on the sale of certain fund investments are determined on an average cost basis. Unrealized appreciation or decline in the value of available for sale securities, which are carried at fair value, is excluded from net income and recorded as a separate component of accumulated other comprehensive income, net of applicable deferred income tax.

(i) Derivative Instruments

The Company recognizes all derivative instruments, including embedded derivative instruments, at fair value in its consolidated balance sheets. The Company employs the use of derivative instruments within its operations to mitigate risks arising from assets and liabilities held in foreign currencies as well as part of its overall investment strategy. For such instruments, changes in assets and liabilities measured at fair value are recorded as “Net realized gains (losses)” in the consolidated statements of income. In addition, the Company’s derivative instruments include amounts related to underwriting activities where an insurance or reinsurance contract meets the accounting definition of a derivative instrument. For such contracts, changes in fair value are reflected in “Other underwriting income” in the consolidated statements of income as the underlying contract originates from the Company’s underwriting operations. For the periods ended 2022, 2021, and 2020, the Company did not designate any derivative instruments as hedges under the relevant accounting guidance. See note 11, “Derivative Instruments” for additional information.

(j) Reserves for Losses and Loss Adjustment Expenses

Insurance and Reinsurance. The reserve for losses and loss adjustment expenses consists of estimates of unpaid reported losses and loss adjustment expenses and estimates for losses incurred but not reported. The reserve for unpaid reported losses and loss adjustment expenses, established by management based on reports from ceding companies and claims from insureds, excludes estimates of amounts related to losses under high deductible policies, and represents the estimated ultimate cost of events or conditions that have been reported to or specifically identified by the Company. Such reserves are supplemented by management’s estimates of reserves for losses incurred for which reports or claims have not been received. The Company’s reserves are based on a combination of reserving methods, incorporating both Company and industry loss development patterns. The Company selects the initial expected loss and loss adjustment expense ratios based on information derived by its underwriters and actuaries during the initial pricing of the business, supplemented by industry data where appropriate. Such ratios consider, among other things, rate changes and

changes in terms and conditions that have been observed in the market. These estimates are reviewed regularly and, as experience develops and new information becomes known, the reserves are adjusted as necessary. Such adjustments, if any, are reflected in income in the period in which they are determined. As actual loss information has been reported, the Company has developed its own loss experience and its reserving methods include other actuarial techniques. Over time, such techniques have been given further weight in its reserving process based on the continuing maturation of the Company’s reserves. Inherent in the estimates of ultimate losses and loss adjustment expenses are expected trends in claims severity and frequency and other factors which may vary significantly as claims are settled. Accordingly, ultimate losses and loss adjustment expenses may differ materially from the amounts recorded in the accompanying consolidated financial statements. Losses and loss adjustment expenses are recorded on an undiscounted basis, except for excess workers’ compensation and employers’ liability business written by the Company’s insurance operations.

Mortgage. The reserves for mortgage guaranty insurance losses and loss adjustment expenses are the estimated claim settlement costs on notices of delinquency that have been received by the Company, as well as loan delinquencies that have been incurred but have not been reported by the lenders. Consistent with primary mortgage insurance industry accounting practice, the Company does not establish loss reserves for future claims on insured loans that are not currently delinquent (defined as two or more payments in arrears). The Company establishes loss reserves on a case-by-case basis when insured loans are reported delinquent using estimated claim rates and average claim sizes for each cohort, net of any salvage recoverable. The Company also reserves for delinquencies that have occurred but have not yet been reported to the Company prior to the close of an accounting period. To determine this reserve, the Company estimates the number of delinquencies not yet reported using historical information regarding late reported delinquencies and applies estimated claim rates and claim sizes for the estimated delinquencies not yet reported.

The establishment of reserves across the Company’s segments is an inherently uncertain process, are necessarily based on estimates, and the ultimate net cost may vary from such estimates. The methods for making such estimates and for establishing the resulting liability are reviewed and updated using the most current information available. Any resulting adjustments, which may be material, are reflected in current operations.

(k) Contractholder Receivables and Payables and Collateral Held for Insured Obligations

Certain insurance policies written by the Company’s U.S. insurance operations feature large deductibles, primarily in its construction and national accounts line of business. Under such contracts, the Company is obligated to pay the claimant for the full amount of the claim. The Company is subsequently reimbursed by the policy holder for the deductible amount. These amounts are included on a gross basis in the consolidated balance sheet as contractholder payables and contractholder receivables. In the event that the Company is unable to collect from the policyholder, the Company would be liable for such defaulted amounts. Collateral, primarily in the form of letters of credit, cash and trusts, is obtained from the policyholder to mitigate the Company’s credit risk. In the instances where the Company receives collateral in the form of cash, the Company reflects it in “Collateral held for insured obligations.”

Contractholder receivables are reported net of an allowance for expected credit losses. The allowance is based upon the Company’s ongoing review of amounts outstanding, changes in policyholder credit standing, amounts and form of collateral obtained, and other relevant factors. A ratings based probability-of-default and loss-given-default methodology is used to estimate the allowance for expected credit losses. Any allowance for credit losses is charged to net realized gains (losses) in the period the receivable is recorded and revised in subsequent periods to reflect changes in the Company’s estimate of expected credit losses. See note 7, “Allowance for Expected Credit Losses” for additional information.

(l) Foreign Exchange

Assets and liabilities of foreign operations whose functional currency is not the U.S. Dollar are translated at the prevailing exchange rates at each balance sheet date. Revenues and expenses of such foreign operations are translated at average exchange rates during the year. The net effect of the translation adjustments for foreign operations is included in accumulated other comprehensive income, net of applicable deferred income tax. Monetary assets and liabilities, such as premiums receivable and the reserve for losses and loss adjustment expenses, denominated in foreign currencies are revalued at the exchange rate in effect at the balance sheet date with the resulting foreign exchange gains and losses included in net income. Accounts that are classified as non-monetary, such as deferred acquisition costs and the unearned premium reserves, are not revalued. In the case of foreign currency denominated fixed maturity securities which are classified as “available for sale,” the change in exchange rates between the local currency in which the investments are denominated and the Company’s functional currency at each balance sheet date is included in unrealized appreciation or

decline in value of securities, a component of accumulated other comprehensive income, net of applicable deferred income tax.

(m) Income Taxes

Deferred income taxes reflect the expected future tax consequences of temporary differences between the carrying amounts of assets and liabilities for financial reporting purposes and amounts used for income tax purposes. A valuation allowance is recorded if it is more likely than not that some or all of a deferred tax asset may not be realized. The Company considers future taxable income and feasible tax planning strategies in assessing the need for a valuation allowance. In the event the Company determines that it will not be able to realize all or part of its deferred income tax assets in the future, an adjustment to the deferred income tax assets would be charged to income in the period in which such determination is made. In addition, if the Company subsequently assesses that the valuation allowance is no longer needed, a benefit would be recorded to income in the period in which such determination is made. See note 15, “Income Taxes” for additional information.

The Company recognizes a tax benefit where it concludes that it is more likely than not that the tax benefit will be sustained on audit by the taxing authority based solely on the technical merits of the associated tax position. If the recognition threshold is met, the Company recognizes a tax benefit measured at the largest amount of the tax benefit that, in the Company’s judgment, is greater than 50% likely to be realized. The Company records interest and penalties related to unrecognized tax benefits in the provision for income taxes.

(n) Share-Based Payment Arrangements

The Company applies a fair value based measurement method in accounting for its share-based payment arrangements with eligible employees and directors. Compensation expense is estimated based on the fair value of the award at the grant date and is recognized in net income over the requisite service period with a corresponding increase in shareholders’ equity. No value is attributed to awards that employees forfeit because they fail to satisfy vesting conditions. The Company’s (i) time-based awards generally vest over a three year period with one-third vesting on the first, second and third anniversaries of the grant date and (ii) performance-based awards cliff vest after each three year performance period based on achievement of the specified performance criteria. The share-based compensation expense associated with awards that have graded vesting features and vest based on service conditions only is calculated on a straight-line basis over the requisite service period for the entire award. Compensation expense recognized in connection with performance awards is based

on the achievement of the specified performance and service conditions. The final measure of compensation expense recognized over the requisite service period reflects the final performance outcome. During the recognition period compensation expense is accrued based on the performance condition that is probable of achievement. For awards granted to retirement-eligible employees where no service is required for the employee to retain the award, the grant date fair value is immediately recognized as compensation expense at the grant date because the employee is able to retain the award without continuing to provide service. For employees near retirement eligibility, attribution of compensation cost is over the period from the grant date to the retirement eligibility date. These charges had no impact on the Company’s cash flows or total shareholders’ equity. See note 22, “Share-Based Compensation” for information relating to the Company’s share-based payment awards.

(o) Guaranty Fund and Other Related Assessments

Liabilities for guaranty fund and other related assessments in the Company’s insurance and reinsurance operations are accrued when the Company receives notice that an amount is payable, or earlier if a reasonable estimate of the assessment can be made.

(p) Treasury Shares

Treasury shares are common shares purchased by the Company and not subsequently canceled. These shares are recorded at cost and result in a reduction of the Company’s shareholders’ equity in its Consolidated Balance Sheets.

(q) Goodwill and Intangible Assets

Goodwill represents the excess of the purchase price of business combination over the fair value of the net assets acquired and is assigned to the applicable reporting unit at acquisition. Goodwill is evaluated for impairment on an annual basis. Impairment tests may be performed more frequently if the facts and circumstances indicate a possible impairment. In performing impairment tests, the Company may first assess qualitative factors to determine whether it is more likely than not (that is, more than a 50% probability) that the fair value of a reporting unit exceeds its carrying amount as a basis for determining whether it is necessary to perform goodwill impairment test described in the accounting guidance.

Indefinite-lived intangible assets, such as insurance licenses are evaluated for impairment similar to goodwill. Finite-lived intangible assets and liabilities include the value of acquired insurance and reinsurance contracts, which are estimated based on the present value of future expected cash flows and amortized in proportion to the estimated profits expected to be realized. Other finite-lived intangible assets, including

customer lists, trade name and IT platforms, are amortized over their useful lives. Finite-lived intangible assets and liabilities are periodically reviewed for indicators of impairment. An impairment is recognized when the carrying amount is not recoverable from its undiscounted cash flows and is measured as the difference between the carrying amount and fair value.

If goodwill or intangible assets are impaired, such assets are written down to their fair values with the related expense recorded in the Company’s results of operations.

(r) Investment in Operating Affiliates

Investment in operating affiliates primarily represent the Company’s investments in which it has significant influence and which are accounted for under the equity method of accounting. In applying the equity method of accounting, investments in operating affiliates are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of net income or loss of the operating affiliate. The Company records its proportionate share of other comprehensive income or loss of the operating affiliate as a component of other comprehensive income. Adjustments are based on the most recently available financial information from the operating affiliate. Changes in the carrying value of these investments are recorded in income (loss) from operating affiliates.

(s) Funds Held Arrangements

Funds held arrangements are agreements with a third party reinsurance company, where the reinsured retains the related assets on a funds held basis. Such amounts are included in “Other assets” on the Company’s balance sheet. Investment returns produced by those assets are recorded as part of net investment income and net realized gains (losses) in the Company's consolidated results of operations. Funds held as collateral by the Company are included in “Other liabilities” and changes to the funds held liability are reflected as part of interest expense in the Company’s consolidated results of operations.

(t) Recent Accounting Pronouncements

Recently Issued Accounting Standards Adopted

The Company adopted ASU 2019-12, “Simplifying the Accounting for Income Taxes.” This ASU eliminates certain exceptions for recognizing deferred taxes for investments, performing intraperiod tax allocations and calculating income taxes in interim periods. The ASU also clarifies the accounting for transactions that result in a step-up in the tax basis of goodwill. The adoption of this guidance did not have a material effect on the Company’s consolidated financial statements.

Recently Issued Accounting Standards Not Yet Adopted

ASU 2020-04, “Facilitation of the Effects of Reference Rate Reform on Financial Reporting,” was issued in March 2020 and amended in December 2022 with ASU 2022-06, “Reference Rate Reform (Topic 848)”. This ASU provides optional expedients and exceptions for applying GAAP to investments, derivatives, or other transactions that reference the London Interbank Offered Rate (“LIBOR”) or another reference rate expected to be discontinued because of reference rate reform. Along with the optional expedients, the amendments include a general principle that permits an entity to consider contract modifications due to reference reform to be an event that does not require contract re-measurement at the modification date or reassessment of a previous accounting determination. The amendment deferred the sunset date from December 31, 2022 to December 31, 2024. As a result, this standard can be adopted no later than December 31, 2024, with early adoption permitted. Based on its current analysis, the Company does not expect that the new guidance will have a material effect on the Company’s consolidated financial statements.

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Segment Information

12 Months Ended

Dec. 31, 2022

Segment Reporting [Abstract]

Segment Information

The Company classifies its businesses into three underwriting segments – insurance, reinsurance and mortgage – and two operating segments – corporate and ‘other.’ The Company determined its reportable segments using the management approach described in accounting guidance regarding disclosures about segments of an enterprise and related information. The accounting policies of the segments are the same as those used for the preparation of the Company’s consolidated financial statements. Intersegment business is allocated to the segment accountable for the underwriting results.

The Company’s insurance, reinsurance and mortgage segments each have managers who are responsible for the overall profitability of their respective segments and who are directly accountable to the Company’s chief operating decision makers, the Chief Executive Officer of Arch Capital, Chief Financial Officer and Treasurer of Arch Capital and the President and Chief Underwriting Officer of Arch Capital. The chief operating decision makers do not assess performance, measure return on equity or make resource allocation decisions on a line of business basis. Management measures segment performance for its three underwriting segments based on underwriting income or loss. The Company does not manage its assets by underwriting segment, with the exception of goodwill and intangible assets, and, accordingly, investment income is not allocated to each underwriting segment.

The insurance segment consists of the Company’s insurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include:

•    Construction and national accounts: primary and excess casualty coverages for middle market and large construction accounts, a comprehensive range of products for middle market accounts in specialty industries and casualty solutions for large national accounts, including loss sensitive primary insurance programs (large deductible, self-insured retention and retrospectively rated programs).

•    Excess and surplus casualty: primary and excess casualty insurance coverages written on a non-admitted basis.

•    Professional lines: directors’ and officers’ liability, errors and omissions liability, employment practices liability, fiduciary liability, crime, professional indemnity and other financial related coverages for corporate, private equity, venture capital, real estate investment trust, limited partnership, financial institution and not-for-profit clients of all sizes, cyber insurance, and medical professional and general liability

insurance coverages for the healthcare industry. The business is predominately written on a claims-made basis.

•    Programs: primarily targeting program managers with unique expertise and niche products offering some combination of general liability, commercial automobile, property, inland marine, umbrella and workers’ compensation.

•    Property, energy, marine and aviation: primary and excess general property insurance coverages, including catastrophe-exposed property coverage, for commercial clients. Coverages for marine include hull, cargo, war, specie and liability. Aviation, stand-alone terrorism and political risks are also offered. Coverage may be provided for operational and construction risk.

•    Travel, accident and health: specialty travel and accident and related insurance products for individual, group travelers, travel agents and suppliers, as well as accident and health, which provides accident, disability and medical plan insurance coverages for employer groups, medical plan members, students and other participant groups.

•    Warranty and lenders solutions: collateral protection, debt cancellation and service contract reimbursement products to banks, credit unions, automotive dealerships and original equipment manufacturers and other specialty programs that pertain to automotive lending and leasing.

•    Other: includes alternative market risks (including captive insurance programs), excess workers’ compensation and employer’s liability insurance coverages for qualified self-insured groups, associations and trusts, and contract, commercial and transactional surety coverages.

The reinsurance segment consists of the Company’s reinsurance underwriting units which offer specialty product lines on a worldwide basis. Reinsurance agreements are typically offered on a proportional and/or excess of loss basis and provide coverage to ceding company clients for specific underlying written policies. Product lines include:

•Casualty: provides coverage on third party liability exposures including, among others, executive assurance, professional liability, excess and umbrella liability, excess motor and healthcare business, and workers’ compensation. Business is assumed primarily on a treaty basis, with some facultative coverages also offered.

•Marine and aviation: provides coverage for energy, hull, cargo, specie, liability and transit, and aviation business, including airline and general aviation risks. Business written may also include space business, which

includes coverages for satellite assembly, launch and operation for commercial space programs.

•Other specialty: provides coverage for proportional motor reinsurance, whole account multi-line treaties, cyber, trade credit and surety, accident and health, workers’ compensation catastrophe, agriculture and political risk, among others.

•Property catastrophe: provides protection for most types of catastrophic losses, including hurricane, earthquake, flood, tornado, hail and fire, and for other perils on a case-by-case basis. Excess of loss coverages are triggered when aggregate losses and loss adjustment expense from a single occurrence of a covered peril exceed the retention specified in the contract.

•Property excluding property catastrophe: provides coverage for personal lines and/or commercial property exposures and principally covers buildings, structures, equipment and contents. The primary perils in this business include fire, explosion, collapse, riot, vandalism, wind, tornado, flood and earthquake. Business is assumed on either a treaty or facultative basis.

•Other: includes life reinsurance business, casualty clash business and, in limited instances, non-traditional business which is intended to provide insurers with risk management solutions that complement traditional reinsurance.

The mortgage segment includes the Company’s underwriting units which offer mortgage insurance and reinsurance products on a worldwide basis. Underwriting units include:

•U.S. primary mortgage insurance: offers private mortgage insurance through Arch Mortgage Insurance Company and United Guaranty Residential Insurance Company (combined “Arch MI U.S.”), both approved eligible mortgage insurers by Fannie Mae and Freddie Mac. Arch MI U.S. also includes AMG, which is not a government sponsored enterprise (“GSE”) approved entity.

•U.S. credit risk transfer (“CRT”) and other: underwrites CRT transactions, which are predominantly with GSEs, and other U.S. reinsurance transactions.

•International mortgage insurance/reinsurance: underwrites mortgage insurance and reinsurance outside of the U.S.

The corporate segment results include net investment income, net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings), equity in net income or loss of investments accounted for using the equity method, other income (loss), corporate expenses, transaction costs and other, amortization of intangible assets, interest expense, net foreign exchange gains or losses, income taxes, income or loss from operating affiliates and items related to the Company’s non-cumulative preferred shares. Such amounts exclude the results of the ‘other’ segment.

Through June 30, 2021, the ‘other’ segment included the results of Somers. In July 2021, the Company announced the completion of the previously disclosed acquisition of Somers by Greysbridge. Based on the governing documents of Greysbridge, the Company has concluded that, while it retains significant influence over Somers, Somers no longer constitutes a variable interest entity. Accordingly, effective July 1, 2021, Arch no longer consolidates the results of Somers in its consolidated financial statements. See note 12, “Variable Interest Entity and Noncontrolling Interests.”

The following tables summarize the Company’s underwriting income or loss by segment, together with a reconciliation of underwriting income or loss to net income available to Arch common shareholders, summary information regarding net premiums written and earned by major line of business and net premiums written by location:

	Year Ended December 31, 2022
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	6,930,864		$	6,948,438		$	1,454,971		$	15,326,447		$	—		$	15,326,447
Premiums ceded	(1,910,222)			(2,024,462)			(322,400)			(4,249,258)			—			(4,249,258)
Net premiums written	5,020,642			4,923,976			1,132,571			11,077,189			—			11,077,189
Change in unearned premiums	(461,307)			(964,595)			26,790			(1,399,112)			—			(1,399,112)
Net premiums earned	4,559,335			3,959,381			1,159,361			9,678,077			—			9,678,077
Other underwriting income	—			4,871			8,356			13,227			—			13,227
Losses and loss adjustment expenses	(2,782,945)			(2,568,843)			324,271			(5,027,517)			—			(5,027,517)
Acquisition expenses	(885,866)			(813,555)			(40,159)			(1,739,580)			—			(1,739,580)
Other operating expenses	(665,472)			(267,531)			(195,172)			(1,128,175)			—			(1,128,175)
Underwriting income	$	225,052		$	314,323		$	1,256,657		1,796,032			—			1,796,032
Net investment income										496,547			—			496,547
Net realized gains (losses)										(662,734)			—			(662,734)
Equity in net income (loss) of investments accounted for using the equity method										115,856			—			115,856
Other income (loss)										(26,165)			—			(26,165)
Corporate expenses										(94,390)			—			(94,390)
Transaction costs and other										(1,092)			—			(1,092)
Amortization of intangible assets										(106,200)			—			(106,200)
Interest expense										(130,266)			—			(130,266)
Net foreign exchange gains (losses)										100,905			—			100,905
Income (loss) before income taxes and income (loss) from operating affiliates										1,488,493			—			1,488,493
Income tax expense										(79,961)			—			(79,961)
Income (loss) from operating affiliates										73,891			—			73,891
Net income (loss)										1,482,423			—			1,482,423
Amounts attributable to redeemable noncontrolling interests										(5,490)			—			(5,490)
Net income (loss) available to Arch										1,476,933			—			1,476,933
Preferred dividends										(40,736)			—			(40,736)
Net income (loss) available to Arch common shareholders										$	1,436,197		$	—		$	1,436,197
Underwriting Ratios
Loss ratio	61.0		%	64.9		%	-28.0		%	51.9		%	—		%	51.9		%
Acquisition expense ratio	19.4		%	20.5		%	3.5		%	18.0		%	—		%	18.0		%
Other operating expense ratio	14.6		%	6.8		%	16.8		%	11.7		%	—		%	11.7		%
Combined ratio	95.0		%	92.2		%	-7.7		%	81.6		%	—		%	81.6		%
Goodwill and intangible assets	$	228,532		$	144,846		$	430,911		$	804,289		$	—		$	804,289
Total investable assets										$	28,065,497		$	—		$	28,065,497
Total assets										47,990,507			—			47,990,507
Total liabilities										35,069,605			—			35,069,605

(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

	Year Ended December 31, 2021
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	5,867,734		$	5,093,930		$	1,507,825		$	12,463,788		$	457,465		$	12,752,487
Premiums ceded	(1,719,541)			(1,839,556)			(246,757)			(3,800,153)			(102,763)			(3,734,150)
Net premiums written	4,148,193			3,254,374			1,261,068			8,663,635			354,702			9,018,337
Change in unearned premiums	(521,725)			(413,931)			22,351			(913,305)			(22,734)			(936,039)
Net premiums earned	3,626,468			2,840,443			1,283,419			7,750,330			331,968			8,082,298
Other underwriting income	—			3,669			17,665			21,334			739			22,073
Losses and loss adjustment expenses	(2,344,365)			(1,924,719)			(56,677)			(4,325,761)			(259,042)			(4,584,803)
Acquisition expenses, net	(606,265)			(536,754)			(97,418)			(1,240,437)			(62,741)			(1,303,178)
Other operating expenses	(558,906)			(212,810)			(194,010)			(965,726)			(32,869)			(998,595)
Underwriting income (loss)	$	116,932		$	169,829		$	952,979		1,239,740			(21,945)			1,217,795
Net investment income										346,808			42,310			389,118
Net realized gains (losses)										299,207			80,638			379,845
Equity in net income (loss) of investments accounted for using the equity method										366,402			—			366,402
Other income (loss)										10,244			—			10,244
Corporate expenses										(77,119)			—			(77,119)
Transaction costs and other										(1,103)			(935)			(2,038)
Amortization of intangible assets										(82,057)			(898)			(82,955)
Interest expense										(131,060)			(8,410)			(139,470)
Net foreign exchange gains (losses)										42,854			(1,325)			41,529
Income (loss) before income taxes and income (loss) from operating affiliates										2,013,916			89,435			2,103,351
Income tax expense										(128,348)			(234)			(128,582)
Income (loss) from operating affiliates										264,693			—			264,693
Net income (loss)										2,150,261			89,201			2,239,462
Amounts attributable to redeemable noncontrolling interests										(2,346)			(1,953)			(4,299)
Amounts attributable to nonredeemable noncontrolling interests										—			(78,314)			(78,314)
Net income (loss) available to Arch										2,147,915			8,934			2,156,849
Preferred dividends										(48,343)			—			(48,343)
Loss on redemption of preferred shares										(15,101)			—			(15,101)
Net income (loss) available to Arch common shareholders										$	2,084,471		$	8,934		$	2,093,405
Underwriting Ratios
Loss ratio	64.6		%	67.8		%	4.4		%	55.8		%	78.0		%	56.7		%
Acquisition expense ratio	16.7		%	18.9		%	7.6		%	16.0		%	18.9		%	16.1		%
Other operating expense ratio	15.4		%	7.5		%	15.1		%	12.5		%	9.9		%	12.4		%
Combined ratio	96.7		%	94.2		%	27.1		%	84.3		%	106.8		%	85.2		%
Goodwill and intangible assets	$	256,434		$	183,523		$	505,026		$	944,983		$	—		$	944,983
Total investable assets										$	27,442,153		$	—		$	27,442,153
Total assets										45,100,945			—			45,100,945
Total liabilities										31,545,816			—			31,545,816

(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

	Year Ended December 31, 2020
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	4,688,562		$	3,472,086		$	1,473,999		$	9,632,691		$	728,546		$	10,088,068
Premiums ceded	(1,525,655)			(1,014,716)			(194,149)			(2,732,564)			(190,957)			(2,650,352)
Net premiums written	3,162,907			2,457,370			1,279,850			6,900,127			537,589			7,437,716
Change in unearned premiums	(291,487)			(295,141)			118,085			(468,543)			22,762			(445,781)
Net premiums earned	2,871,420			2,162,229			1,397,935			6,431,584			560,351			6,991,935
Other underwriting income	(31)			4,454			20,316			24,739			2,045			26,784
Losses and loss adjustment expenses	(2,092,453)			(1,628,320)			(528,344)			(4,249,117)			(440,482)			(4,689,599)
Acquisition expenses, net	(418,483)			(354,048)			(134,240)			(906,771)			(98,071)			(1,004,842)
Other operating expenses	(489,153)			(168,011)			(162,202)			(819,366)			(55,810)			(875,176)
Underwriting income (loss)	$	(128,700)		$	16,304		$	593,465		481,069			(31,967)			449,102
Net investment income										401,908			117,700			519,608
Net realized gains (losses)										813,781			9,679			823,460
Equity in net income (loss) of investments accounted for using the equity method										146,693			—			146,693
Other income (loss)										29			—			29
Corporate expenses										(68,492)			—			(68,492)
Transaction costs and other										(9,456)			(4,040)			(13,496)
Amortization of intangible assets										(69,031)			—			(69,031)
Interest expense										(120,214)			(23,242)			(143,456)
Net foreign exchange gains (losses)										(80,161)			(3,473)			(83,634)
Income (loss) before income taxes and income (loss) from operating affiliates										1,496,126			64,657			1,560,783
Income tax expense										(111,812)			(26)			(111,838)
Income (loss) from operating affiliates										16,766			—			16,766
Net income										1,401,080			64,631			1,465,711
Amounts attributable to redeemable noncontrolling interests										(2,997)			(4,117)			(7,114)
Amounts attributable to nonredeemable noncontrolling interests										—			(53,076)			(53,076)
Net income (loss) available to Arch										1,398,083			7,438			1,405,521
Preferred dividends										(41,612)			—			(41,612)
Net income (loss) available to Arch common shareholders										$	1,356,471		$	7,438		$	1,363,909
Underwriting Ratios
Loss ratio	72.9		%	75.3		%	37.8		%	66.1		%	78.6		%	67.1		%
Acquisition expense ratio	14.6		%	16.4		%	9.6		%	14.1		%	17.5		%	14.4		%
Other operating expense ratio	17.0		%	7.8		%	11.6		%	12.7		%	10.0		%	12.5		%
Combined ratio	104.5		%	99.5		%	59.0		%	92.9		%	106.1		%	94.0		%
Goodwill and intangible assets	$	280,978		$	18,963		$	385,272		$	685,213		$	7,650		$	692,863
Total investable assets										$	26,856,295		$	2,657,612		$	29,513,907
Total assets										39,791,983			3,490,314			43,282,297
Total liabilities										26,789,149			2,505,707			29,294,856

(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

The following tables provide summary information regarding net premiums earned by major line of business and net premiums written by underwriting location:

INSURANCE SEGMENT	Year Ended December 31,
	2022		2021		2020
Net premiums earned (1)
Professional lines	$	1,314,236	$	942,817	$	655,872
Property, energy, marine and aviation	772,388		667,892		506,182
Programs	589,860		506,867		432,854
Travel, accident and health	491,847		255,590		190,944
Construction and national accounts	432,020		416,107		398,999
Excess and surplus casualty	393,353		318,027		270,620
Warranty and lenders solutions	127,222		153,958		114,687
Other	438,409		365,210		301,262
Total	$	4,559,335	$	3,626,468	$	2,871,420
Net premiums written by underwriting location (1)
United States	$	3,340,038	$	2,813,039	$	2,158,415
Europe	1,405,719		1,125,192		856,572
Other	274,885		209,962		147,920
Total	$	5,020,642	$	4,148,193	$	3,162,907

REINSURANCE SEGMENT	Year Ended December 31,
	2022		2021		2020
Net premiums earned (1)
Other specialty	$	1,377,880	$	818,801	$	626,409
Property excluding property catastrophe	1,091,440		836,573		562,208
Casualty	854,543		666,754		549,056
Property catastrophe	366,991		280,738		237,736
Marine and aviation	159,401		152,955		109,624
Other	109,126		84,622		77,196
Total	$	3,959,381	$	2,840,443	$	2,162,229
Net premiums written by underwriting location (1)
United States	$	1,246,507	$	828,504	$	687,622
Bermuda	2,561,771		1,557,294		1,001,990
Europe and other	1,115,698		868,576		767,758
Total	$	4,923,976	$	3,254,374	$	2,457,370

MORTGAGE SEGMENT	Year Ended December 31,
	2022		2021		2020
Net premiums earned by underwriting location
United States	$	815,519	$	970,507	$	1,158,563
Other	343,842		312,912		239,372
Total	$	1,159,361	$	1,283,419	$	1,397,935
Net premiums written by underwriting location
United States	$	780,256	$	914,477	$	1,021,950
Other	352,315		346,591		257,900
Total	$	1,132,571	$	1,261,068	$	1,279,850

(1)    Segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions.

OTHER SEGMENT	Year Ended December 31,
	2022		2021		2020
Net premiums earned (1)
Casualty	$	—	$	138,551	$	245,272
Other specialty	—		118,356		186,717
Property catastrophe	—		15,235		23,037
Property excluding property catastrophe	—		6,578		1,130
Marine and aviation	—		190		429
Other	—		53,058		103,766
Total	$	—	$	331,968	$	560,351
Net premiums written by underwriting location (1)
United States	$	—	$	63,403	$	115,471
Europe	—		91,499		97,753
Bermuda	—		199,800		324,365
Total	$	—	$	354,702	$	537,589

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Reserve for Losses and Loss Adjustment Expenses

12 Months Ended

Dec. 31, 2022

Liability for Future Policy Benefits and Unpaid Claims and Claims Adjustment Expense [Abstract]

Reserve for losses and loss adjustment expenses

The following table represents an analysis of losses and loss adjustment expenses and a reconciliation of the beginning and ending reserve for losses and loss adjustment expenses:

	Year Ended December 31,
	2022		2021		2020
Reserve for losses and loss adjustment expenses at beginning of year	$	17,757,156	$	16,513,929	$	13,891,842
Unpaid losses and loss adjustment expenses recoverable	5,599,231		4,314,855		4,082,650
Net reserve for losses and loss adjustment expenses at beginning of year	12,157,925		12,199,074		9,809,192
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year	5,798,528		4,940,987		4,851,051
Prior years	(771,011)		(356,184)		(161,452)
Total net incurred losses and loss adjustment expenses	5,027,517		4,584,803		4,689,599
Net losses and loss adjustment expense reserves of acquired business (1)	—		104,176		—
Retroactive reinsurance transactions (2)	—		(444,147)		182,210
Impact of deconsolidation of Somers (3)	—		(1,460,611)		—
Foreign exchange (gains) losses and other	(290,376)		1,181		179,190
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year	(887,464)		(734,846)		(661,529)
Prior years	(2,254,484)		(2,091,705)		(1,999,588)
Total net paid losses and loss adjustment expenses	(3,141,948)		(2,826,551)		(2,661,117)
Net reserve for losses and loss adjustment expenses at end of year	13,753,118		12,157,925		12,199,074
Unpaid losses and loss adjustment expenses recoverable	6,278,825		5,599,231		4,314,855
Reserve for losses and loss adjustment expenses at end of year	$	20,031,943	$	17,757,156	$	16,513,929

(1)    Represents activity related to the Company’s acquisitions in the 2021 period. See note 2, “Acquisitions.”

(2)    See ‘Retroactive Reinsurance Transactions’ section.

(3)    See note 12, “Variable Interest Entity and Noncontrolling Interests.”

Development on Prior Year Loss Reserves

Year Ended December 31, 2022

During 2022, the Company recorded estimated net favorable development on prior year loss reserves of $771.0 million, which consisted of net favorable development of $25.3 million from the insurance segment, $191.6 million from the reinsurance segment and $554.1 million from the mortgage segment.

The insurance segment’s net favorable development of $25.3 million, or 0.6 points of net earned premium, consisted of $55.3 million of net favorable development in short-tailed lines partially offset by $29.9 million of net adverse development from medium-tailed and long-tailed lines. Net favorable development in short-tailed lines reflected $37.4 million of favorable development in warranty and lenders solutions, primarily from the 2021 accident year (i.e., the year in which a loss occurred), and $14.8 million of favorable development related to travel and accident

business, primarily from the 2020 and 2021 accident years. Net adverse development in medium-tailed lines reflected $24.7 million of adverse development in professional liability business, primarily from the 2013 to 2015 and 2018 to 2020 accident years, and $6.4 million of adverse development in contract binding business, across most accident years, partially offset by $12.9 million of favorable development in marine business, across most accident years. Net adverse development in long-tail lines reflected $18.5 million of adverse development related to casualty business, primarily from the 2020 and 2021 accident years, and $7.3 million of adverse development on construction and national accounts, primarily from the 2017, 2020 and 2021 accident years. This is partially offset by $21.5 million of favorable development in other business, including alternative markets and excess workers’ compensation, primarily from the 2019 and prior accident years.

The reinsurance segment’s net favorable development of $191.6 million, or 4.8 points of net earned premium, consisted of $196.2 million of net favorable development from short-tailed and medium-tailed lines, partially offset by $4.6 million of net adverse development from long-tailed lines. Net favorable development in short-tailed lines reflected $109.4 million of favorable development from property other than property catastrophe business, primarily from the 2018 to 2021 underwriting years (i.e., all premiums and losses attributable to contracts having an inception or renewal date within the given twelve-month period), $24.0 million of favorable development from property catastrophe business, primarily from the 2018 to 2020 underwriting years, and $35.0 million from other specialty business, primarily from the 2016 and 2021 underwriting years. Net favorable development in medium-tailed lines reflected $28.0 million in marine and aviation lines, across most underwriting years. Net adverse development in long-tailed lines primarily reflected $4.6 million in casualty, spread across many prior underwriting years.

The mortgage segment experienced net favorable development of $554.1 million, or 47.8 points of net earned premium, with the majority of reserve releases being on COVID-related delinquencies associated with the U.S. first lien portfolio from the 2020 and 2021 accident years. The Company’s credit risk transfer, international, second lien and student loan businesses also contributed to the favorable development.

Year Ended December 31, 2021

During 2021, the Company recorded estimated net favorable development on prior year loss reserves of $356.2 million, which consisted of net favorable development of $16.2 million from the insurance segment, $178.8 million from the reinsurance segment, $169.6 million from the mortgage segment, partially offset by $8.4 million of adverse development from the ‘other’ segment (activity prior to the deconsolidation of Somers).

The insurance segment’s net favorable development of $16.2 million, or 0.4 points of net earned premium, consisted of $109.8 million of net favorable development in short-tailed and long-tailed lines mostly offset by $93.5 million of net adverse development from medium-tailed lines. Net favorable development of $81.7 million in short-tailed lines reflected $38.9 million of favorable development from property (excluding marine), primarily from the 2018 to 2020 accident years, $26.7 million of favorable development in warranty and lenders solutions, primarily from the 2020 accident year, and $16.2 million of favorable development on travel and accident, primarily from the 2016 to 2020 accident years. Net favorable development of $28.1 million in long-tailed lines reflected favorable development in construction, national accounts and alternative markets, primarily from the

2016 to 2019 accident years, partially offset by adverse development in executive assurance, primarily from the 2015, 2017 and 2018 accident years. Net adverse development in medium-tailed lines reflected $57.6 million of adverse development in contract binding, primarily from the 2013 to 2019 accident years and $30.8 million of adverse development in professional liability, primarily from the 2018 to 2020 accident years.

The reinsurance segment’s net favorable development of $178.8 million, or 6.3 points of net earned premium, consisted of $184.1 million of net favorable development from short-tailed and medium-tailed lines, partially offset by $5.3 million of net adverse development from long-tailed lines. Net favorable development of $175.5 million in short-tailed lines reflected $123.3 million from other specialty lines, primarily from the 2014 to 2019 underwriting years, and $88.6 million of favorable development from property other than property catastrophe business, primarily from the 2015 to 2020 underwriting years. Such amounts were partially offset by adverse development of $36.4 million from property catastrophe, primarily from the 2020 underwriting year. Adverse development in long-tailed lines reflected an increase in casualty, primarily from the 2018 underwriting year.

The mortgage segment experienced net favorable development of $169.6 million, or 13.2 points of net earned premium. Approximately a third of this development came from the U.S. first lien portfolio, which benefited from improving economic conditions and rising home prices, resulting in reduced claim rate assumptions primarily associated with pre-pandemic delinquencies. Various vintage CRT contracts also experienced similar effects and contributed to the favorable development, including the effect of contracts called by the GSEs. Subrogation recoveries on second lien and student loan business and international business also contributed to the favorable development.

Year Ended December 31, 2020

During 2020, the Company recorded estimated net favorable development on prior year loss reserves of $161.5 million, which consisted of net favorable development of $7.8 million from the insurance segment, $134.0 million from the reinsurance segment, $19.0 million from the mortgage segment, and $0.7 million from the ‘other’ segment.

The insurance segment’s net favorable development of $7.8 million, or 0.3 points of net earned premium, consisted of $83.0 million of net favorable development in short-tailed and long-tailed lines partially offset by $75.2 million of net adverse development from medium-tailed lines. Net favorable development of $33.6 million in short-tailed lines reflected $21.6 million of favorable development from property (excluding marine), primarily from the 2015 to 2018

accident years, and $8.4 million of favorable development on travel and accident, primarily from the 2019 accident year. Net favorable development of $49.4 million in long-tailed lines included $38.8 million of favorable development related to other business, including alternative markets and excess workers’ compensation, across all accident years, and $9.3 million of favorable development related to construction business. Net adverse development in medium-tailed lines reflected $37.9 million of adverse development in surety business, primarily from the 2019 accident year, $23.1 million in contract binding business, primarily from the 2016 to 2019 accident years, and $16.0 million in program business, primarily from the 2016 to 2019 accident years.

The reinsurance segment’s net favorable development of $134.0 million, or 6.2 points of net earned premium, consisted of $155.9 million of net favorable development from short-tailed and medium-tailed lines, partially offset by $21.9 million of net adverse development from long-tailed lines. Net favorable development of $144.0 million in short-tailed lines reflected $87.7 million related to property catastrophe and property other than property catastrophe business, primarily from the 2015 to 2019 underwriting years, and $53.6 million from other specialty lines, across most underwriting years. The net reduction of loss estimates for the reinsurance segment’s short-tailed lines primarily resulted from varying levels of reported and paid claims activity than previously anticipated which led to decreases in

certain loss ratio selections during 2020. Adverse development in long-tailed lines reflected an increase in casualty, primarily from the 2012 to 2015 underwriting years.

The mortgage segment’s net favorable development of $19.0 million, or 1.4 points of net earned premium, included $16.2 million of favorable development on U.S. primary mortgage insurance business. Such development was primarily driven by subrogation recoveries on second lien business and student loan business.

Retroactive Reinsurance Transactions

In 2021, the Company entered into a retroactive reinsurance transaction with third party reinsurer to reinsure run-off liabilities associated with certain U.S. insurance exposures.

In 2021, the Company entered into a reinsurance to close with the related party, in connection with the 2018 and prior years of account for certain London syndicate business. See note 16, “Transactions with Related Parties”.

In 2020, the Company entered into a reinsurance-to-close agreement related to a third party arrangement covering the 2017 and prior years of account for certain London syndicate business.

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Short Duration Contracts

12 Months Ended

Dec. 31, 2022

Short Duration Contracts Disclosure [Abstract]

Short duration contracts

The Company’s reserves for losses and loss adjustment expenses primarily relate to short-duration contracts with various characteristics (e.g., type of coverage, geography, claims duration). The Company considered such information in determining the level of disaggregation for disclosures related to its short-duration contracts, as detailed in the table below:

Reportable segment	Level of disaggregation	Included lines of business
Insurance	Property energy, marine and aviation	Property energy, marine and aviation
	Third party occurrence business	Excess and surplus casualty (excluding contract binding); construction and national accounts; and other (including alternative market risks, excess workers’ compensation and employer’s liability insurance coverages)
	Third party claims-made business	Professional lines
	Multi-line and other specialty	Programs; contract binding (part of excess and surplus casualty); travel, accident and health; warranty and lenders solutions; and other (contract and commercial surety coverages)
Reinsurance	Casualty	Casualty
	Property catastrophe	Property catastrophe
	Property excluding property catastrophe	Property excluding property catastrophe
	Marine and aviation	Marine and aviation
	Other specialty	Other specialty
Mortgage	Direct mortgage insurance in the U.S.	Mortgage insurance on U.S. primary exposures

The Company determined the following to be insignificant for disclosure purposes: (i) certain mortgage business, including non-U.S. primary business, second lien and student loan exposures, global mortgage reinsurance and participation in various GSE credit risk-sharing products and (ii) certain reinsurance business, including casualty clash and non-traditional lines. Such amounts are included as reconciling items.

The Company is required to establish reserves for losses and loss adjustment expenses (“Loss Reserves”) that arise from the business the Company underwrites. Loss Reserves for the insurance, reinsurance and mortgage segments represent estimates of future amounts required to pay losses and loss adjustment expenses for insured or reinsured events which have occurred at or before the balance sheet date. Loss Reserves do not reflect contingency reserve allowances to account for future loss occurrences. Losses arising from future events will be estimated and recognized at the time the losses are incurred and could be substantial.

Insurance Segment

Loss Reserves for the insurance segment are comprised of estimated amounts for (1) reported losses (“case reserves”) and (2) incurred but not reported losses (“IBNR reserves”). Generally, claims personnel determine whether to establish a case reserve for the estimated amount of the ultimate settlement of individual claims. The estimate reflects the judgment of claims personnel based on general corporate reserving practices, the experience and knowledge of such personnel regarding the nature and value of the specific type of claim and, where appropriate, advice of counsel. The Company also contracts with a number of outside third party administrators in the claims process who, in certain cases, have limited authority to establish case reserves. The work of such administrators is reviewed and monitored by our claims personnel. Loss Reserves are also established to provide for loss adjustment expenses and represent the estimated expense of settling claims, including legal and other fees and the general expenses of administering the claims adjustment process. Periodically, adjustments to the case reserves may be made as additional information is reported or payments are made. IBNR reserves are established to provide for incurred claims which have not yet been reported at the balance sheet date as well as to adjust for any projected variance in case reserving. Actuaries estimate ultimate losses and loss adjustment expenses using various generally accepted actuarial methods applied to known losses and other relevant information. Like case reserves, IBNR reserves are adjusted as additional information becomes known or payments are made. The process of estimating reserves involves a considerable degree of judgment by management and, as of any given date, is inherently uncertain.

Ultimate losses and loss adjustment expenses are generally determined by projection of claim emergence and settlement patterns observed in the past that can reasonably be expected to persist into the future. In forecasting ultimate losses and loss adjustment expenses with respect to any line of business, past experience with respect to that line of business is the primary resource, developed through both industry and company experience, but cannot be relied upon in isolation. Uncertainties in estimating ultimate losses and loss adjustment expenses are magnified by the length of the time lag between when a claim actually occurs and when it is reported and settled. This time lag is sometimes referred to as the “claim-tail.” During this period additional facts regarding coverages written in prior accident years, as well as about actual claims and trends, may become known and, as a result, may lead to adjustments of the related Loss Reserves. If the Company determines that an adjustment is appropriate, the adjustment is recorded in the accounting period in which such determination is made. Accordingly, should Loss Reserves need to be increased or decreased in the future from amounts currently established, future results of operations would be negatively or positively impacted respectively. The

Company authorizes managing general agents, general agents and other producers to write program business on the Company’s behalf within prescribed underwriting authorities. This delegated authority process introduces additional complexity to the actuarial determination of unpaid future losses and loss adjustment expenses. In order to monitor adherence to the underwriting guidelines given to such parties, the Company periodically performs underwriting and claims due diligence reviews.

In determining ultimate losses and loss adjustment expenses, the cost to indemnify claimants, provide needed legal defense and other services for insureds and administer the investigation and adjustment of claims are considered. These claim costs are influenced by many factors that change over time, such as expanded coverage definitions as a result of new court decisions, inflation in costs to repair or replace damaged property, inflation in the cost of medical services and legislated changes in statutory benefits, as well as by the particular, unique facts that pertain to each claim. As a result, the rate at which claims arose in the past and the costs to settle them may not always be representative of what will occur in the future. The factors influencing changes in claim costs are often difficult to isolate or quantify and developments in paid and incurred losses from historical trends are frequently subject to multiple and conflicting interpretations. Changes in coverage terms or claims handling practices may also cause future experience and/or development patterns to vary from the past. A key objective of actuaries in developing estimates of ultimate losses and loss adjustment expenses, and resulting IBNR reserves, is to identify aberrations and systemic changes occurring within historical experience and adjust for them so that the future can be projected more reliably. Because of the factors previously discussed, this process requires the substantial use of informed judgment and is inherently uncertain.

Although Loss Reserves are initially determined based on underwriting and pricing analyses, the Company’s insurance segment applies several generally accepted actuarial methods, as discussed below, on a quarterly basis to evaluate the Loss Reserves, in addition to the expected loss method, in particular for Loss Reserves from more mature accident years (the year in which a loss occurred). Each quarter, as part of the reserving process, the segments’ actuaries reaffirm that the assumptions used in the reserving process continue to form a sound basis for the projection of liabilities. If actual loss activity differs substantially from expectations based on historical information, an adjustment to Loss Reserves may be supported. The Company places more or less reliance on a particular actuarial method based on the facts and circumstances at the time the estimates of Loss Reserves are made.

These methods generally fall into one of the following categories or are hybrids of one or more of the following categories:

•Expected loss methods - these methods are based on the assumption that ultimate losses vary proportionately with premiums. Expected loss and loss adjustment expense ratios are typically developed based upon the information derived by underwriters and actuaries during the initial pricing of the business, supplemented by industry data available from organizations, such as statistical bureaus and consulting firms, where appropriate. These ratios consider, among other things, rate increases and changes in terms and conditions that have been observed in the market. Expected loss methods are useful for estimating ultimate losses and loss adjustment expenses in the early years of long-tailed lines of business, when little or no paid or incurred loss information is available, and is commonly applied when limited loss experience exists for a company.

•Historical incurred loss development methods - these methods assume that the ratio of losses in one period to losses in an earlier period will remain constant in the future. These methods use incurred losses (i.e., the sum of cumulative historical loss payments plus outstanding case reserves) over discrete periods of time to estimate future losses. Historical incurred loss development methods may be preferable to historical paid loss development methods because they explicitly take into account open cases and the claims adjusters’ evaluations of the cost to settle all known claims. However, historical incurred loss development methods necessarily assume that case reserving practices are consistently applied over time. Therefore, when there have been significant changes in how case reserves are established, using incurred loss data to project ultimate losses may be less reliable than other methods.

•Historical paid loss development methods - these methods, like historical incurred loss development methods, assume that the ratio of losses in one period to losses in an earlier period will remain constant. These methods use historical loss payments over discrete periods of time to estimate future losses and necessarily assume that factors that have affected paid losses in the past, such as inflation or the effects of litigation, will remain constant in the future. Because historical paid loss development methods do not use incurred losses to estimate ultimate losses, they may be more reliable than the other methods that use incurred losses in situations where there are significant changes in how incurred losses are established by a company’s claims adjusters. However, historical paid loss development methods are more leveraged (meaning that small changes in payments have a larger impact on estimates of ultimate losses) than

actuarial methods that use incurred losses because cumulative loss payments take much longer to equal the expected ultimate losses than cumulative incurred amounts. In addition, and for similar reasons, historical paid loss development methods are often slow to react to situations when new or different factors arise than those that have affected paid losses in the past.

•Adjusted historical paid and incurred loss development methods - these methods take traditional historical paid and incurred loss development methods and adjust them for the estimated impact of changes from the past in factors such as inflation, the speed of claim payments or the adequacy of case reserves. Adjusted historical paid and incurred loss development methods are often more reliable methods of predicting ultimate losses in periods of significant change, provided the actuaries can develop methods to reasonably quantify the impact of changes. As such, these methods utilize more judgment than historical paid and incurred loss development methods.

•Bornhuetter-Ferguson (“B-F”) paid and incurred loss methods - these methods utilize actual paid and incurred losses and expected patterns of paid and incurred losses, taking the initial expected ultimate losses into account to determine an estimate of expected ultimate losses. The B-F paid and incurred loss methods are useful when there are few reported claims and a relatively less stable pattern of reported losses.

•Frequency-Severity methods - These methods utilize actual paid and incurred claim experience, but break the data down into its component pieces: claim counts, often expressed as a ratio to exposure or premium (frequency), and average claim size (severity). The component pieces are projected to an ultimate level and multiplied together to result in an estimate of ultimate loss. These methods are especially useful when the severity of claims can be confined to a relatively stable range of estimated ultimate average claim value.

•Additional analyses - other methodologies are often used in the reserving process for specific types of claims or events, such as catastrophic or other specific major events. These include vendor catastrophe models, which are typically used in the estimation of Loss Reserves at the early stage of known catastrophic events before information has been reported to an insurer or reinsurer.

In the initial reserving process for short-tail insurance lines (consisting of property, energy, marine and aviation and other exposures including travel, accident and health, and warranty and lenders solutions), the Company relies on a combination of the reserving methods discussed above. For catastrophe-exposed business, the reserving process also includes the usage of catastrophe models for known events

and a heavy reliance on analysis of individual catastrophic events and management judgment. The development of losses on short-tail business can be unstable, especially for policies characterized by high severity, low frequency losses. As time passes, for a given accident year, additional weight is given to the paid and incurred B-F loss development methods and eventually to the historical paid and incurred loss development methods in the reserving process. The Company makes a number of key assumptions in their reserving process, including that historical paid and reported development patterns are stable, catastrophe models provide useful information about our exposure to catastrophic events that have occurred and underwriters’ judgment as to potential loss exposures can be relied on. The expected loss ratios used in the initial reserving process for short-tail business have varied over time due to changes in pricing, reinsurance structure, estimates of catastrophe losses, policy changes (such as attachment points, class and limits) and geographical distribution. As losses in short-tail lines are reported relatively quickly, expected loss ratios are selected for the current accident year based upon actual attritional loss ratios for earlier accident years, adjusted for rate changes, inflation, changes in reinsurance programs and expected attritional losses based on modeling. Furthermore, ultimate losses for short-tail business are known in a reasonably short period of time.

In the initial reserving process for medium-tail and long-tail insurance lines (consisting of third party occurrence business, third party claims made business, and other exposures including surety, programs and contract binding exposures), the Company primarily relies on the expected loss method. The development of the Company’s medium-tail and long-tail business may be unstable, especially if there are high severity major events, as a portion of the Company’s casualty business is in high excess layers. As time passes, for a given accident year, additional weight is given to the paid and incurred B-F loss development methods and historical paid and incurred loss development methods in the reserving process. The Company makes a number of key assumptions

in reserving for medium-tail and long-tail lines, including that the pricing loss ratio is the best estimate of the ultimate loss ratio at the time the policy is entered into, that the loss development patterns, which are based on a combination of company and industry loss development patterns and adjusted to reflect differences in the insurance segment’s mix of business, are reasonable and that claims personnel and underwriters analyses of our exposure to major events are assumed to be the best estimate of exposure to the known claims on those events. The expected loss ratios used in the initial reserving process for medium-tail and long-tail business for recent accident years have varied over time, in some cases significantly, from earlier accident years. As the credibility of historical experience for earlier accident years increases, the experience from these accident years will be given a greater weighting in the actuarial analysis to determine future accident year expected loss ratios, adjusted for changes in pricing, loss trends, terms and conditions and reinsurance structure.

From time to time, the Company enters into loss portfolio transfer and adverse development cover reinsurance agreements accounted for as retroactive reinsurance. These agreements transfer Loss Reserves and future favorable or adverse development on certain runoff programs and certain third party occurrence business, within multi-line and other specialty business (the “Covered Lines”). As incurred losses and allocated loss adjustment expenses for the Covered Lines are ceded to the reinsurer, the Company is not exposed to changes in the amount, timing and uncertainty of cash flows arising from the Covered Lines. To avoid distortion, the incurred losses and allocated loss adjustment expenses and cumulative paid losses and loss adjustment expenses for the Covered Lines are excluded entirely from the tables below. Unpaid loss and loss adjustment expenses recoverable at December 31, 2022 included $280.2 million related to such reinsurance agreements.

The following tables present information on the insurance segment’s short-duration insurance contracts:

Property, energy, marine and aviation ($000’s except claim count)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	158,548	$	156,147	$	148,622	$	142,889	$	134,473	$	133,400	$	128,157	$	126,825	$	125,813	$	124,868	$	27	3,982
2014			148,104		145,679		147,248		136,050		132,166		134,192		134,895		134,803		133,605		1,674		3,557
2015					112,299		109,769		103,921		102,449		97,789		91,770		91,833		90,816		2,654		4,244
2016							104,002		100,843		105,184		100,003		95,989		92,108		87,618		61		5,704
2017									280,686		246,264		235,924		230,413		231,199		225,298		3,268		6,287
2018											180,981		186,030		173,693		170,057		170,411		7,177		5,048
2019													179,056		178,564		165,477		161,156		4,162		5,942
2020															359,394		329,362		335,747		28,330		8,546
2021																	426,870		428,719		54,746		7,566
2022																			521,750		208,080		8,965
																	Total		$	2,279,988
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	32,216	$	84,680	$	110,432	$	119,649	$	121,779	$	125,014	$	122,894	$	124,227	$	124,381	$	124,402
2014			25,849		53,632		77,764		84,061		87,681		98,423		115,253		122,165		122,792
2015					23,561		64,900		76,282		86,196		87,870		86,190		87,260		87,564
2016							24,684		83,218		98,303		97,089		94,570		90,808		87,232
2017									30,215		139,849		195,512		211,688		215,874		217,764
2018											30,026		102,285		134,858		142,838		149,663
2019													26,130		105,380		133,911		139,141
2020															55,619		194,487		251,055
2021																	90,423		267,677
2022																			100,476
									Total										1,547,766
									All outstanding liabilities before 2013, net of reinsurance										18,239
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	750,461

Third party occurrence business ($000’s except claim count)
	Incurred losses and allocated loss adjustment expenses, net of reinsurance																				December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	282,852	$	296,668	$	306,572	$	301,622	$	281,637	$	274,246	$	272,385	$	269,297	$	270,110	$	263,430	$	43,148	66,118
2014			329,718		335,587		338,505		342,759		339,403		343,904		342,641		343,286		345,024		60,263		75,557
2015					358,769		391,570		398,565		391,797		391,132		382,427		386,465		379,226		75,540		78,507
2016							389,530		394,190		405,803		399,315		374,654		367,586		363,453		93,800		78,576
2017									417,097		417,662		422,360		412,231		406,857		406,165		114,603		84,418
2018											430,128		452,879		450,647		451,164		458,050		156,700		77,685
2019													455,928		487,080		480,535		471,279		195,283		84,985
2020															606,640		616,314		640,231		309,019		90,795
2021																	621,972		662,716		431,302		89,718
2022																			688,082		614,366		70,380
																	Total		$	4,677,656
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	6,840	$	29,215	$	71,335	$	101,153	$	122,045	$	149,012	$	164,090	$	174,591	$	184,444	$	192,159
2014			9,200		40,226		71,473		112,541		161,935		191,108		211,440		223,895		237,135
2015					11,110		44,514		88,411		139,364		181,505		211,510		227,439		249,399
2016							11,679		41,920		87,543		136,759		164,534		194,637		215,481
2017									13,391		52,309		99,806		134,988		165,468		220,660
2018											16,991		63,776		115,049		154,138		198,502
2019													18,375		73,075		121,646		172,948
2020															24,407		76,567		154,902
2021																	26,235		90,791
2022																			23,981
									Total										1,755,958
									All outstanding liabilities before 2013, net of reinsurance										263,297
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	3,184,995

Third party claims-made business ($000’s except claim count)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	301,608	$	320,266	$	324,044	$	320,177	$	294,372	$	290,852	$	281,642	$	271,156	$	273,607	$	281,584	$	14,639	14,953
2014			264,273		279,410		298,541		278,556		281,271		297,248		291,498		287,573		296,153		21,206		15,482
2015					258,740		277,358		276,256		259,830		255,207		252,263		267,725		266,758		18,198		14,392
2016							274,996		291,258		308,080		314,412		321,764		326,960		329,534		29,356		15,083
2017									270,272		285,738		311,724		308,172		323,128		316,673		45,042		15,198
2018											272,543		314,112		319,646		336,106		347,449		61,612		15,934
2019													289,128		317,312		317,363		322,178		93,422		15,858
2020															383,497		413,156		423,375		187,245		15,438
2021																	514,676		517,975		351,736		15,751
2022																			657,664		575,484		18,190
																	Total		$	3,759,343
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	19,007	$	87,386	$	137,857	$	179,261	$	197,861	$	216,984	$	238,730	$	245,423	$	246,813	$	253,570
2014			13,814		63,288		129,409		172,722		207,447		229,314		243,137		249,307		260,333
2015					9,059		52,007		100,030		126,431		174,084		193,105		216,892		220,871
2016							10,537		68,157		127,203		158,127		205,478		242,300		256,705
2017									9,281		67,529		112,975		143,064		195,788		232,508
2018											12,241		68,244		118,105		158,389		208,063
2019													12,373		65,286		122,046		154,630
2020															17,070		87,248		151,750
2021																	23,253		90,487
2022																			25,244
									Total										1,854,161
									All outstanding liabilities before 2013, net of reinsurance										86,120
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	1,991,302

Multi-line and other specialty ($000’s except claim count)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	264,243	$	272,335	$	263,631	$	263,928	$	251,894	$	253,271	$	248,634	$	245,825	$	245,069	$	244,191	$	2,761	86,371
2014			301,548		325,705		318,453		318,268		317,197		313,221		310,051		309,061		310,977		3,968		130,844
2015					334,684		357,939		356,777		364,815		356,657		349,432		347,206		344,974		5,632		170,579
2016							408,686		430,976		427,829		416,108		409,987		408,004		408,716		8,616		189,406
2017									482,436		501,026		491,347		500,947		504,322		512,717		12,776		229,570
2018											512,406		564,563		562,848		565,116		564,693		21,722		256,621
2019													566,864		612,179		640,262		651,004		38,672		250,441
2020															618,340		569,123		515,016		87,261		162,214
2021																	635,186		618,581		153,336		113,165
2022																			678,479		425,107		89,859
																	Total		$	4,849,348
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	86,680	$	150,925	$	180,428	$	213,461	$	225,324	$	234,330	$	236,375	$	237,293	$	238,321	$	238,257
2014			107,726		196,899		234,267		267,079		281,195		291,727		293,131		294,630		295,896
2015					138,153		236,108		277,850		305,895		320,971		326,652		330,431		331,320
2016							175,948		304,743		341,789		362,823		379,305		385,314		390,350
2017									181,102		342,385		380,696		423,480		446,002		471,978
2018											211,711		389,047		442,643		479,824		508,649
2019													211,970		385,794		486,882		548,844
2020															171,994		309,106		358,967
2021																	156,992		334,549
2022																			177,092
									Total										3,655,902
									All outstanding liabilities before 2013, net of reinsurance										22,275
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	1,215,721

The following table presents the average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance, as of December 31, 2022:

	Average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance
	Year 1		Year 2		Year 3		Year 4		Year 5		Year 6		Year 7		Year 8		Year 9		Year 10
Property, energy, marine and aviation	20.3	%	44.2	%	18.4	%	5.2	%	1.5	%	1.1	%	2.0	%	2.2	%	0.3	%	—	%
Third party occurrence business	3.4	%	9.3	%	11.8	%	11.2	%	9.7	%	9.7	%	5.4	%	4.5	%	3.8	%	2.9	%
Third party claims-made business	4.1	%	17.2	%	17.2	%	11.4	%	13.6	%	8.8	%	6.4	%	2.0	%	2.1	%	2.4	%
Multi-line and other specialty	34.3	%	28.9	%	10.9	%	8.8	%	4.5	%	3.1	%	0.9	%	0.4	%	0.4	%	—	%

Reinsurance Segment

Loss Reserves for the Company’s reinsurance segment are comprised of (1) case reserves, (2) additional case reserves (“ACRs”) and (3) IBNR reserves. The Company receives reports of claims notices from ceding companies and records case reserves based upon the amount of reserves recommended by the ceding company. Case reserves may be supplemented by ACRs, which may be estimated by the Company’s claims personnel ahead of official notification from the ceding company, or when judgment regarding the size or severity of the known event differs from the ceding company. In certain instances, the Company establishes ACRs even when the ceding company does not report any liability on a known event. In addition, specific claim information reported by ceding companies or obtained through claim audits can alert the Company to emerging trends such as changing legal interpretations of coverage and liability, claims from unexpected sources or classes of business, and significant changes in the frequency or severity of individual claims. Such information is often used in the process of estimating IBNR reserves. IBNR reserves are established to provide for incurred claims which have not yet been reported at the balance sheet date as well as to adjust for any projected variance in case reserving. Actuaries estimate ultimate losses and loss adjustment expenses using various generally accepted actuarial methods applied to known losses and other relevant information. Like case reserves, IBNR reserves are adjusted as additional information becomes known or payments are made. The process of estimating Loss Reserves involves a considerable degree of judgment by management and, as of any given date, is inherently uncertain.

The estimation of Loss Reserves for the reinsurance segment is subject to the same risk factors as the estimation of Loss Reserves for the insurance segment. In addition, the inherent uncertainties of estimating such reserves are even greater for reinsurers, due primarily to the following factors: (1) the claim-tail for reinsurers is generally longer because claims are first reported to the ceding company and then to the reinsurer through one or more intermediaries, (2) the reliance on premium estimates, where reports have not been received from the ceding company, in the reserving process, (3) the potential for writing a number of reinsurance contracts with different ceding companies with the same exposure to a single loss event, (4) the diversity of loss development

patterns among different types of reinsurance contracts, (5) the necessary reliance on the ceding companies for information regarding reported claims and (6) the differing reserving practices among ceding companies.

Ultimate losses and loss adjustment expenses are generally determined by projection of claim emergence and settlement patterns observed in the past that can reasonably be expected to persist into the future. As with the insurance segment, the process of estimating Loss Reserves for the reinsurance segment involves a considerable degree of judgment by management and, as of any given date, is inherently uncertain. As discussed above, such uncertainty is greater for reinsurers compared to insurers. As a result, our reinsurance operations obtain information from numerous sources to assist in the process. Pricing actuaries from the reinsurance segment devote considerable effort to understanding and analyzing a ceding company’s operations and loss history during the underwriting of the business, using a combination of ceding company and industry statistics. Such statistics normally include historical premium and loss data by class of business, individual claim information for larger claims, distributions of insurance limits provided, loss reporting and payment patterns, and rate change history. This analysis is used to project expected loss ratios for each treaty during the upcoming contract period.

As mentioned above, there can be a considerable time lag from the time a claim is reported to a ceding company to the time it is reported to the reinsurer. The lag can be several years in some cases and may be attributed to a number of reasons, including the time it takes to investigate a claim, delays associated with the litigation process, the deterioration in a claimant’s physical condition many years after an accident occurs, the case reserving approach of the ceding company, etc. In the reserving process, the Company assumes that such lags are predictable, on average, over time and therefore the lags are contemplated in the loss reporting patterns used in their actuarial methods. This means that the reinsurance segment must rely on estimates for a longer period of time than does an insurance company. Backlogs in the recording of assumed reinsurance can also complicate the accuracy of loss reserve estimation. As of December 31, 2022 there were no significant backlogs related to the processing of assumed reinsurance information at our reinsurance operations.

The reinsurance segment relies heavily on information reported by ceding companies, as discussed above. In order to determine the accuracy and completeness of such information, underwriters, actuaries, and claims personnel often perform audits of ceding companies and regularly review information received from ceding companies for unusual or unexpected results. Material findings are usually discussed with the ceding companies. The Company sometimes encounters situations where they determine that a claim presentation from a ceding company is not in accordance with contract terms. In these situations, the Company attempts to resolve the dispute with the ceding company. Most situations are resolved amicably and without the need for litigation or arbitration. However, in the infrequent situations where a resolution is not possible, the Company will vigorously defend its position in such disputes.

Although Loss Reserves are initially determined based on underwriting and pricing analysis, the Company applies several generally accepted actuarial methods, as discussed above, on a quarterly basis to evaluate its Loss Reserves in addition to the expected loss method, in particular for reserves from more mature underwriting years (the year in which business is underwritten). Each quarter, as part of the reserving process, the Company’s actuaries reaffirm that the assumptions used in the reserving process continue to form a sound basis for projection of liabilities. If actual loss activity differs substantially from expectations based on historical information, an adjustment to Loss Reserves may be supported. Estimated Loss Reserves for more mature underwriting years are now based more on actual loss activity and historical patterns than on the initial assumptions based on pricing indications. More recent underwriting years rely more heavily on internal pricing assumptions. The Company places more or less reliance on a particular actuarial method based on the facts and circumstances at the time the estimates of Loss Reserves are made.

In the initial reserving process for short-tail reinsurance lines (consisting of property excluding property catastrophe and property catastrophe exposures), the Company relies on a combination of the reserving methods discussed above. For known catastrophic events, the reserving process also includes the usage of catastrophe models and a heavy reliance on analysis which includes ceding company inquiries and management judgment. The development of property losses may be unstable, especially where there is high catastrophic exposure, may be characterized by high severity, low frequency losses for excess and catastrophe-exposed business and may be highly correlated across contracts. As time passes, for a given underwriting year, additional weight is given to the paid and incurred B-F loss development methods and historical paid and incurred loss development

methods in the reserving process. The Company makes a number of key assumptions in reserving for short-tail lines, including that historical paid and reported development patterns are stable, catastrophe models provide useful information about our exposure to catastrophic events that have occurred and our underwriters’ judgment and guidance received from ceding companies as to potential loss exposures may be relied on. The expected loss ratios used in the initial reserving process for property exposures have varied over time due to changes in pricing, reinsurance structure, estimates of catastrophe losses, terms and conditions and geographical distribution. As losses in property lines are reported relatively quickly, expected loss ratios are selected for the current underwriting year incorporating the experience for earlier underwriting years, adjusted for rate changes, inflation, changes in reinsurance programs, expectations about present and future market conditions and expected attritional losses based on modeling. Due to the short-tail nature of property business, reported loss experience emerges quickly and ultimate losses are known in a reasonably short period of time.

In the initial reserving process for medium-tail and long-tail reinsurance lines (consisting of casualty, other specialty, marine and aviation and other exposures), the Company primarily relies on the expected loss method. The development of medium-tail and long-tail business may be unstable, especially if there are high severity major events, with business written on an excess of loss basis typically having a longer tail than business written on a pro rata basis. As time passes, for a given underwriting year, additional weight is given to the paid and incurred B-F loss development methods and eventually to the historical paid and incurred loss development methods in the reserving process. Our reinsurance operations make a number of key assumptions in reserving for medium-tail and long-tail lines, including that the pricing loss ratio is the best estimate of the ultimate loss ratio at the time the contract is entered into, historical paid and reported development patterns are stable and claims personnel and underwriters’ analyses of our exposure to major events are our best estimate of our exposure to the known claims on those events. The expected loss ratios used in our reinsurance operations’ initial reserving process for medium-tail and long-tail contracts have varied over time due to changes in pricing, terms and conditions and reinsurance structure. As the credibility of historical experience for earlier underwriting years increases, the experience from these underwriting years is used in the actuarial analysis to determine future underwriting year expected loss ratios, adjusted for changes in pricing, loss trends, terms and conditions and reinsurance structure.

The following tables present information on the reinsurance segment’s short-duration insurance contracts:

Casualty ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	163,425	$	156,619	$	152,392	$	146,230	$	134,204	$	132,701	$	129,120	$	133,401	$	133,687	$	133,094	$	26,542	N/A
2014			212,923		217,991		214,724		227,485		224,105		233,922		234,293		230,944		231,175		33,255		N/A
2015					217,343		216,759		224,385		231,473		235,637		242,554		245,756		247,419		44,753		N/A
2016							208,192		221,004		242,089		257,214		264,573		264,475		268,079		46,122		N/A
2017									262,894		251,827		267,173		293,381		304,194		310,858		52,415		N/A
2018											270,621		284,405		276,802		281,852		293,320		56,325		N/A
2019													325,359		334,755		361,549		372,669		93,310		N/A
2020															378,668		367,595		349,831		169,909		N/A
2021																	434,187		431,165		292,696		N/A
2022																			541,941		482,552		N/A
																	Total		$	3,179,551
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	2,421	$	9,822	$	22,886	$	42,861	$	54,323	$	62,751	$	70,289	$	76,141	$	81,167	$	87,485
2014			3,885		15,973		40,651		63,214		90,530		113,596		133,263		143,929		152,586
2015					4,440		20,208		46,933		70,523		95,988		119,096		136,138		151,119
2016							5,720		25,626		51,494		86,362		112,818		131,341		155,584
2017									6,417		30,316		63,922		112,474		136,489		163,243
2018											7,576		31,240		106,443		128,728		154,173
2019													15,798		57,568		96,593		129,766
2020															17,646		50,383		90,156
2021																	14,633		53,264
2022																			17,638
									Total										1,155,014
									All outstanding liabilities before 2013, net of reinsurance										299,288
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	2,323,825

Property catastrophe ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	65,372	$	45,962	$	34,959	$	30,518	$	27,974	$	27,248	$	26,415	$	26,543	$	26,344	$	26,221	$	(138)	N/A
2014			43,800		29,801		24,500		21,764		20,026		19,326		19,229		19,004		19,045		(10)		N/A
2015					32,748		17,558		11,425		5,531		3,779		3,133		2,932		2,569		68		N/A
2016							23,224		16,582		12,749		9,190		6,886		5,987		5,181		877		N/A
2017									86,410		53,699		49,507		35,893		24,239		21,026		(803)		N/A
2018											73,041		52,001		33,425		19,831		10,722		3,039		N/A
2019													25,526		14,252		13,093		4,590		4,576		N/A
2020															260,244		322,680		326,262		33,413		N/A
2021																	308,014		302,124		29,963		N/A
2022																			299,636		73,474		N/A
																	Total		$	1,017,376
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	12,035	$	18,496	$	23,001	$	24,697	$	26,329	$	26,549	$	26,549	$	27,233	$	26,998	$	27,023
2014			13,619		19,544		17,902		18,679		18,244		18,421		18,550		18,629		18,592
2015					(3,141)		(2,109)		1,843		2,103		1,659		1,745		1,817		1,874
2016							(7,039)		1,759		1,870		2,932		2,086		2,433		2,594
2017									30,625		31,621		37,084		27,060		14,215		16,034
2018											27,424		7,344		18,253		(10,934)		(8,100)
2019													4,374		8,845		12,895		(11,472)
2020															52,592		152,075		200,510
2021																	64,408		167,806
2022																			69,969
									Total										484,830
									All outstanding liabilities before 2013, net of reinsurance										2,612
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	535,158

Property excluding property catastrophe ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	114,775	$	76,290	$	69,981	$	65,734	$	64,013	$	63,247	$	62,070	$	62,774	$	62,288	$	63,390	$	29	N/A
2014			142,092		116,331		98,263		90,031		87,768		83,476		81,812		80,348		79,307		443		N/A
2015					213,681		187,932		183,709		187,569		186,861		175,812		172,189		166,580		3,909		N/A
2016							174,506		144,323		136,367		134,362		138,216		135,116		128,941		6,208		N/A
2017									266,628		247,462		235,310		227,891		212,133		204,128		8,794		N/A
2018											222,932		238,876		234,794		211,852		201,429		7,370		N/A
2019													214,513		204,620		194,164		189,456		8,407		N/A
2020															366,726		338,712		319,097		36,912		N/A
2021																	545,101		497,059		83,934		N/A
2022																			742,703		360,528		N/A
																	Total		$	2,592,090
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	25,943	$	42,418	$	49,433	$	52,614	$	53,400	$	55,272	$	60,777	$	61,640	$	61,665	$	63,228
2014			23,342		62,414		71,144		76,060		77,687		78,067		78,029		77,728		77,894
2015					75,458		118,396		148,887		159,482		164,637		158,293		158,537		159,054
2016							33,236		94,121		97,918		103,202		111,039		113,300		114,432
2017									27,456		124,220		155,139		162,933		177,737		181,029
2018											29,654		107,172		151,632		166,598		174,778
2019													42,919		123,293		149,377		161,573
2020															100,927		207,061		242,844
2021																	135,815		269,481
2022																			142,938
									Total										1,587,251
									All outstanding liabilities before 2013, net of reinsurance										5,765
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	1,010,604

Marine and aviation ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	38,167	$	36,765	$	35,669	$	34,293	$	34,207	$	33,453	$	33,001	$	29,434	$	26,728	$	25,695	$	1,012	N/A
2014			30,566		28,757		26,995		25,297		23,302		22,919		21,698		21,651		18,511		800		N/A
2015					33,134		37,019		31,499		31,373		30,423		28,120		27,299		25,008		1,514		N/A
2016							27,258		22,625		23,448		19,122		16,834		14,896		11,952		4,080		N/A
2017									28,590		26,165		23,613		20,749		19,842		17,329		4,178		N/A
2018											27,613		25,680		24,058		24,192		21,052		3,738		N/A
2019													48,383		54,684		60,321		60,635		5,574		N/A
2020															82,716		75,695		79,338		28,621		N/A
2021																	110,129		95,586		51,391		N/A
2022																			125,685		99,917		N/A
																	Total		$	480,791
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	4,751	$	13,054	$	17,678	$	20,580	$	21,557	$	22,803	$	23,176	$	22,941	$	22,912	$	23,648
2014			4,005		7,795		11,335		12,209		14,368		14,794		15,650		15,729		17,084
2015					(6)		13,321		18,852		20,623		22,318		21,971		22,114		22,297
2016							(7,371)		(1,739)		445		3,169		5,764		6,656		7,028
2017									1,650		6,433		9,249		10,897		11,488		11,817
2018											1,993		6,817		11,021		13,332		13,923
2019													10,537		21,261		28,680		34,637
2020															9,096		26,129		42,203
2021																	8,407		24,108
2022																			12,101
									Total										208,846
									All outstanding liabilities before 2013, net of reinsurance										17,999
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	289,944

Other specialty ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	304,905	$	280,398	$	269,105	$	267,106	$	266,970	$	264,418	$	263,713	$	257,960	$	255,453	$	254,380	$	4,327	N/A
2014			328,056		308,074		310,153		303,589		298,357		299,789		295,270		289,460		287,941		6,034		N/A
2015					271,235		269,237		267,079		263,826		263,985		261,158		250,103		248,848		6,340		N/A
2016							313,982		310,907		303,432		295,116		301,277		296,251		293,571		8,371		N/A
2017									382,884		375,347		357,762		357,212		355,763		351,478		22,234		N/A
2018											402,372		395,484		390,135		413,116		408,905		32,668		N/A
2019													414,049		393,864		387,810		383,491		38,889		N/A
2020															579,367		511,136		506,164		57,946		N/A
2021																	589,452		590,091		148,264		N/A
2022																			924,130		601,334		N/A
																	Total		$	4,248,999
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	81,609	$	155,936	$	188,651	$	209,775	$	222,292	$	229,228	$	237,023	$	237,559	$	240,669	$	243,881
2014			92,743		181,222		223,243		240,680		250,427		263,123		266,898		270,529		271,712
2015					80,453		157,176		190,699		204,444		216,683		227,879		230,640		231,384
2016							103,649		196,496		231,761		249,699		265,763		271,609		277,028
2017									130,150		245,165		285,299		299,405		312,273		322,863
2018											124,996		265,000		303,141		323,868		340,061
2019													116,762		204,625		267,972		293,260
2020															129,621		285,729		361,031
2021																	146,503		300,025
2022																			175,834
									Total										2,817,079
									All outstanding liabilities before 2013, net of reinsurance										13,001
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	1,444,921

The following table presents the average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance, as of December 31, 2022:

	Average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance
	Year 1		Year 2		Year 3		Year 4		Year 5		Year 6		Year 7		Year 8		Year 9		Year 10
Casualty	2.8	%	7.8	%	12.4	%	11.3	%	9.5	%	8.2	%	7.5	%	5.0	%	3.8	%	4.7	%
Property catastrophe	41.7	%	27.3	%	49.4	%	(115.6)	%	(10.7)	%	4.1	%	1.7	%	1.7	%	(0.5)	%	0.1	%
Property excluding property catastrophe	27.0	%	37.4	%	13.2	%	5.6	%	4.0	%	0.6	%	2.4	%	0.4	%	0.1	%	2.5	%
Marine and aviation	4.5	%	28.8	%	18.3	%	10.9	%	8.4	%	3.0	%	2.4	%	0.1	%	3.6	%	2.9	%
Other specialty	29.9	%	29.9	%	13.1	%	6.0	%	4.4	%	3.3	%	1.8	%	0.6	%	0.8	%	1.3	%

Mortgage Segment

The Company’s mortgage segment includes (1) U.S. primary mortgage insurance (2) U.S. credit risk transfer and other, and (3) international mortgage insurance and reinsurance. The latter two categories along with second lien and student loan exposures are excluded on the basis of insignificance for the purposes of presenting disclosures related to short duration contracts.

For primary mortgage insurance business, the Company establishes case reserves for loans that have been reported as delinquent by loan servicers as well as those that are delinquent but not reported (IBNR reserves). The Company also reserves for the expenses of adjusting claims related to these delinquencies. The trigger that creates a case reserve estimate is that an insured loan is reported to us as being two payments in arrears. The actuarial reviews and documentation created in the reserving process are completed in accordance with generally accepted actuarial standards.

The selected assumptions reflect actuarial judgment based on the analysis of historical data and experience combined with information concerning current underwriting, economic, judicial, regulatory and other influences on ultimate claim settlements.

Because the reserving process requires the Company to forecast future conditions, it is inherently uncertain and requires significant judgment and estimation. The use of different estimates would result in the establishment of different reserve levels. Additionally, changes in estimates are likely to occur from period to period as economic conditions change, and the ultimate liability may vary significantly from the estimates used. Major risk factors include (but are not limited to) changes in home prices and borrower equity, which can limit the borrower’s ability to sell the property and satisfy the outstanding loan balance, and changes in unemployment, which can affect the borrower’s income and ability to make mortgage payments. The unique nature of the COVID-19 pandemic, with no historical

precedent, adds further uncertainty to current reserve estimates.

The lead actuarial methodology used by the Company is a frequency-severity method based on the inventory of pending delinquencies. Each month the loan servicers report the delinquency status of each insured loan. Using the frequency-severity method allows the Company to take advantage of its knowledge of the number of delinquent loans and the coverage provided (“risk size”) on those loans by directly relating the reserves to these amounts. The delinquencies are grouped into homogeneous cohorts for analysis, reflecting the age of delinquency. A claim rate is then developed for each cohort which represents the frequency with which the delinquencies become claims. The claim frequency rates are based on an analysis of the patterns of emerging cure counts and claim counts, the foreclosure status of the pending delinquencies, the product and geographical mix of the delinquencies and our view of future economic and claim conditions, which include trends in home prices and unemployment. Claim rates can vary materially by age of delinquency, depending on the mix of delinquencies and economic conditions.

Claim size severity estimates are determined by examining the risk sizes on the delinquent loans and estimating the portion of risk that will be paid, as well as any expenses. This is done based on a review of historical development patterns, an assessment of economic conditions and the level of equity the borrowers may have in their homes, as well as considering economic conditions and loss mitigation opportunities. Mortgage insurance is generally not subject to large claim sizes, as with some other lines of insurance. A claim size over $250,000 is rare, and this helps reduce the volatility of claim size estimates.

The claim rate and claim size assumptions generate case reserves for the population of reported delinquencies. The reserve for unreported delinquencies (included in IBNR reserves) is estimated by looking at historical patterns of reporting. Claim rates and claim sizes can then be assigned to estimated unreported delinquencies using assumptions made in the establishment of case reserves.

Mortgage insurance Loss Reserves are short-tail, in the sense that the vast majority of delinquencies are resolved within two years of being reported. Due to the forbearances and foreclosure moratoriums associated with COVID-19, settlement timelines have been extended. While reserves are initially analyzed by reserve cohort, as described above, they are also rolled up by underwriting year to ensure that reserve assumptions are consistent with the performance of the underwriting year. The accuracy of prior reserve assumptions is also checked in hindsight to determine if adjustments to the assumptions are needed.

Loss Reserves for the Company’s mortgage reinsurance business and GSE credit risk sharing transactions are comprised of case reserves and IBNR reserves. The Company’s mortgage reinsurance operations receive reports of delinquent loans and claims notices from ceding companies and record case reserves based upon the amount of reserves recommended by the ceding company. In addition, specific claim and delinquency information reported by ceding companies is used in the process of estimating IBNR reserves.

The following table presents information on the mortgage segment’s short-duration insurance contracts:

U.S. primary mortgage insurance ($000’s except claim count)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims	Cumulative number of paid claims
Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	469,311	$	419,668	$	411,793	$	405,809	$	395,693	$	393,149	$	390,987	$	391,062	$	391,324	$	390,299	2	9,474
2014			316,095		297,151		279,434		266,027		265,992		261,091		262,682		262,829		260,554		4	6,311
2015					222,790		197,238		198,001		194,677		189,235		190,913		190,560		188,649		1	4,573
2016							183,556		170,532		148,715		140,608		142,392		141,657		137,415		—	3,445
2017									179,376		132,220		107,255		108,181		109,242		102,005		(1)	2,516
2018											132,318		96,357		89,120		87,962		71,976		(4)	1,718
2019													108,424		119,253		110,362		63,485		74	1,002
2020															420,003		373,533		78,334		476	299
2021																	144,375		77,212		379	72
2022																			173,327		2,147	7
															Total				$	1,543,256
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	41,447		203,957		308,956		353,189		373,909		382,200		386,853		387,894		387,879		388,036
2014			20,099		129,159		201,925		233,879		247,038		254,175		256,285		256,875		257,232
2015					16,159		92,431		151,222		171,337		180,321		183,472		184,025		184,955
2016							11,462		72,201		113,357		127,286		131,161		131,717		132,387
2017									8,622		48,112		78,650		87,317		89,756		91,645
2018											3,966		31,478		50,135		55,853		58,687
2019													2,899		20,105		29,102		34,178
2020															1,040		4,144		7,740
2021																	469		1,687
2022																			176
																			1,156,723
									All outstanding liabilities before 2013, net of reinsurance										10,585
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	397,118

The following table presents the average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance, as of December 31, 2022:

Average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance
	Year 1		Year 2		Year 3		Year 4		Year 5		Year 6		Year 7		Year 8		Year 9		Year 10
U.S. Primary	5.6	%	30.9	%	23.8	%	9.8	%	4.0	%	1.8	%	0.7	%	0.3	%	0.1	%	—	%

The following table represents a reconciliation of the disclosures of net incurred and paid loss development tables to the reserve for losses and loss adjustment expenses at December 31, 2022:

	December 31, 2022
Net outstanding liabilities
Insurance
Property, energy, marine and aviation	$	750,461
Third party occurrence business	3,184,995
Third party claims-made business	1,991,302
Multi-line and other specialty	1,215,721
Reinsurance
Casualty	2,323,825
Property catastrophe	535,158
Property excluding property catastrophe	1,010,604
Marine and aviation	289,944
Other specialty	1,444,921
Mortgage
U.S. primary	397,118
Other short duration lines not included in disclosures	301,222
Total for short duration lines	13,445,271
Unpaid losses and loss adjustment expenses recoverable
Insurance
Property, energy, marine and aviation	423,740
Third party occurrence business	1,761,871
Third party claims-made business	995,921
Multi-line and other specialty	173,051
Reinsurance
Casualty	684,663
Property catastrophe	595,740
Property excluding property catastrophe	206,867
Marine and aviation	186,416
Other specialty	656,130
Mortgage
U.S. primary	37,531
Other short duration lines not included in disclosures (1)	560,642
Intercompany eliminations	(3,747)
Total for short duration lines	6,278,825
Lines other than short duration	102,283
Discounting	(60,536)
Unallocated claims adjustment expenses	266,100
	307,847
Total gross reserves for losses and loss adjustment expenses	$	20,031,943

(1)    Includes unpaid loss and loss adjustment expenses recoverable of $280.2 million related to the loss portfolio transfer reinsurance agreements.

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Allowance for Expected Credit Losses

12 Months Ended

Dec. 31, 2022

Credit Loss [Abstract]

Allowance for expected credit losses

Premiums Receivable

The following table provides a roll forward of the allowance for expected credit losses of the Company’s premium receivables:

Year Ended December 31, 2022	Premium Receivables, Net of Allowance		Allowance for Expected Credit Losses
Balance at beginning of period	$	2,633,280	$	39,958
Change for provision of expected credit losses (1)			(4,556)
Balance at end of period	$	3,624,777	$	35,402
Year Ended December 31, 2021
Balance at beginning of period	$	2,064,586	$	37,781
Change for provision of expected credit losses (1)			2,177
Balance at end of period	$	2,633,280	$	39,958

(1) Amounts deemed uncollectible are written-off in operating expenses. For the 2022 and 2021 periods, amounts written off totaled $11.4 million and $3.8 million, respectively.

Reinsurance Recoverables

The Company monitors the financial condition of its reinsurers and attempts to place coverages only with substantial, financially sound carriers. Although the Company has not experienced any material credit losses to date, an inability of its reinsurers or retrocessionaires to meet their obligations to it over the relevant exposure periods for any reason could have a material adverse effect on its financial condition and results of operations.

The following table provides a roll forward of the allowance for expected credit losses of the Company’s reinsurance recoverables:

Year Ended December 31, 2022	Reinsurance Recoverables, Net of Allowance		Allowance for Expected Credit Losses
Balance at beginning of period	$	5,880,735	$	13,230
Change for provision of expected credit losses			8,314
Balance at end of period	$	6,563,654	$	21,544
Year Ended December 31, 2021
Balance at beginning of period	$	4,500,802	$	11,636
Change for provision of expected credit losses			1,594
Balance at end of period	5,880,735		$	13,230

The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums) at December 31, 2022 and 2021:

	December 31,
	2022			2021
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	$	6,563,654		$	5,880,735
% due from carriers with A.M. Best rating of “A-” or better	68.8		%	69.7		%
% due from all other rated carriers	0.1		%	0.1		%
% due from all other carriers with no A.M. Best rating (1)	31.1		%	30.2		%
Largest balance due from any one carrier as % of total shareholders’ equity	9.0		%	6.7		%

(1)    At December 31, 2022 and 2021 period, over 95% and 91% of such amount is collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other, respectively.

Contractholder Receivables

The following table provides a roll forward of the allowance for expected credit losses of the Company’s contractholder receivables:

Year Ended December 31, 2022	Contractholder Receivables, Net of Allowance		Allowance for Expected Credit Losses
Balance at beginning of period	$	1,828,691	$	3,437
Change for provision of expected credit losses			(746)
Balance at end of period	$	1,731,293	$	2,691
Year Ended December 31, 2021
Balance at beginning of period	$	1,986,924	$	8,638
Change for provision of expected credit losses			(5,201)
Balance at end of period	1,828,691		$	3,437

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Reinsurance

12 Months Ended

Dec. 31, 2022

Reinsurance Disclosures [Abstract]

Reinsurance

In the normal course of business, the Company’s insurance subsidiaries cede a portion of their premium through pro rata and excess of loss reinsurance agreements on a treaty or facultative basis to third parties. The Company’s reinsurance subsidiaries participate in “common account” retrocessional arrangements for certain pro rata treaties. Such arrangements reduce the effect of individual or aggregate losses to all companies participating on such treaties, including the reinsurers, such as the Company’s reinsurance subsidiaries, and the ceding company. In addition, the Company’s reinsurance subsidiaries may purchase retrocessional coverage as part of their risk management program. The Company’s mortgage subsidiaries cede a portion of their premium through quota share arrangements and enter into various aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies. Reinsurance recoverables are recorded as assets, predicated on the reinsurers’ ability to meet their obligations under the reinsurance agreements. If the reinsurers are unable to satisfy their obligations under the agreements, the Company’s insurance or reinsurance subsidiaries would be liable for such defaulted amounts.

The effects of reinsurance on the Company’s written and earned premiums and losses and loss adjustment expenses with unaffiliated reinsurers were as follows:

	Year Ended December 31,
	2022		2021		2020
Premiums Written
Direct	$	8,540,787	$	7,706,832	$	6,553,910
Assumed	6,785,660		5,045,655		3,534,158
Ceded	(4,249,258)		(3,734,150)		(2,650,352)
Net	$	11,077,189	$	9,018,337	$	7,437,716
Premiums Earned
Direct	$	8,057,635	$	7,149,794	$	6,361,451
Assumed	5,767,738		4,333,873		3,213,873
Ceded	(4,147,296)		(3,401,369)		(2,583,389)
Net	$	9,678,077	$	8,082,298	$	6,991,935
Losses and Loss Adjustment Expenses
Direct	$	3,990,768	$	4,266,758	$	4,392,392
Assumed	3,559,133		2,826,820		2,204,323
Ceded	(2,522,384)		(2,508,775)		(1,907,116)
Net	$	5,027,517	$	4,584,803	$	4,689,599

Bellemeade Re

The Company has entered into various aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda (the “Bellemeade Agreements”). For the respective coverage periods, the Company will retain the first layer of the respective aggregate losses and the special purpose reinsurance companies will provide second layer coverage up to the outstanding coverage amount. The Company will then retain losses in excess of the outstanding coverage limit. The aggregate excess of loss reinsurance coverage decreases over a ten-year period as the underlying covered mortgages amortize. See note 12, “Variable Interest Entity and Noncontrolling Interests.”

The following table summarizes the respective coverages and retentions at December 31, 2022:

			December 31, 2022
Bellemeade Entities (Issue Date)	Initial Coverage at Issuance		Current Coverage		Remaining Retention, Net
2017-1 Ltd. (1)	$	368,114	$	36,679	$	142,461
2018-1 Ltd. (2)	374,460		89,698		143,592
2018-3 Ltd. (3)	506,110		199,237		152,861
2019-1 Ltd. (4)	341,790		107,880		118,908
2019-2 Ltd. (5)	621,022		325,462		191,550
2019-3 Ltd. (6)	700,920		222,977		208,931
2019-4 Ltd. (7)	577,267		266,124		142,564
2020-2 Ltd. (8)	449,167		105,110		237,709
2020-3 Ltd. (9)	451,816		250,971		161,544
2020-4 Ltd. (10)	337,013		101,729		138,131
2021-1 Ltd. (11)	643,577		503,267		153,525
2021-2 Ltd. (12)	616,017		535,461		138,524
2021-3 Ltd. (13)	639,391		616,959		132,492
2022-1 Ltd. (14)	316,760		316,760		143,577
2022-2 Ltd. (15)	327,165		327,165		217,436
Total	$	7,270,589	$	4,005,479	$	2,423,805

(1)    Issued in October 2017, covering in-force policies issued between January 1, 2017 and June 30, 2017.

(2)    Issued in April 2018, covering in-force policies issued between July 1, 2017 and December 31, 2017.

(3)    Issued in October 2018, covering in-force policies issued between January 1, 2018 and June 30, 2018.

(4)    Issued in March 2019, covering in-force policies primarily issued between 2005 to 2008 under United Guaranty Residential Insurance Company (“UGRIC”); as well as policies issued through 2015 under both UGRIC and Arch Mortgage Insurance Company.

(5)    Issued in April 2019, covering in-force policies issued between July 1, 2018 and December 31, 2018.

(6)    Issued in July 2019, covering in-force policies issued in 2016.

(7)    Issued in October 2019, covering in-force policies issued between January 1, 2019 and June 30, 2019.

(8)    Issued in September 2020, covering in-force policies issued between January 1, 2020 and May 31, 2020. $423 million was directly funded by Bellemeade 2020-2 Ltd. with an additional $26 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(9)    Issued in November 2020, covering in-force policies issued between June 1, 2020 and August 31, 2020. $418 million was directly funded by Bellemeade 2020-3 Ltd. with an additional $34 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(10)    Issued in December 2020, covering in-force policies issued between July 1, 2019 and December 31, 2019. $321 million was directly funded by Bellemeade 2020-4 Ltd. with an additional $16 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(11) Issued in March 2021, covering in-force policies issued between September 1, 2020 and November 30, 2020. $580 million was directly funded by Bellemeade Re 2021-1 Ltd. with an additional $64 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(12) Issued in June 2021, covering in-force policies issued between December 1, 2020 and March 31, 2021. $523 million was directly funded by Bellemeade Re 2021-2 Ltd. via insurance-linked notes, with an additional $93 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(13) Issued in September 2021, covering in-force policies issued between April 1, 2021 and June 30, 2021. $508 million was directly funded by Bellemeade Re 2021-3 Ltd. via insurance-linked notes, with an additional $131 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(14) Issued in January 2022, covering in-force policies issued between July 1, 2021 and November 30, 2021. $284 million was directly funded by Bellemeade Re 2022-1 Ltd. via insurance-linked notes, with an additional $33 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(15) Issued in September 2022, covering in-force policies issued between November 1, 2021 and June 30, 2022. $201 million was directly funded by Bellemeade Re 2022-2 Ltd. via insurance-linked notes, with an additional $126 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

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Investment Information

12 Months Ended

Dec. 31, 2022

Disclosure Investment Information [Abstract]

Investment Information

Available For Sale Investments

The following table summarizes the fair value and cost or amortized cost of the Company’s securities classified as available for sale:

	Estimated Fair Value		Gross Unrealized Gains		Gross Unrealized Losses		Allowance for Expected Credit Losses		Cost or Amortized Cost
December 31, 2022
Fixed maturities:
Corporate bonds	$	8,020,128	$	55,468	$	(781,353)	$	(29,950)	$	8,775,963
Mortgage backed securities	795,391		4,933		(86,587)		2		877,043
Municipal bonds	419,166		3,149		(33,360)		(100)		449,477
Commercial mortgage backed securities	1,047,275		608		(57,667)		(3,415)		1,107,749
U.S. government and government agencies	5,161,193		14,891		(342,963)		—		5,489,265
Non-U.S. government securities	2,312,819		8,870		(237,846)		(1,882)		2,543,677
Asset backed securities	1,926,817		761		(106,623)		(6,010)		2,038,689
Total	19,682,789		88,680		(1,646,399)		(41,355)		21,281,863
Short-term investments	1,331,662		554		(1,888)		—		1,332,996
Total	$	21,014,451	$	89,234	$	(1,648,287)	$	(41,355)	$	22,614,859
December 31, 2021
Fixed maturities:
Corporate bonds	$	6,553,333	$	104,170	$	(69,194)	$	(2,037)	$	6,520,394
Mortgage backed securities	408,477		2,825		(5,410)		(48)		411,110
Municipal bonds	404,666		18,724		(1,409)		(2)		387,353
Commercial mortgage backed securities	1,046,484		1,740		(3,117)		(6)		1,047,867
U.S. government and government agencies	4,772,764		10,076		(45,967)		—		4,808,655
Non-U.S. government securities	2,120,294		54,048		(34,749)		(82)		2,101,077
Asset backed securities	2,692,091		6,540		(11,108)		(708)		2,697,367
Total	17,998,109		198,123		(170,954)		(2,883)		17,973,823
Short-term investments	1,734,716		568		(590)		—		1,734,738
Total	$	19,732,825	$	198,691	$	(171,544)	$	(2,883)	$	19,708,561

The following table summarizes, for all available for sale securities in an unrealized loss position, the fair value and gross unrealized loss by length of time the security has been in a continual unrealized loss position:

	Less than 12 Months				12 Months or More				Total
	Estimated Fair Value		Gross Unrealized Losses		Estimated Fair Value		Gross Unrealized Losses		Estimated Fair Value		Gross Unrealized Losses
December 31, 2022
Fixed maturities:
Corporate bonds	$	4,822,624	$	(393,112)	$	2,559,399	$	(388,241)	$	7,382,023	$	(781,353)
Mortgage backed securities	545,844		(51,673)		154,154		(34,914)		699,998		(86,587)
Municipal bonds	363,936		(29,924)		16,282		(3,436)		380,218		(33,360)
Commercial mortgage backed securities	598,392		(34,899)		445,175		(22,768)		1,043,567		(57,667)
U.S. government and government agencies	3,556,676		(197,259)		1,442,542		(145,704)		4,999,218		(342,963)
Non-U.S. government securities	1,702,973		(153,587)		541,652		(84,259)		2,244,625		(237,846)
Asset backed securities	1,148,220		(65,189)		512,376		(41,434)		1,660,596		(106,623)
Total	12,738,665		(925,643)		5,671,580		(720,756)		18,410,245		(1,646,399)
Short-term investments	236,735		(1,888)		—		—		236,735		(1,888)
Total	$	12,975,400	$	(927,531)	$	5,671,580	$	(720,756)	$	18,646,980	$	(1,648,287)
December 31, 2021
Fixed maturities:
Corporate bonds	$	3,639,582	$	(63,938)	$	98,867	$	(5,256)	$	3,738,449	$	(69,194)
Mortgage backed securities	222,176		(3,545)		46,809		(1,865)		268,985		(5,410)
Municipal bonds	26,665		(385)		16,361		(1,024)		43,026		(1,409)
Commercial mortgage backed securities	675,603		(2,805)		5,908		(312)		681,511		(3,117)
U.S. government and government agencies	4,211,621		(44,180)		33,373		(1,787)		4,244,994		(45,967)
Non-U.S. government securities	1,511,301		(31,983)		62,957		(2,766)		1,574,258		(34,749)
Asset backed securities	1,667,002		(9,853)		33,082		(1,255)		1,700,084		(11,108)
Total	11,953,950		(156,689)		297,357		(14,265)		12,251,307		(170,954)
Short-term investments	284,733		(590)		—		—		284,733		(590)
Total	$	12,238,683	$	(157,279)	$	297,357	$	(14,265)	$	12,536,040	$	(171,544)

At December 31, 2022, on a lot level basis, approximately 9,810 security lots out of a total of approximately 12,590 security lots were in an unrealized loss position and the largest single unrealized loss from a single lot in the Company’s fixed maturity portfolio was $7.2 million. The Company believes that such securities were temporarily impaired at December 31, 2022. At December 31, 2021, on a lot level basis, approximately 4,700 security lots out of a total of approximately 10,240 security lots were in an unrealized loss position and the largest single unrealized loss from a single lot in the Company’s fixed maturity portfolio was $1.1 million.

The contractual maturities of the Company’s fixed maturities are shown in the following table. Expected maturities, which are management’s best estimates, will differ from contractual maturities because borrowers may have the right to call or prepay obligations with or without call or prepayment penalties.

	December 31, 2022				December 31, 2021
Maturity	Estimated Fair Value		Amortized Cost		Estimated Fair Value		Amortized Cost
Due in one year or less	$	510,669	$	536,962	$	300,889	$	299,772
Due after one year through five years	11,014,753		11,714,427		8,355,255		8,339,387
Due after five years through 10 years	3,984,497		4,527,447		4,689,155		4,684,393
Due after 10 years	403,387		479,546		505,758		493,927
	15,913,306		17,258,382		13,851,057		13,817,479
Mortgage backed securities	795,391		877,043		408,477		411,110
Commercial mortgage backed securities	1,047,275		1,107,749		1,046,484		1,047,867
Asset backed securities	1,926,817		2,038,689		2,692,091		2,697,367
Total	$	19,682,789	$	21,281,863	$	17,998,109	$	17,973,823

Equity Securities, at Fair Value

At December 31, 2022, the Company held $860.0 million of equity securities, at fair value, compared to $1.8 billion at December 31, 2021.

Net Investment Income

The components of net investment income were derived from the following sources:

	Year Ended December 31,
	2022		2021		2020
Fixed maturities	$	468,659	$	330,061	$	412,481
Term loans	2,038		34,843		84,149
Equity securities	22,497		42,396		28,958
Short-term investments	29,519		6,928		10,840
Other (1)	44,609		62,895		72,395
Gross investment income	567,322		477,123		608,823
Investment expenses	(70,775)		(88,005)		(89,215)
Net investment income	$	496,547	$	389,118	$	519,608

(1)    Includes income distributions from investment funds and other items

Net Realized Gains (Losses)

Net realized gains (losses) were as follows:

	Year Ended December 31,
	2022		2021		2020
Available for sale securities:
Gross gains on investment sales	$	81,161	$	313,886	$	595,941
Gross losses on investment sales	(317,150)		(156,791)		(117,282)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	(70,951)		7,953		15,881
Other investments	(19,498)		116,781		13,656
Equity securities	(4,520)		13,028		14,629
Short-term investments	(3,012)		601		2,279
Equity securities, at fair value :
Net realized gains (losses) on securities sold	74,922		122,606		26,849
Net unrealized gains (losses) on equity securities still held at reporting date	(267,927)		48,746		102,394
Allowance for credit losses:
Investments related	(43,909)		(2,100)		(3,597)
Underwriting related	(13,274)		1,062		(10,007)
Net impairment losses	—		—		(533)
Derivative instruments (1)	(75,023)		(32,390)		179,675
Other (2)	(3,553)		(53,537)		3,575
Net realized gains (losses)	$	(662,734)	$	379,845	$	823,460

(1)    See note 11, “Derivative Instruments” for information on the Company’s derivative instruments.

(2)    2021 period reflected $33.1 million of losses related to the Company’s

deconsolidation of Somers.

Other Investments

The following table summarizes the Company’s other investments and other investable assets:

	December 31,
	2022		2021
Fixed maturities	$	554,120	$	416,698
Other investments	1,043,184		1,432,553
Short-term investments	33,101		97,806
Equity securities	13,792		26,493
Total other investments	$	1,644,197	$	1,973,550

The following table summarizes the Company’s other investments, as detailed in the previous table, by strategy:

	December 31,
	2022		2021
Lending	405,871		536,345
Investment grade fixed income	271,143		147,810
Term loan investments	163,941		484,950
Private equity	123,266		91,126
Energy	22,627		81,692
Credit related funds	56,336		70,278
Infrastructure	—		20,352
Total	$	1,043,184	$	1,432,553

Investments Accounted For Using the Equity Method

The following table summarizes the Company’s investments accounted for using the equity method, by strategy:

	December 31,
	2022		2021
Credit related funds	$	1,135,818	$	1,022,334
Private equity	916,534		436,042
Real estate	535,238		396,395
Lending	531,339		376,649
Infrastructure	245,246		230,070
Equities	169,156		395,090
Fixed income	130,062		101,890
Energy	110,917		119,141
Total	$	3,774,310	$	3,077,611

In applying the equity method, investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the fair value of the underlying securities in the funds). Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds.

Equity in Net Income (Loss) of Investments Accounted For Using the Equity Method

The Company recorded equity in net income related to investments accounted for using the equity method of $115.9 million for 2022, compared to $366.4 million for 2021 and $146.7 million for 2020. In applying the equity method, investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the market value of the underlying securities in the funds).

A summary of financial information for the Company’s investment funds and operating affiliates accounted for using the equity method is as follows:

	December 31,
	2022		2021
Invested assets	$	74,960,738	$	58,508,009
Total assets	88,062,991		69,648,905
Total liabilities	27,553,307		17,944,325
Net assets	$	60,509,684	$	51,704,580

	Year Ended December 31,
	2022		2021		2020
Total revenues	$	12,305,082	$	11,785,949	$	5,762,098
Total expenses	5,374,047		3,238,606		1,656,029
Net income (loss)	$	6,931,035	$	8,547,343	$	4,106,069

Certain of the Company’s other investments and investments accounted for using the equity method are in investment funds for which the Company has the option to redeem at agreed upon values as described in each investment fund’s subscription agreement. Depending on the terms of the various subscription agreements, investments in investment funds may be redeemed daily, monthly, quarterly or on other terms. Two common redemption restrictions which may impact the Company’s ability to redeem these investment funds are gates and lockups. A gate is a suspension of redemptions which may be implemented by the general partner or investment manager of the fund in order to defer, in whole or in part, the redemption request in the event the aggregate amount of redemption requests exceeds a predetermined percentage of the investment fund's net assets which may otherwise hinder the general partner or investment manager's ability to liquidate holdings in an orderly fashion in order to generate the cash necessary to fund extraordinarily large redemption payouts. A lockup period is the initial amount of time an investor is contractually required to hold the security before having the ability to redeem. If the investment funds are eligible to be redeemed, the time to redeem such fund can take weeks or months following the notification.

Limited Partnership Interests

In the normal course of its activities, the Company invests in limited partnerships as part of its overall investment strategy. Such amounts are included in ‘investments accounted for using the equity method’ and ‘investments accounted for using the fair value option.’ The Company determined that these limited partnership interests represented variable interests in the funds. The Company’s maximum exposure to loss with respect to these investments is limited to the investment carrying amounts reported in the Company’s consolidated balance sheet and any unfunded commitment.

The following table summarizes investments in limited partnership interests where the Company has a variable interest by balance sheet item:

	December 31,
	2022		2021
Investments accounted for using the equity method (1)	$	3,774,310	$	3,077,611
Investments accounted for using the fair value option (2)	130,466		170,595
Total	$	3,904,776	$	3,248,206

(1)     Aggregate unfunded commitments were $2.6 billion at December 31, 2022, consistent with $2.6 billion at December 31, 2021.

(2)    Aggregate unfunded commitments were $16.7 million at December 31, 2022, compared to $18.8 million at December 31, 2021.

Investments in Operating Affiliates

Investments in which the Company has significant influence over the operating and financial policies are classified as ‘investments in operating affiliates’ on the Company’s balance sheets and are accounted for under the equity method. Such investments primarily include the Company’s investment in Coface SA (“Coface”), Greysbridge and Premia. Investments in Coface and Premia are generally recorded on a three month lag, while the Company’s investment in Greysbridge is not recorded on a lag.

In 2021, the Company completed the share purchase agreement with Natixis to purchase 29.5% of the common

equity of Coface, a France-based leader in the global trade credit insurance market. The consideration paid was €9.95 per share, or an aggregate €453 million (approximately $546 million) including related fees. Income (loss) from operating affiliates reflected a one-time gain of $74.5 million realized from the acquisition. As a result of equity method accounting rules, approximately $36 million of additional gain was deferred and will generally be recognized over the next five years. As of December 31, 2022, the Company owned approximately 29.9% of the issued shares of Coface, or 30.1% excluding treasury shares, with a carrying value of $562.9 million, compared to $630.5 million at December 31, 2021.

In July 2021, the Company announced the completion of the previously disclosed acquisition of Somers by Greysbridge for a cash purchase price of $35.00 per common share.

Effective July 1, 2021, Somers is wholly owned by Greysbridge, and Greysbridge is owned 40% by the Company, 30% by certain investment funds managed by Kelso and 30% by certain investment funds managed by Warburg. At December 31, 2022 the Company’s carrying value in Greysbridge was $305.6 million, compared to $375.7 million at December 31, 2021. The Company’s carrying value in Greysbridge at December 31, 2021 reflected aggregate purchase price of $278.9 million along with income (loss) from operating affiliates, which included a one-time gain of $95.7 million recognized from the acquisition. In addition, the ‘net realized gains (losses)’ line on the Company’s consolidated statements of income included a $33.1 million loss as a result of deconsolidation of Somers in the Company’s financial statements following the close of the transaction. See note 12, “Variable Interest Entity and Noncontrolling Interests.”

The Company recorded income from operating affiliates of $73.9 million for 2022, compared to income of $264.7 million for 2021 and $16.8 million for 2020.

Allowance for Expected Credit Losses

The following table provides a roll forward of the allowance for expected credit losses of the Company’s securities classified as available for sale:

Year Ended December 31, 2022	Structured Securities (1)		Municipal Bonds		Non-U.S. Government Securities		Corporate Bonds		Total
Balance at beginning of period	$	802	$	2	$	82	$	1,997	$	2,883
Additions for current-period provision for expected credit losses	14,184		359		1,616		39,477		55,636
Additions (reductions) for previously recognized expected credit losses	(3,184)		(261)		275		(8,619)		(11,789)
Reductions due to disposals	(2,379)		—		(91)		(2,905)		(5,375)
Balance at end of period	$	9,423	$	100	$	1,882	$	29,950	$	41,355
Year Ended December 31, 2021
Balance at beginning of period	$	1,490	$	11	$	—	$	896	$	2,397
Additions for current-period provision for expected credit losses	602		—		82		2,858		3,542
Additions (reductions) for previously recognized expected credit losses	(847)		(9)		—		(402)		(1,258)
Reductions due to disposals (2)	(443)		—		—		(1,355)		(1,798)
Balance at end of period	$	802	$	2	$	82	$	1,997	$	2,883

(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed

(2)    Reduction for the 2021 periods primarily related to the Company’s deconsolidation of Somers.

Restricted Assets

The Company is required to maintain assets on deposit, which primarily consist of fixed maturities, with various regulatory authorities to support its underwriting operations. The Company’s subsidiaries maintain assets in trust accounts as collateral for transactions with affiliated companies and also have investments in segregated portfolios primarily to provide collateral or guarantees for letters of credit to third parties

The following table details the value of the Company’s restricted assets:

	December 31,
	2022		2021
Assets used for collateral or guarantees:
Affiliated transactions	$	4,254,398	$	4,223,955
Third party agreements	2,632,892		2,289,631
Deposits with U.S. regulatory authorities	776,342		798,100
Other (1)	1,037,848		938,046
Total restricted assets	$	8,701,480	$	8,249,732

(1) Primarily includes Funds at Lloyds, deposits with non-U.S. regulatory authorities and other restricted assets.

Reconciliation of Cash and Restricted Cash

The following table details reconciliation of cash and restricted cash within the Consolidated Balance Sheets:

	December 31,
	2022		2021		2020
Cash	$	855,118	$	858,668	$	906,448
Restricted cash (included in ‘other assets’)	418,210		456,103		384,096
Cash and restricted cash	$	1,273,328	$	1,314,771	$	1,290,544

XML

Fair Value

12 Months Ended

Dec. 31, 2022

Fair Value Disclosures [Abstract]

Fair Value

Accounting guidance regarding fair value measurements addresses how companies should measure fair value when they are required to use a fair value measure for recognition or disclosure purposes under GAAP and provides a common definition of fair value to be used throughout GAAP. It defines fair value as the price that would be received to sell an asset or paid to transfer a liability in an orderly fashion between market participants at the measurement date. In addition, it establishes a three-level valuation hierarchy for the disclosure of fair value measurements. The valuation hierarchy is based upon the transparency of inputs to the valuation of an asset or liability as of the measurement date. The level in the hierarchy within which a given fair value measurement falls is determined based on the lowest level input that is significant to the measurement (Level 1 being the highest priority and Level 3 being the lowest priority).

The levels in the hierarchy are defined as follows:

Level 1:	Inputs to the valuation methodology are observable inputs that reflect quoted prices (unadjusted) for identical assets or liabilities in active markets
Level 2:	Inputs to the valuation methodology include quoted prices for similar assets and liabilities in active markets, and inputs that are observable for the asset or liability, either directly or indirectly, for substantially the full term of the financial instrument
Level 3:	Inputs to the valuation methodology are unobservable and significant to the fair value measurement

Following is a description of the valuation methodologies used for securities measured at fair value, as well as the general classification of such securities pursuant to the valuation hierarchy. The Company reviews its securities measured at fair value and discusses the proper classification of such investments with investment advisers and others.

The Company determines the existence of an active market based on its judgment as to whether transactions for the financial instrument occur in such market with sufficient frequency and volume to provide reliable pricing information. The independent pricing sources obtain market quotations and actual transaction prices for securities that have quoted prices in active markets. The Company uses quoted values and other data provided by nationally recognized independent pricing sources as inputs into its process for determining fair values of its fixed maturity investments. To validate the techniques or models used by pricing sources, the Company's review process includes, but is not limited to: (i) quantitative analysis (e.g., comparing the quarterly return for each managed portfolio to its target

benchmark, with significant differences identified and investigated); (ii) a review of the prices obtained in the pricing process and the range of resulting fair values; (iii) initial and ongoing evaluation of methodologies used by outside parties to calculate fair value; (iv) a comparison of the fair value estimates to the Company’s knowledge of the current market; (v) a comparison of the pricing services' fair values to other pricing services' fair values for the same investments; and (vi) periodic back-testing, which includes randomly selecting purchased or sold securities and comparing the executed prices to the fair value estimates from the pricing service. A price source hierarchy was maintained in order to determine which price source would be used (i.e., a price obtained from a pricing service with more seniority in the hierarchy will be used over a less senior one in all cases). The hierarchy prioritizes pricing services based on availability and reliability and assigns the highest priority to index providers. Based on the above review, the Company will challenge any prices for a security or portfolio which are considered not to be representative of fair value.

In certain circumstances, when fair values are unavailable from these independent pricing sources, quotes are obtained directly from broker-dealers who are active in the corresponding markets. Such quotes are subject to the validation procedures noted above. Of the $23.8 billion of financial assets and liabilities measured at fair value at December 31, 2022, approximately $12.6 million, or 0.1%, were priced using non-binding broker-dealer quotes. Of the $23.8 billion of financial assets and liabilities measured at fair value at December 31, 2021, approximately $7.7 million, or 0.0%, were priced using non-binding broker-dealer quotes.

Fixed maturities

The Company uses the market approach valuation technique to estimate the fair value of its fixed maturity securities, when possible. The market approach includes obtaining prices from independent pricing services, such as index providers and pricing vendors, as well as to a lesser extent quotes from broker-dealers. The independent pricing sources obtain market quotations and actual transaction prices for securities that have quoted prices in active markets. Each source has its own proprietary method for determining the fair value of securities that are not actively traded. In general, these methods involve the use of “matrix pricing” in which the independent pricing source uses observable market inputs including, but not limited to, investment yields, credit risks and spreads, benchmarking of like securities, broker-dealer quotes, reported trades and sector groupings to determine a reasonable fair value. The following describes the significant inputs generally used to determine the fair value of the Company’s fixed maturity securities by asset class:

U.S. government and government agencies – valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The Company determined that all U.S. Treasuries would be classified as Level 1 securities due to observed levels of trading activity, the high number of strongly correlated pricing quotes received on U.S. Treasuries and other factors. The fair values of U.S. government agency securities are generally determined using the spread above the risk-free yield curve. As the yields for the risk-free yield curve and the spreads for these securities are observable market inputs, the fair values of U.S. government agency securities are classified within Level 2.

Corporate bonds – valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined using the spread above the risk-free yield curve. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. As the significant inputs used in the pricing process for corporate bonds are observable market inputs, the fair value of these securities are classified within Level 2. A small number of securities are included in Level 3 due to the lack of an available independent price source for such securities. As the significant inputs used to price these securities are unobservable, the fair value of such securities are classified as Level 3.

Mortgage-backed securities – valuations provided by independent pricing services, substantially all through pricing vendors and index providers with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models (including Option Adjusted Spread) which use spreads to determine the expected average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. The pricing services also review prepayment speeds and other indicators, when applicable. As the significant inputs used in the pricing process for mortgage-backed securities are observable market inputs, the fair value of these securities are classified within Level 2.

Municipal bonds – valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The fair values of these securities are generally determined using spreads obtained from broker-dealers who trade in the relevant security market, trade prices and the new issue market. As the significant inputs used in the pricing process for municipal bonds are observable market inputs, the fair value of these securities are classified within Level 2.

Commercial mortgage-backed securities – valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models which use spreads to determine the appropriate average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. As the significant inputs used in the pricing process for commercial mortgage-backed securities are observable market inputs, the fair value of these securities are classified within Level 2.

Non-U.S. government securities – valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The fair values of these securities are generally based on international indices or valuation models which include daily observed yield curves, cross-currency basis index spreads and country credit spreads. As the significant inputs used in the pricing process for non-U.S. government securities are observable market inputs, the fair value of these securities are classified within Level 2.

Asset-backed securities – valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models (including Option Adjusted Spread) which use spreads to determine the appropriate average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. As the significant inputs used in the pricing process for asset-backed securities are observable market inputs, the fair value of these securities are classified within Level 2. A small number of securities are included in Level 3 due to a low level of transparency on the inputs used in the pricing process.

Equity securities

The Company determined that exchange-traded equity securities would be included in Level 1 as their fair values are based on quoted market prices in active markets. Other equity securities are included in Level 2 of the valuation hierarchy. A small number of securities are included in Level 3 due to the lack of an available independent price source for such securities. As the significant inputs used to price these securities are unobservable, the fair value of such securities are classified as Level 3.

Other investments

The Company determined that exchange-traded investments would be included in Level 1 as their fair values are based on quoted market prices in active markets. Other investments also include term loan investments for which fair values are estimated by using quoted prices of term loan investments with similar characteristics, pricing models or matrix pricing. Such investments are generally classified within Level 2. A small number of securities are included in Level 3 due to the lack of an available independent price source for such securities.

Derivative instruments

The Company’s futures contracts, foreign currency forward contracts, interest rate swaps and other derivatives trade in the over-the-counter derivative market. The Company uses the market approach valuation technique to estimate the fair value for these derivatives based on significant observable market inputs from third party pricing vendors, non-binding broker-dealer quotes and/or recent trading activity. As the significant inputs used in the pricing process for these derivative instruments are observable market inputs, the fair value of these securities are classified within Level 2.

Short-term investments

The Company determined that certain of its short-term investments held in highly liquid money market-type funds, Treasury bills and commercial paper would be included in Level 1 as their fair values are based on quoted market prices in active markets. The fair values of other short-term investments are generally determined using the spread above the risk-free yield curve and are classified within Level 2.

Residential mortgage loans

The Company’s residential mortgage loans (included in ‘other assets’ in the consolidated balance sheets) include amounts related to the Company’s whole mortgage loan purchase and sell program. Fair values of residential mortgage loans are generally determined based on market prices. As significant inputs used in pricing process for these residential mortgage loans are observable market inputs, the fair value of these securities are classified within Level 2.

Other liabilities

The Company’s other liabilities include contingent and deferred consideration liabilities related to the Company’s acquisitions. Contingent consideration liabilities are remeasured at fair value at each balance sheet date with changes in fair value recognized in ‘net realized gains (losses)’. To determine the fair value of contingent consideration liabilities, the Company estimates the future payments using an income approach based on modeled inputs which include a weighted average cost of capital. Deferred consideration liabilities are measured at fair value on the transaction date. The Company determined that contingent and deferred consideration liabilities would be included within Level 3.

The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2022:

			Fair Value Measurement Using:
	Estimated Fair Value		Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Assets measured at fair value:
Available for sale securities:
Fixed maturities:
Corporate bonds	$	8,020,128	$	—	$	7,898,901	$	121,227
Mortgage backed securities	795,391		—		795,391		—
Municipal bonds	419,166		—		419,166		—
Commercial mortgage backed securities	1,047,275		—		1,047,275		—
U.S. government and government agencies	5,161,193		5,144,467		16,726		—
Non-U.S. government securities	2,312,819		—		2,312,819		—
Asset backed securities	1,926,817		—		1,926,817		—
Total	19,682,789		5,144,467		14,417,095		121,227
Short-term investments	1,331,662		1,197,304		134,358		—
Equity securities, at fair value	859,969		828,513		28,042		3,414
Derivative instruments (2)	148,301		—		148,301		—
Residential mortgage loans	2,283		—		2,283		—
Fair value option:
Corporate bonds	542,755		—		542,755		—
Non-U.S. government bonds	4,315		—		4,315		—
Asset backed securities	1,652		—		1,652		—
U.S. government and government agencies	5,398		5,398		—		—
Short-term investments	33,101		699		32,402		—
Equity securities	13,792		9,619		—		4,173
Other investments	196,215		—		162,956		33,259
Other investments measured at net asset value (1)	846,969
Total	1,644,197		15,716		744,080		37,432
Total assets measured at fair value	$	23,669,201	$	7,186,000	$	15,474,159	$	162,073
Liabilities measured at fair value:
Contingent consideration liabilities	$	(14,246)	$	—	$	—	$	(14,246)
Derivative instruments (2)	(75,961)		—		(75,961)		—
Total liabilities measured at fair value	$	(90,207)	$	—	$	(75,961)	$	(14,246)

(1)    In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.

(2)    See note 11, “Derivative Instruments.”

The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2021:

			Fair Value Measurement Using:
	Estimated Fair Value		Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Assets measured at fair value:
Available for sale securities:
Fixed maturities:
Corporate bonds	$	6,553,333	$	—	$	6,553,320	$	13
Mortgage backed securities	408,477		—		408,477		—
Municipal bonds	404,666		—		404,666		—
Commercial mortgage backed securities	1,046,484		—		1,046,484		—
U.S. government and government agencies	4,772,764		4,744,517		28,247		—
Non-U.S. government securities	2,120,294		—		2,120,294		—
Asset backed securities	2,692,091		—		2,688,744		3,347
Total	17,998,109		4,744,517		13,250,232		3,360
Equity securities, at fair value	1,804,170		1,762,864		38,388		2,918
Short-term investments	1,734,716		1,052,822		681,894		—
Derivative instruments (2)	127,121		—		127,121		—
Residential mortgage loans	49,847		—		49,847		—
Fair value option:
Corporate bonds	388,546		—		388,546		—
Non-U.S. government bonds	23,785		—		23,785		—
Asset backed securities	4,367		—		4,367		—
U.S. government and government agencies	—		—		—		—
Short-term investments	97,806		528		97,278		—
Equity securities	26,493		21,745		—		4,748
Other investments	310,798		20,352		262,465		27,981
Other investments measured at net asset value (1)	1,121,755
Total	1,973,550		42,625		776,441		32,729
Total assets measured at fair value	$	23,687,513	$	7,602,828	$	14,923,923	$	39,007
Liabilities measured at fair value:
Contingent consideration liabilities	$	(16,960)	$	—	$	—	$	(16,960)
Derivative instruments (2)	(54,224)		—		(54,224)		—
Total liabilities measured at fair value	$	(71,184)	$	—	$	(54,224)	$	(16,960)

(1)    In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.

(2)    See note 11, “Derivative Instruments.”

The following table presents a reconciliation of the beginning and ending balances for all financial assets and liabilities measured at fair value on a recurring basis using Level 3 inputs for 2022 and 2021:

			Assets										Liabilities
	Available For Sale				Fair Value Option						Fair Value
	Structured Securities (1)		Corporate Bonds		Corporate Bonds		Other Investments		Equity Securities		Equity Securities		Other Liabilities
Year Ended December 31, 2022
Balance at beginning of year	$	3,347	$	13	$	—	$	27,981	$	4,748	$	2,918	$	(16,960)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	(592)		352		—		(781)		(575)		(470)		(364)
Included in other comprehensive income	(1)		(1,095)		—		—		—		—		1,170
Purchases, issuances, sales and settlements
Purchases	—		150,013		—		12,381		—		969		—
Issuances	—		—		—		—		—		—		—
Sales	(2,051)		(5,363)		—		(3,339)		—		(3)		—
Settlements	(703)		(26,250)		—		(2,983)		—		—		1,908
Transfers in and/or out of Level 3	—		3,557		—		—		—		—		—
Balance at end of year	$	—	$	121,227	$	—	$	33,259	$	4,173	$	3,414	$	(14,246)
Year Ended December 31, 2021
Balance at beginning of year	$	3,426	$	13	$	985	$	67,103	$	68,988	$	42,015	$	(461)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	(135)		—		13		868		4,941		1,958		—
Included in other comprehensive income	133		—		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		—		13,213		—		5,718		(16,494)
Issuances	—		—		—		—		—		—		—
Sales (3)	—		—		(998)		(53,203)		(69,181)		(46,773)		—
Settlements	(77)		—		—		—		—		—		(5)
Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of year	$	3,347	$	13	$	—	$	27,981	$	4,748	$	2,918	$	(16,960)

(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

(2)    Gains or losses were included in net realized gains (losses).

(3)     Sales for the 2021 period primarily relates to the Company’s deconsolidation of Somers.

Financial Instruments Disclosed, But Not Carried, At Fair Value

The Company uses various financial instruments in the normal course of its business. The carrying values of cash, accrued investment income, receivable for securities sold, certain other assets, payable for securities purchased and certain other liabilities approximated their fair values at December 31, 2022, due to their respective short maturities. As these financial instruments are not actively traded, their respective fair values are classified within Level 2.

At December 31, 2022, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.7 billion and had a fair value of $2.4 billion. At December 31, 2021, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.7 billion and had a fair value of $3.3 billion. The fair values of the senior notes were obtained

from a third party pricing service and are based on observable market inputs. As such, the fair value of the senior notes is classified within Level 2.

Fair Value Measurements on a Non-Recurring Basis

The Company measures the fair value of certain assets on a non-recurring basis, generally quarterly, annually, or when events or changes in circumstances indicate that the carrying amount of the assets may not be recoverable. These assets include investments accounted for using the equity method, certain other investments, goodwill and intangible assets, and long-lived assets. The Company uses a variety of techniques to measure the fair value of these assets when appropriate, as described below:

Investments accounted for using the equity method. When the Company determines that the carrying value of these assets may not be recoverable, the Company records the assets at fair value with the loss recognized in income. In such cases, the Company measures the fair value of these assets using the techniques discussed above in “—Fair Value Measurements on a Recurring Basis.”

Goodwill and Intangible Assets. The Company tests goodwill and intangible assets annually for impairment whenever events or changes in circumstances indicate the carrying amount may not be recoverable. When the Company determines goodwill and intangible assets may be impaired, the Company uses techniques including discounted expected future cash flows, to measure fair value.

Long-Lived Assets. The Company tests its long-lived assets for impairment whenever events or changes in circumstances indicate the carrying amount of a long-lived asset may not be recoverable.

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Derivative Instruments

12 Months Ended

Dec. 31, 2022

Derivative Instruments and Hedging Activities Disclosure [Abstract]

Derivative Instruments

The Company’s investment strategy allows for the use of derivative instruments. The Company’s derivative instruments are recorded on its consolidated balance sheets at fair value. The Company utilizes exchange traded U.S. Treasury note, Eurodollar and other futures contracts and commodity futures to manage portfolio duration or replicate investment positions in its portfolios and the Company routinely utilizes foreign currency forward contracts, currency options, index futures contracts and other derivatives as part of its total return objective. In addition, certain of the Company’s investments are managed in portfolios which incorporate the use of foreign currency forward contracts which are intended to provide an economic hedge against foreign currency movements.

In addition, the Company purchases to-be-announced mortgage backed securities (“TBAs”) as part of its investment strategy. TBAs represent commitments to purchase a future issuance of agency mortgage backed securities. For the period between purchase of a TBA and issuance of the underlying security, the Company’s position is accounted for as a derivative. The Company purchases TBAs in both long and short positions to enhance investment performance and as part of its overall investment strategy.

The following table summarizes information on the fair values and notional values of the Company’s derivative instruments:

	Estimated Fair Value
	Asset Derivatives (1)		Liability Derivatives (1)		Notional Value (2)
December 31, 2022
Futures contracts	$	50,629	$	(16,963)	$	3,138,446
Foreign currency forward contracts	38,891		(35,446)		1,136,126
Other	58,781		(23,552)		3,591,793
Total	$	148,301	$	(75,961)
December 31, 2021
Futures contracts	$	34,999	$	(9,808)	$	2,826,564
Foreign currency forward contracts	7,734		(11,390)		915,962
TBAs	11,227		—		11,227
Other	73,161		(33,026)		3,736,773
Total	$	127,121	$	(54,224)

(1)    The fair value of asset derivatives are included in ‘other assets’ and the fair value of liability derivatives are included in ‘other liabilities.’

(2)    Represents the absolute notional value of all outstanding contracts, consisting of long and short positions.

The Company did not hold any derivatives which were designated as hedging instruments at December 31, 2022 or 2021.

The Company’s derivative instruments can be traded under master netting agreements, which establish terms that apply to all derivative transactions with a counterparty. In the event of a bankruptcy or other stipulated event of default, such agreements provide that the non-defaulting party may elect to terminate all outstanding derivative transactions, in which case all individual derivative positions (loss or gain) with a counterparty are closed out and netted and replaced with a single amount, usually referred to as the termination amount, which is expressed in a single currency. The resulting single net amount, where positive, is payable to the party “in-the-money” regardless of whether or not it is the defaulting party, unless the parties have agreed that only the non-defaulting party is entitled to receive a termination payment where the net amount is positive and is in its favor.

At December 31, 2022, $147.4 million and $73.2 million, respectively, of asset derivatives and liability derivatives were subject to a master netting agreement compared to $122.3 million and $53.9 million, respectively, at December 31, 2021. The remaining derivatives included in the table above were not subject to a master netting agreement.

Realized and unrealized contract gains and losses on the Company’s derivative instruments are reflected in ‘net realized gains (losses)’ in the consolidated statements of income, as summarized in the following table:

Derivatives not designated as hedging instruments	Year Ended December 31,
	2022		2021		2020
Net realized gains (losses):
Futures contracts	$	(86,634)	$	(15,262)	$	114,987
Foreign currency forward contracts	6,144		(39,755)		49,974
TBAs	(51)		(233)		1,129
Other	5,518		22,860		13,585
Total	$	(75,023)	$	(32,390)	$	179,675

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Variable Interest Entity and Noncontrolling Interests

12 Months Ended

Dec. 31, 2022

Variable Interest Entity and Noncontrolling Interest Disclosure [Abstract]

Variable Interest Entity and Noncontrolling Interests

Somers Holdings Ltd.

In March 2014, the Company invested $100.0 million and acquired 2,500,000 common shares of Somers. Somers was considered a VIE and the Company concluded that it was the primary beneficiary of Somers. In the 2020 fourth quarter, Arch Capital, Somers and Greysbridge, a wholly-owned subsidiary of Arch Capital, entered into an Agreement and Plan of Merger (as amended, the “Merger Agreement”). The merger and the related Greysbridge equity financing closed on July 1, 2021. Effective July 1, 2021, Somers is wholly owned by Greysbridge, and Greysbridge is owned 40% by the Company, 30% by certain investment funds managed by Kelso and 30% by certain investment funds managed by Warburg. Based on the governing documents of Greysbridge, the Company concluded that, while it retains significant influence over Somers, Somers no longer constitutes a variable interest entity. Accordingly, effective July 1, 2021, the Company no longer consolidates the results of Somers in its consolidated financial statements and footnotes. The Company classifies its investment as ‘investments in operating affiliates’ on the Company’s balance sheets and is accounted for under the equity method.

The following table summarizes Somers’ cash flow from operating, investing and financing activities.

	Year Ended December 31,
	2022	2021	2020
Total cash provided by (used for):
Operating activities	—	46,991	181,736
Investing activities	—	96,325	258,589
Financing activities	—	(2,042)	(335,776)

Non-redeemable noncontrolling interests

The following table sets forth activity in the non-redeemable noncontrolling interests:

	December 31,
	2022		2021
Balance, beginning of year	$	—	$	823,007
Impact of deconsolidation of Somers	—		(918,874)
Additional paid in capital attributable to noncontrolling interests	—		22,113
Amounts attributable to noncontrolling interests	—		78,314
Other comprehensive (income) loss attributable to noncontrolling interests	—		(4,560)
Balance, end of year	$	—	$	—

Redeemable noncontrolling interests

The following table sets forth activity in the redeemable noncontrolling interests:

	December 31,
	2022		2021		2020
Balance, beginning of year	$	9,233	$	58,548	$	55,404
Impact of deconsolidation of Somers	—		(48,919)		—
Other	1,596		(396)		3,144
Balance, end of year	$	10,829	$	9,233	$	58,548

The portion of income or loss attributable to third party investors is recorded in the consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests’ as summarized in the table below:

	December 31,
	2022		2021		2020
Amounts attributable to non-redeemable noncontrolling interests	$	—	$	(78,314)	$	(53,076)
Amounts attributable to redeemable noncontrolling interests	(5,490)		(4,299)		(7,114)
Net (income) loss attributable to noncontrolling interests	$	(5,490)	$	(82,613)	$	(60,190)

Bellemeade Re

The Company has entered into aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda (the “Bellemeade Agreements”). At the time the Bellemeade Agreements were entered into, the applicability of the accounting guidance that addresses VIEs was evaluated. As a result of the evaluation of the Bellemeade Agreements, the Company concluded that these entities are VIEs. However, given that the ceding insurers do not have the unilateral power to direct those activities that are significant to their economic performance, the Company does not consolidate such entities in its consolidated financial statements.

The following table presents the total assets of the Bellemeade entities, as well as the Company’s maximum exposure to loss associated with these VIEs, calculated as the maximum historical observable spread between the benchmark index for each respective transaction and short term invested trust asset yields. The benchmark index for agreements effective prior to 2021 is based on one-month LIBOR, while the 2021 and later agreements benchmark index is based on the Secured Overnight Financing Rate (“SOFR”). SOFR is a measure of the cost of borrowing cash overnight, collateralized by U.S. Treasury securities, and is based on directly observable U.S. Treasury-backed repurchase transactions.

			December 31, 2022										December 31, 2021
			Maximum Exposure to Loss										Maximum Exposure to Loss
Bellemeade Entities (Issue Date)	Total VIE Assets		On-Balance Sheet (Asset) Liability		Off-Balance Sheet		Total		Coverage Remaining from Reinsurers (1)		Total VIE Assets		On-Balance Sheet (Asset) Liability		Off-Balance Sheet		Total
2017-1 Ltd. (Oct-17)	$	36,679	$	(6)	$	14	$	8	$	—	$	108,368	$	(159)	$	424	$	265
2018-1 Ltd. (Apr-18)	89,698		(153)		508		355		—		181,136		(528)		1,268		740
2018-3 Ltd. (Oct-18)	199,237		(250)		771		521		—		302,563		(1,018)		2,496		1,478
2019-1 Ltd. (Mar-19)	107,880		(48)		593		545		—		181,324		(380)		5,807		5,427
2019-2 Ltd. (Apr-19)	325,462		(206)		4,356		4,150		—		398,316		(515)		3,998		3,483
2019-3 Ltd. (Jul-19)	222,977		(104)		1,229		1,125		—		409,859		(584)		3,190		2,606
2019-4 Ltd. (Oct-19)	266,124		(142)		3,640		3,498		—		411,954		(462)		4,759		4,297
2020-2 Ltd. (Sep-20)	105,110		(8)		492		484		—		217,766		(177)		1,984		1,807
2020-3 Ltd. (Nov-20)	243,891		53		2,872		2,925		7,079		348,818		(128)		5,793		5,665
2020-4 Ltd. (Dec-20)	97,563		32		642		674		4,165		176,826		(50)		1,630		1,580
2021-1 Ltd. (Mar-21)	467,469		239		2,743		2,982		35,798		568,986		(303)		3,283		2,980
2021-2 Ltd. (Jun-21)	458,362		581		2,855		3,436		77,099		522,807		281		4,124		4,405
2021-3 Ltd. (Sep-21)	489,927		217		2,704		2,921		127,032		507,873		(411)		3,446		3,035
2022-1 Ltd. (Jan-22)	283,500		399		1,765		2,164		33,260
2022-2 Ltd. (Sep-22)	201,005		1,172		1,616		2,788		126,160
Total	$	3,594,884	$	1,776	$	26,800	$	28,576	$	410,593	$	4,336,596	$	(4,434)	$	42,202	$	37,768

(1) Coverage from a separate panel of reinsurers remaining at December 31, 2022.

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Other Comprehensive Income

12 Months Ended

Dec. 31, 2022

Comprehensive Income Note Disclosure [Abstract]

Other Comprehensive Income (Loss)

The following table presents the changes in each component of AOCI, net of noncontrolling interests:

	Unrealized Appreciation on Available-For-Sale Investments		Foreign Currency Translation Adjustments		Total
Year Ended December 31, 2022
Beginning balance	$	13,486	$	(78,086)	$	(64,600)
Other comprehensive income (loss) before reclassifications	(1,772,649)		(56,720)		(1,829,369)
Amounts reclassified from accumulated other comprehensive income	247,799		—		247,799
Net current period other comprehensive income (loss)	(1,524,850)		(56,720)		(1,581,570)
Ending balance	$	(1,511,364)	$	(134,806)	$	(1,646,170)
Year Ended December 31, 2021
Beginning balance	$	501,295	$	(12,400)	$	488,895
Other comprehensive income (loss) before reclassifications	(371,741)		(65,686)		(437,427)
Amounts reclassified from accumulated other comprehensive income	(116,068)		—		(116,068)
Net current period other comprehensive income (loss)	(487,809)		(65,686)		(553,495)
Ending balance	$	13,486	$	(78,086)	$	(64,600)
Year Ended December 31, 2020
Beginning balance	$	258,486	$	(46,395)	$	212,091
Other comprehensive income (loss) before reclassifications	668,996		33,995		702,991
Amounts reclassified from accumulated other comprehensive income	(426,187)		—		(426,187)
Net current period other comprehensive income (loss)	242,809		33,995		276,804
Ending balance	$	501,295	$	(12,400)	$	488,895

The following tables present details about amounts reclassified from accumulated other comprehensive income and the tax effects allocated to each component of other comprehensive income (loss):

	Consolidated Statement of Income	Amounts Reclassified from AOCI
Details About	Line Item That Includes	Year Ended December 31,
AOCI Components	Reclassification	2022		2021		2020
Unrealized appreciation on available-for-sale investments
	Net realized gains (losses)	$	(235,989)	$	157,095	$	478,659
	Provision for credit losses	(43,909)		(2,099)		(3,597)
	Other-than-temporary impairment losses	—		—		(533)
	Total before tax	(279,898)		154,996		474,529
	Income tax (expense) benefit	32,099		(38,928)		(48,342)
	Net of tax	$	(247,799)	$	116,068	$	426,187

Following are the related tax effects allocated to each component of other comprehensive income (loss):

	Before Tax		Tax Expense		Net of Tax
	Amount		(Benefit)		Amount
Year Ended December 31, 2022
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(2,010,443)	$	(237,794)	$	(1,772,649)
Less reclassification of net realized gains (losses) included in net income	(279,898)		(32,099)		(247,799)
Foreign currency translation adjustments	(56,554)		166		(56,720)
Other comprehensive income (loss)	$	(1,787,099)	$	(205,529)	$	(1,581,570)
Year Ended December 31, 2021
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(406,774)	$	(19,845)	$	(386,929)
Less reclassification of net realized gains (losses) included in net income	154,996		38,928		116,068
Foreign currency translation adjustments	(64,423)		59		(64,482)
Other comprehensive income (loss)	$	(626,193)	$	(58,714)	$	(567,479)
Year Ended December 31, 2020
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	754,572	$	75,855	$	678,717
Less reclassification of net realized gains (losses) included in net income	474,529		48,342		426,187
Foreign currency translation adjustments	33,706		370		33,336
Other comprehensive income (loss)	$	313,749	$	27,883	$	285,866

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Earnings Per Common Share

12 Months Ended

Dec. 31, 2022

Earnings Per Share [Abstract]

Earnings Per Common Share

The calculation of basic earnings per common share is computed by dividing income available to Arch common shareholders by the weighted average number of Common Shares and common share equivalents outstanding. The following table sets forth the computation of basic and diluted earnings per common share:

	Year Ended December 31,
	2022		2021		2020
Numerator:
Net income	$	1,482,423	$	2,239,462	$	1,465,711
Amounts attributable to noncontrolling interests	(5,490)		(82,613)		(60,190)
Net income available to Arch	1,476,933		2,156,849		1,405,521
Preferred dividends	(40,736)		(48,343)		(41,612)
Loss on redemption of preferred shares	—		(15,101)		—
Net income available to Arch common shareholders	$	1,436,197	$	2,093,405	$	1,363,909
Denominator:
Weighted average common shares outstanding	368,612,197		391,748,715		403,062,179
Effect of dilutive common share equivalents:
Nonvested restricted shares	2,103,036		1,996,524		1,682,309
Stock options (1)	6,894,534		6,600,697		5,514,967
Weighted average common shares and common share equivalents outstanding – diluted	377,609,767		400,345,936		410,259,455
Earnings per common share:
Basic	$	3.90	$	5.34	$	3.38
Diluted	$	3.80	$	5.23	$	3.32

(1)    Certain stock options were not included in the computation of diluted earnings per share where the exercise price of the stock options exceeded the average market price and would have been anti-dilutive or where, when applying the treasury stock method to in-the-money options, the sum of the proceeds, including unrecognized compensation, exceeded the average market price and would have been anti-dilutive. For 2022, 2021 and 2020, the number of stock options excluded were 798,053, 2,398,608 and 2,249,821, respectively.

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Income Taxes

12 Months Ended

Dec. 31, 2022

Income Tax Disclosure [Abstract]

Income Taxes

Arch Capital is incorporated under the laws of Bermuda and, under current Bermuda law, is not obligated to pay any taxes in Bermuda based upon income or capital gains. The Company has received a written undertaking from the Minister of Finance in Bermuda under the Exempted Undertakings Tax Protection Act 1966 that, in the event that any legislation is enacted in Bermuda imposing any tax computed on profits, income, gain or appreciation on any capital asset, or any tax in the nature of estate duty or inheritance tax, such tax will not be applicable to Arch Capital or any of its operations until March 31, 2035. This undertaking does not, however, prevent the imposition of taxes on any person ordinarily resident in Bermuda or any company in respect of its ownership of real property or leasehold interests in Bermuda.

Arch Capital and its non-U.S. subsidiaries will be subject to U.S. federal income tax only to the extent that they derive U.S. source income that is subject to U.S. withholding tax, or income that is effectively connected with the conduct of a trade or business within the U.S. and is not exempt from U.S.

tax under an applicable income tax treaty with the U.S., or because a non-U.S. subsidiary has elected to be treated as a U.S. taxpayer. Arch Capital and its non-U.S. subsidiaries will be subject to a withholding tax on dividends from U.S. investments and interest from certain U.S. payors (subject to reduction by any applicable income tax treaty). Arch Capital and its non-U.S. subsidiaries intend to conduct their operations in a manner that will not cause them to be treated as engaged in a trade or business in the United States and, therefore, will not be required to pay U.S. federal income taxes (other than U.S. excise taxes on insurance and reinsurance premium and withholding taxes on dividends and certain other U.S. source investment income). However, because there is uncertainty as to the activities which constitute being engaged in a trade or business within the United States, there can be no assurances that the U.S. Internal Revenue Service will not contend successfully that Arch Capital, or its non-U.S. subsidiaries that do not elect to become U.S. taxpayers, are engaged in a trade or business in the United States. If Arch Capital or any of its non-U.S. subsidiaries were subject to U.S. income tax, Arch Capital’s shareholders’ equity and earnings could be materially adversely affected. Arch Capital has subsidiaries and branches that operate in various jurisdictions around the world that are subject to tax in the jurisdictions in which they

operate. The significant jurisdictions in which Arch Capital’s subsidiaries and branches are subject to tax are the United States, United Kingdom, Ireland, Canada, Switzerland, Australia and Denmark.

The components of income taxes attributable to operations were as follows:

	Year Ended December 31,
	2022		2021		2020
Current expense (benefit):
United States	$	195,588	$	284,274	$	181,571
Non-U.S.	5,628		11,259		16,091
	201,216		295,533		197,662
Deferred expense (benefit):
United States	(96,599)		(123,261)		(89,170)
Non-U.S.	(24,656)		(43,690)		3,346
	(121,255)		(166,951)		(85,824)
Income tax expense	$	79,961	$	128,582	$	111,838

The Company’s income or loss before income taxes was earned in the following jurisdictions:

	Year Ended December 31,
	2022		2021		2020
Income (Loss) Before Income Taxes:
Bermuda	$	985,828	$	1,518,616	$	1,114,117
United States	400,865		643,239		409,893
Other	175,691		206,187		53,539
Total	$	1,562,384	$	2,368,042	$	1,577,549

The expected tax provision computed on pre-tax income or loss at the weighted average tax rate has been calculated as the sum of the pre-tax income in each jurisdiction multiplied by that jurisdiction’s applicable statutory tax rate. The 2022 applicable statutory tax rates by jurisdiction were as follows: Bermuda (0.0%), United States (21.0%), United Kingdom (19.0%), Ireland (12.5%), Denmark (22.0%), Canada (26.5%), Gibraltar (12.5%), Australia (30.0%), Hong Kong (16.5%) and the Netherlands (25.8%).

A reconciliation of the difference between the provision for income taxes and the expected tax provision at the weighted average tax rate follows:

	Year Ended December 31,
	2022		2021		2020
Expected income tax expense (benefit) computed on pre-tax income at weighted average income tax rate	$	110,337	$	158,269	$	111,947
Addition (reduction) in income tax expense (benefit) resulting from:
Investment income	(12,762)		(23,572)		(1,824)
State taxes, net of U.S. federal tax benefit	10,650		20,978		5,027
Dividend withholding taxes	10,559		12,211		7,105
Change in valuation allowance	(22,726)		(40,425)		13,190
Base eroding tax	7,694		—		—
Share based compensation	(9,159)		(5,339)		(2,533)
Tax credits	(9,736)		—		—
Intercompany loan write-off	(3,544)		—		(22,083)
Other	(1,352)		6,460		1,009
Income tax expense (benefit)	$	79,961	$	128,582	$	111,838

The effect of a change in tax laws or rates on deferred tax assets and liabilities is recognized in income in the period in which such change is enacted.

Deferred income tax assets and liabilities reflect temporary differences based on enacted tax rates between the carrying amounts of assets and liabilities for financial reporting and income tax purposes.

Significant components of the Company’s deferred income tax assets and liabilities were as follows:

	December 31,
	2022		2021
Deferred income tax assets:
Net operating loss	$	76,665	$	87,960
Discounting of net loss reserves	77,556		72,001
Net unearned premium reserve	96,581		75,483
Compensation liabilities	55,269		28,062
Foreign tax credit carryforward	16,738		20,058
Bad debt reserves	17,365		10,252
Depreciation and amortization	141,409		115,041
Lease liability	26,681		21,453
Net unrealized decline of investments	192,949		—
Lloyds year of account deferral	1,385		—
Other, net	14,450		703
Deferred tax assets before valuation allowance	717,048		431,013
Valuation allowance	(6,968)		(43,953)
Deferred tax assets net of valuation allowance	710,080		387,060
Deferred income tax liabilities:
Deposit accounting liability	(2,658)		(1,578)
Goodwill and intangibles	(38,905)		(70,549)
Lloyds year of account deferral	—		(12,514)
Contingency reserve	(43,870)		(49,486)
Deferred policy acquisition costs	(63,708)		(25,612)
Investment related	(9,225)		(7,492)
Net unrealized appreciation of investments	—		(8,377)
Right-of-use asset	(20,781)		(17,406)
Total deferred tax liabilities	(179,147)		(193,014)
Net deferred income tax assets	$	530,933	$	194,046

The Company provides a valuation allowance to reduce the net value of certain deferred tax assets to an amount which management expects to more likely than not be realized. As of December 31, 2022, the Company’s valuation allowance was $7.0 million, compared to $44.0 million at December 31, 2021. The valuation allowance at December 31, 2022, was primarily attributable to valuation allowances on the Company’s Ireland and Hong Kong operations and certain other deferred tax assets relating to tax attributes that have a limited use.

At December 31, 2022, the Company’s net operating loss carryforwards and tax credits were as follows:

	Year Ended December 31,
	2022		Expiration
Operating Loss Carryforwards
United Kingdom	$	198,571	No expiration
Ireland	61,685		No expiration
Australia	32,333		No expiration
Hong Kong	28,080		No expiration
Netherlands	60		No expiration
United States (1)	23,766		2029 - 2038
Tax Credits
U.K. foreign tax credits	13,907		No expiration
U.S. foreign tax credits	2,830		2029 - 2032

(1) On January 30, 2014, the Company’s U.S. mortgage operations underwent an ownership change for U.S. federal income tax purposes as a result of the Company’s acquisition of the CMG Entities. As a result of this ownership change, a limitation has been imposed upon the utilization of approximately $7.0 million of the Company’s existing U.S. net operating loss carryforwards. Utilization is limited to approximately $0.6 million per year in accordance with Section 382 of the Internal Revenue Code of 1986 as amended (“the Code”).

The Company’s U.S. mortgage operations are eligible for a tax deduction, subject to certain limitations, under Section 832(e) of the Code for amounts required by state law or regulation to be set aside in statutory contingency reserves. The deduction is allowed only to the extent that the Company purchases non-interest bearing U.S. Mortgage Guaranty Tax and Loss Bonds (“T&L Bonds”) issued by the U.S. Treasury Department in an amount equal to the tax benefit derived from deducting any portion of the statutory contingency reserves. T&L Bonds are reflected in ‘other assets’ on the Company’s balance sheet and totaled approximately $12.4 million at December 31, 2022, compared to $31.6 million at December 31, 2021.

Deferred income tax liabilities have not been accrued with respect to the undistributed earnings of the Company's U.S., U.K. and Ireland subsidiaries as it is the Company’s intention that all such earnings will be indefinitely reinvested. If the earnings were to be distributed, as dividends or otherwise, such amounts may be subject to withholding tax in the jurisdiction of the paying entity. The Company no longer intends to indefinitely reinvest earnings from the Company's Canada subsidiary, however, no income or withholding taxes have been accrued as the Canada subsidiary does not have positive cumulative earnings and profits and therefore a distribution from this particular subsidiary would not be subject to income taxes or withholding taxes. Potential tax implications of repatriation from the Company’s unremitted earnings that are indefinitely reinvested are driven by facts at the time of distribution. Therefore, it is not practicable to estimate the income tax liabilities that might be incurred if

such earnings were remitted. Distributions from the U.K. or Ireland would not be subject to withholding tax and no deferred income tax liability would need to be accrued.

The Company recognizes interest and penalties relating to unrecognized tax benefits in the provision for income taxes. As of December 31, 2022, the Company’s total unrecognized tax benefits, including interest and penalties, were $2.0 million. If recognized, the full amount of the unrecognized tax benefit would impact the consolidated effective tax rate. A reconciliation of the beginning and ending amount of unrecognized tax benefits is as follows:

	December 31,
	2022		2021
Balance at beginning of year	$	2,008	$	2,008
Additions based on tax positions related to the current year	—		—
Additions for tax positions of prior years	—		—
Reductions for tax positions of prior years	—		—
Settlements	—		—
Balance at end of year	$	2,008	$	2,008

The Company, its subsidiaries and branches file income tax returns in various federal, state and local jurisdictions. The following table details open tax years that are potentially subject to examination by local tax authorities, in the following major jurisdictions:

Jurisdiction	Tax Years
United States	2015-2022
United Kingdom	2020-2022
Ireland	2018-2022
Canada	2018-2022
Switzerland	2018-2022
Denmark	2018-2022
Australia	2018-2022

As of December 31, 2022, the Company’s current income tax payable (included in “Other liabilities”) was $40.6 million.

Inflation Reduction Act of 2022.

On August 16, 2022, the U.S. government enacted the Inflation Reduction Act of 2022, which among other things implements a 15% minimum tax on book income of certain large corporations, a 1% excise tax on net stock repurchases and several tax incentives to promote clean energy. The effective date of these provisions is January 1, 2023. Based on its current analysis of the provisions, the Company does not expect that this legislation will have a material effect on the Company’s consolidated financial statements.

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Transactions with Related Parties

12 Months Ended

Dec. 31, 2022

Related Party Transactions [Abstract]

Transactions with Related Parties

In 2017, the Company acquired approximately 25% of Premia Holdings Ltd. Premia Holdings Ltd. is the parent of Premia Reinsurance Ltd., a multi-line Bermuda reinsurance company (together with Premia Holdings Ltd., “Premia”). Premia’s strategy is to reinsure or acquire companies or reserve portfolios in the non-life property and casualty insurance and reinsurance run-off market. Arch Re Bermuda and certain Arch co-investors invested $100.0 million and acquired approximately 25% of Premia as well as warrants to purchase additional common equity. Arch has appointed two directors to serve on the seven person board of directors of Premia. Arch Re Bermuda is providing a 25% quota share reinsurance treaty on certain business written by Premia. During 2022, Arch Re Bermuda entered into certain reinsurance transactions with Premia which generated net premiums written and earned of $121.1 million and $119.9 million, respectively, compared to $40.4 million of net premiums written and earned in 2021. At December 31, 2022, Arch Re Bermuda recorded a funds held asset from Premia of $118.7 million, compared to $53.5 million at December 31, 2021.

In the 2021 first quarter, as part of the Company’s acquisition of Barbican, the Company entered into an agreement with Premia Managing Agency Limited for the reinsurance to close of Syndicate 1955’s 2018 underwriting year of account into Premia Syndicate 1884’s 2021 underwriting year of account. The reinsurance to close covers legacy business underwritten by Syndicate 1955 on the underwriting 2018 and prior years of account and under the agreement, approximately $380 million of net liabilities was transferred to Syndicate 1884, with an effective date of January 1, 2021. The Company had no reinsurance recoverable on unpaid and paid losses or funds held liability at December 31, 2022 and December 31, 2021.

In July 2021, following consummation of the Merger Agreement and the related Greysbridge equity financing, pursuant to which Somers became wholly owned by Greysbridge, and Greysbridge is owned 40% by the Company, 30% by certain funds managed by Kelso and 30% by certain funds managed by Warburg. During the 2022 and 2021 period, the Company entered into certain reinsurance transactions with Somers. The Company’s net premiums written was reduced by $519.4 million and $379.1 million, for the 2022 and 2021 periods, respectively (which included reinsurance transactions as well as those entered into in conjunction with the Merger Agreement). In addition, Somers paid certain acquisition costs and administrative fees to the Company. At December 31, 2022, the Company recorded a reinsurance recoverable on unpaid and paid losses from Somers of $1.2 billion and a reinsurance balance payable to Somers of $413.8 million. At December 31, 2021,

reinsurance recoverable on unpaid and paid losses from Somers was $902.8 million, with a reinsurance balance payable to Somers of $258.4 million. See note 12, “Variable Interest Entity and Noncontrolling Interests.”

The Company has a put/call option that was entered into in connection with the Greysbridge equity financing, whereby beginning January 1, 2024 the Company will have a call right (but not the obligation) and Warburg and Kelso will each have a put right (but not the obligation) to buy/sell one third of their initial shares annually at the tangible book value per share of Greysbridge for the most recently ended fiscal quarter.

As of December 31, 2022, the Company owns $35.0 million in aggregate principal amount of Somers 6.5% senior notes, due July 2, 2029

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Leases

12 Months Ended

Dec. 31, 2022

Leases [Abstract]

Leases

In the ordinary course of business, the Company renews and enters into new leases for office property and equipment. At the lease inception date, the Company determines whether a contract contains a lease and its classification as a finance or operating lease. Primarily all of the Company’s leases are classified as operating leases. The Company’s operating leases have remaining lease terms of up to 10 years, some of which include options to extend the lease term. The Company considers these options when determining the lease term and measuring its lease liability and right-of-use asset. In addition, the Company’s lease agreements do not contain any material residual value guarantees or material restrictive covenants.

Short-term operating leases with an initial term of twelve months or less were excluded on the Company's consolidated balance sheet and represent an inconsequential amount of operating lease expense.

As most leases do not provide an implicit rate, the Company uses its incremental borrowing rate based on the information available at the lease commencement date in determining the present value of lease payments.

Additional information regarding the Company’s operating leases is as follows:

	December 31,
	2022			2021
Operating lease costs	$	33,571		$	31,691
Sublease income (1)	$	(988)		$	—
Cash payments included in the measurement of lease liabilities reported in operating cash flows	$	26,051		$	32,094
Right-of-use assets obtained in exchange for new lease liabilities	$	42,841		$	22,686
Right-of-use assets (2)	$	123,083		$	106,836
Operating lease liability (2)	$	151,890		$	126,711
Weighted average discount rate	4.2		%	3.9		%
Weighted average remaining lease term	6.6 years			5.9 years

(1)    The sublease income primarily relates to office property in Raleigh, North Carolina.

(2)    The right-of-use assets are included in ‘other assets’ while the operating lease liability is included in ‘other liabilities.’

The following table presents the contractual maturities of the Company's operating lease liabilities at December 31, 2022:

Years Ending December 31,
2023	$	31,861
2024	30,091
2025	24,651
2026	21,939
2027	17,859
2028 and thereafter	48,522
Total undiscounted lease liability	$	174,923
Less: present value adjustment	(23,033)
Operating lease liability	$	151,890

Rental expense was approximately $38.9 million, $39.1 million and $37.4 million for 2022, 2021 and 2020, respectively.

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Commitments and Contingencies

12 Months Ended

Dec. 31, 2022

Commitments and Contingencies Disclosure [Abstract]

Commitments and Contingencies

Concentrations of Credit Risk

The creditworthiness of a counterparty is evaluated by the Company, taking into account credit ratings assigned by independent agencies. The credit approval process involves an assessment of factors, including, among others, the counterparty, country and industry credit exposure limits. Collateral may be required, at the discretion of the Company, on certain transactions based on the creditworthiness of the counterparty.

The areas where significant concentrations of credit risk may exist include unpaid losses and loss adjustment expenses recoverable, contractholder receivables, ceded unearned premiums, paid losses and loss adjustment expenses recoverable net of reinsurance balances payable, investments and cash and cash equivalent balances. A credit exposure exists with respect to reinsurance recoverables as they may

become uncollectible. The Company manages its credit risk in its reinsurance relationships by transacting with reinsurers that it considers financially sound and, if necessary, the Company may hold collateral in the form of funds, trust accounts and/or irrevocable letters of credit. This collateral can be drawn on for amounts that remain unpaid beyond specified time periods on an individual reinsurer basis. In addition, certain insurance policies written by the Company’s insurance operations feature large deductibles, primarily in its construction and national accounts lines of business. Under such contracts, the Company is obligated to pay the claimant for the full amount of the claim. The Company is subsequently reimbursed by the policyholder for the deductible amount. These amounts are included on a gross basis in the consolidated balance sheet in contractholder payables and contractholder receivables, respectively. In the event that the Company is unable to collect from the policyholder, the Company would be liable for such defaulted amounts. Collateral, primarily in the form of letters of credit, cash and trusts, is obtained from the policyholder to mitigate the Company’s credit risk. In the instances where the company receives collateral in the form of cash, the Company records a related liability in “Collateral held for insured obligations.”

In addition, the Company underwrites a significant amount of its business through brokers and a credit risk exists should any of these brokers be unable to fulfill their contractual obligations with respect to the payments of insurance and reinsurance balances owed to the Company. The following table summarizes the percentage of the Company’s gross premiums written generated from or placed by the largest brokers:

Broker	Year Ended December 31,
	2022		2021		2020
Marsh & McLennan Companies and its subsidiaries	17.3	%	18.3	%	13.3	%
Aon Corporation and its subsidiaries	13.8	%	12.2	%	12.0	%

No other broker and no one insured or reinsured accounted for more than 10% of gross premiums written for 2022, 2021 and 2020.

The Company’s available for sale investment portfolio is managed in accordance with guidelines that have been tailored to meet specific investment strategies, including standards of diversification, which limit the allowable holdings of any single issue. There were no investments in any entity in excess of 10% of the Company’s shareholders’ equity at December 31, 2022 other than investments issued or guaranteed by the United States government or its agencies.

Investment Commitments

The Company’s investment commitments, which are primarily related to agreements entered into by the Company to invest in funds and separately managed accounts when called upon, were approximately $2.9 billion and $3.0 billion at December 31, 2022 and 2021, respectively.

Purchase Obligations

The Company has also entered into certain agreements which commit the Company to purchase goods or services, primarily related to software and computerized systems. Such purchase obligations were approximately $150.1 million and $114.1 million at December 31, 2022 and 2021, respectively.

Employment and Other Arrangements

At December 31, 2022, the Company has entered into employment agreements with certain of its executive officers. Such employment arrangements provide for compensation in the form of base salary, annual bonus, share-based awards, participation in the Company’s employee benefit programs and the reimbursements of expenses.

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Debt and Financing Arrangements

12 Months Ended

Dec. 31, 2022

Debt Disclosure [Abstract]

Debt and Financing Arrangements

The Company’s senior notes payable at December 31, 2022 and 2021 were as follows:

					Carrying Amount at
	Interest		Principal		December 31,
	(Fixed)		Amount		2022		2021
2034 notes (1)	7.350	%	300,000		297,618		297,488
2043 notes (2)	5.144	%	500,000		495,188		495,063
2026 notes (3)	4.011	%	500,000		498,073		497,633
2046 notes (4)	5.031	%	450,000		445,582		445,490
2050 notes (5)	3.635	%	1,000,000		988,949		988,720
			$	2,750,000	$	2,725,410	$	2,724,394

(1) Senior notes of Arch Capital issued on May 4, 2004 and due May 1, 2034 (“2034 notes”).

(2) Senior notes of Arch-U.S., a wholly-owned subsidiary of Arch Capital, issued on December 13, 2013 and due November 1, 2043 (“2043 notes”), fully and unconditionally guaranteed by Arch Capital.

(3) Senior notes of Arch Capital Finance LLC (“Arch Finance”), a wholly-owned finance subsidiary of Arch Capital, issued on December 8, 2016 and due December 15, 2026 (“2026 notes”), fully and unconditionally guaranteed by Arch Capital.

(4) Senior notes of Arch Finance issued on December 8, 2016 and due December 15, 2046 (“2046 notes”), fully and unconditionally guaranteed by Arch Capital

(5) Senior notes of Arch Capital issued on June 30, 2020 and due June 30, 2050 (“2050 notes”).

The 2034 notes are Arch Capital’s senior unsecured obligations and rank equally with all of its existing and future senior unsecured indebtedness. Interest payments on the 2034 notes are due on May 1st and November 1st of each year.

Arch Capital may redeem the 2034 notes at any time and from time to time, in whole or in part, at a “make-whole” redemption price.

The 2043 notes are unsecured and unsubordinated obligations of Arch-U.S. and Arch Capital, respectively, and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch-U.S. and Arch Capital, respectively. Interest payments on the 2043 notes are due on May 1st and November 1st of each year. Arch-U.S. may redeem the 2043 notes at any time and from time to time, in whole or in part, at a “make-whole” redemption price.

The 2026 notes are unsecured and unsubordinated obligations of Arch Finance and Arch Capital, respectively, and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch Finance and Arch Capital, respectively. Interest payments on the 2026 notes are due on June 15th and December 15th of each year. Arch Finance may redeem the 2026 notes at any time and from time to time, in whole or in part, at a “make-whole” redemption price.

The 2046 notes are unsecured and unsubordinated obligations of Arch Finance and Arch Capital, respectively, and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch Finance and Arch Capital, respectively. Interest payments on the 2046 notes are due on June 15th and December 15th of each year. Arch Finance may redeem the 2046 notes at any time and from time to time, in whole or in part, at a “make-whole” redemption price.

The 2050 notes are Arch Capital’s senior unsecured obligations and rank equally with all of its existing and future senior unsecured indebtedness. Interest payments on the 2050 notes are due on June 30 and December 30 of each year. Arch Capital may redeem the 2050 notes at any time and from time to time, in whole or in part, at a “make-whole” redemption price.

Letter of Credit and Revolving Credit Facilities

In the normal course of its operations, the Company enters into agreements with financial institutions to obtain secured and unsecured credit facilities. On April 7, 2022, Arch Capital and certain of its subsidiaries amended its existing credit agreement into a $925.0 million facility (the “Credit Facility”) with a syndication of lenders. The Credit Facility, as amended, consists of a $425.0 million secured facility for letters of credit (the “Secured Facility”) and a $500.0 million unsecured facility for revolving loans and letters of credit (the “Unsecured Facility”). Obligations of each borrower under the Secured Facility for letters of credit are secured by cash and eligible securities of such borrower held in collateral accounts. Commitments under the Credit Facility may be increased up to, but not exceeding, an aggregate of $1.25 billion. Arch Capital has a one-time option to convert

any or all outstanding revolving loans of Arch Capital and/or Arch-U.S. to term loans with the same terms as the revolving loans except that any prepayments may not be re-borrowed. Arch-U.S. guarantees the obligations of Arch Capital, and Arch Capital guarantees the obligations of Arch-U.S. Borrowings of revolving loans may be made at a variable rate based on SOFR. Secured letters of credit are available for issuance on behalf of certain Arch Capital subsidiaries. At December 31, 2022, the Secured Facility had $323.1 million of letters of credit outstanding and remaining capacity of $101.9 million, and the Unsecured Facility had no outstanding revolving loans or letters of credit, with remaining capacity of $500.0 million.

The Credit Facility contains certain restrictive and maintenance covenants customary for facilities of this type, including restrictions on indebtedness, minimum consolidated tangible net worth, maximum leverage levels and minimum financial strength ratings. Arch Capital and its subsidiaries which are party to the agreement were in compliance with all covenants contained therein at December 31, 2022.

Commitments under the Credit Facility will expire on December 17, 2024, and all loans then outstanding must be repaid. Letters of credit issued under the Unsecured Facility will not have an expiration date later than December 17, 2025.

In addition, certain of Arch Capital’s subsidiaries had outstanding secured and unsecured letters of credit through other facilities of $24.6 million and $400.0 million respectively, which were issued in the normal course of business (“LOC Facilities”). The principal purpose of the LOC Facilities is to issue, as required, evergreen standby letters of credit in favor of primary insurance or reinsurance counterparties with which certain of Arch Capital’s subsidiaries has entered into reinsurance arrangements. This is required to ensure that such counterparties are permitted to take credit for reinsurance obtained in United States jurisdictions where such subsidiaries are not licensed or otherwise admitted as an insurer, as required under insurance regulations in the United States, and to comply with requirements of Lloyd’s of London in connection with qualifying quota share and other arrangements. The amount of letters of credit issued is driven by, among other things, the timing and payment of catastrophe losses, loss development of existing reserves, the payment pattern of such reserves, the further expansion of business and the loss experience of such business.

When issued, all secured letters of credit are secured by a portion of the investment portfolio. At December 31, 2022, these letters of credit were secured by investments with a fair value of $465.2 million. The Company had no outstanding revolving credit agreement borrowings at December 31, 2022 and 2021.

Federal Home Loan Bank Membership

Certain subsidiaries of the Company are members of Federal Home Loan Banks (“FHLBs”). Members may borrow from the FHLBs at competitive rates subject to certain conditions. Conditions include maintaining sufficient collateral deposits for funding and a requirement to hold stock in the FHLBs related to both membership and outstanding advances. At December 31, 2022 the Company had no advances outstanding under the FHLB program, compared to $80.0 million of advances outstanding under the FHLB program, which was secured by investments with a fair value of $80.2 million at December 31, 2021. Advances outstanding under the FHLB program are included in ‘other liabilities’ on the Company’s balance sheet.

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Goodwill and Intangible Assets

12 Months Ended

Dec. 31, 2022

Goodwill and Intangible Assets Disclosure [Abstract]

Goodwill and Intangible Assets

The following table shows an analysis of goodwill and intangible assets:

	Goodwill		Intangible assets (indefinite life)		Intangible assets (finite life)		Total
Net balance at Dec. 31, 2020	$	314,629	$	79,219	$	299,015	$	692,863
Acquisitions (1)	31,677		—		318,459		350,136
Amortization	—		—		(82,955)		(82,955)
Impact of deconsolidation of Somers (2)	—		(7,650)		—		(7,650)
Foreign currency movements and other adjustments	(1,441)		(212)		(5,758)		(7,411)
Net balance at Dec. 31, 2021	344,865		71,357		528,761		944,983
Acquisitions (1)	8,389		—		—		8,389
Amortization	—		—		(106,200)		(106,200)
Foreign currency movements and other adjustments	(11,181)		(2,576)		(29,126)		(42,883)
Net balance at Dec. 31, 2022	$	342,073	$	68,781	$	393,435	$	804,289
Gross balance at Dec. 31, 2022	$	351,231	$	70,246	$	1,102,298	$	1,523,775
Accumulated amortization	—		—		(678,020)		(678,020)
Foreign currency movements and other adjustments	(9,158)		(1,465)		(30,843)		(41,466)
Net balance at Dec. 31, 2022	$	342,073	$	68,781	$	393,435	$	804,289

(1)    See note 2, “Acquisitions.”

(2)    See note 12, “Variable Interest Entity and Noncontrolling Interests.”

The following table presents the components of goodwill and intangible assets:

	Gross Balance		Accumulated Amortization		Foreign Currency Translation Adjustment and Other		Net Balance
Dec. 31, 2022
Acquired insurance contracts	$	451,505	$	(426,202)	$	339	$	25,642
Operating platform	52,674		(50,302)		2		2,374
Distribution relationships	602,518		(207,908)		(31,110)		363,500
Goodwill	351,231		—		(9,158)		342,073
Insurance licenses	48,331		—		—		48,331
Syndicate capacity	21,915		—		(1,465)		20,450
Unfavorable service contract	(9,533)		9,533		—		—
Other	5,134		(3,141)		(74)		1,919
Total	$	1,523,775	$	(678,020)	$	(41,466)	$	804,289
Dec. 31, 2021
Acquired insurance contracts	$	451,505	$	(409,592)	$	339	$	42,252
Operating platform	52,674		(48,838)		56		3,892
Distribution relationships	602,518		(120,302)		(2,207)		480,009
Goodwill	342,842		—		2,023		344,865
Insurance licenses	48,331		—		—		48,331
Syndicate capacity	21,915		—		1,111		23,026
Unfavorable service contract	(9,533)		9,435		—		(98)
Other	5,134		(2,542)		114		2,706
Total	$	1,515,386	$	(571,839)	$	1,436	$	944,983

The estimated remaining amortization expense for the Company’s intangible assets with finite lives is as follows:

2023	$	91,605
2024	73,366
2025	41,060
2026	32,091
2027	29,268
2028 and thereafter	126,045
Total	$	393,435

The estimated remaining useful lives of these assets range from one to fourteen years at December 31, 2022.

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Shareholders' Equity

12 Months Ended

Dec. 31, 2022

Stockholders' Equity Note [Abstract]

Shareholders' Equity

Authorized and Issued

The authorized share capital of Arch Capital consists of 1.8 billion Common Shares, par value of $0.0011 per share, and 50 million Preferred Shares, par value of $0.01 per share.

Common Shares

The following table presents a roll-forward of changes in Arch Capital’s issued and outstanding Common Shares:

	Year Ended December 31,
	2022	2021	2020
Common Shares:
Shares issued and outstanding, beginning of year	583,289,850	579,000,841	574,617,195
Shares issued (1)	3,517,399	2,669,229	2,646,164
Restricted shares issued, net of cancellations	1,443,513	1,619,780	1,737,482
Shares issued and outstanding, end of year	588,250,762	583,289,850	579,000,841
Common shares in treasury, end of year	(217,904,765)	(204,365,956)	(172,280,199)
Shares issued and outstanding, end of year	370,345,997	378,923,894	406,720,642

(1)    Includes shares issued from the exercise of stock options and stock appreciation rights, the vesting of restricted share units and shares issued from the employee share purchase plan.

Share Repurchase Program

The Board of Directors of Arch Capital (the “Board”) has authorized the investment in Arch Capital’s common shares through a share repurchase program. At December 31, 2022, $1.0 billion of share repurchases were available under the program. Repurchases under the program may be effected from time to time in open market or privately negotiated transactions through December 31, 2024. The timing and amount of the repurchase transactions under this program will depend on a variety of factors, including market conditions and corporate and regulatory considerations.

Repurchases of Arch Capital’s common shares in connection with the share repurchase plan and other share-based transactions were held in the treasury under the cost method, and the cost of the common shares acquired is included in ‘Common shares held in treasury, at cost.’ At December 31, 2022, Arch Capital held 217.9 million shares for an aggregate cost of $4.4 billion in treasury, at cost.

The Company’s repurchases under the share repurchase program were as follows:

	Year Ended December 31,
	2022		2021		2020
Aggregate cost of shares repurchased	$	585,823	$	1,234,294	$	83,472
Shares repurchased	12,891,405		31,486,830		2,850,102
Average price per share repurchased	$	45.44	$	39.20	$	29.29

Since the inception of the share repurchase program through December 31, 2022, Arch Capital has repurchased approximately 433.6 million common shares for an aggregate purchase price of $5.9 billion.

Series G Preferred Shares

In June 2021, Arch Capital completed a $500 million underwritten public offering of 20.0 million depositary shares

(the “Depositary Shares”), each of which represents a 1/1,000th interest in a share of its 4.55% Non-Cumulative Preferred Shares, Series G, $0.01 par value and $25,000 liquidation preference per share (equivalent to $25 liquidation preference per Depositary Share) (the “Series G Preferred Shares”). Each Depositary Share, evidenced by a depositary receipt, entitles the holder, through the depositary,

to a proportional fractional interest in all rights and preferences of the Series G Preferred Shares represented thereby (including any dividend, liquidation, redemption and voting rights).

Holders of Series G Preferred Shares will be entitled to receive dividend payments only when, as and if declared by the Board or a duly authorized committee of the Board. Any such dividends will be payable from, and including, the date of original issue on a noncumulative basis, quarterly in arrears on the last day of March, June, September and December of each year, at an annual rate of 4.55%. Dividends on the Series G Preferred Shares are not cumulative. The Company will be restricted from paying dividends on or repurchasing its common shares unless certain dividend payments are made on the Series G Preferred Shares. The Company may not declare or pay a dividend on the Series G Preferred Shares under certain circumstances, including if the Company is or, after giving effect to such payment, would be in breach of applicable individual or group solvency and liquidity requirements or applicable individual or group enhanced capital requirements (“ECR”). The Series G Preferred Shares may not be redeemed at any time if the ECR would be breached immediately before or after giving effect to such redemption, unless the Company replaces the capital represented by preference shares to be redeemed with capital having equal or better capital treatment.

Except in specified circumstances relating to certain tax or corporate events, the Series G Preferred Shares are not redeemable prior to June 11, 2026. On and after that date, the

Series G Preferred Shares will be redeemable at the Company’s option, in whole or in part, at a redemption price of $25,000 per share of the Series G Preferred Shares (equivalent to $25 per depositary share), plus any declared and unpaid dividends, without accumulation of any undeclared dividends to, but excluding, the redemption date. The Depositary Shares will be redeemed if and to the extent the related Series G Preferred Shares are redeemed by the Company. Neither the Depositary Shares nor the Series G Preferred Shares have a stated maturity, nor will they be subject to any sinking fund or mandatory redemption. The Series G Preferred Shares are not convertible into any other securities. The Series G Preferred Shares do not have voting rights, except under limited circumstances. The net proceeds from the Series G Preferred Share offerings were used to redeem the Company’s outstanding 5.25% Series E Non-Cumulative Preferred Shares.

Series F Preferred Shares

In August 2017 and November 2017, Arch Capital completed combined $330 million of underwritten public offerings ($230 million in August 2017 and $100 million in November 2017) of 13.2 million depositary shares (the “Series F Depositary Shares”), each of which represents a 1/1,000th interest in a share of its 5.45% Non-Cumulative Preferred Shares, Series F, with a $0.01 par value and $25,000 liquidation preference per share (equivalent to $25 liquidation preference per Series F Depositary Share) (the “Series F Preferred Shares”). Each Series F Depositary Share, evidenced by a depositary receipt, entitles the holder, through the depositary, to a proportional fractional interest in all rights and preferences of the Series F Preferred Shares represented thereby (including any dividend, liquidation, redemption and voting rights).

Holders of Series F Preferred Shares will be entitled to receive dividend payments only when, as and if declared by the Board or a duly authorized committee of the board. Any such dividends will be payable from, and including, the date of original issue on a noncumulative basis, quarterly in arrears on the last day of March, June, September and December of each year, at an annual rate of 5.45%. Dividends on the Series F Preferred Shares are not cumulative. The Company will be restricted from paying dividends on or repurchasing its common shares unless certain dividend payments are made on the Series F Preferred Shares.

Except in specified circumstances relating to certain tax or corporate events, the Series F Preferred Shares are not redeemable prior to August 17, 2022 (the fifth anniversary of the issue date). On and after that date, the Series F Preferred

Shares will be redeemable at the Company’s option, in whole or in part, at a redemption price of $25,000 per share of the Series F Preferred Shares (equivalent to $25 per depositary share), plus any declared and unpaid dividends, without accumulation of any undeclared dividends to, but excluding, the redemption date. The Series F Depositary Shares will be redeemed if and to the extent the related Series F Preferred Shares are redeemed by the Company. Neither the Series F Depositary Shares nor the Series F Preferred Shares have a stated maturity, nor will they be subject to any sinking fund or mandatory redemption. The Series F Preferred Shares are not convertible into any other securities. The Series F Preferred Shares will not have voting rights, except under limited circumstances. The net proceeds from the Series F Preferred Share offerings were used to redeem the Company’s outstanding 6.75% Series C Non-Cumulative Preferred Shares.

Series E Preferred Shares

In September, 2021, Arch Capital redeemed all outstanding 5.25% Series E non-cumulative preferred shares. The preferred shares were redeemed at a redemption price equal to $25 per share, plus all declared and unpaid dividends to (but excluding) the redemption date. In accordance with GAAP, following the redemption, original issuance costs related to such shares have been removed from additional paid-in capital and recorded as a “loss on redemption of preferred shares.” Such adjustment had no impact on total shareholders’ equity or cash flows.

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Share-Based Compensation

12 Months Ended

Dec. 31, 2022

Share-Based Payment Arrangement [Abstract]

Share-Based Compensation

Long Term Incentive and Share Award Plans

The Company utilizes share-based compensation plans for officers, other employees and directors of Arch Capital and its subsidiaries to provide competitive compensation opportunities, to encourage long-term service, to recognize individual contributions and reward achievement of performance goals and to promote the creation of long-term value for shareholders by aligning the interests of such persons with those of shareholders.

The 2022 Long-Term Incentive and Share Award Plan (“the 2022 Plan”) became effective as of May 4, 2022 following approval by shareholders of the Company. The 2022 Plan provides for the issuance of stock options, stock appreciation rights, restricted shares, restricted share units payable in common shares or cash, dividend equivalents, performance shares and performance units and other share-based awards to Arch Capital’s eligible employees and directors. The number of common shares reserved for grants under the 2022 Plan, subject to anti-dilution adjustments in the event of certain changes in Arch Capital’s capital structure, is 9,000,000; provided that no more than 6,000,000 common

shares may be issued as incentive stock options under Section 422 of the Code. The 2022 Plan will terminate as to future awards on February 25, 2032. At December 31, 2022, 9,000,000 shares are available for future issuance.

The 2018 Long-Term Incentive and Share Award Plan (the “2018 Plan”) became effective as of May 9, 2018 following approval by shareholders of the Company. The 2018 Plan provides for the issuance of restricted stock units, performance units, restricted shares, performance shares, stock options and stock appreciation rights and other equity-based awards to our employees and directors. The 2018 Plan authorizes the issuance of 34,500,000 common shares and will terminate as to future awards on February 28, 2028. At December 31, 2022, 4,577,991 shares are available for future issuance.

The 2015 Long Term Incentive and Share Award Plan (the (“2015 Plan”) authorizes the issuance of 12,900,000 common shares and became effective as of May 7, 2015 following approval by shareholders of the Company. The 2015 Plan provides for the issuance of share-based awards to our employees and directors and will terminate as to future awards on February 26, 2025. At December 31, 2022, 504,872 shares are available for future issuance.

Upon shareholder approval on May 6, 2016, the Amended and Restated Arch Capital Group Ltd. 2007 Employee Share Purchase Plan (the “ESPP”) became effective and a total of 4,689,777 common shares were reserved for issuance. The purpose of the ESPP is to give employees of Arch Capital and its subsidiaries an opportunity to purchase common shares through payroll deductions, thereby encouraging employees to share in the economic growth and success of Arch Capital and its subsidiaries. The ESPP is designed to qualify as an “employee share purchase plan” under Section 423 of the Code. At December 31, 2022, 1,041,837 shares remain available for issuance.

Stock Options and Stock Appreciation Rights

The Company generally issues stock options and SARs to eligible employees, with exercise prices equal to the fair market values of the Company’s Common Shares on the grant dates. Such grants generally vest over a three year period with one-third vesting on the first, second and third anniversaries of the grant date.

The grant date fair value is determined using the Black-Scholes option valuation model. The expected life assumption is based on an expected term analysis, which incorporates the Company’s historical exercise experience. Expected volatility is based on the Company’s daily historical trading data of its common shares. The table below summarizes the assumptions used.

	Year Ended December 31,
	2022		2021		2020
Dividend yield	—	%	—	%	—	%
Expected volatility	24.0	%	24.2	%	16.6	%
Risk free interest rate	2.0	%	1.0	%	1.2	%
Expected option life	6.0 years		6.0 years		6.0 years

A summary of stock option and SAR activity under the Company’s Long Term Incentive and Share Award Plans during 2022 is presented below:

	Year Ended December 31, 2022
	Number of Options / SARs	Weighted Average Exercise Price		Weighted Average Contractual Term	Aggregate Intrinsic Value
Outstanding, beginning of year	17,083,160	$	25.06
Granted	784,963	$	47.46
Exercised	(3,412,371)	$	16.91
Forfeited or expired	(34,851)	$	39.96
Outstanding, end of year	14,420,901	$	28.17	4.37	$	499,051
Exercisable, end of year	12,433,470	$	26.20	3.77	$	454,769

The aggregate intrinsic value of stock options and SARs exercised represents the difference between the exercise price of the stock options and SARs and the closing market price of the Company’s common shares on the exercise dates. During 2022, the Company received proceeds of $17.2 million from the exercise of stock options and recognized a tax benefit of $8.7 million from the exercise of stock options and SARs.

	Year Ended December 31,
	2022		2021		2020
Weighted average grant date fair value	$	13.26	$	9.22	$	8.14
Aggregate intrinsic value of Options/SARs exercised	$	113,409	$	47,074	$	59,723

Restricted Common Shares and Restricted Units

The Company also issues restricted share and unit awards to eligible employees and directors, for which the fair value is equal to the fair market values of the Company’s Common Shares on the grant dates. Restricted share and unit awards generally vest over a three year period with one-third vesting on the first, second and third anniversaries of the grant date.

A summary of restricted share and restricted unit activity under the Company’s Long Term Incentive and Share Award Plans for 2022 is presented below:

	Restricted Common Shares		Restricted Unit Awards
Unvested Shares:
Unvested balance, beginning of year	2,070,837		699,866
Granted	914,694		174,699
Vested	(744,096)		(330,144)
Forfeited	(75,881)		(27,128)
Unvested balance, end of year	2,165,554		517,293
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year	$	36.35	$	33.29
Granted	$	47.45	$	47.50
Vested	$	38.21	$	34.38
Forfeited	$	41.13	$	37.51
Unvested balance, end of year	$	40.23	$	37.17

The following table presents the weighted average grant date fair value of restricted shares and restricted unit awards granted and the aggregate fair value of restricted shares and unit awards vesting in each year.

	Year Ended December 31,
	2022		2021		2020
Restricted shares and restricted unit awards granted	1,089,393		1,261,773		1,535,330
Weighted average grant date fair value	$	47.45	$	36.12	$	37.55
Aggregate fair value of vested restricted share and unit awards	$	78,129	$	65,477	$	39,703

The aggregate intrinsic value of restricted units outstanding at December 31, 2022 was $32.5 million.

Performance Awards

The Company also issues performance share and unit awards (“performance awards”) to eligible employees, which are earned based on the achievement of pre-established threshold, target and maximum goals over three-year performance periods. Final payouts depend on the level of achievement along with each employees continued service through the vest date, and can vary between 0% and 200%. The grant date fair value of the performance awards is measured using a Monte Carlo simulation model, which incorporated the assumptions summarized in the table below. Expected volatility is based on the Company’s daily historical trading data of its common shares. The cumulative compensation expense recognized and unrecognized as of any reporting period date represents the adjusted estimate of performance shares and units that will ultimately be awarded, valued at their original grant date fair values.

	Year Ended December 31,
	2022		2021		2020
Expected volatility	38.1	%	37.5	%	18.1	%
Risk free interest rate	1.7	%	0.3	%	1.1	%

	Performance Shares		Performance Units
Unvested Shares:
Unvested balance, beginning of year	1,861,760		29,770
Granted	669,742		21,030
Performance adjustment (1) (2)	(54,904)		8,921
Vested	(583,544)		(19,695)
Forfeited	(10,138)		(316)
Unvested balance, end of year	1,882,916		39,710
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year	$	38.93	$	38.71
Granted	$	49.91	$	49.91
Performance adjustment (1) (2)	$	36.07	$	35.83
Vested	$	36.07	$	35.83
Forfeited	$	49.91	$	49.91
Unvested balance, end of year	$	43.75	$	45.33

(1)    The performance adjustment represents the difference between the number of performance shares granted and earned, which vested following the end of the performance period. The performance shares were granted at the maximum level of achievement.

(2)    The performance adjustment represents the change in PSUs, which vested following the end of the performance period. The performance units were granted at the target level of achievement.

The following table presents the weighted average grant date fair values of performance awards granted.

	Year Ended December 31,
	2022		2021		2020
Performance awards	690,772		685,104		557,204
Weighted average grant date fair value	$	49.91	$	37.38	$	44.17

The issuance of share-based awards and amortization thereon has no effect on the Company’s consolidated shareholders’ equity.

Share-Based Compensation Expense

The following tables present pre-tax and after-tax share-based compensation expense recognized as well as the unrecognized compensation cost associated with unvested awards and the weighted average period over which it is expected to be recognized.

	Year Ended December 31,
	2022		2021		2020
Pre-Tax
Stock options and SARs	$	11,891	$	12,316	$	11,744
Restricted share and unit awards	50,278		46,817		41,284
Performance awards	21,510		23,696		14,729
ESPP	3,993		3,751		2,135
Total	$	87,672	$	86,580	$	69,892
After-Tax
Stock options and SARs	$	10,726	$	10,927	$	10,388
Restricted share and unit awards	42,346		39,349		34,599
Performance awards	19,794		21,920		13,380
ESPP	3,660		3,471		1,978
Total	$	76,526	$	75,667	$	60,345

	December 31, 2022
	Stock Options and SARs		Restricted Common Shares and Units		Performance Common Shares and Units
Unrecognized compensation cost related to unvested awards	$	6,357	$	42,096	$	7,520
Weighted average recognition period (years)	0.75		1.00		0.48

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Retirement Plans	12 Months Ended
	Dec. 31, 2022
Retirement Benefits [Abstract]
Retirement Plans	For purposes of providing employees with retirement benefits, the Company maintains defined contribution retirement plans. Contributions are based on the participants’ eligible compensation. For 2022, 2021 and 2020, the Company expensed $67.0 million, $60.4 million and $52.0 million, respectively, related to these retirement plans.

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Legal Proceedings	12 Months Ended
	Dec. 31, 2022
Disclosure Legal Proceedings [Abstract]
Legal Proceedings	The Company, in common with the insurance industry in general, is subject to litigation and arbitration in the normal course of its business. As of December 31, 2022, the Company was not a party to any litigation or arbitration which is expected by management to have a material adverse effect on the Company’s results of operations and financial condition and liquidity.

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Statutory Information

12 Months Ended

Dec. 31, 2022

Disclosure Statutory Information [Abstract]

Statutory Information

The Company’s insurance and reinsurance subsidiaries are subject to insurance and/or reinsurance laws and regulations in the jurisdictions in which they operate. These regulations include certain restrictions on the amount of dividends or other distributions available to shareholders without prior approval of the insurance regulatory authorities.

The actual and required statutory capital and surplus for the Company’s principal operating subsidiaries at December 31, 2022 and 2021:

	December 31,
	2022		2021
Actual capital and surplus (1):
Bermuda	$	19,546,128	$	17,528,510
Ireland	968,443		958,200
United States	6,194,954		5,600,652
United Kingdom	1,018,092		902,002
Canada	68,637		70,063
Australia	284,998		283,693
Required capital and surplus:
Bermuda	$	6,449,878	$	5,661,301
Ireland	815,194		794,933
United States	1,748,543		1,717,646
United Kingdom	543,104		563,164
Canada	47,825		42,513
Australia	175,885		214,022

(1)Such amounts include ownership interests in affiliated insurance and reinsurance subsidiaries.

There were no state-prescribed or permitted regulatory accounting practices for any of the Company’s insurance or reinsurance entities that resulted in reported statutory surplus that differed from that which would have been reported under the prescribed practices of the respective regulatory authorities, including the National Association of Insurance Commissioners. The differences between statutory financial statements and statements prepared in accordance with GAAP vary by jurisdiction, however, with the primary differences being that statutory financial statements may not reflect deferred acquisition costs, certain net deferred tax assets, goodwill and intangible assets, unrealized appreciation or depreciation on debt securities and certain unauthorized reinsurance recoverables and include contingency reserves.

The statutory net income (loss) for the Company’s principal operating subsidiaries for 2022, 2021 and 2020 was as follows:

	Year Ended December 31,
	2022		2021		2020
Statutory net income (loss):
Bermuda	$	1,729,925	$	2,370,746	$	1,579,889
Ireland	(52,757)		25,191		18,397
United States	219,524		345,790		143,271
United Kingdom	56,818		35,286		4,078
Canada	9,215		6,985		(1,049)
Australia	38,538		11,874		(8,601)

Bermuda

The Company’s Bermuda insurance and reinsurance subsidiaries are subject to the Bermuda Insurance Act 1978 and related regulations, each as amended (the “Insurance Act”). Arch Re Bermuda, the Company’s principal reinsurance and insurance subsidiary, is registered as a Class 4 insurer and long-term insurer while Arch Group Reinsurance Ltd. (“AGRL”) is registered as a Class 3A general business insurer and provides affiliated quota share reinsurance covering certain U.S. business. The Insurance Act requires that both entities maintain minimum statutory capital and surplus equal to the greater of a minimum solvency margin and the enhanced capital requirement (“ECR”) as determined by the Bermuda Monetary Authority (“BMA”). The ECR is calculated based on the Bermuda Solvency Capital Requirement model, a risk-based model that takes into account the risk characteristics of different aspects of the company’s business. At December 31, 2022 and 2021, the actual and required capital and surplus were based on the economic balance sheet requirements.

Under the Insurance Act, Arch Re Bermuda and AGRL are restricted with respect to the payment of dividends. Each entity is prohibited from declaring or paying in any financial year dividends of more than 25% of its total statutory capital and surplus (as shown on its previous financial year’s

statutory balance sheet) unless it files, at least seven days before payment of such dividends, with the BMA an affidavit stating that it will continue to meet the required margins following the declaration of those dividends. Accordingly, Arch Re Bermuda can pay approximately $3.7 billion to Arch Capital during 2023 without providing an affidavit to the BMA. Dividends or distributions, if any, made by AGRL would result in an increase in available capital at Arch-U.S.

Ireland

The Company has three Irish subsidiaries: Arch Re Europe, an authorized life and non-life reinsurer, Arch Insurance (EU), an authorized non-life insurer and Arch Underwriting Europe, a registered insurance and reinsurance intermediary. Irish authorized reinsurers and insurers, such as Arch Re Europe, Arch Insurance (EU) and Irish intermediaries, such as Arch Underwriters Europe, are also subject to the general body of Irish laws and regulations including the provisions of the Companies Act 2014. As part of the Company’s Brexit plan, Arch Insurance (EU) received approval from the Central Bank of Ireland (“CBI”) to expand the nature of its business in 2019 commenced writing insurance lines in the European Economic Area in 2020, and the Part VII Transfer was completed at the end of December 2020. Arch Re Europe, Arch Insurance (EU) and Arch Underwriters Europe are subject to the supervision of the CBI and must comply with Irish insurance acts and regulations as well as with directions and guidance issued by the CBI. Arch Re Europe and Arch Insurance (EU) are required to maintain a minimum level of capital. At December 31, 2022 and 2021, these requirements were met.

The amount of dividends these subsidiaries are permitted to declare is limited to accumulated, realized profits, so far as not previously utilized by distribution or capitalization, less its accumulated, realized losses, so far as not previously written off in a reduction or reorganization of capital duly made. The solvency and capital requirements must still be met following any distribution. Dividends or distributions, if any, made by Arch Re Europe would result in an increase in available capital at Arch Re Bermuda.

United States

The Company’s U.S. insurance and reinsurance subsidiaries are subject to insurance laws and regulations in the jurisdictions in which they operate. The ability of the Company’s regulated insurance subsidiaries to pay dividends or make distributions is dependent on their ability to meet applicable regulatory standards. These regulations include restrictions that limit the amount of dividends or other distributions, such as loans or cash advances, available to shareholders without prior approval of the insurance regulatory authorities.

Dividends or distributions, if any, made by Arch Re U.S. would result in an increase in available capital at Arch-U.S., the Company’s U.S. holding company. Arch Re U.S. can declare a maximum of approximately $255.4 million of dividends during 2023 subject to the approval of the Commissioner of the Delaware Department of Insurance.

AMIC and UGRIC are approved as eligible mortgage insurers by Fannie Mae and Freddie Mac, subject to maintaining certain requirements (“eligible mortgage insurers”). In April 2015, the GSEs published their original comprehensive, requirements, known as the Private Mortgage Insurer Eligibility Requirements or “PMIERs.” Revised and restated in September 2018, and clarified thereafter by the Guidance Letters 2020-1 and 2021-1 issued by the GSEs in 2020 and 2021, respectively, the PMIERs apply to the Company’s eligible mortgage insurers, but do not apply to AMG, which is not GSE-approved.

The amount of assets required to satisfy the revised financial requirements of the PMIERs may be affected by many factors, including macro-economic conditions, the size and composition of our mortgage insurance portfolio, and the amount of risk ceded to reinsurers that may be deducted in our calculation of “minimum required assets.”

The Company’s U.S. mortgage insurance subsidiaries are subject to regulation by their domiciliary and primary regulators, the Wisconsin Office of the Commissioner of Insurance (“Wisconsin OCI”) for AMIC and AMG, the North Carolina Department of Insurance (“NC DOI”) for UGRIC, and by state insurance departments in each state in which they are licensed. As mandated by state insurance laws, mortgage insurers are generally mono-line companies. Each company is subject to the statutory requirements of their domiciliary regulator as to payment of dividends and return of capital; the GSEs may also impart limitations on the Company’s eligible mortgage insurers, such as required minimum assets. Under respective state law, the Company’s U.S. mortgage subsidiaries can declare a maximum of approximately $156.5 million of ordinary dividends in 2023, however, dividend capacity is limited by the respective companies unassigned surplus amounts. Such dividends would increase the available capital at Arch U.S. MI Holdings Inc., a subsidiary of Arch-U.S.

Mortgage insurance companies licensed in Wisconsin or North Carolina are required to establish contingency loss reserves for purposes of statutory accounting in an amount equal to at least 50% of net earned premiums. These amounts generally cannot be withdrawn for a period of 10 years and are separate liabilities for statutory accounting purposes, which affects the ability to pay dividends. However, with prior regulatory approval, a mortgage insurance company may make early withdrawals from the contingency reserve

when incurred losses exceed 35% of net premiums earned in a calendar year.

Under Wisconsin and North Carolina law, as well as that of 14 other states, a mortgage insurer must maintain a minimum amount of statutory capital relative to its risk in force in order for the mortgage insurer to continue to write new business. While formulations of minimum capital vary in certain jurisdictions, the most common measure applied allows for a maximum risk-to-capital ratio of 25 to 1. Wisconsin and North Carolina require mortgage insurers to maintain a “minimum policyholder position” calculated in accordance with their respective regulations. Policyholders' position consists primarily of statutory policyholders' surplus plus the contingency loss reserves.

United Kingdom

The Prudential Regulation Authority (“PRA”) and the Financial Conduct Authority (“FCA”) regulate insurance and reinsurance companies and the FCA regulates firms carrying on insurance mediation activities operating in the U.K., both under the Financial Services and Markets Act 2000. In May 2004, Arch Insurance (U.K.) was granted the relevant permissions for the classes of insurance business which it underwrites in the U.K. AMAL currently manages Arch Syndicate 2012 and Arch Syndicate 1955 pursuant to its authorizations by the U.K. regulators and Lloyd’s. All U.K. companies are also subject to a range of statutory provisions, including the laws and regulations of the Companies Act 2006 (as amended) (the “U.K. Companies Act”).

Arch Insurance (U.K.) and AMAL must maintain a margin of solvency at all times under the Solvency II Directive from the European Insurance and Occupational Pensions Authority. The regulations stipulate that insurers are required to maintain the minimum capital requirement and solvency capital requirement at all times. At December 31, 2022 and 2021, these requirements were met.

As corporate members of Lloyd’s, AMAL (as managing agent of the Company’s Lloyd’s Syndicates) and each syndicate’s respective corporate members are subject to the oversight of the Council of Lloyd’s. The capital required to support a Syndicate’s underwriting capacity, or funds at Lloyd’s, is assessed annually and is determined by Lloyd’s in accordance with the capital adequacy rules established by the PRA. The Company has provided capital to support the underwriting of Arch Syndicate 2012 and Arch Syndicate 1955 in the form of pledged assets and letters of credit provided by Arch Re Bermuda. The amount which the Company provides as funds at Lloyd’s is not available for distribution to the Company for the payment of dividends. Lloyd’s is supervised by the PRA and required to implement certain rules prescribed by the PRA under the Lloyd’s Act of 1982 regarding the operation of the Lloyd’s market. With

respect to managing agents and corporate members, Lloyd’s prescribes certain minimum standards relating to management and control, solvency and other requirements and monitors managing agents’ compliance with such standards.

Under U.K. law, all U.K. companies are restricted from declaring a dividend to their shareholders unless they have “profits available for distribution.” The calculation as to whether a company has sufficient profits is based on its accumulated realized profits minus its accumulated realized losses. U.K. insurance regulatory laws do not prohibit the payment of dividends, but the PRA or FCA, as applicable, requires that insurance companies and insurance intermediaries maintain certain solvency margins and may restrict the payment of a dividend by Arch Insurance (U.K.) and AMAL.

Canada

Arch Insurance Canada and the Canadian branch of Arch Re U.S. (“Arch Re Canada”) are subject to federal, as well as provincial and territorial, regulation in Canada. The Office of the Superintendent of Financial Institutions (“OSFI”) is the federal regulatory body that, under the Insurance Companies Act (Canada), regulates federal Canadian and non-Canadian insurance companies operating in Canada. Arch Insurance Canada and Arch Re Canada are subject to regulation in the provinces and territories in which they underwrite insurance/reinsurance, and the primary goal of insurance/reinsurance regulation at the provincial and territorial levels is to govern the market conduct of insurance/reinsurance companies. Arch Insurance Canada is licensed to carry on insurance business by OSFI and in each province and territory. Arch Re Canada is licensed to carry-on reinsurance business by OSFI and in the provinces of Ontario and Quebec.

Under the Insurance Companies Act (Canada), Arch Insurance Canada is required to maintain an adequate amount of capital in Canada, calculated in accordance with a test promulgated by OSFI called the Minimum Capital Test (“MCT”), and Arch Re Canada is required to maintain an adequate margin of assets over liabilities in Canada, calculated in accordance with a test promulgated by OSFI called the Branch Adequacy of Assets Test. Under the Insurance Companies Act (Canada), approval of the Minister of Finance (Canada) is required in connection with certain acquisitions of shares of, or control of, Canadian insurance companies such as Arch Insurance Canada, and notice to and/or approval of OSFI is required in connection with the payment of dividends by or redemption of shares by Canadian insurance companies such as Arch Insurance Canada.

Australia

The Australian Prudential Regulation Authority (“APRA”) is an independent statutory authority responsible for prudential supervision of institutions across banking, insurance and superannuation and promotes financial stability in Australia. Arch Indemnity has been authorized to conduct monoline lenders’ mortgage insurance business in Australia since June 2002 and was acquired by Arch Capital on August 30, 2021 and since that date is the primary provider of lenders’ mortgage insurance for the group. Arch Indemnity has also been licensed by the Australian Securities and Investments Commission (“ASIC”) since March 2011 to engage in credit activities in Australia. Arch LMI Pty Ltd. (“Arch LMI”) was formerly authorized by APRA in January 2019 to conduct monoline lenders’ mortgage insurance business in Australia; however, in December 2022, we converted Arch LMI to a services company for our Australian lenders mortgage insurance operations and the company relinquished its APRA authorization. Major regulatory requirements that are applicable to Arch Indemnity in general as an insurance provider and financial institution in Australia include requirements and compliance with minimum capital levels; risk management strategy; corporate governance standards, privacy legislation on the collection, use and storage of personal information; cyber security obligations imposed by APRA and ASIC; modern slavery legislation; anti-money laundering and counter-terrorism legislation. At December 31, 2022 and 2021, these requirements were met.

Arch Capital also conducts property and casualty insurance business in Australia through the Company’s Lloyd’s platform. This insurance business is managed by and distributed through local coverholders and is subject to Lloyd’s Supervision. In addition, the business is subject to local Australian prudential regulatory oversight by APRA, and additional separate financial services market conduct regulation by the Australian Securities and Investments Commission.

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Schedule II - Condensed Financial Information of Registrant

12 Months Ended

Dec. 31, 2022

Condensed Financial Information Disclosure [Abstract]

Condensed Financial Information of Registrant

SCHEDULE II

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONDENSED FINANCIAL INFORMATION OF REGISTRANT

(U.S. dollars in thousands)

Balance Sheet

(Parent Company Only)

	December 31,
	2022		2021
Assets
Total investments	$	7,282	$	2,038
Cash	11,393		16,317
Investments in subsidiaries	14,191,188		14,822,024
Investment in operating affiliates	5,259		6,877
Due from subsidiaries and affiliates	1,554		11
Other assets	17,203		9,604
Total assets	$	14,233,879	$	14,856,871
Liabilities
Senior notes	$	1,286,567	$	1,286,208
Other liabilities	37,239		24,767
Total liabilities	1,323,806		1,310,975
Shareholders' Equity
Non-cumulative preferred shares	830,000		830,000
Common shares ($0.0011 par, shares issued: 588,250,762 and 583,289,850)	654		648
Additional paid-in capital	2,211,444		2,085,075
Retained earnings	15,892,065		14,455,868
Accumulated other comprehensive income (loss), net of deferred income tax	(1,646,170)		(64,600)
Common shares held in treasury, at cost (shares: 217,904,765 and 204,365,956)	(4,377,920)		(3,761,095)
Total shareholders' equity	$	12,910,073	$	13,545,896
Total liabilities and shareholders' equity	$	14,233,879	$	14,856,871

The financial information for the parent company (Arch Capital Group Ltd.) should be read in conjunction with the Consolidated Financial Statements and Notes thereto.

Statement of Income

(Parent Company Only)

	Year Ended
	December 31,
	2022		2021		2020
Revenues
Net investment income	$	2,058	$	1,524	$	53
Net realized gains (losses)	29		—		(2,110)
Total revenues	2,087		1,524		(2,057)
Expenses
Corporate expenses	85,997		71,818		65,566
Interest expense	58,759		58,741		40,445
Net foreign exchange (gains) losses	(1)		7		3
Total expenses	144,755		130,566		106,014
Income (loss) before income taxes and income (loss) from operating affiliates	(142,668)		(129,042)		(108,071)
Income (loss) from operating affiliates	(1,047)		(590)		(437)
Income (loss) before equity in net income of subsidiaries	(143,715)		(129,632)		(108,508)
Equity in net income of subsidiaries	1,592,929		2,286,481		1,514,029
Net income available to Arch	1,449,214		2,156,849		1,405,521
Preferred dividends	(40,736)		(48,343)		(41,612)
Loss on redemption of preferred shares	—		(15,101)		—
Net income available to Arch common shareholders	$	1,408,478	$	2,093,405	$	1,363,909

The financial information for the parent company (Arch Capital Group Ltd.) should be read in conjunction with the Consolidated Financial Statements and Notes thereto.

Statement of Cash Flows

(Parent Company Only)

	Year Ended
	December 31,
	2022		2021		2020
Operating Activities:
Net Cash Provided By Operating Activities	$	621,307	$	1,727,529	$	124,751
Investing Activities:
Net (purchases) sales of short-term investments	(4,838)		(1,866)		(130)
Capital contributed to subsidiaries	—		(487,161)		(988,975)
Purchase of fixed assets	(22)		(783)		(15)
Other	(1,462)		—		—
Net Cash Used For Investing Activities	(6,322)		(489,810)		(989,120)
Financing Activities:
Purchases of common shares under share repurchase program	(585,823)		(1,234,294)		(83,472)
Proceeds from common shares issued, net	6,660		6,418		1,876
Proceeds from issuance of preferred shares, net	—		485,821		—
Redemption of preferred shares	—		(450,000)		—
Proceeds from borrowings	—		—		988,393
Preferred dividends paid	(40,736)		(48,280)		(41,612)
Net Cash Used For Financing Activities	(619,899)		(1,240,335)		865,185
Increase (decrease) in cash and restricted cash	(4,914)		(2,616)		816
Cash and restricted cash, beginning of year	16,344		18,960		18,144
Cash and restricted cash, end of period	$	11,430	$	16,344	$	18,960

The financial information for the parent company (Arch Capital Group Ltd.) should be read in conjunction with the Consolidated Financial Statements and Notes thereto.

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Schedule III - Supplementary Insurance Information

12 Months Ended

Dec. 31, 2022

SEC Schedule, 12-16, Insurance Companies, Supplementary Insurance Information [Abstract]

Supplementary Insurance Information

SCHEDULE III

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

SUPPLEMENTARY INSURANCE INFORMATION

(U.S. dollars in thousands)

	Deferred Acquisition Costs	Reserves for Losses and Loss Adjustment Expenses	Unearned Premiums	Net Premiums Earned	Net Investment Income (1)	Net Losses and Loss Adjustment Expenses Incurred	Amortization of Deferred Acquisition Costs	Other Operating Expenses (2)	Net Premiums Written
December 31, 2022
Insurance	$301,398	$11,017,327	$3,381,810	$4,559,335	NM	$2,782,945	$885,866	$665,472	$5,020,642
Reinsurance	992,339	8,305,854	3,206,284	3,959,381	NM	2,568,843	813,555	267,531	4,923,976
Mortgage	(29,867)	708,762	748,908	1,159,361	NM	(324,271)	40,159	195,172	1,132,571
Other
Total	$1,263,870	$20,031,943	$7,337,002	$9,678,077	NM	$5,027,517	$1,739,580	$1,128,175	$11,077,189
December 31, 2021
Insurance	$378,265	$9,810,622	$2,937,664	$3,626,468	NM	$2,344,365	$606,265	$558,906	$4,148,193
Reinsurance	424,390	6,878,721	2,263,264	2,840,443	NM	1,924,719	536,754	212,810	3,254,374
Mortgage	99,186	1,067,813	811,014	1,283,419	NM	56,677	97,418	194,010	1,261,068
Other				331,968	NM	259,042	62,741	32,869	354,702
Total	$901,841	$17,757,156	$6,011,942	$8,082,298	NM	$4,584,803	$1,303,178	$998,595	$9,018,337
December 31, 2020
Insurance	$254,833	$8,989,930	$2,334,225	$2,871,420	NM	$2,092,453	$418,483	$489,153	$3,162,907
Reinsurance	278,422	5,027,742	1,356,983	2,162,229	NM	1,628,320	354,048	168,011	2,457,370
Mortgage	203,748	976,673	740,043	1,397,935	NM	528,344	134,240	162,202	1,279,850
Other	53,705	1,519,583	407,714	560,351	NM	440,482	98,071	55,810	537,589
Total	$790,708	$16,513,928	$4,838,965	$6,991,935	NM	$4,689,599	$1,004,842	$875,176	$7,437,716

(1)    The Company does not manage its assets by segment and, accordingly, net investment income is not allocated to each underwriting segment. See note 4, “Segment Information,” to our consolidated financial statements in Item 8 for information related to the ‘other’ segment.

(2)    Certain other operating expenses relate to the Company’s corporate segment. Such amounts are not reflected in the table above. See note 4, “Segment Information,” to our consolidated financial statements in Item 8 for information related to the corporate segment.

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Schedule IV - Reinsurance

12 Months Ended

Dec. 31, 2022

SEC Schedule, 12-17, Insurance Companies, Reinsurance [Abstract]

Reinsurance

SCHEDULE IV

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

REINSURANCE

(U.S. dollars in thousands)

	Gross Amount		Ceded to Other Companies (1)		Assumed From Other Companies (1)		Net Amount		Percentage of Amount Assumed to Net
Year Ended December 31, 2022
Premiums Written:
Insurance	$	6,889,358	$	(1,910,222)	$	41,506	$	5,020,642	0.8	%
Reinsurance	395,063		(2,024,462)		6,553,375		4,923,976		133.1	%
Mortgage	1,256,366		(322,400)		198,605		1,132,571		17.5	%
Total	$	8,540,787	$	(4,249,258)	$	6,785,660	$	11,077,189	61.3	%
Year Ended December 31, 2021
Premiums Written:
Insurance	$	5,833,873	$	(1,719,541)	$	33,861	$	4,148,193	0.8	%
Reinsurance	408,520		(1,839,556)		4,685,410		3,254,374		144.0	%
Mortgage	1,213,333		(246,757)		294,492		1,261,068		23.4	%
Other	251,106		(102,763)		206,359		354,702		58.2	%
Total	$	7,706,832	$	(3,734,150)	$	5,045,655	$	9,018,337	55.9	%
Year Ended December 31, 2020
Premiums Written:
Insurance	$	4,659,416	$	(1,525,655)	$	29,146	$	3,162,907	0.9	%
Reinsurance	305,435		(1,014,716)		3,166,651		2,457,370		128.9	%
Mortgage	1,192,316		(194,149)		281,683		1,279,850		22.0	%
Other	396,743		(190,957)		331,803		537,589		61.7	%
Total	$	6,553,910	$	(2,650,352)	$	3,534,158	$	7,437,716	47.5	%

(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions and are included in the gross premiums written of each segment. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

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Schedule VI - Supplementary Information For Property and Casualty Insurance Underwriters

12 Months Ended

Dec. 31, 2022

SEC Schedule, 12-18, Supplemental Information, Property-Casualty Insurance Underwriters [Abstract]

Supplementary Information for Property and Casualty Insurance Underwriters

SCHEDULE VI

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

SUPPLEMENTARY INFORMATION FOR PROPERTY AND CASUALTY INSURANCE UNDERWRITERS

(U.S. dollars in thousands)

Column A	Column B		Column C		Column D		Column E		Column F		Column G		Column H				Column I		Column J		Column K
Affiliation with Registrant	Deferred Acquisition Costs		Reserves for Losses and Loss Adjustment Expenses		Discount, if any, deducted in Column C		Unearned Premiums		Net Premiums Earned		Net Investment Income		Net Losses and Loss Adjustment Expenses Incurred Related to				Amortization of Deferred Acquisition Costs		Net Paid Losses and Loss Adjustment Expenses		Net Premiums Written
													(a) Current Year		(b) Prior Years
Consolidated Subsidiaries
2022	$	1,263,870	$	20,031,943	$	60,536	$	7,337,002	$	9,678,077	$	496,547	$	5,798,528	$	(771,011)	$	1,739,580	$	3,141,948	$	11,077,189
2021	901,841		17,757,156		55,575		6,011,942		8,082,298		389,118		4,940,987		(356,184)		1,303,178		2,826,551		9,018,337
2020	790,708		16,513,929		23,326		4,838,965		6,991,935		519,608		4,851,051		(161,452)		1,004,842		2,661,117		7,437,716

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Significant Accounting Policies (Policies)

12 Months Ended

Dec. 31, 2022

Accounting Policies [Abstract]

Basis of presentation

The consolidated financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America (“GAAP”) and include the accounts of Arch Capital and its subsidiaries, including Arch Reinsurance Ltd. (“Arch Re Bermuda”), Arch Reinsurance Company (“Arch Re U.S.”), Arch Capital Group (U.S.) Inc.(“Arch-U.S.”), Arch Insurance Company, Arch Specialty Insurance Company, Arch Property Casualty Insurance Company (“Arch P&C”), Arch Indemnity Insurance Company (“Arch Indemnity Insurance”), Arch Insurance Canada Ltd. (“Arch Insurance Canada”), Arch Reinsurance Europe Designated Activity Company (“Arch Re Europe”), Arch Mortgage Insurance Company (“AMIC”), Arch Mortgage Guaranty Company (“AMG”), United Guaranty Residential Insurance Company (“UGRIC”), Arch Indemnity, Arch Insurance (EU) Designated Activity Company (“Arch Insurance (EU)”), Arch Insurance (U.K.) Limited (“Arch Insurance (U.K.)”) and the Company’s participation on Lloyd’s of London syndicates: 2012 (“Arch Syndicate 2012”) and 1955 (“Arch Syndicate 1955” and together with Arch Syndicate 2012, the Company’s “Lloyd’s Syndicates”). All significant intercompany transactions and balances have been eliminated in consolidation.

Use of estimates

The preparation of financial statements in conformity with GAAP requires management to make estimates and assumptions that affect the reported amounts of assets and liabilities and disclosure of contingent assets and liabilities at the date of the financial statements and the reported amounts of revenues and expenses during the reporting period. Actual results could differ materially from those estimates and assumptions. The Company’s principal estimates include:

•The reserve for losses and loss adjustment expenses;

•Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses, including the provision for uncollectible amounts;

•Estimates of written and earned premiums;

•The valuation of the investment portfolio and assessment of allowance for credit losses;

•The valuation of purchased intangible assets;

•The assessment of goodwill and intangible assets for impairment; and

•The valuation of deferred tax assets.

Premiums

Insurance. Insurance premiums written are generally recorded at the policy inception and are primarily earned on a pro rata basis over the terms of the policies for all products, usually 12 months. Premiums written include estimates that are derived from multiple sources which include the historical experience of the underlying business, similar business and available industry information. Unearned premium reserves represent the portion of premiums written that relates to the unexpired terms of in-force insurance policies.

Reinsurance. Reinsurance premiums written include amounts reported by brokers and ceding companies, supplemented by the Company’s own estimates of premiums where reports have not been received. The determination of premium estimates requires a review of the Company’s experience with the ceding companies, familiarity with each market, the timing of the reported information, an analysis and understanding of the characteristics of each line of business, and management’s judgment of the impact of various factors, including premium or loss trends, on the volume of business written and ceded to the Company. On an ongoing basis, the Company’s underwriters review the amounts reported by these third parties for reasonableness based on their experience and knowledge of the subject class of business, taking into account the Company’s historical experience with the brokers or ceding companies. In addition, reinsurance contracts under which the Company assumes business generally contain specific provisions which allow the Company to perform audits of the ceding company to ensure compliance with the terms and conditions of the contract, including accurate and timely reporting of information. Based on a review of all available information, management establishes premium estimates where reports have not been received. Premium estimates are updated when new information is received and differences between such estimates and actual amounts are recorded in the period in which estimates are changed or the actual amounts are determined.

Reinsurance premiums written are recorded based on the type of contracts the Company writes. Premiums on the Company’s excess of loss and pro rata reinsurance contracts are estimated when the business is underwritten. For excess of loss contracts, premiums are recorded as written based on

the terms of the contract. Estimates of premiums written under pro rata contracts are recorded in the period in which the underlying risks are expected to incept and are based on information provided by the brokers and the ceding companies. For multi-year reinsurance treaties which are payable in annual installments, generally, only the initial annual installment is included as premiums written at policy inception due to the ability of the reinsured to commute or cancel coverage during the term of the policy. The remaining annual installments are included as premiums written at each successive anniversary date within the multi-year term.

Reinsurance premiums written, irrespective of the class of business, are generally earned on a pro rata basis over the terms of the underlying policies or reinsurance contracts. Contracts and policies written on a “losses occurring” basis cover claims that may occur during the term of the contract or policy, which is typically 12 months. Accordingly, the premium is earned evenly over the term. Contracts which are written on a “risks attaching” basis cover claims which attach to the underlying insurance policies written during the terms of such contracts. Premiums earned on such contracts usually extend beyond the original term of the reinsurance contract, typically resulting in recognition of premiums earned over a 24-month period. Certain of the Company’s reinsurance contracts include provisions that adjust premiums or acquisition expenses based upon the experience under the contracts. Premiums written and earned, as well as related acquisition expenses, are recorded based upon the projected experience under such contracts.

The Company also writes certain reinsurance business that is intended to provide insurers with risk management solutions that complement traditional reinsurance. Under these contracts, the Company assumes a measured amount of insurance risk in exchange for an anticipated margin, which is typically lower than on traditional reinsurance contracts. The terms and conditions of these contracts may include additional or return premiums based on loss experience, loss corridors, sublimits and caps. Examples of such business include aggregate stop-loss coverages, financial quota share coverages and multi-year retrospectively rated excess of loss coverages. If these contracts are deemed to transfer risk, they are accounted for as reinsurance. Otherwise, such contracts are accounted for under the deposit method.

Mortgage. Mortgage guaranty insurance policies are contracts that are generally non-cancelable by the insurer, are renewable at a fixed price, and provide for payment of premiums on a monthly, annual or single basis. Upon renewal, the Company is not able to re-underwrite or re-price its policies. Consistent with industry accounting practices, premiums written on a monthly basis are earned as coverage is provided. Premiums written on an annual basis are amortized on a monthly pro rata basis over the year of coverage. Primary mortgage insurance premiums written on

policies covering more than one year are referred to as single premiums. A portion of the revenue from single premiums is recognized in premiums earned in the current period, and the remaining portion is deferred as unearned premiums and earned over the estimated expiration of risk of the policy. If single premium policies related to insured loans are canceled due to repayment by the borrower and the policy is a non-refundable product, the remaining unearned premium related to each canceled policy is recognized as earned premium upon notification of the cancellation.

Reinstatement premiums for the Company’s insurance and reinsurance operations are recognized at the time a loss event occurs, where coverage limits for the remaining life of the contract are reinstated under pre-defined contract terms. Reinstatement premiums, if obligatory, are fully earned when recognized. The accrual of reinstatement premiums is based on an estimate of losses and loss adjustment expenses, which reflects management’s judgment.

Premium estimates are reviewed by management at least quarterly. Such review includes a comparison of actual reported premiums to expected ultimate premiums along with a review of the aging and collection of premium estimates. Based on management’s review, the appropriateness of the premium estimates is evaluated, and any adjustment to these estimates is recorded in the period in which it becomes known. Adjustments to premium estimates could be material and such adjustments could directly and significantly impact earnings favorably or unfavorably in the period they are determined because the estimated premium may be fully or substantially earned. A significant portion of amounts included as premiums receivable, which represent estimated premiums written, net of commissions, are not currently due based on the terms of the underlying contracts.

Unearned premiums represent the portion of premiums written that is applicable to the estimated unexpired risk of insured loans. A portion of premium payments may be refundable if the insured cancels coverage, which generally occurs when the loan is repaid, the loan amortizes to a sufficiently low amount to trigger a lender permitted or legally required cancellation, or the value of the property has increased sufficiently in accordance with the terms of the contract. Premium refunds reduce premiums earned in the consolidated statements of income. Generally, only unearned premiums are refundable.

Premiums receivable include amounts receivable from agents, brokers and insured that are both currently due and amounts not yet due on insurance, reinsurance and mortgage insurance policies. Premiums receivable balances are reported net of an allowance for expected credit losses. The Company monitors credit risk associated with premiums receivable through its ongoing review of amounts outstanding, aging of the receivable, historical loss data, and

counterparty financial strength measures. The allowance also includes estimated uncollectible amounts related to dispute risk. In certain instances, credit risk may be reduced by the Company’s right to offset loss obligations or unearned premiums against premiums receivable. Any allowance for credit losses is charged to net realized gains (losses) in the period the receivable is recorded and revised in subsequent periods to reflect changes in the Company’s estimate of expected credit losses. See note 7, “Allowance for Expected Credit Losses” for additional information.

Acquisition costs

Acquisition Costs. Acquisition costs that are directly related and incremental to the successful acquisition or renewal of business are deferred and amortized based on the type of contract. The Company’s insurance and reinsurance operations capitalize incremental direct external costs that result from acquiring a contract but do not capitalize salaries, benefits and other internal underwriting costs. For the Company’s mortgage insurance operations, which include a substantial direct sales force, both external and certain internal direct costs are deferred and amortized. For property and casualty insurance and reinsurance contracts, deferred acquisition costs are amortized over the period in which the related premiums are earned. Consistent with mortgage insurance industry accounting practice, amortization of acquisition costs related to the mortgage insurance contracts for each underwriting year’s book of business is recorded in proportion to estimated gross profits. Estimated gross profits are comprised of earned premiums and losses and loss adjustment expenses. For each underwriting year, the Company estimates the rate of amortization to reflect actual experience and any changes to persistency or loss development.

Deferred acquisition costs are carried at their estimated realizable value and take into account anticipated losses and loss adjustment expenses, based on historical and current experience, and anticipated investment income.

A premium deficiency occurs if the sum of anticipated losses and loss adjustment expenses, unamortized acquisition costs and maintenance costs exceed unearned premiums (including expected future premiums) and anticipated investment income. A premium deficiency reserve (“PDR”) is recorded by charging any unamortized acquisition costs to expense to the extent required in order to eliminate the deficiency. If the premium deficiency exceeds unamortized acquisition costs then a liability is accrued for the excess deficiency.

To assess the need for a PDR on mortgage exposures, the Company develops loss projections based on modeled loan defaults related to its current policies in force. This projection is based on recent trends in default experience, severity and rates of defaulted loans moving to claim, as well as recent trends in the rate at which loans are prepaid, and incorporates anticipated interest income. Evaluating the expected

profitability of the Company’s existing mortgage insurance business and the need for a PDR for its mortgage business involves significant reliance upon assumptions and estimates with regard to the likelihood, magnitude and timing of potential losses and premium revenues. No premium deficiency charges were recorded by the Company during 2022, 2021 or 2020.

Deposit accounting

Certain assumed reinsurance contracts that are deemed not to transfer insurance risk, are accounted for using the deposit method of accounting. However, it is possible that the Company could incur financial losses on such contracts. Management exercises significant judgment in the assumptions used in determining whether assumed contracts should be accounted for as reinsurance contracts or deposit contracts. For those contracts that contain only significant underwriting risk, the estimated profit margin is deferred and amortized over the contract period and such amount is included in the Company’s underwriting results. When the estimated profit margin is explicit, the margin is reflected as other underwriting income and any adverse financial results on such contracts are reflected as incurred losses. When the estimated profit margin is implicit, the margin is reflected as an offset to paid losses and any adverse financial results on such contracts are reflected as incurred losses. Additional judgments are required when applying the accounting guidance with respect to the revenue recognition criteria for contracts deemed to transfer only significant underwriting risk. For those contracts that contain only significant timing risk, an accretion rate is established at inception of the contract based on actuarial estimates whereby the deposit accounting liability is increased to the estimated amount payable over the contract term. The accretion on the deposit is based on the expected rate of return required to fund the expected future payment obligations. Periodically the Company reassesses the estimated ultimate liability and the related expected rate of return. The accretion of the deposit accounting liability as well as changes to the estimated ultimate liability and the accretion rate would be reflected as part of interest expense in the Company’s results of operations. Any negative accretion in a deposit accounting liability is shown in other underwriting income in the Company’s results of operations.

Under some of these contracts, the ceding company retains the related assets on a funds held basis. Such amounts are included in “Other assets” on the Company’s balance sheet. Interest income produced by those assets are recorded as part of net investment income in the Company's results of operations.

Retroactive accounting

Retroactive reinsurance reimburses a ceding company for liabilities incurred as a result of past insurable events covered by the underlying policies reinsured. In certain instances, reinsurance contracts cover losses both on a prospective basis and on a retroactive basis and, accordingly, the Company bifurcates the prospective and retrospective elements of these reinsurance contracts and accounts for each element separately where practical. Underwriting income generated in connection with retroactive reinsurance contracts is deferred and amortized into income over the settlement period while losses are charged to income immediately. Subsequent changes in estimated amount or timing of cash flows under such retroactive reinsurance contracts are accounted for by adjusting the previously deferred amount to the balance that would have existed had the revised estimate been available at the inception of the reinsurance transaction, with a corresponding charge or credit to income.

Reinsurance ceded

In the normal course of business, the Company purchases reinsurance to increase capacity and to limit the impact of individual losses and events on its underwriting results by reinsuring certain levels of risk with other insurance enterprises or reinsurers. The Company uses pro rata, excess of loss and facultative reinsurance contracts. Reinsurance ceding commissions that represent a recovery of acquisition costs are recognized as a reduction to acquisition costs while the remaining portion is deferred. The accompanying consolidated statement of income reflects premiums and losses and loss adjustment expenses and acquisition costs, net of reinsurance ceded. See note 8, “Reinsurance” for information on the Company's reinsurance usage. Reinsurance premiums ceded and unpaid losses and loss adjustment expenses recoverable are estimated in a manner consistent with that of the original policies issued and the terms of the reinsurance contracts. If the reinsurers are unable to satisfy their obligations under the agreements, the Company’s insurance or reinsurance subsidiaries would be liable for such defaulted amounts.

Reinsurance recoverables are recorded as assets, predicated on the reinsurers’ ability to meet their obligations under the reinsurance agreements. In certain instances, the Company obtains collateral, including letters of credit and trust accounts to further reduce the credit exposure on its reinsurance recoverables. The Company reports its reinsurance recoverables net of an allowance for expected credit loss. The allowance is based upon the Company’s ongoing review of amounts outstanding, the financial condition of its reinsurers, amounts and form of collateral obtained and other relevant factors. A ratings based probability-of-default and loss-given-default methodology is used to estimate the allowance for expected credit loss. Any

allowance for credit losses is charged to net realized gains (losses) in the period the recoverable is recorded and revised in subsequent periods to reflect changes in the Company’s estimate of expected credit losses. See note 7, “Allowance for Expected Credit Losses” for additional information.

Cash

Cash includes cash equivalents, which are investments with original maturities of three months or less which are not part of the investment portfolio.

Restricted cash

Restricted cash represents amounts held for the benefit of third parties or is legally or contractually restricted as to withdrawal or usage by the Company. Such amounts are included in “Other assets” on the Company’s balance sheet.

Investments

The Company currently classifies substantially all of its fixed maturity investments and short-term investments as “available for sale” and, accordingly, they are carried at estimated fair value (also known as fair value) with the changes in fair value recorded as an unrealized gain or loss component of accumulated other comprehensive income in shareholders’ equity. The fair value of fixed maturity securities and equity securities is generally determined from quotations received from nationally recognized pricing services, or when such prices are not available, by reference to broker or underwriter bid indications. Short-term investments comprise securities due to mature within one year of the date of issue. Short-term investments include certain cash equivalents which are part of investment portfolios under the management of external and internal investment managers.

The Company’s investment portfolio includes certain funds that, due to their ownership structure, are accounted for by the Company using the equity method. In applying the equity method, these investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the fair value of the underlying securities in the funds). Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds. Changes in the carrying value of such investments are recorded in net income as “Equity in net income (loss) of investments accounted for using the equity method.” As such, fluctuations in the carrying value of the investments accounted for using the equity method may increase the volatility of the Company’s reported results of operations.

The Company’s investment portfolio includes equity securities that are accounted for at fair value. Such holdings primarily include publicly traded common stocks. Dividend income on equities is reflected in net investment income. Changes in fair value on equity securities are included in “Net realized gains (losses)” in the consolidated statement of income.

The Company elected to carry certain fixed maturity securities, equity securities, short-term investments and other investments at fair value under the fair value option afforded by accounting guidance regarding the fair value option for financial assets and liabilities. The fair value for certain of the Company’s other investments are determined using net asset values (“NAVs”) as advised by external fund managers. The NAV is based on the fund manager’s valuation of the underlying holdings in accordance with the fund’s governing documents.

Changes in fair value of investments accounted for using the fair value option are included in “Net realized gains (losses).” The primary reasons for electing the fair value option were to address simplification and cost-benefit considerations.

The Company invests in reverse repurchase agreements that are generally treated as collateralized receivables. Receivables for reverse repurchase agreements are reflected in “Other investments” or “Short-term investments” in the Company's consolidated balance sheet depending on their terms. These agreements are recorded at their contracted resale amount plus accrued interest, other than those that are accounted for at fair value. In reverse repurchase transactions, the Company obtains an interest in the purchased assets that are received as collateral.

The Company invests in limited partner interests and shares of limited liability companies. Such amounts are included in investments accounted for using the equity method and other investments. These investments can often have characteristics of a variable interest entity (“VIE”). A VIE refers to entities that have characteristics such as (i) insufficient equity at risk to allow the entity to finance its activities without additional financial support or (ii) instances where the equity investors, as a group, do not have the characteristic of a controlling financial interest. If the Company is determined to be the primary beneficiary, it is required to consolidate the VIE. The primary beneficiary is defined as the variable interest holder that is determined to have the controlling financial interest as a result of having both (i) the power to direct the activities of a VIE that most significantly impact the economic performance of the VIE and (ii) the obligation to absorb losses or right to receive benefits from the VIE that could potentially be significant to the VIE. At inception of the VIE as well as on an ongoing basis, the Company determines whether it is the primary beneficiary based on an analysis of the Company’s level of involvement in the VIE, the

contractual terms, and the overall structure of the VIE. The Company's maximum exposure to loss with respect to these investments is limited to the investment carrying amounts reported in the Company's consolidated balance sheet and any unfunded commitment.

The Company conducts a periodic review to identify and evaluate credit based impairments related to the Company’s available for sale investments. The Company derives estimated credit losses by comparing expected future cash flows to be collected to the amortized cost of the security. Estimates of expected future cash flows consider among other things, macroeconomic conditions as well as the financial condition, near-term and long-term prospects for the issuer, and the likelihood of the recoverability of principal and interest. Effective January 1, 2020, credit losses are recognized through an allowance account subject to reversal, rather than a reduction in amortized cost. Declines in value attributable to factors other than credit are reported as an unrealized loss in other comprehensive income while the allowance for credit loss is charged to net realized gains (losses) in the consolidated statement of income.

For available for sale investments that the Company intends to sell or for which it is more likely than not that the Company would be required to sell before an anticipated recovery in value, the full amount of the impairment is included in net realized gains (losses). The new cost basis of the investment is the previous amortized cost basis reduced by the impairment recognized in net realized gains (losses). The new cost basis is not adjusted for any subsequent recoveries in fair value.

The Company reports accrued investment income separately from investment balances and has elected not to measure an allowance for credit losses for accrued investment income. Any uncollectible accrued interest income is written off in the period it is deemed uncollectible.

Net investment income includes interest and dividend income together with amortization of market premiums and discounts and is net of investment management and custody fees. Anticipated prepayments and expected maturities are used in applying the interest method for certain investments such as mortgage and other asset-backed securities. When actual prepayments differ significantly from anticipated prepayments, the effective yield is recalculated to reflect actual payments to date and anticipated future payments. The net investment in such securities is adjusted to the amount that would have existed had the new effective yield been applied since the acquisition of the security. Such adjustments, if any, are included in net investment income when determined.

Investment gains or losses realized on the sale of investments, except for certain fund investments, are determined on a first-in, first-out basis and are reflected in net income. Investment gains or losses realized on the sale of certain fund investments are determined on an average cost basis. Unrealized appreciation or decline in the value of available for sale securities, which are carried at fair value, is excluded from net income and recorded as a separate component of accumulated other comprehensive income, net of applicable deferred income tax.

Derivative instruments

The Company recognizes all derivative instruments, including embedded derivative instruments, at fair value in its consolidated balance sheets. The Company employs the use of derivative instruments within its operations to mitigate risks arising from assets and liabilities held in foreign currencies as well as part of its overall investment strategy. For such instruments, changes in assets and liabilities measured at fair value are recorded as “Net realized gains (losses)” in the consolidated statements of income. In addition, the Company’s derivative instruments include amounts related to underwriting activities where an insurance or reinsurance contract meets the accounting definition of a derivative instrument. For such contracts, changes in fair value are reflected in “Other underwriting income” in the consolidated statements of income as the underlying contract originates from the Company’s underwriting operations. For the periods ended 2022, 2021, and 2020, the Company did not designate any derivative instruments as hedges under the relevant accounting guidance. See note 11, “Derivative Instruments” for additional information.

Reserves for losses and loss adjustment expenses

Insurance and Reinsurance. The reserve for losses and loss adjustment expenses consists of estimates of unpaid reported losses and loss adjustment expenses and estimates for losses incurred but not reported. The reserve for unpaid reported losses and loss adjustment expenses, established by management based on reports from ceding companies and claims from insureds, excludes estimates of amounts related to losses under high deductible policies, and represents the estimated ultimate cost of events or conditions that have been reported to or specifically identified by the Company. Such reserves are supplemented by management’s estimates of reserves for losses incurred for which reports or claims have not been received. The Company’s reserves are based on a combination of reserving methods, incorporating both Company and industry loss development patterns. The Company selects the initial expected loss and loss adjustment expense ratios based on information derived by its underwriters and actuaries during the initial pricing of the business, supplemented by industry data where appropriate. Such ratios consider, among other things, rate changes and

changes in terms and conditions that have been observed in the market. These estimates are reviewed regularly and, as experience develops and new information becomes known, the reserves are adjusted as necessary. Such adjustments, if any, are reflected in income in the period in which they are determined. As actual loss information has been reported, the Company has developed its own loss experience and its reserving methods include other actuarial techniques. Over time, such techniques have been given further weight in its reserving process based on the continuing maturation of the Company’s reserves. Inherent in the estimates of ultimate losses and loss adjustment expenses are expected trends in claims severity and frequency and other factors which may vary significantly as claims are settled. Accordingly, ultimate losses and loss adjustment expenses may differ materially from the amounts recorded in the accompanying consolidated financial statements. Losses and loss adjustment expenses are recorded on an undiscounted basis, except for excess workers’ compensation and employers’ liability business written by the Company’s insurance operations.

Mortgage. The reserves for mortgage guaranty insurance losses and loss adjustment expenses are the estimated claim settlement costs on notices of delinquency that have been received by the Company, as well as loan delinquencies that have been incurred but have not been reported by the lenders. Consistent with primary mortgage insurance industry accounting practice, the Company does not establish loss reserves for future claims on insured loans that are not currently delinquent (defined as two or more payments in arrears). The Company establishes loss reserves on a case-by-case basis when insured loans are reported delinquent using estimated claim rates and average claim sizes for each cohort, net of any salvage recoverable. The Company also reserves for delinquencies that have occurred but have not yet been reported to the Company prior to the close of an accounting period. To determine this reserve, the Company estimates the number of delinquencies not yet reported using historical information regarding late reported delinquencies and applies estimated claim rates and claim sizes for the estimated delinquencies not yet reported.

The establishment of reserves across the Company’s segments is an inherently uncertain process, are necessarily based on estimates, and the ultimate net cost may vary from such estimates. The methods for making such estimates and for establishing the resulting liability are reviewed and updated using the most current information available. Any resulting adjustments, which may be material, are reflected in current operations.

Contractholders receivables and payables

Certain insurance policies written by the Company’s U.S. insurance operations feature large deductibles, primarily in its construction and national accounts line of business. Under such contracts, the Company is obligated to pay the claimant for the full amount of the claim. The Company is subsequently reimbursed by the policy holder for the deductible amount. These amounts are included on a gross basis in the consolidated balance sheet as contractholder payables and contractholder receivables. In the event that the Company is unable to collect from the policyholder, the Company would be liable for such defaulted amounts. Collateral, primarily in the form of letters of credit, cash and trusts, is obtained from the policyholder to mitigate the Company’s credit risk. In the instances where the Company receives collateral in the form of cash, the Company reflects it in “Collateral held for insured obligations.”

Contractholder receivables are reported net of an allowance for expected credit losses. The allowance is based upon the Company’s ongoing review of amounts outstanding, changes in policyholder credit standing, amounts and form of collateral obtained, and other relevant factors. A ratings based probability-of-default and loss-given-default methodology is used to estimate the allowance for expected credit losses. Any allowance for credit losses is charged to net realized gains (losses) in the period the receivable is recorded and revised in subsequent periods to reflect changes in the Company’s estimate of expected credit losses. See note 7, “Allowance for Expected Credit Losses” for additional information.

Foreign exchange

Assets and liabilities of foreign operations whose functional currency is not the U.S. Dollar are translated at the prevailing exchange rates at each balance sheet date. Revenues and expenses of such foreign operations are translated at average exchange rates during the year. The net effect of the translation adjustments for foreign operations is included in accumulated other comprehensive income, net of applicable deferred income tax. Monetary assets and liabilities, such as premiums receivable and the reserve for losses and loss adjustment expenses, denominated in foreign currencies are revalued at the exchange rate in effect at the balance sheet date with the resulting foreign exchange gains and losses included in net income. Accounts that are classified as non-monetary, such as deferred acquisition costs and the unearned premium reserves, are not revalued. In the case of foreign currency denominated fixed maturity securities which are classified as “available for sale,” the change in exchange rates between the local currency in which the investments are denominated and the Company’s functional currency at each balance sheet date is included in unrealized appreciation or decline in value of securities, a component of accumulated other comprehensive income, net of applicable deferred income tax.

Income taxes

Deferred income taxes reflect the expected future tax consequences of temporary differences between the carrying amounts of assets and liabilities for financial reporting purposes and amounts used for income tax purposes. A valuation allowance is recorded if it is more likely than not that some or all of a deferred tax asset may not be realized. The Company considers future taxable income and feasible tax planning strategies in assessing the need for a valuation allowance. In the event the Company determines that it will not be able to realize all or part of its deferred income tax assets in the future, an adjustment to the deferred income tax assets would be charged to income in the period in which such determination is made. In addition, if the Company subsequently assesses that the valuation allowance is no longer needed, a benefit would be recorded to income in the period in which such determination is made. See note 15, “Income Taxes” for additional information.

The Company recognizes a tax benefit where it concludes that it is more likely than not that the tax benefit will be sustained on audit by the taxing authority based solely on the technical merits of the associated tax position. If the recognition threshold is met, the Company recognizes a tax benefit measured at the largest amount of the tax benefit that, in the Company’s judgment, is greater than 50% likely to be realized. The Company records interest and penalties related to unrecognized tax benefits in the provision for income taxes.

Share-based payment arrangements

The Company applies a fair value based measurement method in accounting for its share-based payment arrangements with eligible employees and directors. Compensation expense is estimated based on the fair value of the award at the grant date and is recognized in net income over the requisite service period with a corresponding increase in shareholders’ equity. No value is attributed to awards that employees forfeit because they fail to satisfy vesting conditions. The Company’s (i) time-based awards generally vest over a three year period with one-third vesting on the first, second and third anniversaries of the grant date and (ii) performance-based awards cliff vest after each three year performance period based on achievement of the specified performance criteria. The share-based compensation expense associated with awards that have graded vesting features and vest based on service conditions only is calculated on a straight-line basis over the requisite service period for the entire award. Compensation expense recognized in connection with performance awards is based on the achievement of the specified performance and service conditions. The final measure of compensation expense recognized over the requisite service period reflects the final performance outcome. During the recognition period compensation expense is accrued based on the performance condition that is probable of achievement. For awards granted to retirement-eligible employees where no service is required for the employee to retain the award, the grant date fair value is immediately recognized as compensation expense at the grant date because the employee is able to retain the award without continuing to provide service. For employees near retirement eligibility, attribution of compensation cost is over the period from the grant date to the retirement eligibility date. These charges had no impact on the Company’s cash flows or total shareholders’ equity. See note 22, “Share-Based Compensation” for information relating to the Company’s share-based payment awards.

Guaranty fund and other related assessments

Liabilities for guaranty fund and other related assessments in the Company’s insurance and reinsurance operations are accrued when the Company receives notice that an amount is payable, or earlier if a reasonable estimate of the assessment can be made.

Treasury shares

Treasury shares are common shares purchased by the Company and not subsequently canceled. These shares are recorded at cost and result in a reduction of the Company’s shareholders’ equity in its Consolidated Balance Sheets.

Goodwill and intangible assets

Goodwill represents the excess of the purchase price of business combination over the fair value of the net assets acquired and is assigned to the applicable reporting unit at acquisition. Goodwill is evaluated for impairment on an annual basis. Impairment tests may be performed more frequently if the facts and circumstances indicate a possible impairment. In performing impairment tests, the Company may first assess qualitative factors to determine whether it is more likely than not (that is, more than a 50% probability) that the fair value of a reporting unit exceeds its carrying amount as a basis for determining whether it is necessary to perform goodwill impairment test described in the accounting guidance.

Indefinite-lived intangible assets, such as insurance licenses are evaluated for impairment similar to goodwill. Finite-lived intangible assets and liabilities include the value of acquired insurance and reinsurance contracts, which are estimated based on the present value of future expected cash flows and amortized in proportion to the estimated profits expected to be realized. Other finite-lived intangible assets, including

customer lists, trade name and IT platforms, are amortized over their useful lives. Finite-lived intangible assets and liabilities are periodically reviewed for indicators of impairment. An impairment is recognized when the carrying amount is not recoverable from its undiscounted cash flows and is measured as the difference between the carrying amount and fair value.

If goodwill or intangible assets are impaired, such assets are written down to their fair values with the related expense recorded in the Company’s results of operations.

Investment in operating affiliates

Investment in operating affiliates primarily represent the Company’s investments in which it has significant influence and which are accounted for under the equity method of accounting. In applying the equity method of accounting, investments in operating affiliates are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of net income or loss of the operating affiliate. The Company records its proportionate share of other comprehensive income or loss of the operating affiliate as a component of other comprehensive income. Adjustments are based on the most recently available financial information from the operating affiliate. Changes in the carrying value of these investments are recorded in income (loss) from operating affiliates.

Recent accounting pronouncements

Recently Issued Accounting Standards Adopted

The Company adopted ASU 2019-12, “Simplifying the Accounting for Income Taxes.” This ASU eliminates certain exceptions for recognizing deferred taxes for investments, performing intraperiod tax allocations and calculating income taxes in interim periods. The ASU also clarifies the accounting for transactions that result in a step-up in the tax basis of goodwill. The adoption of this guidance did not have a material effect on the Company’s consolidated financial statements.

Recently Issued Accounting Standards Not Yet Adopted

ASU 2020-04, “Facilitation of the Effects of Reference Rate Reform on Financial Reporting,” was issued in March 2020 and amended in December 2022 with ASU 2022-06, “Reference Rate Reform (Topic 848)”. This ASU provides optional expedients and exceptions for applying GAAP to investments, derivatives, or other transactions that reference the London Interbank Offered Rate (“LIBOR”) or another reference rate expected to be discontinued because of reference rate reform. Along with the optional expedients, the amendments include a general principle that permits an entity to consider contract modifications due to reference reform to be an event that does not require contract re-measurement at the modification date or reassessment of a previous accounting determination. The amendment deferred the sunset date from December 31, 2022 to December 31, 2024. As a result, this standard can be adopted no later than December 31, 2024, with early adoption permitted. Based on its current analysis, the Company does not expect that the new guidance will have a material effect on the Company’s consolidated financial statements.

Funds held arrangements

Funds held arrangements are agreements with a third party reinsurance company, where the reinsured retains the related assets on a funds held basis. Such amounts are included in “Other assets” on the Company’s balance sheet. Investment returns produced by those assets are recorded as part of net investment income and net realized gains (losses) in the Company's consolidated results of operations. Funds held as collateral by the Company are included in “Other liabilities” and changes to the funds held liability are reflected as part of interest expense in the Company’s consolidated results of operations.

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Segment Information (Tables)

12 Months Ended

Dec. 31, 2022

Segment Reporting [Abstract]

Analysis of underwriting income (loss) by segment and reconciliation to net income (loss) available to common shareholders

The following tables summarize the Company’s underwriting income or loss by segment, together with a reconciliation of underwriting income or loss to net income available to Arch common shareholders, summary information regarding net premiums written and earned by major line of business and net premiums written by location:

	Year Ended December 31, 2022
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	6,930,864		$	6,948,438		$	1,454,971		$	15,326,447		$	—		$	15,326,447
Premiums ceded	(1,910,222)			(2,024,462)			(322,400)			(4,249,258)			—			(4,249,258)
Net premiums written	5,020,642			4,923,976			1,132,571			11,077,189			—			11,077,189
Change in unearned premiums	(461,307)			(964,595)			26,790			(1,399,112)			—			(1,399,112)
Net premiums earned	4,559,335			3,959,381			1,159,361			9,678,077			—			9,678,077
Other underwriting income	—			4,871			8,356			13,227			—			13,227
Losses and loss adjustment expenses	(2,782,945)			(2,568,843)			324,271			(5,027,517)			—			(5,027,517)
Acquisition expenses	(885,866)			(813,555)			(40,159)			(1,739,580)			—			(1,739,580)
Other operating expenses	(665,472)			(267,531)			(195,172)			(1,128,175)			—			(1,128,175)
Underwriting income	$	225,052		$	314,323		$	1,256,657		1,796,032			—			1,796,032
Net investment income										496,547			—			496,547
Net realized gains (losses)										(662,734)			—			(662,734)
Equity in net income (loss) of investments accounted for using the equity method										115,856			—			115,856
Other income (loss)										(26,165)			—			(26,165)
Corporate expenses										(94,390)			—			(94,390)
Transaction costs and other										(1,092)			—			(1,092)
Amortization of intangible assets										(106,200)			—			(106,200)
Interest expense										(130,266)			—			(130,266)
Net foreign exchange gains (losses)										100,905			—			100,905
Income (loss) before income taxes and income (loss) from operating affiliates										1,488,493			—			1,488,493
Income tax expense										(79,961)			—			(79,961)
Income (loss) from operating affiliates										73,891			—			73,891
Net income (loss)										1,482,423			—			1,482,423
Amounts attributable to redeemable noncontrolling interests										(5,490)			—			(5,490)
Net income (loss) available to Arch										1,476,933			—			1,476,933
Preferred dividends										(40,736)			—			(40,736)
Net income (loss) available to Arch common shareholders										$	1,436,197		$	—		$	1,436,197
Underwriting Ratios
Loss ratio	61.0		%	64.9		%	-28.0		%	51.9		%	—		%	51.9		%
Acquisition expense ratio	19.4		%	20.5		%	3.5		%	18.0		%	—		%	18.0		%
Other operating expense ratio	14.6		%	6.8		%	16.8		%	11.7		%	—		%	11.7		%
Combined ratio	95.0		%	92.2		%	-7.7		%	81.6		%	—		%	81.6		%
Goodwill and intangible assets	$	228,532		$	144,846		$	430,911		$	804,289		$	—		$	804,289
Total investable assets										$	28,065,497		$	—		$	28,065,497
Total assets										47,990,507			—			47,990,507
Total liabilities										35,069,605			—			35,069,605

(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

	Year Ended December 31, 2021
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	5,867,734		$	5,093,930		$	1,507,825		$	12,463,788		$	457,465		$	12,752,487
Premiums ceded	(1,719,541)			(1,839,556)			(246,757)			(3,800,153)			(102,763)			(3,734,150)
Net premiums written	4,148,193			3,254,374			1,261,068			8,663,635			354,702			9,018,337
Change in unearned premiums	(521,725)			(413,931)			22,351			(913,305)			(22,734)			(936,039)
Net premiums earned	3,626,468			2,840,443			1,283,419			7,750,330			331,968			8,082,298
Other underwriting income	—			3,669			17,665			21,334			739			22,073
Losses and loss adjustment expenses	(2,344,365)			(1,924,719)			(56,677)			(4,325,761)			(259,042)			(4,584,803)
Acquisition expenses, net	(606,265)			(536,754)			(97,418)			(1,240,437)			(62,741)			(1,303,178)
Other operating expenses	(558,906)			(212,810)			(194,010)			(965,726)			(32,869)			(998,595)
Underwriting income (loss)	$	116,932		$	169,829		$	952,979		1,239,740			(21,945)			1,217,795
Net investment income										346,808			42,310			389,118
Net realized gains (losses)										299,207			80,638			379,845
Equity in net income (loss) of investments accounted for using the equity method										366,402			—			366,402
Other income (loss)										10,244			—			10,244
Corporate expenses										(77,119)			—			(77,119)
Transaction costs and other										(1,103)			(935)			(2,038)
Amortization of intangible assets										(82,057)			(898)			(82,955)
Interest expense										(131,060)			(8,410)			(139,470)
Net foreign exchange gains (losses)										42,854			(1,325)			41,529
Income (loss) before income taxes and income (loss) from operating affiliates										2,013,916			89,435			2,103,351
Income tax expense										(128,348)			(234)			(128,582)
Income (loss) from operating affiliates										264,693			—			264,693
Net income (loss)										2,150,261			89,201			2,239,462
Amounts attributable to redeemable noncontrolling interests										(2,346)			(1,953)			(4,299)
Amounts attributable to nonredeemable noncontrolling interests										—			(78,314)			(78,314)
Net income (loss) available to Arch										2,147,915			8,934			2,156,849
Preferred dividends										(48,343)			—			(48,343)
Loss on redemption of preferred shares										(15,101)			—			(15,101)
Net income (loss) available to Arch common shareholders										$	2,084,471		$	8,934		$	2,093,405
Underwriting Ratios
Loss ratio	64.6		%	67.8		%	4.4		%	55.8		%	78.0		%	56.7		%
Acquisition expense ratio	16.7		%	18.9		%	7.6		%	16.0		%	18.9		%	16.1		%
Other operating expense ratio	15.4		%	7.5		%	15.1		%	12.5		%	9.9		%	12.4		%
Combined ratio	96.7		%	94.2		%	27.1		%	84.3		%	106.8		%	85.2		%
Goodwill and intangible assets	$	256,434		$	183,523		$	505,026		$	944,983		$	—		$	944,983
Total investable assets										$	27,442,153		$	—		$	27,442,153
Total assets										45,100,945			—			45,100,945
Total liabilities										31,545,816			—			31,545,816

(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

	Year Ended December 31, 2020
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	4,688,562		$	3,472,086		$	1,473,999		$	9,632,691		$	728,546		$	10,088,068
Premiums ceded	(1,525,655)			(1,014,716)			(194,149)			(2,732,564)			(190,957)			(2,650,352)
Net premiums written	3,162,907			2,457,370			1,279,850			6,900,127			537,589			7,437,716
Change in unearned premiums	(291,487)			(295,141)			118,085			(468,543)			22,762			(445,781)
Net premiums earned	2,871,420			2,162,229			1,397,935			6,431,584			560,351			6,991,935
Other underwriting income	(31)			4,454			20,316			24,739			2,045			26,784
Losses and loss adjustment expenses	(2,092,453)			(1,628,320)			(528,344)			(4,249,117)			(440,482)			(4,689,599)
Acquisition expenses, net	(418,483)			(354,048)			(134,240)			(906,771)			(98,071)			(1,004,842)
Other operating expenses	(489,153)			(168,011)			(162,202)			(819,366)			(55,810)			(875,176)
Underwriting income (loss)	$	(128,700)		$	16,304		$	593,465		481,069			(31,967)			449,102
Net investment income										401,908			117,700			519,608
Net realized gains (losses)										813,781			9,679			823,460
Equity in net income (loss) of investments accounted for using the equity method										146,693			—			146,693
Other income (loss)										29			—			29
Corporate expenses										(68,492)			—			(68,492)
Transaction costs and other										(9,456)			(4,040)			(13,496)
Amortization of intangible assets										(69,031)			—			(69,031)
Interest expense										(120,214)			(23,242)			(143,456)
Net foreign exchange gains (losses)										(80,161)			(3,473)			(83,634)
Income (loss) before income taxes and income (loss) from operating affiliates										1,496,126			64,657			1,560,783
Income tax expense										(111,812)			(26)			(111,838)
Income (loss) from operating affiliates										16,766			—			16,766
Net income										1,401,080			64,631			1,465,711
Amounts attributable to redeemable noncontrolling interests										(2,997)			(4,117)			(7,114)
Amounts attributable to nonredeemable noncontrolling interests										—			(53,076)			(53,076)
Net income (loss) available to Arch										1,398,083			7,438			1,405,521
Preferred dividends										(41,612)			—			(41,612)
Net income (loss) available to Arch common shareholders										$	1,356,471		$	7,438		$	1,363,909
Underwriting Ratios
Loss ratio	72.9		%	75.3		%	37.8		%	66.1		%	78.6		%	67.1		%
Acquisition expense ratio	14.6		%	16.4		%	9.6		%	14.1		%	17.5		%	14.4		%
Other operating expense ratio	17.0		%	7.8		%	11.6		%	12.7		%	10.0		%	12.5		%
Combined ratio	104.5		%	99.5		%	59.0		%	92.9		%	106.1		%	94.0		%
Goodwill and intangible assets	$	280,978		$	18,963		$	385,272		$	685,213		$	7,650		$	692,863
Total investable assets										$	26,856,295		$	2,657,612		$	29,513,907
Total assets										39,791,983			3,490,314			43,282,297
Total liabilities										26,789,149			2,505,707			29,294,856

(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

Summary of information regarding net premiums written and earned by major line of business and net premiums written by location

The following tables provide summary information regarding net premiums earned by major line of business and net premiums written by underwriting location:

INSURANCE SEGMENT	Year Ended December 31,
	2022		2021		2020
Net premiums earned (1)
Professional lines	$	1,314,236	$	942,817	$	655,872
Property, energy, marine and aviation	772,388		667,892		506,182
Programs	589,860		506,867		432,854
Travel, accident and health	491,847		255,590		190,944
Construction and national accounts	432,020		416,107		398,999
Excess and surplus casualty	393,353		318,027		270,620
Warranty and lenders solutions	127,222		153,958		114,687
Other	438,409		365,210		301,262
Total	$	4,559,335	$	3,626,468	$	2,871,420
Net premiums written by underwriting location (1)
United States	$	3,340,038	$	2,813,039	$	2,158,415
Europe	1,405,719		1,125,192		856,572
Other	274,885		209,962		147,920
Total	$	5,020,642	$	4,148,193	$	3,162,907

REINSURANCE SEGMENT	Year Ended December 31,
	2022		2021		2020
Net premiums earned (1)
Other specialty	$	1,377,880	$	818,801	$	626,409
Property excluding property catastrophe	1,091,440		836,573		562,208
Casualty	854,543		666,754		549,056
Property catastrophe	366,991		280,738		237,736
Marine and aviation	159,401		152,955		109,624
Other	109,126		84,622		77,196
Total	$	3,959,381	$	2,840,443	$	2,162,229
Net premiums written by underwriting location (1)
United States	$	1,246,507	$	828,504	$	687,622
Bermuda	2,561,771		1,557,294		1,001,990
Europe and other	1,115,698		868,576		767,758
Total	$	4,923,976	$	3,254,374	$	2,457,370

MORTGAGE SEGMENT	Year Ended December 31,
	2022		2021		2020
Net premiums earned by underwriting location
United States	$	815,519	$	970,507	$	1,158,563
Other	343,842		312,912		239,372
Total	$	1,159,361	$	1,283,419	$	1,397,935
Net premiums written by underwriting location
United States	$	780,256	$	914,477	$	1,021,950
Other	352,315		346,591		257,900
Total	$	1,132,571	$	1,261,068	$	1,279,850

(1)    Segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions.

OTHER SEGMENT	Year Ended December 31,
	2022		2021		2020
Net premiums earned (1)
Casualty	$	—	$	138,551	$	245,272
Other specialty	—		118,356		186,717
Property catastrophe	—		15,235		23,037
Property excluding property catastrophe	—		6,578		1,130
Marine and aviation	—		190		429
Other	—		53,058		103,766
Total	$	—	$	331,968	$	560,351
Net premiums written by underwriting location (1)
United States	$	—	$	63,403	$	115,471
Europe	—		91,499		97,753
Bermuda	—		199,800		324,365
Total	$	—	$	354,702	$	537,589

(1)    Segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions.

XML

Reserve for Losses and Loss Adjustment Expenses (Tables)

12 Months Ended

Dec. 31, 2022

Liability for Future Policy Benefits and Unpaid Claims and Claims Adjustment Expense [Abstract]

Analysis of losses and loss adjustment expenses and reconciliation of beginning and ending reserve balances

The following table represents an analysis of losses and loss adjustment expenses and a reconciliation of the beginning and ending reserve for losses and loss adjustment expenses:

	Year Ended December 31,
	2022		2021		2020
Reserve for losses and loss adjustment expenses at beginning of year	$	17,757,156	$	16,513,929	$	13,891,842
Unpaid losses and loss adjustment expenses recoverable	5,599,231		4,314,855		4,082,650
Net reserve for losses and loss adjustment expenses at beginning of year	12,157,925		12,199,074		9,809,192
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year	5,798,528		4,940,987		4,851,051
Prior years	(771,011)		(356,184)		(161,452)
Total net incurred losses and loss adjustment expenses	5,027,517		4,584,803		4,689,599
Net losses and loss adjustment expense reserves of acquired business (1)	—		104,176		—
Retroactive reinsurance transactions (2)	—		(444,147)		182,210
Impact of deconsolidation of Somers (3)	—		(1,460,611)		—
Foreign exchange (gains) losses and other	(290,376)		1,181		179,190
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year	(887,464)		(734,846)		(661,529)
Prior years	(2,254,484)		(2,091,705)		(1,999,588)
Total net paid losses and loss adjustment expenses	(3,141,948)		(2,826,551)		(2,661,117)
Net reserve for losses and loss adjustment expenses at end of year	13,753,118		12,157,925		12,199,074
Unpaid losses and loss adjustment expenses recoverable	6,278,825		5,599,231		4,314,855
Reserve for losses and loss adjustment expenses at end of year	$	20,031,943	$	17,757,156	$	16,513,929

(1)    Represents activity related to the Company’s acquisitions in the 2021 period. See note 2, “Acquisitions.”

(2)    See ‘Retroactive Reinsurance Transactions’ section.

(3)    See note 12, “Variable Interest Entity and Noncontrolling Interests.”

XML

Short Duration Contracts (Tables)

12 Months Ended

Dec. 31, 2022

Short Duration Contracts Disclosure [Abstract]

Levels of disaggregation

The Company’s reserves for losses and loss adjustment expenses primarily relate to short-duration contracts with various characteristics (e.g., type of coverage, geography, claims duration). The Company considered such information in determining the level of disaggregation for disclosures related to its short-duration contracts, as detailed in the table below:

Reportable segment	Level of disaggregation	Included lines of business
Insurance	Property energy, marine and aviation	Property energy, marine and aviation
	Third party occurrence business	Excess and surplus casualty (excluding contract binding); construction and national accounts; and other (including alternative market risks, excess workers’ compensation and employer’s liability insurance coverages)
	Third party claims-made business	Professional lines
	Multi-line and other specialty	Programs; contract binding (part of excess and surplus casualty); travel, accident and health; warranty and lenders solutions; and other (contract and commercial surety coverages)
Reinsurance	Casualty	Casualty
	Property catastrophe	Property catastrophe
	Property excluding property catastrophe	Property excluding property catastrophe
	Marine and aviation	Marine and aviation
	Other specialty	Other specialty
Mortgage	Direct mortgage insurance in the U.S.	Mortgage insurance on U.S. primary exposures

Claims Development [Line Items]

Reconciliation of claims development to liability

The following table represents a reconciliation of the disclosures of net incurred and paid loss development tables to the reserve for losses and loss adjustment expenses at December 31, 2022:

	December 31, 2022
Net outstanding liabilities
Insurance
Property, energy, marine and aviation	$	750,461
Third party occurrence business	3,184,995
Third party claims-made business	1,991,302
Multi-line and other specialty	1,215,721
Reinsurance
Casualty	2,323,825
Property catastrophe	535,158
Property excluding property catastrophe	1,010,604
Marine and aviation	289,944
Other specialty	1,444,921
Mortgage
U.S. primary	397,118
Other short duration lines not included in disclosures	301,222
Total for short duration lines	13,445,271
Unpaid losses and loss adjustment expenses recoverable
Insurance
Property, energy, marine and aviation	423,740
Third party occurrence business	1,761,871
Third party claims-made business	995,921
Multi-line and other specialty	173,051
Reinsurance
Casualty	684,663
Property catastrophe	595,740
Property excluding property catastrophe	206,867
Marine and aviation	186,416
Other specialty	656,130
Mortgage
U.S. primary	37,531
Other short duration lines not included in disclosures (1)	560,642
Intercompany eliminations	(3,747)
Total for short duration lines	6,278,825
Lines other than short duration	102,283
Discounting	(60,536)
Unallocated claims adjustment expenses	266,100
	307,847
Total gross reserves for losses and loss adjustment expenses	$	20,031,943

(1)    Includes unpaid loss and loss adjustment expenses recoverable of $280.2 million related to the loss portfolio transfer reinsurance agreements.

Insurance

Claims Development [Line Items]

Claims development tables

The following tables present information on the insurance segment’s short-duration insurance contracts:

Property, energy, marine and aviation ($000’s except claim count)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	158,548	$	156,147	$	148,622	$	142,889	$	134,473	$	133,400	$	128,157	$	126,825	$	125,813	$	124,868	$	27	3,982
2014			148,104		145,679		147,248		136,050		132,166		134,192		134,895		134,803		133,605		1,674		3,557
2015					112,299		109,769		103,921		102,449		97,789		91,770		91,833		90,816		2,654		4,244
2016							104,002		100,843		105,184		100,003		95,989		92,108		87,618		61		5,704
2017									280,686		246,264		235,924		230,413		231,199		225,298		3,268		6,287
2018											180,981		186,030		173,693		170,057		170,411		7,177		5,048
2019													179,056		178,564		165,477		161,156		4,162		5,942
2020															359,394		329,362		335,747		28,330		8,546
2021																	426,870		428,719		54,746		7,566
2022																			521,750		208,080		8,965
																	Total		$	2,279,988
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	32,216	$	84,680	$	110,432	$	119,649	$	121,779	$	125,014	$	122,894	$	124,227	$	124,381	$	124,402
2014			25,849		53,632		77,764		84,061		87,681		98,423		115,253		122,165		122,792
2015					23,561		64,900		76,282		86,196		87,870		86,190		87,260		87,564
2016							24,684		83,218		98,303		97,089		94,570		90,808		87,232
2017									30,215		139,849		195,512		211,688		215,874		217,764
2018											30,026		102,285		134,858		142,838		149,663
2019													26,130		105,380		133,911		139,141
2020															55,619		194,487		251,055
2021																	90,423		267,677
2022																			100,476
									Total										1,547,766
									All outstanding liabilities before 2013, net of reinsurance										18,239
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	750,461

Third party occurrence business ($000’s except claim count)
	Incurred losses and allocated loss adjustment expenses, net of reinsurance																				December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	282,852	$	296,668	$	306,572	$	301,622	$	281,637	$	274,246	$	272,385	$	269,297	$	270,110	$	263,430	$	43,148	66,118
2014			329,718		335,587		338,505		342,759		339,403		343,904		342,641		343,286		345,024		60,263		75,557
2015					358,769		391,570		398,565		391,797		391,132		382,427		386,465		379,226		75,540		78,507
2016							389,530		394,190		405,803		399,315		374,654		367,586		363,453		93,800		78,576
2017									417,097		417,662		422,360		412,231		406,857		406,165		114,603		84,418
2018											430,128		452,879		450,647		451,164		458,050		156,700		77,685
2019													455,928		487,080		480,535		471,279		195,283		84,985
2020															606,640		616,314		640,231		309,019		90,795
2021																	621,972		662,716		431,302		89,718
2022																			688,082		614,366		70,380
																	Total		$	4,677,656
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	6,840	$	29,215	$	71,335	$	101,153	$	122,045	$	149,012	$	164,090	$	174,591	$	184,444	$	192,159
2014			9,200		40,226		71,473		112,541		161,935		191,108		211,440		223,895		237,135
2015					11,110		44,514		88,411		139,364		181,505		211,510		227,439		249,399
2016							11,679		41,920		87,543		136,759		164,534		194,637		215,481
2017									13,391		52,309		99,806		134,988		165,468		220,660
2018											16,991		63,776		115,049		154,138		198,502
2019													18,375		73,075		121,646		172,948
2020															24,407		76,567		154,902
2021																	26,235		90,791
2022																			23,981
									Total										1,755,958
									All outstanding liabilities before 2013, net of reinsurance										263,297
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	3,184,995

Third party claims-made business ($000’s except claim count)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	301,608	$	320,266	$	324,044	$	320,177	$	294,372	$	290,852	$	281,642	$	271,156	$	273,607	$	281,584	$	14,639	14,953
2014			264,273		279,410		298,541		278,556		281,271		297,248		291,498		287,573		296,153		21,206		15,482
2015					258,740		277,358		276,256		259,830		255,207		252,263		267,725		266,758		18,198		14,392
2016							274,996		291,258		308,080		314,412		321,764		326,960		329,534		29,356		15,083
2017									270,272		285,738		311,724		308,172		323,128		316,673		45,042		15,198
2018											272,543		314,112		319,646		336,106		347,449		61,612		15,934
2019													289,128		317,312		317,363		322,178		93,422		15,858
2020															383,497		413,156		423,375		187,245		15,438
2021																	514,676		517,975		351,736		15,751
2022																			657,664		575,484		18,190
																	Total		$	3,759,343
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	19,007	$	87,386	$	137,857	$	179,261	$	197,861	$	216,984	$	238,730	$	245,423	$	246,813	$	253,570
2014			13,814		63,288		129,409		172,722		207,447		229,314		243,137		249,307		260,333
2015					9,059		52,007		100,030		126,431		174,084		193,105		216,892		220,871
2016							10,537		68,157		127,203		158,127		205,478		242,300		256,705
2017									9,281		67,529		112,975		143,064		195,788		232,508
2018											12,241		68,244		118,105		158,389		208,063
2019													12,373		65,286		122,046		154,630
2020															17,070		87,248		151,750
2021																	23,253		90,487
2022																			25,244
									Total										1,854,161
									All outstanding liabilities before 2013, net of reinsurance										86,120
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	1,991,302

Multi-line and other specialty ($000’s except claim count)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	264,243	$	272,335	$	263,631	$	263,928	$	251,894	$	253,271	$	248,634	$	245,825	$	245,069	$	244,191	$	2,761	86,371
2014			301,548		325,705		318,453		318,268		317,197		313,221		310,051		309,061		310,977		3,968		130,844
2015					334,684		357,939		356,777		364,815		356,657		349,432		347,206		344,974		5,632		170,579
2016							408,686		430,976		427,829		416,108		409,987		408,004		408,716		8,616		189,406
2017									482,436		501,026		491,347		500,947		504,322		512,717		12,776		229,570
2018											512,406		564,563		562,848		565,116		564,693		21,722		256,621
2019													566,864		612,179		640,262		651,004		38,672		250,441
2020															618,340		569,123		515,016		87,261		162,214
2021																	635,186		618,581		153,336		113,165
2022																			678,479		425,107		89,859
																	Total		$	4,849,348
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	86,680	$	150,925	$	180,428	$	213,461	$	225,324	$	234,330	$	236,375	$	237,293	$	238,321	$	238,257
2014			107,726		196,899		234,267		267,079		281,195		291,727		293,131		294,630		295,896
2015					138,153		236,108		277,850		305,895		320,971		326,652		330,431		331,320
2016							175,948		304,743		341,789		362,823		379,305		385,314		390,350
2017									181,102		342,385		380,696		423,480		446,002		471,978
2018											211,711		389,047		442,643		479,824		508,649
2019													211,970		385,794		486,882		548,844
2020															171,994		309,106		358,967
2021																	156,992		334,549
2022																			177,092
									Total										3,655,902
									All outstanding liabilities before 2013, net of reinsurance										22,275
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	1,215,721

Percentage annual payout by age

The following table presents the average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance, as of December 31, 2022:

	Average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance
	Year 1		Year 2		Year 3		Year 4		Year 5		Year 6		Year 7		Year 8		Year 9		Year 10
Property, energy, marine and aviation	20.3	%	44.2	%	18.4	%	5.2	%	1.5	%	1.1	%	2.0	%	2.2	%	0.3	%	—	%
Third party occurrence business	3.4	%	9.3	%	11.8	%	11.2	%	9.7	%	9.7	%	5.4	%	4.5	%	3.8	%	2.9	%
Third party claims-made business	4.1	%	17.2	%	17.2	%	11.4	%	13.6	%	8.8	%	6.4	%	2.0	%	2.1	%	2.4	%
Multi-line and other specialty	34.3	%	28.9	%	10.9	%	8.8	%	4.5	%	3.1	%	0.9	%	0.4	%	0.4	%	—	%

Reinsurance

Claims Development [Line Items]

Claims development tables

The following tables present information on the reinsurance segment’s short-duration insurance contracts:

Casualty ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	163,425	$	156,619	$	152,392	$	146,230	$	134,204	$	132,701	$	129,120	$	133,401	$	133,687	$	133,094	$	26,542	N/A
2014			212,923		217,991		214,724		227,485		224,105		233,922		234,293		230,944		231,175		33,255		N/A
2015					217,343		216,759		224,385		231,473		235,637		242,554		245,756		247,419		44,753		N/A
2016							208,192		221,004		242,089		257,214		264,573		264,475		268,079		46,122		N/A
2017									262,894		251,827		267,173		293,381		304,194		310,858		52,415		N/A
2018											270,621		284,405		276,802		281,852		293,320		56,325		N/A
2019													325,359		334,755		361,549		372,669		93,310		N/A
2020															378,668		367,595		349,831		169,909		N/A
2021																	434,187		431,165		292,696		N/A
2022																			541,941		482,552		N/A
																	Total		$	3,179,551
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	2,421	$	9,822	$	22,886	$	42,861	$	54,323	$	62,751	$	70,289	$	76,141	$	81,167	$	87,485
2014			3,885		15,973		40,651		63,214		90,530		113,596		133,263		143,929		152,586
2015					4,440		20,208		46,933		70,523		95,988		119,096		136,138		151,119
2016							5,720		25,626		51,494		86,362		112,818		131,341		155,584
2017									6,417		30,316		63,922		112,474		136,489		163,243
2018											7,576		31,240		106,443		128,728		154,173
2019													15,798		57,568		96,593		129,766
2020															17,646		50,383		90,156
2021																	14,633		53,264
2022																			17,638
									Total										1,155,014
									All outstanding liabilities before 2013, net of reinsurance										299,288
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	2,323,825

Property catastrophe ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	65,372	$	45,962	$	34,959	$	30,518	$	27,974	$	27,248	$	26,415	$	26,543	$	26,344	$	26,221	$	(138)	N/A
2014			43,800		29,801		24,500		21,764		20,026		19,326		19,229		19,004		19,045		(10)		N/A
2015					32,748		17,558		11,425		5,531		3,779		3,133		2,932		2,569		68		N/A
2016							23,224		16,582		12,749		9,190		6,886		5,987		5,181		877		N/A
2017									86,410		53,699		49,507		35,893		24,239		21,026		(803)		N/A
2018											73,041		52,001		33,425		19,831		10,722		3,039		N/A
2019													25,526		14,252		13,093		4,590		4,576		N/A
2020															260,244		322,680		326,262		33,413		N/A
2021																	308,014		302,124		29,963		N/A
2022																			299,636		73,474		N/A
																	Total		$	1,017,376
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	12,035	$	18,496	$	23,001	$	24,697	$	26,329	$	26,549	$	26,549	$	27,233	$	26,998	$	27,023
2014			13,619		19,544		17,902		18,679		18,244		18,421		18,550		18,629		18,592
2015					(3,141)		(2,109)		1,843		2,103		1,659		1,745		1,817		1,874
2016							(7,039)		1,759		1,870		2,932		2,086		2,433		2,594
2017									30,625		31,621		37,084		27,060		14,215		16,034
2018											27,424		7,344		18,253		(10,934)		(8,100)
2019													4,374		8,845		12,895		(11,472)
2020															52,592		152,075		200,510
2021																	64,408		167,806
2022																			69,969
									Total										484,830
									All outstanding liabilities before 2013, net of reinsurance										2,612
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	535,158

Property excluding property catastrophe ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	114,775	$	76,290	$	69,981	$	65,734	$	64,013	$	63,247	$	62,070	$	62,774	$	62,288	$	63,390	$	29	N/A
2014			142,092		116,331		98,263		90,031		87,768		83,476		81,812		80,348		79,307		443		N/A
2015					213,681		187,932		183,709		187,569		186,861		175,812		172,189		166,580		3,909		N/A
2016							174,506		144,323		136,367		134,362		138,216		135,116		128,941		6,208		N/A
2017									266,628		247,462		235,310		227,891		212,133		204,128		8,794		N/A
2018											222,932		238,876		234,794		211,852		201,429		7,370		N/A
2019													214,513		204,620		194,164		189,456		8,407		N/A
2020															366,726		338,712		319,097		36,912		N/A
2021																	545,101		497,059		83,934		N/A
2022																			742,703		360,528		N/A
																	Total		$	2,592,090
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	25,943	$	42,418	$	49,433	$	52,614	$	53,400	$	55,272	$	60,777	$	61,640	$	61,665	$	63,228
2014			23,342		62,414		71,144		76,060		77,687		78,067		78,029		77,728		77,894
2015					75,458		118,396		148,887		159,482		164,637		158,293		158,537		159,054
2016							33,236		94,121		97,918		103,202		111,039		113,300		114,432
2017									27,456		124,220		155,139		162,933		177,737		181,029
2018											29,654		107,172		151,632		166,598		174,778
2019													42,919		123,293		149,377		161,573
2020															100,927		207,061		242,844
2021																	135,815		269,481
2022																			142,938
									Total										1,587,251
									All outstanding liabilities before 2013, net of reinsurance										5,765
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	1,010,604

Marine and aviation ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	38,167	$	36,765	$	35,669	$	34,293	$	34,207	$	33,453	$	33,001	$	29,434	$	26,728	$	25,695	$	1,012	N/A
2014			30,566		28,757		26,995		25,297		23,302		22,919		21,698		21,651		18,511		800		N/A
2015					33,134		37,019		31,499		31,373		30,423		28,120		27,299		25,008		1,514		N/A
2016							27,258		22,625		23,448		19,122		16,834		14,896		11,952		4,080		N/A
2017									28,590		26,165		23,613		20,749		19,842		17,329		4,178		N/A
2018											27,613		25,680		24,058		24,192		21,052		3,738		N/A
2019													48,383		54,684		60,321		60,635		5,574		N/A
2020															82,716		75,695		79,338		28,621		N/A
2021																	110,129		95,586		51,391		N/A
2022																			125,685		99,917		N/A
																	Total		$	480,791
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	4,751	$	13,054	$	17,678	$	20,580	$	21,557	$	22,803	$	23,176	$	22,941	$	22,912	$	23,648
2014			4,005		7,795		11,335		12,209		14,368		14,794		15,650		15,729		17,084
2015					(6)		13,321		18,852		20,623		22,318		21,971		22,114		22,297
2016							(7,371)		(1,739)		445		3,169		5,764		6,656		7,028
2017									1,650		6,433		9,249		10,897		11,488		11,817
2018											1,993		6,817		11,021		13,332		13,923
2019													10,537		21,261		28,680		34,637
2020															9,096		26,129		42,203
2021																	8,407		24,108
2022																			12,101
									Total										208,846
									All outstanding liabilities before 2013, net of reinsurance										17,999
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	289,944

Other specialty ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	304,905	$	280,398	$	269,105	$	267,106	$	266,970	$	264,418	$	263,713	$	257,960	$	255,453	$	254,380	$	4,327	N/A
2014			328,056		308,074		310,153		303,589		298,357		299,789		295,270		289,460		287,941		6,034		N/A
2015					271,235		269,237		267,079		263,826		263,985		261,158		250,103		248,848		6,340		N/A
2016							313,982		310,907		303,432		295,116		301,277		296,251		293,571		8,371		N/A
2017									382,884		375,347		357,762		357,212		355,763		351,478		22,234		N/A
2018											402,372		395,484		390,135		413,116		408,905		32,668		N/A
2019													414,049		393,864		387,810		383,491		38,889		N/A
2020															579,367		511,136		506,164		57,946		N/A
2021																	589,452		590,091		148,264		N/A
2022																			924,130		601,334		N/A
																	Total		$	4,248,999
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	$	81,609	$	155,936	$	188,651	$	209,775	$	222,292	$	229,228	$	237,023	$	237,559	$	240,669	$	243,881
2014			92,743		181,222		223,243		240,680		250,427		263,123		266,898		270,529		271,712
2015					80,453		157,176		190,699		204,444		216,683		227,879		230,640		231,384
2016							103,649		196,496		231,761		249,699		265,763		271,609		277,028
2017									130,150		245,165		285,299		299,405		312,273		322,863
2018											124,996		265,000		303,141		323,868		340,061
2019													116,762		204,625		267,972		293,260
2020															129,621		285,729		361,031
2021																	146,503		300,025
2022																			175,834
									Total										2,817,079
									All outstanding liabilities before 2013, net of reinsurance										13,001
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	1,444,921

Percentage annual payout by age

The following table presents the average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance, as of December 31, 2022:

	Average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance
	Year 1		Year 2		Year 3		Year 4		Year 5		Year 6		Year 7		Year 8		Year 9		Year 10
Casualty	2.8	%	7.8	%	12.4	%	11.3	%	9.5	%	8.2	%	7.5	%	5.0	%	3.8	%	4.7	%
Property catastrophe	41.7	%	27.3	%	49.4	%	(115.6)	%	(10.7)	%	4.1	%	1.7	%	1.7	%	(0.5)	%	0.1	%
Property excluding property catastrophe	27.0	%	37.4	%	13.2	%	5.6	%	4.0	%	0.6	%	2.4	%	0.4	%	0.1	%	2.5	%
Marine and aviation	4.5	%	28.8	%	18.3	%	10.9	%	8.4	%	3.0	%	2.4	%	0.1	%	3.6	%	2.9	%
Other specialty	29.9	%	29.9	%	13.1	%	6.0	%	4.4	%	3.3	%	1.8	%	0.6	%	0.8	%	1.3	%

Mortgage

Claims Development [Line Items]

Claims development tables

The following table presents information on the mortgage segment’s short-duration insurance contracts:

U.S. primary mortgage insurance ($000’s except claim count)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2022
																					Total of IBNR liabilities plus expected development on reported claims	Cumulative number of paid claims
Year ended December 31,
Accident year	2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020 unaudited		2021 unaudited		2022
2013	$	469,311	$	419,668	$	411,793	$	405,809	$	395,693	$	393,149	$	390,987	$	391,062	$	391,324	$	390,299	2	9,474
2014			316,095		297,151		279,434		266,027		265,992		261,091		262,682		262,829		260,554		4	6,311
2015					222,790		197,238		198,001		194,677		189,235		190,913		190,560		188,649		1	4,573
2016							183,556		170,532		148,715		140,608		142,392		141,657		137,415		—	3,445
2017									179,376		132,220		107,255		108,181		109,242		102,005		(1)	2,516
2018											132,318		96,357		89,120		87,962		71,976		(4)	1,718
2019													108,424		119,253		110,362		63,485		74	1,002
2020															420,003		373,533		78,334		476	299
2021																	144,375		77,212		379	72
2022																			173,327		2,147	7
															Total				$	1,543,256
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013	41,447		203,957		308,956		353,189		373,909		382,200		386,853		387,894		387,879		388,036
2014			20,099		129,159		201,925		233,879		247,038		254,175		256,285		256,875		257,232
2015					16,159		92,431		151,222		171,337		180,321		183,472		184,025		184,955
2016							11,462		72,201		113,357		127,286		131,161		131,717		132,387
2017									8,622		48,112		78,650		87,317		89,756		91,645
2018											3,966		31,478		50,135		55,853		58,687
2019													2,899		20,105		29,102		34,178
2020															1,040		4,144		7,740
2021																	469		1,687
2022																			176
																			1,156,723
									All outstanding liabilities before 2013, net of reinsurance										10,585
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	397,118

Percentage annual payout by age

The following table presents the average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance, as of December 31, 2022:

Average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance
	Year 1		Year 2		Year 3		Year 4		Year 5		Year 6		Year 7		Year 8		Year 9		Year 10
U.S. Primary	5.6	%	30.9	%	23.8	%	9.8	%	4.0	%	1.8	%	0.7	%	0.3	%	0.1	%	—	%

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Allowance for Expected Credit Losses (Tables)

12 Months Ended

Dec. 31, 2022

Credit Loss [Abstract]

Allowance for credit losses on premiums receivable

The following table provides a roll forward of the allowance for expected credit losses of the Company’s premium receivables:

Year Ended December 31, 2022	Premium Receivables, Net of Allowance		Allowance for Expected Credit Losses
Balance at beginning of period	$	2,633,280	$	39,958
Change for provision of expected credit losses (1)			(4,556)
Balance at end of period	$	3,624,777	$	35,402
Year Ended December 31, 2021
Balance at beginning of period	$	2,064,586	$	37,781
Change for provision of expected credit losses (1)			2,177
Balance at end of period	$	2,633,280	$	39,958

(1) Amounts deemed uncollectible are written-off in operating expenses. For the 2022 and 2021 periods, amounts written off totaled $11.4 million and $3.8 million, respectively.

Allowance for credit losses on reinsurance recoverable

The following table provides a roll forward of the allowance for expected credit losses of the Company’s reinsurance recoverables:

Year Ended December 31, 2022	Reinsurance Recoverables, Net of Allowance		Allowance for Expected Credit Losses
Balance at beginning of period	$	5,880,735	$	13,230
Change for provision of expected credit losses			8,314
Balance at end of period	$	6,563,654	$	21,544
Year Ended December 31, 2021
Balance at beginning of period	$	4,500,802	$	11,636
Change for provision of expected credit losses			1,594
Balance at end of period	5,880,735		$	13,230

Summary of reinsurance recoverables on paid and unpaid losses

The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums) at December 31, 2022 and 2021:

	December 31,
	2022			2021
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	$	6,563,654		$	5,880,735
% due from carriers with A.M. Best rating of “A-” or better	68.8		%	69.7		%
% due from all other rated carriers	0.1		%	0.1		%
% due from all other carriers with no A.M. Best rating (1)	31.1		%	30.2		%
Largest balance due from any one carrier as % of total shareholders’ equity	9.0		%	6.7		%

(1)    At December 31, 2022 and 2021 period, over 95% and 91% of such amount is collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other, respectively.

Allowance for credit losses on contractholder receivables

The following table provides a roll forward of the allowance for expected credit losses of the Company’s contractholder receivables:

Year Ended December 31, 2022	Contractholder Receivables, Net of Allowance		Allowance for Expected Credit Losses
Balance at beginning of period	$	1,828,691	$	3,437
Change for provision of expected credit losses			(746)
Balance at end of period	$	1,731,293	$	2,691
Year Ended December 31, 2021
Balance at beginning of period	$	1,986,924	$	8,638
Change for provision of expected credit losses			(5,201)
Balance at end of period	1,828,691		$	3,437

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Reinsurance (Tables)

12 Months Ended

Dec. 31, 2022

Reinsurance Disclosures [Abstract]

Effects of reinsurance

The effects of reinsurance on the Company’s written and earned premiums and losses and loss adjustment expenses with unaffiliated reinsurers were as follows:

	Year Ended December 31,
	2022		2021		2020
Premiums Written
Direct	$	8,540,787	$	7,706,832	$	6,553,910
Assumed	6,785,660		5,045,655		3,534,158
Ceded	(4,249,258)		(3,734,150)		(2,650,352)
Net	$	11,077,189	$	9,018,337	$	7,437,716
Premiums Earned
Direct	$	8,057,635	$	7,149,794	$	6,361,451
Assumed	5,767,738		4,333,873		3,213,873
Ceded	(4,147,296)		(3,401,369)		(2,583,389)
Net	$	9,678,077	$	8,082,298	$	6,991,935
Losses and Loss Adjustment Expenses
Direct	$	3,990,768	$	4,266,758	$	4,392,392
Assumed	3,559,133		2,826,820		2,204,323
Ceded	(2,522,384)		(2,508,775)		(1,907,116)
Net	$	5,027,517	$	4,584,803	$	4,689,599

Coverage and retention

The following table summarizes the respective coverages and retentions at December 31, 2022:

			December 31, 2022
Bellemeade Entities (Issue Date)	Initial Coverage at Issuance		Current Coverage		Remaining Retention, Net
2017-1 Ltd. (1)	$	368,114	$	36,679	$	142,461
2018-1 Ltd. (2)	374,460		89,698		143,592
2018-3 Ltd. (3)	506,110		199,237		152,861
2019-1 Ltd. (4)	341,790		107,880		118,908
2019-2 Ltd. (5)	621,022		325,462		191,550
2019-3 Ltd. (6)	700,920		222,977		208,931
2019-4 Ltd. (7)	577,267		266,124		142,564
2020-2 Ltd. (8)	449,167		105,110		237,709
2020-3 Ltd. (9)	451,816		250,971		161,544
2020-4 Ltd. (10)	337,013		101,729		138,131
2021-1 Ltd. (11)	643,577		503,267		153,525
2021-2 Ltd. (12)	616,017		535,461		138,524
2021-3 Ltd. (13)	639,391		616,959		132,492
2022-1 Ltd. (14)	316,760		316,760		143,577
2022-2 Ltd. (15)	327,165		327,165		217,436
Total	$	7,270,589	$	4,005,479	$	2,423,805

(1)    Issued in October 2017, covering in-force policies issued between January 1, 2017 and June 30, 2017.

(2)    Issued in April 2018, covering in-force policies issued between July 1, 2017 and December 31, 2017.

(3)    Issued in October 2018, covering in-force policies issued between January 1, 2018 and June 30, 2018.

(4)    Issued in March 2019, covering in-force policies primarily issued between 2005 to 2008 under United Guaranty Residential Insurance Company (“UGRIC”); as well as policies issued through 2015 under both UGRIC and Arch Mortgage Insurance Company.

(5)    Issued in April 2019, covering in-force policies issued between July 1, 2018 and December 31, 2018.

(6)    Issued in July 2019, covering in-force policies issued in 2016.

(7)    Issued in October 2019, covering in-force policies issued between January 1, 2019 and June 30, 2019.

(8)    Issued in September 2020, covering in-force policies issued between January 1, 2020 and May 31, 2020. $423 million was directly funded by Bellemeade 2020-2 Ltd. with an additional $26 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(9)    Issued in November 2020, covering in-force policies issued between June 1, 2020 and August 31, 2020. $418 million was directly funded by Bellemeade 2020-3 Ltd. with an additional $34 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(10)    Issued in December 2020, covering in-force policies issued between July 1, 2019 and December 31, 2019. $321 million was directly funded by Bellemeade 2020-4 Ltd. with an additional $16 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(11) Issued in March 2021, covering in-force policies issued between September 1, 2020 and November 30, 2020. $580 million was directly funded by Bellemeade Re 2021-1 Ltd. with an additional $64 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(12) Issued in June 2021, covering in-force policies issued between December 1, 2020 and March 31, 2021. $523 million was directly funded by Bellemeade Re 2021-2 Ltd. via insurance-linked notes, with an additional $93 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(13) Issued in September 2021, covering in-force policies issued between April 1, 2021 and June 30, 2021. $508 million was directly funded by Bellemeade Re 2021-3 Ltd. via insurance-linked notes, with an additional $131 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(14) Issued in January 2022, covering in-force policies issued between July 1, 2021 and November 30, 2021. $284 million was directly funded by Bellemeade Re 2022-1 Ltd. via insurance-linked notes, with an additional $33 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(15) Issued in September 2022, covering in-force policies issued between November 1, 2021 and June 30, 2022. $201 million was directly funded by Bellemeade Re 2022-2 Ltd. via insurance-linked notes, with an additional $126 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

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Investment Information (Tables)

12 Months Ended

Dec. 31, 2022

Disclosure Investment Information [Abstract]

Summary of fair value and cost or amortized cost of available for sale securities

The following table summarizes the fair value and cost or amortized cost of the Company’s securities classified as available for sale:

	Estimated Fair Value		Gross Unrealized Gains		Gross Unrealized Losses		Allowance for Expected Credit Losses		Cost or Amortized Cost
December 31, 2022
Fixed maturities:
Corporate bonds	$	8,020,128	$	55,468	$	(781,353)	$	(29,950)	$	8,775,963
Mortgage backed securities	795,391		4,933		(86,587)		2		877,043
Municipal bonds	419,166		3,149		(33,360)		(100)		449,477
Commercial mortgage backed securities	1,047,275		608		(57,667)		(3,415)		1,107,749
U.S. government and government agencies	5,161,193		14,891		(342,963)		—		5,489,265
Non-U.S. government securities	2,312,819		8,870		(237,846)		(1,882)		2,543,677
Asset backed securities	1,926,817		761		(106,623)		(6,010)		2,038,689
Total	19,682,789		88,680		(1,646,399)		(41,355)		21,281,863
Short-term investments	1,331,662		554		(1,888)		—		1,332,996
Total	$	21,014,451	$	89,234	$	(1,648,287)	$	(41,355)	$	22,614,859
December 31, 2021
Fixed maturities:
Corporate bonds	$	6,553,333	$	104,170	$	(69,194)	$	(2,037)	$	6,520,394
Mortgage backed securities	408,477		2,825		(5,410)		(48)		411,110
Municipal bonds	404,666		18,724		(1,409)		(2)		387,353
Commercial mortgage backed securities	1,046,484		1,740		(3,117)		(6)		1,047,867
U.S. government and government agencies	4,772,764		10,076		(45,967)		—		4,808,655
Non-U.S. government securities	2,120,294		54,048		(34,749)		(82)		2,101,077
Asset backed securities	2,692,091		6,540		(11,108)		(708)		2,697,367
Total	17,998,109		198,123		(170,954)		(2,883)		17,973,823
Short-term investments	1,734,716		568		(590)		—		1,734,738
Total	$	19,732,825	$	198,691	$	(171,544)	$	(2,883)	$	19,708,561

Summary of available for sale securities in a continual unrealized loss position

The following table summarizes, for all available for sale securities in an unrealized loss position, the fair value and gross unrealized loss by length of time the security has been in a continual unrealized loss position:

	Less than 12 Months				12 Months or More				Total
	Estimated Fair Value		Gross Unrealized Losses		Estimated Fair Value		Gross Unrealized Losses		Estimated Fair Value		Gross Unrealized Losses
December 31, 2022
Fixed maturities:
Corporate bonds	$	4,822,624	$	(393,112)	$	2,559,399	$	(388,241)	$	7,382,023	$	(781,353)
Mortgage backed securities	545,844		(51,673)		154,154		(34,914)		699,998		(86,587)
Municipal bonds	363,936		(29,924)		16,282		(3,436)		380,218		(33,360)
Commercial mortgage backed securities	598,392		(34,899)		445,175		(22,768)		1,043,567		(57,667)
U.S. government and government agencies	3,556,676		(197,259)		1,442,542		(145,704)		4,999,218		(342,963)
Non-U.S. government securities	1,702,973		(153,587)		541,652		(84,259)		2,244,625		(237,846)
Asset backed securities	1,148,220		(65,189)		512,376		(41,434)		1,660,596		(106,623)
Total	12,738,665		(925,643)		5,671,580		(720,756)		18,410,245		(1,646,399)
Short-term investments	236,735		(1,888)		—		—		236,735		(1,888)
Total	$	12,975,400	$	(927,531)	$	5,671,580	$	(720,756)	$	18,646,980	$	(1,648,287)
December 31, 2021
Fixed maturities:
Corporate bonds	$	3,639,582	$	(63,938)	$	98,867	$	(5,256)	$	3,738,449	$	(69,194)
Mortgage backed securities	222,176		(3,545)		46,809		(1,865)		268,985		(5,410)
Municipal bonds	26,665		(385)		16,361		(1,024)		43,026		(1,409)
Commercial mortgage backed securities	675,603		(2,805)		5,908		(312)		681,511		(3,117)
U.S. government and government agencies	4,211,621		(44,180)		33,373		(1,787)		4,244,994		(45,967)
Non-U.S. government securities	1,511,301		(31,983)		62,957		(2,766)		1,574,258		(34,749)
Asset backed securities	1,667,002		(9,853)		33,082		(1,255)		1,700,084		(11,108)
Total	11,953,950		(156,689)		297,357		(14,265)		12,251,307		(170,954)
Short-term investments	284,733		(590)		—		—		284,733		(590)
Total	$	12,238,683	$	(157,279)	$	297,357	$	(14,265)	$	12,536,040	$	(171,544)

Contractual maturities of the Company's fixed maturities and fixed maturities pledged under securities lending arrangements

	December 31, 2022				December 31, 2021
Maturity	Estimated Fair Value		Amortized Cost		Estimated Fair Value		Amortized Cost
Due in one year or less	$	510,669	$	536,962	$	300,889	$	299,772
Due after one year through five years	11,014,753		11,714,427		8,355,255		8,339,387
Due after five years through 10 years	3,984,497		4,527,447		4,689,155		4,684,393
Due after 10 years	403,387		479,546		505,758		493,927
	15,913,306		17,258,382		13,851,057		13,817,479
Mortgage backed securities	795,391		877,043		408,477		411,110
Commercial mortgage backed securities	1,047,275		1,107,749		1,046,484		1,047,867
Asset backed securities	1,926,817		2,038,689		2,692,091		2,697,367
Total	$	19,682,789	$	21,281,863	$	17,998,109	$	17,973,823

Components of net investment income

The components of net investment income were derived from the following sources:

	Year Ended December 31,
	2022		2021		2020
Fixed maturities	$	468,659	$	330,061	$	412,481
Term loans	2,038		34,843		84,149
Equity securities	22,497		42,396		28,958
Short-term investments	29,519		6,928		10,840
Other (1)	44,609		62,895		72,395
Gross investment income	567,322		477,123		608,823
Investment expenses	(70,775)		(88,005)		(89,215)
Net investment income	$	496,547	$	389,118	$	519,608

(1)    Includes income distributions from investment funds and other items

Summary of net realized gains (losses)

Net realized gains (losses) were as follows:

	Year Ended December 31,
	2022		2021		2020
Available for sale securities:
Gross gains on investment sales	$	81,161	$	313,886	$	595,941
Gross losses on investment sales	(317,150)		(156,791)		(117,282)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	(70,951)		7,953		15,881
Other investments	(19,498)		116,781		13,656
Equity securities	(4,520)		13,028		14,629
Short-term investments	(3,012)		601		2,279
Equity securities, at fair value :
Net realized gains (losses) on securities sold	74,922		122,606		26,849
Net unrealized gains (losses) on equity securities still held at reporting date	(267,927)		48,746		102,394
Allowance for credit losses:
Investments related	(43,909)		(2,100)		(3,597)
Underwriting related	(13,274)		1,062		(10,007)
Net impairment losses	—		—		(533)
Derivative instruments (1)	(75,023)		(32,390)		179,675
Other (2)	(3,553)		(53,537)		3,575
Net realized gains (losses)	$	(662,734)	$	379,845	$	823,460

(1)    See note 11, “Derivative Instruments” for information on the Company’s derivative instruments.

(2)    2021 period reflected $33.1 million of losses related to the Company’s

deconsolidation of Somers.

Other investments

The following table summarizes the Company’s other investments and other investable assets:

	December 31,
	2022		2021
Fixed maturities	$	554,120	$	416,698
Other investments	1,043,184		1,432,553
Short-term investments	33,101		97,806
Equity securities	13,792		26,493
Total other investments	$	1,644,197	$	1,973,550

The following table summarizes the Company’s other investments, as detailed in the previous table, by strategy:

	December 31,
	2022		2021
Lending	405,871		536,345
Investment grade fixed income	271,143		147,810
Term loan investments	163,941		484,950
Private equity	123,266		91,126
Energy	22,627		81,692
Credit related funds	56,336		70,278
Infrastructure	—		20,352
Total	$	1,043,184	$	1,432,553

Investments accounted for using the equity method

The following table summarizes the Company’s investments accounted for using the equity method, by strategy:

	December 31,
	2022		2021
Credit related funds	$	1,135,818	$	1,022,334
Private equity	916,534		436,042
Real estate	535,238		396,395
Lending	531,339		376,649
Infrastructure	245,246		230,070
Equities	169,156		395,090
Fixed income	130,062		101,890
Energy	110,917		119,141
Total	$	3,774,310	$	3,077,611

A summary of financial information for the Company’s investment funds and operating affiliates accounted for using the equity method is as follows:

	December 31,
	2022		2021
Invested assets	$	74,960,738	$	58,508,009
Total assets	88,062,991		69,648,905
Total liabilities	27,553,307		17,944,325
Net assets	$	60,509,684	$	51,704,580

	Year Ended December 31,
	2022		2021		2020
Total revenues	$	12,305,082	$	11,785,949	$	5,762,098
Total expenses	5,374,047		3,238,606		1,656,029
Net income (loss)	$	6,931,035	$	8,547,343	$	4,106,069

Summary of investments in limited partnership interests where the Company has a variable interest

The following table summarizes investments in limited partnership interests where the Company has a variable interest by balance sheet item:

	December 31,
	2022		2021
Investments accounted for using the equity method (1)	$	3,774,310	$	3,077,611
Investments accounted for using the fair value option (2)	130,466		170,595
Total	$	3,904,776	$	3,248,206

(1)     Aggregate unfunded commitments were $2.6 billion at December 31, 2022, consistent with $2.6 billion at December 31, 2021.

(2)    Aggregate unfunded commitments were $16.7 million at December 31, 2022, compared to $18.8 million at December 31, 2021.

Roll forward of the allowance for expected credit losses of securities classified as available for sale

The following table provides a roll forward of the allowance for expected credit losses of the Company’s securities classified as available for sale:

Year Ended December 31, 2022	Structured Securities (1)		Municipal Bonds		Non-U.S. Government Securities		Corporate Bonds		Total
Balance at beginning of period	$	802	$	2	$	82	$	1,997	$	2,883
Additions for current-period provision for expected credit losses	14,184		359		1,616		39,477		55,636
Additions (reductions) for previously recognized expected credit losses	(3,184)		(261)		275		(8,619)		(11,789)
Reductions due to disposals	(2,379)		—		(91)		(2,905)		(5,375)
Balance at end of period	$	9,423	$	100	$	1,882	$	29,950	$	41,355
Year Ended December 31, 2021
Balance at beginning of period	$	1,490	$	11	$	—	$	896	$	2,397
Additions for current-period provision for expected credit losses	602		—		82		2,858		3,542
Additions (reductions) for previously recognized expected credit losses	(847)		(9)		—		(402)		(1,258)
Reductions due to disposals (2)	(443)		—		—		(1,355)		(1,798)
Balance at end of period	$	802	$	2	$	82	$	1,997	$	2,883

(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed

(2)    Reduction for the 2021 periods primarily related to the Company’s deconsolidation of Somers.

Summary of restricted assets

The following table details the value of the Company’s restricted assets:

	December 31,
	2022		2021
Assets used for collateral or guarantees:
Affiliated transactions	$	4,254,398	$	4,223,955
Third party agreements	2,632,892		2,289,631
Deposits with U.S. regulatory authorities	776,342		798,100
Other (1)	1,037,848		938,046
Total restricted assets	$	8,701,480	$	8,249,732

(1) Primarily includes Funds at Lloyds, deposits with non-U.S. regulatory authorities and other restricted assets.

Reconciliation of cash and restricted cash

The following table details reconciliation of cash and restricted cash within the Consolidated Balance Sheets:

	December 31,
	2022		2021		2020
Cash	$	855,118	$	858,668	$	906,448
Restricted cash (included in ‘other assets’)	418,210		456,103		384,096
Cash and restricted cash	$	1,273,328	$	1,314,771	$	1,290,544

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Fair Value (Tables)

12 Months Ended

Dec. 31, 2022

Fair Value Disclosures [Abstract]

Fair value hierarchy

The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2022:

			Fair Value Measurement Using:
	Estimated Fair Value		Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Assets measured at fair value:
Available for sale securities:
Fixed maturities:
Corporate bonds	$	8,020,128	$	—	$	7,898,901	$	121,227
Mortgage backed securities	795,391		—		795,391		—
Municipal bonds	419,166		—		419,166		—
Commercial mortgage backed securities	1,047,275		—		1,047,275		—
U.S. government and government agencies	5,161,193		5,144,467		16,726		—
Non-U.S. government securities	2,312,819		—		2,312,819		—
Asset backed securities	1,926,817		—		1,926,817		—
Total	19,682,789		5,144,467		14,417,095		121,227
Short-term investments	1,331,662		1,197,304		134,358		—
Equity securities, at fair value	859,969		828,513		28,042		3,414
Derivative instruments (2)	148,301		—		148,301		—
Residential mortgage loans	2,283		—		2,283		—
Fair value option:
Corporate bonds	542,755		—		542,755		—
Non-U.S. government bonds	4,315		—		4,315		—
Asset backed securities	1,652		—		1,652		—
U.S. government and government agencies	5,398		5,398		—		—
Short-term investments	33,101		699		32,402		—
Equity securities	13,792		9,619		—		4,173
Other investments	196,215		—		162,956		33,259
Other investments measured at net asset value (1)	846,969
Total	1,644,197		15,716		744,080		37,432
Total assets measured at fair value	$	23,669,201	$	7,186,000	$	15,474,159	$	162,073
Liabilities measured at fair value:
Contingent consideration liabilities	$	(14,246)	$	—	$	—	$	(14,246)
Derivative instruments (2)	(75,961)		—		(75,961)		—
Total liabilities measured at fair value	$	(90,207)	$	—	$	(75,961)	$	(14,246)

(1)    In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.

(2)    See note 11, “Derivative Instruments.”

The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2021:

			Fair Value Measurement Using:
	Estimated Fair Value		Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Assets measured at fair value:
Available for sale securities:
Fixed maturities:
Corporate bonds	$	6,553,333	$	—	$	6,553,320	$	13
Mortgage backed securities	408,477		—		408,477		—
Municipal bonds	404,666		—		404,666		—
Commercial mortgage backed securities	1,046,484		—		1,046,484		—
U.S. government and government agencies	4,772,764		4,744,517		28,247		—
Non-U.S. government securities	2,120,294		—		2,120,294		—
Asset backed securities	2,692,091		—		2,688,744		3,347
Total	17,998,109		4,744,517		13,250,232		3,360
Equity securities, at fair value	1,804,170		1,762,864		38,388		2,918
Short-term investments	1,734,716		1,052,822		681,894		—
Derivative instruments (2)	127,121		—		127,121		—
Residential mortgage loans	49,847		—		49,847		—
Fair value option:
Corporate bonds	388,546		—		388,546		—
Non-U.S. government bonds	23,785		—		23,785		—
Asset backed securities	4,367		—		4,367		—
U.S. government and government agencies	—		—		—		—
Short-term investments	97,806		528		97,278		—
Equity securities	26,493		21,745		—		4,748
Other investments	310,798		20,352		262,465		27,981
Other investments measured at net asset value (1)	1,121,755
Total	1,973,550		42,625		776,441		32,729
Total assets measured at fair value	$	23,687,513	$	7,602,828	$	14,923,923	$	39,007
Liabilities measured at fair value:
Contingent consideration liabilities	$	(16,960)	$	—	$	—	$	(16,960)
Derivative instruments (2)	(54,224)		—		(54,224)		—
Total liabilities measured at fair value	$	(71,184)	$	—	$	(54,224)	$	(16,960)

(1)    In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.

(2)    See note 11, “Derivative Instruments.”

Rollforward of Level 3 investments

The following table presents a reconciliation of the beginning and ending balances for all financial assets and liabilities measured at fair value on a recurring basis using Level 3 inputs for 2022 and 2021:

			Assets										Liabilities
	Available For Sale				Fair Value Option						Fair Value
	Structured Securities (1)		Corporate Bonds		Corporate Bonds		Other Investments		Equity Securities		Equity Securities		Other Liabilities
Year Ended December 31, 2022
Balance at beginning of year	$	3,347	$	13	$	—	$	27,981	$	4,748	$	2,918	$	(16,960)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	(592)		352		—		(781)		(575)		(470)		(364)
Included in other comprehensive income	(1)		(1,095)		—		—		—		—		1,170
Purchases, issuances, sales and settlements
Purchases	—		150,013		—		12,381		—		969		—
Issuances	—		—		—		—		—		—		—
Sales	(2,051)		(5,363)		—		(3,339)		—		(3)		—
Settlements	(703)		(26,250)		—		(2,983)		—		—		1,908
Transfers in and/or out of Level 3	—		3,557		—		—		—		—		—
Balance at end of year	$	—	$	121,227	$	—	$	33,259	$	4,173	$	3,414	$	(14,246)
Year Ended December 31, 2021
Balance at beginning of year	$	3,426	$	13	$	985	$	67,103	$	68,988	$	42,015	$	(461)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	(135)		—		13		868		4,941		1,958		—
Included in other comprehensive income	133		—		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		—		13,213		—		5,718		(16,494)
Issuances	—		—		—		—		—		—		—
Sales (3)	—		—		(998)		(53,203)		(69,181)		(46,773)		—
Settlements	(77)		—		—		—		—		—		(5)
Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of year	$	3,347	$	13	$	—	$	27,981	$	4,748	$	2,918	$	(16,960)

(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

(2)    Gains or losses were included in net realized gains (losses).

(3)     Sales for the 2021 period primarily relates to the Company’s deconsolidation of Somers.

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Derivative Instruments (Tables)

12 Months Ended

Dec. 31, 2022

Derivative Instruments and Hedging Activities Disclosure [Abstract]

Fair value and notional amount of derivatives

The following table summarizes information on the fair values and notional values of the Company’s derivative instruments:

	Estimated Fair Value
	Asset Derivatives (1)		Liability Derivatives (1)		Notional Value (2)
December 31, 2022
Futures contracts	$	50,629	$	(16,963)	$	3,138,446
Foreign currency forward contracts	38,891		(35,446)		1,136,126
Other	58,781		(23,552)		3,591,793
Total	$	148,301	$	(75,961)
December 31, 2021
Futures contracts	$	34,999	$	(9,808)	$	2,826,564
Foreign currency forward contracts	7,734		(11,390)		915,962
TBAs	11,227		—		11,227
Other	73,161		(33,026)		3,736,773
Total	$	127,121	$	(54,224)

(1)    The fair value of asset derivatives are included in ‘other assets’ and the fair value of liability derivatives are included in ‘other liabilities.’

(2)    Represents the absolute notional value of all outstanding contracts, consisting of long and short positions.

Summary of net realized gains (losses) recorded in the consolidated statements of income

Realized and unrealized contract gains and losses on the Company’s derivative instruments are reflected in ‘net realized gains (losses)’ in the consolidated statements of income, as summarized in the following table:

Derivatives not designated as hedging instruments	Year Ended December 31,
	2022		2021		2020
Net realized gains (losses):
Futures contracts	$	(86,634)	$	(15,262)	$	114,987
Foreign currency forward contracts	6,144		(39,755)		49,974
TBAs	(51)		(233)		1,129
Other	5,518		22,860		13,585
Total	$	(75,023)	$	(32,390)	$	179,675

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Variable Interest Entity and Noncontrolling Interests (Tables)

12 Months Ended

Dec. 31, 2022

Variable Interest Entity and Noncontrolling Interest Disclosure [Abstract]

Summary of VIE cash flows

The following table summarizes Somers’ cash flow from operating, investing and financing activities.

	Year Ended December 31,
	2022	2021	2020
Total cash provided by (used for):
Operating activities	—	46,991	181,736
Investing activities	—	96,325	258,589
Financing activities	—	(2,042)	(335,776)

Activity in non-redeemable noncontrolling interests

The following table sets forth activity in the non-redeemable noncontrolling interests:

	December 31,
	2022		2021
Balance, beginning of year	$	—	$	823,007
Impact of deconsolidation of Somers	—		(918,874)
Additional paid in capital attributable to noncontrolling interests	—		22,113
Amounts attributable to noncontrolling interests	—		78,314
Other comprehensive (income) loss attributable to noncontrolling interests	—		(4,560)
Balance, end of year	$	—	$	—

Activity in redeemable noncontrolling interest

The following table sets forth activity in the redeemable noncontrolling interests:

	December 31,
	2022		2021		2020
Balance, beginning of year	$	9,233	$	58,548	$	55,404
Impact of deconsolidation of Somers	—		(48,919)		—
Other	1,596		(396)		3,144
Balance, end of year	$	10,829	$	9,233	$	58,548

Portion of income or loss attributable to noncontrolling interests

The portion of income or loss attributable to third party investors is recorded in the consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests’ as summarized in the table below:

	December 31,
	2022		2021		2020
Amounts attributable to non-redeemable noncontrolling interests	$	—	$	(78,314)	$	(53,076)
Amounts attributable to redeemable noncontrolling interests	(5,490)		(4,299)		(7,114)
Net (income) loss attributable to noncontrolling interests	$	(5,490)	$	(82,613)	$	(60,190)

Total assets and maximum loss exposure of VIE

The following table presents the total assets of the Bellemeade entities, as well as the Company’s maximum exposure to loss associated with these VIEs, calculated as the maximum historical observable spread between the benchmark index for each respective transaction and short term invested trust asset yields. The benchmark index for agreements effective prior to 2021 is based on one-month LIBOR, while the 2021 and later agreements benchmark index is based on the Secured Overnight Financing Rate (“SOFR”). SOFR is a measure of the cost of borrowing cash overnight, collateralized by U.S. Treasury securities, and is based on directly observable U.S. Treasury-backed repurchase transactions.

			December 31, 2022										December 31, 2021
			Maximum Exposure to Loss										Maximum Exposure to Loss
Bellemeade Entities (Issue Date)	Total VIE Assets		On-Balance Sheet (Asset) Liability		Off-Balance Sheet		Total		Coverage Remaining from Reinsurers (1)		Total VIE Assets		On-Balance Sheet (Asset) Liability		Off-Balance Sheet		Total
2017-1 Ltd. (Oct-17)	$	36,679	$	(6)	$	14	$	8	$	—	$	108,368	$	(159)	$	424	$	265
2018-1 Ltd. (Apr-18)	89,698		(153)		508		355		—		181,136		(528)		1,268		740
2018-3 Ltd. (Oct-18)	199,237		(250)		771		521		—		302,563		(1,018)		2,496		1,478
2019-1 Ltd. (Mar-19)	107,880		(48)		593		545		—		181,324		(380)		5,807		5,427
2019-2 Ltd. (Apr-19)	325,462		(206)		4,356		4,150		—		398,316		(515)		3,998		3,483
2019-3 Ltd. (Jul-19)	222,977		(104)		1,229		1,125		—		409,859		(584)		3,190		2,606
2019-4 Ltd. (Oct-19)	266,124		(142)		3,640		3,498		—		411,954		(462)		4,759		4,297
2020-2 Ltd. (Sep-20)	105,110		(8)		492		484		—		217,766		(177)		1,984		1,807
2020-3 Ltd. (Nov-20)	243,891		53		2,872		2,925		7,079		348,818		(128)		5,793		5,665
2020-4 Ltd. (Dec-20)	97,563		32		642		674		4,165		176,826		(50)		1,630		1,580
2021-1 Ltd. (Mar-21)	467,469		239		2,743		2,982		35,798		568,986		(303)		3,283		2,980
2021-2 Ltd. (Jun-21)	458,362		581		2,855		3,436		77,099		522,807		281		4,124		4,405
2021-3 Ltd. (Sep-21)	489,927		217		2,704		2,921		127,032		507,873		(411)		3,446		3,035
2022-1 Ltd. (Jan-22)	283,500		399		1,765		2,164		33,260
2022-2 Ltd. (Sep-22)	201,005		1,172		1,616		2,788		126,160
Total	$	3,594,884	$	1,776	$	26,800	$	28,576	$	410,593	$	4,336,596	$	(4,434)	$	42,202	$	37,768

(1) Coverage from a separate panel of reinsurers remaining at December 31, 2022.

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Other Comprehensive Income (Tables)

12 Months Ended

Dec. 31, 2022

Comprehensive Income Note Disclosure [Abstract]

Schedule of changes in each component of AOCI

The following table presents the changes in each component of AOCI, net of noncontrolling interests:

	Unrealized Appreciation on Available-For-Sale Investments		Foreign Currency Translation Adjustments		Total
Year Ended December 31, 2022
Beginning balance	$	13,486	$	(78,086)	$	(64,600)
Other comprehensive income (loss) before reclassifications	(1,772,649)		(56,720)		(1,829,369)
Amounts reclassified from accumulated other comprehensive income	247,799		—		247,799
Net current period other comprehensive income (loss)	(1,524,850)		(56,720)		(1,581,570)
Ending balance	$	(1,511,364)	$	(134,806)	$	(1,646,170)
Year Ended December 31, 2021
Beginning balance	$	501,295	$	(12,400)	$	488,895
Other comprehensive income (loss) before reclassifications	(371,741)		(65,686)		(437,427)
Amounts reclassified from accumulated other comprehensive income	(116,068)		—		(116,068)
Net current period other comprehensive income (loss)	(487,809)		(65,686)		(553,495)
Ending balance	$	13,486	$	(78,086)	$	(64,600)
Year Ended December 31, 2020
Beginning balance	$	258,486	$	(46,395)	$	212,091
Other comprehensive income (loss) before reclassifications	668,996		33,995		702,991
Amounts reclassified from accumulated other comprehensive income	(426,187)		—		(426,187)
Net current period other comprehensive income (loss)	242,809		33,995		276,804
Ending balance	$	501,295	$	(12,400)	$	488,895

Details about amounts reclassified from AOCI

The following tables present details about amounts reclassified from accumulated other comprehensive income and the tax effects allocated to each component of other comprehensive income (loss):

	Consolidated Statement of Income	Amounts Reclassified from AOCI
Details About	Line Item That Includes	Year Ended December 31,
AOCI Components	Reclassification	2022		2021		2020
Unrealized appreciation on available-for-sale investments
	Net realized gains (losses)	$	(235,989)	$	157,095	$	478,659
	Provision for credit losses	(43,909)		(2,099)		(3,597)
	Other-than-temporary impairment losses	—		—		(533)
	Total before tax	(279,898)		154,996		474,529
	Income tax (expense) benefit	32,099		(38,928)		(48,342)
	Net of tax	$	(247,799)	$	116,068	$	426,187

Schedule of tax effects allocated to each component of other comprehensive income (loss)

Following are the related tax effects allocated to each component of other comprehensive income (loss):

	Before Tax		Tax Expense		Net of Tax
	Amount		(Benefit)		Amount
Year Ended December 31, 2022
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(2,010,443)	$	(237,794)	$	(1,772,649)
Less reclassification of net realized gains (losses) included in net income	(279,898)		(32,099)		(247,799)
Foreign currency translation adjustments	(56,554)		166		(56,720)
Other comprehensive income (loss)	$	(1,787,099)	$	(205,529)	$	(1,581,570)
Year Ended December 31, 2021
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(406,774)	$	(19,845)	$	(386,929)
Less reclassification of net realized gains (losses) included in net income	154,996		38,928		116,068
Foreign currency translation adjustments	(64,423)		59		(64,482)
Other comprehensive income (loss)	$	(626,193)	$	(58,714)	$	(567,479)
Year Ended December 31, 2020
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	754,572	$	75,855	$	678,717
Less reclassification of net realized gains (losses) included in net income	474,529		48,342		426,187
Foreign currency translation adjustments	33,706		370		33,336
Other comprehensive income (loss)	$	313,749	$	27,883	$	285,866

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Earnings Per Common Share (Tables)

12 Months Ended

Dec. 31, 2022

Earnings Per Share [Abstract]

Schedule of computation of basic and diluted earnings per common share

The following table sets forth the computation of basic and diluted earnings per common share:

	Year Ended December 31,
	2022		2021		2020
Numerator:
Net income	$	1,482,423	$	2,239,462	$	1,465,711
Amounts attributable to noncontrolling interests	(5,490)		(82,613)		(60,190)
Net income available to Arch	1,476,933		2,156,849		1,405,521
Preferred dividends	(40,736)		(48,343)		(41,612)
Loss on redemption of preferred shares	—		(15,101)		—
Net income available to Arch common shareholders	$	1,436,197	$	2,093,405	$	1,363,909
Denominator:
Weighted average common shares outstanding	368,612,197		391,748,715		403,062,179
Effect of dilutive common share equivalents:
Nonvested restricted shares	2,103,036		1,996,524		1,682,309
Stock options (1)	6,894,534		6,600,697		5,514,967
Weighted average common shares and common share equivalents outstanding – diluted	377,609,767		400,345,936		410,259,455
Earnings per common share:
Basic	$	3.90	$	5.34	$	3.38
Diluted	$	3.80	$	5.23	$	3.32

(1)    Certain stock options were not included in the computation of diluted earnings per share where the exercise price of the stock options exceeded the average market price and would have been anti-dilutive or where, when applying the treasury stock method to in-the-money options, the sum of the proceeds, including unrecognized compensation, exceeded the average market price and would have been anti-dilutive. For 2022, 2021 and 2020, the number of stock options excluded were 798,053, 2,398,608 and 2,249,821, respectively.

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Income Taxes (Tables)

12 Months Ended

Dec. 31, 2022

Income Tax Disclosure [Abstract]

Components of income taxes attributable to operations

The components of income taxes attributable to operations were as follows:

	Year Ended December 31,
	2022		2021		2020
Current expense (benefit):
United States	$	195,588	$	284,274	$	181,571
Non-U.S.	5,628		11,259		16,091
	201,216		295,533		197,662
Deferred expense (benefit):
United States	(96,599)		(123,261)		(89,170)
Non-U.S.	(24,656)		(43,690)		3,346
	(121,255)		(166,951)		(85,824)
Income tax expense	$	79,961	$	128,582	$	111,838

Schedule of income or loss before income taxes by jurisdiction

The Company’s income or loss before income taxes was earned in the following jurisdictions:

	Year Ended December 31,
	2022		2021		2020
Income (Loss) Before Income Taxes:
Bermuda	$	985,828	$	1,518,616	$	1,114,117
United States	400,865		643,239		409,893
Other	175,691		206,187		53,539
Total	$	1,562,384	$	2,368,042	$	1,577,549

Reconciliation of the differences between the provision for income taxes and the expected tax provision at the weighted average tax rate

A reconciliation of the difference between the provision for income taxes and the expected tax provision at the weighted average tax rate follows:

	Year Ended December 31,
	2022		2021		2020
Expected income tax expense (benefit) computed on pre-tax income at weighted average income tax rate	$	110,337	$	158,269	$	111,947
Addition (reduction) in income tax expense (benefit) resulting from:
Investment income	(12,762)		(23,572)		(1,824)
State taxes, net of U.S. federal tax benefit	10,650		20,978		5,027
Dividend withholding taxes	10,559		12,211		7,105
Change in valuation allowance	(22,726)		(40,425)		13,190
Base eroding tax	7,694		—		—
Share based compensation	(9,159)		(5,339)		(2,533)
Tax credits	(9,736)		—		—
Intercompany loan write-off	(3,544)		—		(22,083)
Other	(1,352)		6,460		1,009
Income tax expense (benefit)	$	79,961	$	128,582	$	111,838

Significant components of deferred income tax assets and liabilities

Significant components of the Company’s deferred income tax assets and liabilities were as follows:

	December 31,
	2022		2021
Deferred income tax assets:
Net operating loss	$	76,665	$	87,960
Discounting of net loss reserves	77,556		72,001
Net unearned premium reserve	96,581		75,483
Compensation liabilities	55,269		28,062
Foreign tax credit carryforward	16,738		20,058
Bad debt reserves	17,365		10,252
Depreciation and amortization	141,409		115,041
Lease liability	26,681		21,453
Net unrealized decline of investments	192,949		—
Lloyds year of account deferral	1,385		—
Other, net	14,450		703
Deferred tax assets before valuation allowance	717,048		431,013
Valuation allowance	(6,968)		(43,953)
Deferred tax assets net of valuation allowance	710,080		387,060
Deferred income tax liabilities:
Deposit accounting liability	(2,658)		(1,578)
Goodwill and intangibles	(38,905)		(70,549)
Lloyds year of account deferral	—		(12,514)
Contingency reserve	(43,870)		(49,486)
Deferred policy acquisition costs	(63,708)		(25,612)
Investment related	(9,225)		(7,492)
Net unrealized appreciation of investments	—		(8,377)
Right-of-use asset	(20,781)		(17,406)
Total deferred tax liabilities	(179,147)		(193,014)
Net deferred income tax assets	$	530,933	$	194,046

Summary of operating loss carryforwards

At December 31, 2022, the Company’s net operating loss carryforwards and tax credits were as follows:

	Year Ended December 31,
	2022		Expiration
Operating Loss Carryforwards
United Kingdom	$	198,571	No expiration
Ireland	61,685		No expiration
Australia	32,333		No expiration
Hong Kong	28,080		No expiration
Netherlands	60		No expiration
United States (1)	23,766		2029 - 2038
Tax Credits
U.K. foreign tax credits	13,907		No expiration
U.S. foreign tax credits	2,830		2029 - 2032

(1) On January 30, 2014, the Company’s U.S. mortgage operations underwent an ownership change for U.S. federal income tax purposes as a result of the Company’s acquisition of the CMG Entities. As a result of this ownership change, a limitation has been imposed upon the utilization of approximately $7.0 million of the Company’s existing U.S. net operating loss carryforwards. Utilization is limited to approximately $0.6 million per year in accordance with Section 382 of the Internal Revenue Code of 1986 as amended (“the Code”).

Summary of tax credit carryforwards

At December 31, 2022, the Company’s net operating loss carryforwards and tax credits were as follows:

	Year Ended December 31,
	2022		Expiration
Operating Loss Carryforwards
United Kingdom	$	198,571	No expiration
Ireland	61,685		No expiration
Australia	32,333		No expiration
Hong Kong	28,080		No expiration
Netherlands	60		No expiration
United States (1)	23,766		2029 - 2038
Tax Credits
U.K. foreign tax credits	13,907		No expiration
U.S. foreign tax credits	2,830		2029 - 2032

(1) On January 30, 2014, the Company’s U.S. mortgage operations underwent an ownership change for U.S. federal income tax purposes as a result of the Company’s acquisition of the CMG Entities. As a result of this ownership change, a limitation has been imposed upon the utilization of approximately $7.0 million of the Company’s existing U.S. net operating loss carryforwards. Utilization is limited to approximately $0.6 million per year in accordance with Section 382 of the Internal Revenue Code of 1986 as amended (“the Code”).

Reconciliation of the beginning and ending amount of unrecognized tax benefits

A reconciliation of the beginning and ending amount of unrecognized tax benefits is as follows:

	December 31,
	2022		2021
Balance at beginning of year	$	2,008	$	2,008
Additions based on tax positions related to the current year	—		—
Additions for tax positions of prior years	—		—
Reductions for tax positions of prior years	—		—
Settlements	—		—
Balance at end of year	$	2,008	$	2,008

Summary of open tax years potentially subject to examination, by jurisdiction

The following table details open tax years that are potentially subject to examination by local tax authorities, in the following major jurisdictions:

Jurisdiction	Tax Years
United States	2015-2022
United Kingdom	2020-2022
Ireland	2018-2022
Canada	2018-2022
Switzerland	2018-2022
Denmark	2018-2022
Australia	2018-2022

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Leases (Tables)

12 Months Ended

Dec. 31, 2022

Leases [Abstract]

Additional information regarding operating leases

Additional information regarding the Company’s operating leases is as follows:

	December 31,
	2022			2021
Operating lease costs	$	33,571		$	31,691
Sublease income (1)	$	(988)		$	—
Cash payments included in the measurement of lease liabilities reported in operating cash flows	$	26,051		$	32,094
Right-of-use assets obtained in exchange for new lease liabilities	$	42,841		$	22,686
Right-of-use assets (2)	$	123,083		$	106,836
Operating lease liability (2)	$	151,890		$	126,711
Weighted average discount rate	4.2		%	3.9		%
Weighted average remaining lease term	6.6 years			5.9 years

(1)    The sublease income primarily relates to office property in Raleigh, North Carolina.

(2)    The right-of-use assets are included in ‘other assets’ while the operating lease liability is included in ‘other liabilities.’

Contractual maturities of operating lease liabilities

The following table presents the contractual maturities of the Company's operating lease liabilities at December 31, 2022:

Years Ending December 31,
2023	$	31,861
2024	30,091
2025	24,651
2026	21,939
2027	17,859
2028 and thereafter	48,522
Total undiscounted lease liability	$	174,923
Less: present value adjustment	(23,033)
Operating lease liability	$	151,890

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Commitments and Contingencies (Tables)

12 Months Ended

Dec. 31, 2022

Commitments and Contingencies Disclosure [Abstract]

Broker concentration risk

The following table summarizes the percentage of the Company’s gross premiums written generated from or placed by the largest brokers:

Broker	Year Ended December 31,
	2022		2021		2020
Marsh & McLennan Companies and its subsidiaries	17.3	%	18.3	%	13.3	%
Aon Corporation and its subsidiaries	13.8	%	12.2	%	12.0	%

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Debt and Financing Arrangements - (Tables)

12 Months Ended

Dec. 31, 2022

Debt Disclosure [Abstract]

Schedule of senior notes

The Company’s senior notes payable at December 31, 2022 and 2021 were as follows:

					Carrying Amount at
	Interest		Principal		December 31,
	(Fixed)		Amount		2022		2021
2034 notes (1)	7.350	%	300,000		297,618		297,488
2043 notes (2)	5.144	%	500,000		495,188		495,063
2026 notes (3)	4.011	%	500,000		498,073		497,633
2046 notes (4)	5.031	%	450,000		445,582		445,490
2050 notes (5)	3.635	%	1,000,000		988,949		988,720
			$	2,750,000	$	2,725,410	$	2,724,394

(1) Senior notes of Arch Capital issued on May 4, 2004 and due May 1, 2034 (“2034 notes”).

(2) Senior notes of Arch-U.S., a wholly-owned subsidiary of Arch Capital, issued on December 13, 2013 and due November 1, 2043 (“2043 notes”), fully and unconditionally guaranteed by Arch Capital.

(3) Senior notes of Arch Capital Finance LLC (“Arch Finance”), a wholly-owned finance subsidiary of Arch Capital, issued on December 8, 2016 and due December 15, 2026 (“2026 notes”), fully and unconditionally guaranteed by Arch Capital.

(4) Senior notes of Arch Finance issued on December 8, 2016 and due December 15, 2046 (“2046 notes”), fully and unconditionally guaranteed by Arch Capital

(5) Senior notes of Arch Capital issued on June 30, 2020 and due June 30, 2050 (“2050 notes”).

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Goodwill and Intangible Assets (Tables)

12 Months Ended

Dec. 31, 2022

Goodwill and Intangible Assets Disclosure [Abstract]

Analysis of goodwill and intangible assets

The following table shows an analysis of goodwill and intangible assets:

	Goodwill		Intangible assets (indefinite life)		Intangible assets (finite life)		Total
Net balance at Dec. 31, 2020	$	314,629	$	79,219	$	299,015	$	692,863
Acquisitions (1)	31,677		—		318,459		350,136
Amortization	—		—		(82,955)		(82,955)
Impact of deconsolidation of Somers (2)	—		(7,650)		—		(7,650)
Foreign currency movements and other adjustments	(1,441)		(212)		(5,758)		(7,411)
Net balance at Dec. 31, 2021	344,865		71,357		528,761		944,983
Acquisitions (1)	8,389		—		—		8,389
Amortization	—		—		(106,200)		(106,200)
Foreign currency movements and other adjustments	(11,181)		(2,576)		(29,126)		(42,883)
Net balance at Dec. 31, 2022	$	342,073	$	68,781	$	393,435	$	804,289
Gross balance at Dec. 31, 2022	$	351,231	$	70,246	$	1,102,298	$	1,523,775
Accumulated amortization	—		—		(678,020)		(678,020)
Foreign currency movements and other adjustments	(9,158)		(1,465)		(30,843)		(41,466)
Net balance at Dec. 31, 2022	$	342,073	$	68,781	$	393,435	$	804,289

(1)    See note 2, “Acquisitions.”

(2)    See note 12, “Variable Interest Entity and Noncontrolling Interests.”

Summary of components of intangible assets

The following table presents the components of goodwill and intangible assets:

	Gross Balance		Accumulated Amortization		Foreign Currency Translation Adjustment and Other		Net Balance
Dec. 31, 2022
Acquired insurance contracts	$	451,505	$	(426,202)	$	339	$	25,642
Operating platform	52,674		(50,302)		2		2,374
Distribution relationships	602,518		(207,908)		(31,110)		363,500
Goodwill	351,231		—		(9,158)		342,073
Insurance licenses	48,331		—		—		48,331
Syndicate capacity	21,915		—		(1,465)		20,450
Unfavorable service contract	(9,533)		9,533		—		—
Other	5,134		(3,141)		(74)		1,919
Total	$	1,523,775	$	(678,020)	$	(41,466)	$	804,289
Dec. 31, 2021
Acquired insurance contracts	$	451,505	$	(409,592)	$	339	$	42,252
Operating platform	52,674		(48,838)		56		3,892
Distribution relationships	602,518		(120,302)		(2,207)		480,009
Goodwill	342,842		—		2,023		344,865
Insurance licenses	48,331		—		—		48,331
Syndicate capacity	21,915		—		1,111		23,026
Unfavorable service contract	(9,533)		9,435		—		(98)
Other	5,134		(2,542)		114		2,706
Total	$	1,515,386	$	(571,839)	$	1,436	$	944,983

Estimated future amortization expense

The estimated remaining amortization expense for the Company’s intangible assets with finite lives is as follows:

2023	$	91,605
2024	73,366
2025	41,060
2026	32,091
2027	29,268
2028 and thereafter	126,045
Total	$	393,435

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Shareholders' Equity (Tables)

12 Months Ended

Dec. 31, 2022

Stockholders' Equity Note [Abstract]

Roll-forward of changes in issued and outstanding Common Shares

The following table presents a roll-forward of changes in Arch Capital’s issued and outstanding Common Shares:

	Year Ended December 31,
	2022	2021	2020
Common Shares:
Shares issued and outstanding, beginning of year	583,289,850	579,000,841	574,617,195
Shares issued (1)	3,517,399	2,669,229	2,646,164
Restricted shares issued, net of cancellations	1,443,513	1,619,780	1,737,482
Shares issued and outstanding, end of year	588,250,762	583,289,850	579,000,841
Common shares in treasury, end of year	(217,904,765)	(204,365,956)	(172,280,199)
Shares issued and outstanding, end of year	370,345,997	378,923,894	406,720,642

(1)    Includes shares issued from the exercise of stock options and stock appreciation rights, the vesting of restricted share units and shares issued from the employee share purchase plan.

Schedule of share repurchases

The Company’s repurchases under the share repurchase program were as follows:

	Year Ended December 31,
	2022		2021		2020
Aggregate cost of shares repurchased	$	585,823	$	1,234,294	$	83,472
Shares repurchased	12,891,405		31,486,830		2,850,102
Average price per share repurchased	$	45.44	$	39.20	$	29.29

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Share-Based Compensation (Tables)

12 Months Ended

Dec. 31, 2022

Share-Based Payment Arrangement [Abstract]

Valuation assumptions

	Year Ended December 31,
	2022		2021		2020
Dividend yield	—	%	—	%	—	%
Expected volatility	24.0	%	24.2	%	16.6	%
Risk free interest rate	2.0	%	1.0	%	1.2	%
Expected option life	6.0 years		6.0 years		6.0 years

Option activity

A summary of stock option and SAR activity under the Company’s Long Term Incentive and Share Award Plans during 2022 is presented below:

	Year Ended December 31, 2022
	Number of Options / SARs	Weighted Average Exercise Price		Weighted Average Contractual Term	Aggregate Intrinsic Value
Outstanding, beginning of year	17,083,160	$	25.06
Granted	784,963	$	47.46
Exercised	(3,412,371)	$	16.91
Forfeited or expired	(34,851)	$	39.96
Outstanding, end of year	14,420,901	$	28.17	4.37	$	499,051
Exercisable, end of year	12,433,470	$	26.20	3.77	$	454,769

Weighted average grant date fair value

	Year Ended December 31,
	2022		2021		2020
Weighted average grant date fair value	$	13.26	$	9.22	$	8.14
Aggregate intrinsic value of Options/SARs exercised	$	113,409	$	47,074	$	59,723

Unvested restricted share and unit activity

A summary of restricted share and restricted unit activity under the Company’s Long Term Incentive and Share Award Plans for 2022 is presented below:

	Restricted Common Shares		Restricted Unit Awards
Unvested Shares:
Unvested balance, beginning of year	2,070,837		699,866
Granted	914,694		174,699
Vested	(744,096)		(330,144)
Forfeited	(75,881)		(27,128)
Unvested balance, end of year	2,165,554		517,293
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year	$	36.35	$	33.29
Granted	$	47.45	$	47.50
Vested	$	38.21	$	34.38
Forfeited	$	41.13	$	37.51
Unvested balance, end of year	$	40.23	$	37.17

Performance shares and units, valuation assumptions

	Year Ended December 31,
	2022		2021		2020
Expected volatility	38.1	%	37.5	%	18.1	%
Risk free interest rate	1.7	%	0.3	%	1.1	%

Unvested performance share and unit activity

	Performance Shares		Performance Units
Unvested Shares:
Unvested balance, beginning of year	1,861,760		29,770
Granted	669,742		21,030
Performance adjustment (1) (2)	(54,904)		8,921
Vested	(583,544)		(19,695)
Forfeited	(10,138)		(316)
Unvested balance, end of year	1,882,916		39,710
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year	$	38.93	$	38.71
Granted	$	49.91	$	49.91
Performance adjustment (1) (2)	$	36.07	$	35.83
Vested	$	36.07	$	35.83
Forfeited	$	49.91	$	49.91
Unvested balance, end of year	$	43.75	$	45.33

(1)    The performance adjustment represents the difference between the number of performance shares granted and earned, which vested following the end of the performance period. The performance shares were granted at the maximum level of achievement.

(2)    The performance adjustment represents the change in PSUs, which vested following the end of the performance period. The performance units were granted at the target level of achievement.

Share based compensation expense

The following tables present pre-tax and after-tax share-based compensation expense recognized as well as the unrecognized compensation cost associated with unvested awards and the weighted average period over which it is expected to be recognized.

	Year Ended December 31,
	2022		2021		2020
Pre-Tax
Stock options and SARs	$	11,891	$	12,316	$	11,744
Restricted share and unit awards	50,278		46,817		41,284
Performance awards	21,510		23,696		14,729
ESPP	3,993		3,751		2,135
Total	$	87,672	$	86,580	$	69,892
After-Tax
Stock options and SARs	$	10,726	$	10,927	$	10,388
Restricted share and unit awards	42,346		39,349		34,599
Performance awards	19,794		21,920		13,380
ESPP	3,660		3,471		1,978
Total	$	76,526	$	75,667	$	60,345

Unrecognized compensation cost

	December 31, 2022
	Stock Options and SARs		Restricted Common Shares and Units		Performance Common Shares and Units
Unrecognized compensation cost related to unvested awards	$	6,357	$	42,096	$	7,520
Weighted average recognition period (years)	0.75		1.00		0.48

Restricted Common Shares And Restricted Units

Share-based Compensation Arrangement by Share-based Payment Award [Line Items]

Weighted average grant date fair value of restricted stock

The following table presents the weighted average grant date fair value of restricted shares and restricted unit awards granted and the aggregate fair value of restricted shares and unit awards vesting in each year.

	Year Ended December 31,
	2022		2021		2020
Restricted shares and restricted unit awards granted	1,089,393		1,261,773		1,535,330
Weighted average grant date fair value	$	47.45	$	36.12	$	37.55
Aggregate fair value of vested restricted share and unit awards	$	78,129	$	65,477	$	39,703

Performance Common Shares and Units

Share-based Compensation Arrangement by Share-based Payment Award [Line Items]

Weighted average grant date fair value of restricted stock

The following table presents the weighted average grant date fair values of performance awards granted.

	Year Ended December 31,
	2022		2021		2020
Performance awards	690,772		685,104		557,204
Weighted average grant date fair value	$	49.91	$	37.38	$	44.17

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Statutory Information (Tables)

12 Months Ended

Dec. 31, 2022

Disclosure Statutory Information [Abstract]

Summary of statutory capital, surplus and net income

The actual and required statutory capital and surplus for the Company’s principal operating subsidiaries at December 31, 2022 and 2021:

	December 31,
	2022		2021
Actual capital and surplus (1):
Bermuda	$	19,546,128	$	17,528,510
Ireland	968,443		958,200
United States	6,194,954		5,600,652
United Kingdom	1,018,092		902,002
Canada	68,637		70,063
Australia	284,998		283,693
Required capital and surplus:
Bermuda	$	6,449,878	$	5,661,301
Ireland	815,194		794,933
United States	1,748,543		1,717,646
United Kingdom	543,104		563,164
Canada	47,825		42,513
Australia	175,885		214,022

(1)Such amounts include ownership interests in affiliated insurance and reinsurance subsidiaries.

The statutory net income (loss) for the Company’s principal operating subsidiaries for 2022, 2021 and 2020 was as follows:

	Year Ended December 31,
	2022		2021		2020
Statutory net income (loss):
Bermuda	$	1,729,925	$	2,370,746	$	1,579,889
Ireland	(52,757)		25,191		18,397
United States	219,524		345,790		143,271
United Kingdom	56,818		35,286		4,078
Canada	9,215		6,985		(1,049)
Australia	38,538		11,874		(8,601)

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General (Details) - Greysbridge Holdings Ltd	Jul. 01, 2021
Schedule of Equity Method Investments [Line Items]
Percentage ownership	40.00%
Kelso And Company
Schedule of Equity Method Investments [Line Items]
Percentage ownership	30.00%
Warburg Pincus LLC
Schedule of Equity Method Investments [Line Items]
Percentage ownership	30.00%

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Acquisitions (Details) - USD ($) $ in Thousands			12 Months Ended
	Aug. 31, 2021	Aug. 06, 2021	Dec. 31, 2022	Dec. 31, 2021
Business Acquisition [Line Items]
Goodwill and intangible assets, acquisitions			$ 8,389	$ 350,136
Westpac Lenders Mortgage Insurance Limited
Business Acquisition [Line Items]
Term of business exclusivity agreement	10 years
Somerset
Business Acquisition [Line Items]
Goodwill and intangible assets, acquisitions		$ 350,100

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Significant Accounting Policies (Details)	12 Months Ended
	Dec. 31, 2022
Significant Accounting Policies [Line Items]
Premium revenue recognition period	12 months
Investments, time lag for reporting - low end of range	1 month
Investments, time lag for reporting - high end of range	3 months
Vesting period, share-based awards	3 years
Requisite service period, share-based awards	3 years
Losses occurring
Significant Accounting Policies [Line Items]
Premium revenue recognition period	12 months
Risks attaching
Significant Accounting Policies [Line Items]
Premium revenue recognition period	24 months

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Segment Information - Analysis of underwriting income by segment and reconciliation to net income available to common shareholders (Details) $ in Thousands		12 Months Ended
		Dec. 31, 2022 USD ($) segment	Dec. 31, 2021 USD ($)		Dec. 31, 2020 USD ($)
Segment Reporting Information [Line Items]
Gross premiums written		$ 15,326,447	$ 12,752,487		$ 10,088,068
Premiums ceded		(4,249,258)	(3,734,150)		(2,650,352)
Net premiums written		11,077,189	9,018,337		7,437,716
Change in unearned premiums		(1,399,112)	(936,039)		(445,781)
Net premiums earned		9,678,077	8,082,298		6,991,935
Other underwriting income		13,227	22,073		26,784
Losses and loss adjustment expenses		(5,027,517)	(4,584,803)		(4,689,599)
Acquisition expenses, net		(1,739,580)	(1,303,178)		(1,004,842)
Other operating expenses		(1,128,175)	(998,595)		(875,176)
Underwriting income (loss)		1,796,032	1,217,795		449,102
Net investment income		496,547	389,118		519,608
Net realized gains (losses)		(662,734)	379,845		823,460
Equity in net income (loss) of investment funds accounted for using the equity method		115,856	366,402		146,693
Other income (loss)		(26,165)	10,244		29
Corporate expenses		(94,390)	(77,119)		(68,492)
Transaction costs and other		(1,092)	(2,038)		(13,496)
Amortization of intangible assets		(106,200)	(82,955)		(69,031)
Interest expense		(130,266)	(139,470)		(143,456)
Net foreign exchange gains (losses)		100,905	41,529		(83,634)
Income before income taxes and income (loss) from operating affiliates		1,488,493	2,103,351		1,560,783
Income tax (expense) benefit		(79,961)	(128,582)		(111,838)
Income (loss) from operating affiliates		73,891	264,693		16,766
Net income (loss)		1,482,423	2,239,462		1,465,711
Amounts attributable to redeemable noncontrolling interests		(5,490)	(4,299)		(7,114)
Amounts attributable to nonredeemable noncontrolling interests		0	(78,314)		(53,076)
Net income available to Arch		1,476,933	2,156,849		1,405,521
Preferred share dividends		(40,736)	(48,343)		(41,612)
Loss on redemption of preferred shares		0	(15,101)		0
Net income (loss) available to Arch common shareholders		$ 1,436,197	$ 2,093,405		$ 1,363,909
Underwriting Ratios
Loss ratio		51.90%	56.70%		67.10%
Acquisition expense ratio		18.00%	16.10%		14.40%
Other operating expense ratio		11.70%	12.40%		12.50%
Combined ratio		81.60%	85.20%		94.00%
Goodwill and intangible assets		$ 804,289	$ 944,983		$ 692,863
Total investable assets		28,065,497	27,442,153		29,513,907
Total assets		47,990,507	45,100,945		43,282,297
Total liabilities		$ 35,069,605	31,545,816		29,294,856
Operating segments | Underwriting Segments
Segment Reporting Information [Line Items]
Number of segments | segment		3
Gross premiums written	[1]	$ 15,326,447	12,463,788		9,632,691
Premiums ceded		(4,249,258)	(3,800,153)		(2,732,564)
Net premiums written		11,077,189	8,663,635		6,900,127
Change in unearned premiums		(1,399,112)	(913,305)		(468,543)
Net premiums earned		9,678,077	7,750,330		6,431,584
Other underwriting income		13,227	21,334		24,739
Losses and loss adjustment expenses		(5,027,517)	(4,325,761)		(4,249,117)
Acquisition expenses, net		(1,739,580)	(1,240,437)		(906,771)
Other operating expenses		(1,128,175)	(965,726)		(819,366)
Underwriting income (loss)		1,796,032	1,239,740		481,069
Net investment income		496,547	346,808		401,908
Net realized gains (losses)		(662,734)	299,207		813,781
Equity in net income (loss) of investment funds accounted for using the equity method		115,856	366,402		146,693
Other income (loss)		(26,165)	10,244		29
Corporate expenses		(94,390)	(77,119)		(68,492)
Transaction costs and other		(1,092)	(1,103)		(9,456)
Amortization of intangible assets		(106,200)	(82,057)		(69,031)
Interest expense		(130,266)	(131,060)		(120,214)
Net foreign exchange gains (losses)		100,905	42,854		(80,161)
Income before income taxes and income (loss) from operating affiliates		1,488,493	2,013,916		1,496,126
Income tax (expense) benefit		(79,961)	(128,348)		(111,812)
Income (loss) from operating affiliates		73,891	264,693		16,766
Net income (loss)		1,482,423	2,150,261		1,401,080
Amounts attributable to redeemable noncontrolling interests		(5,490)	(2,346)		(2,997)
Amounts attributable to nonredeemable noncontrolling interests			0		0
Net income available to Arch		1,476,933	2,147,915		1,398,083
Preferred share dividends		(40,736)	(48,343)		(41,612)
Loss on redemption of preferred shares			(15,101)
Net income (loss) available to Arch common shareholders		$ 1,436,197	$ 2,084,471		$ 1,356,471
Underwriting Ratios
Loss ratio		51.90%	55.80%		66.10%
Acquisition expense ratio		18.00%	16.00%		14.10%
Other operating expense ratio		11.70%	12.50%		12.70%
Combined ratio		81.60%	84.30%		92.90%
Goodwill and intangible assets		$ 804,289	$ 944,983		$ 685,213
Total investable assets		28,065,497	27,442,153		26,856,295
Total assets		47,990,507	45,100,945		39,791,983
Total liabilities		35,069,605	31,545,816		26,789,149
Operating segments | Insurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	6,930,864	5,867,734		4,688,562
Premiums ceded	[2]	(1,910,222)	(1,719,541)		(1,525,655)
Net premiums written		5,020,642	4,148,193		3,162,907
Change in unearned premiums		(461,307)	(521,725)		(291,487)
Net premiums earned		4,559,335	3,626,468		2,871,420
Other underwriting income		0	0		(31)
Losses and loss adjustment expenses		(2,782,945)	(2,344,365)		(2,092,453)
Acquisition expenses, net		(885,866)	(606,265)		(418,483)
Other operating expenses		(665,472)	(558,906)		(489,153)
Underwriting income (loss)		$ 225,052	$ 116,932		$ (128,700)
Underwriting Ratios
Loss ratio		61.00%	64.60%		72.90%
Acquisition expense ratio		19.40%	16.70%		14.60%
Other operating expense ratio		14.60%	15.40%		17.00%
Combined ratio		95.00%	96.70%		104.50%
Goodwill and intangible assets		$ 228,532	$ 256,434		$ 280,978
Operating segments | Reinsurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	6,948,438	5,093,930		3,472,086
Premiums ceded	[2]	(2,024,462)	(1,839,556)		(1,014,716)
Net premiums written		4,923,976	3,254,374		2,457,370
Change in unearned premiums		(964,595)	(413,931)		(295,141)
Net premiums earned		3,959,381	2,840,443		2,162,229
Other underwriting income		4,871	3,669		4,454
Losses and loss adjustment expenses		(2,568,843)	(1,924,719)		(1,628,320)
Acquisition expenses, net		(813,555)	(536,754)		(354,048)
Other operating expenses		(267,531)	(212,810)		(168,011)
Underwriting income (loss)		$ 314,323	$ 169,829		$ 16,304
Underwriting Ratios
Loss ratio		64.90%	67.80%		75.30%
Acquisition expense ratio		20.50%	18.90%		16.40%
Other operating expense ratio		6.80%	7.50%		7.80%
Combined ratio		92.20%	94.20%		99.50%
Goodwill and intangible assets		$ 144,846	$ 183,523		$ 18,963
Operating segments | Mortgage
Segment Reporting Information [Line Items]
Gross premiums written	[1]	1,454,971	1,507,825		1,473,999
Premiums ceded	[2]	(322,400)	(246,757)		(194,149)
Net premiums written		1,132,571	1,261,068		1,279,850
Change in unearned premiums		26,790	22,351		118,085
Net premiums earned		1,159,361	1,283,419		1,397,935
Other underwriting income		8,356	17,665		20,316
Losses and loss adjustment expenses		324,271	(56,677)		(528,344)
Acquisition expenses, net		(40,159)	(97,418)		(134,240)
Other operating expenses		(195,172)	(194,010)		(162,202)
Underwriting income (loss)		$ 1,256,657	$ 952,979		$ 593,465
Underwriting Ratios
Loss ratio		(28.00%)	4.40%		37.80%
Acquisition expense ratio		3.50%	7.60%		9.60%
Other operating expense ratio		16.80%	15.10%		11.60%
Combined ratio		(7.70%)	27.10%		59.00%
Goodwill and intangible assets		$ 430,911	$ 505,026		$ 385,272
Operating segments | Other
Segment Reporting Information [Line Items]
Number of segments | segment		2
Gross premiums written	[1]	$ 0	457,465		728,546
Premiums ceded		0	(102,763)	[2]	(190,957)	[2]
Net premiums written		0	354,702		537,589
Change in unearned premiums		0	(22,734)		22,762
Net premiums earned		0	331,968		560,351
Other underwriting income		0	739		2,045
Losses and loss adjustment expenses		0	(259,042)		(440,482)
Acquisition expenses, net		0	(62,741)		(98,071)
Other operating expenses		0	(32,869)		(55,810)
Underwriting income (loss)		0	(21,945)		(31,967)
Net investment income		0	42,310		117,700
Net realized gains (losses)		0	80,638		9,679
Equity in net income (loss) of investment funds accounted for using the equity method		0	0		0
Other income (loss)		0	0		0
Corporate expenses		0	0		0
Transaction costs and other		0	(935)		(4,040)
Amortization of intangible assets		0	(898)		0
Interest expense		0	(8,410)		(23,242)
Net foreign exchange gains (losses)		0	(1,325)		(3,473)
Income before income taxes and income (loss) from operating affiliates		0	89,435		64,657
Income tax (expense) benefit		0	(234)		(26)
Income (loss) from operating affiliates		0	0		0
Net income (loss)		0	89,201		64,631
Amounts attributable to redeemable noncontrolling interests		0	(1,953)		(4,117)
Amounts attributable to nonredeemable noncontrolling interests		0	(78,314)		(53,076)
Net income available to Arch		0	8,934		7,438
Preferred share dividends		0	0		0
Loss on redemption of preferred shares			0
Net income (loss) available to Arch common shareholders		$ 0	$ 8,934		$ 7,438
Underwriting Ratios
Loss ratio		0.00%	78.00%		78.60%
Acquisition expense ratio		0.00%	18.90%		17.50%
Other operating expense ratio		0.00%	9.90%		10.00%
Combined ratio		0.00%	106.80%		106.10%
Goodwill and intangible assets		$ 0	$ 0		$ 7,650
Total investable assets		0	0		2,657,612
Total assets		0	0		3,490,314
Total liabilities		$ 0	$ 0		$ 2,505,707

[1] Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

[2] Certain amounts included in the gross premiums written of each segment are related to intersegment transactions and are included in the gross premiums written of each segment. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

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Segment Information - Summary of net premiums written and earned by major line of business and net premiums written by location (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Segment Reporting Information [Line Items]
Net premiums earned		$ 9,678,077	$ 8,082,298	$ 6,991,935
Net premiums written		11,077,189	9,018,337	7,437,716
Operating segments | Insurance
Segment Reporting Information [Line Items]
Net premiums earned		4,559,335	3,626,468	2,871,420
Net premiums written		5,020,642	4,148,193	3,162,907
Operating segments | Insurance | United States
Segment Reporting Information [Line Items]
Net premiums written	[1]	3,340,038	2,813,039	2,158,415
Operating segments | Insurance | Europe
Segment Reporting Information [Line Items]
Net premiums written	[1]	1,405,719	1,125,192	856,572
Operating segments | Insurance | Other geographic location
Segment Reporting Information [Line Items]
Net premiums written	[1]	274,885	209,962	147,920
Operating segments | Insurance | Professional lines
Segment Reporting Information [Line Items]
Net premiums earned	[1]	1,314,236	942,817	655,872
Operating segments | Insurance | Property, energy, marine and aviation
Segment Reporting Information [Line Items]
Net premiums earned	[1]	772,388	667,892	506,182
Operating segments | Insurance | Programs
Segment Reporting Information [Line Items]
Net premiums earned	[1]	589,860	506,867	432,854
Operating segments | Insurance | Travel, accident and health
Segment Reporting Information [Line Items]
Net premiums earned	[1]	491,847	255,590	190,944
Operating segments | Insurance | Construction and national accounts
Segment Reporting Information [Line Items]
Net premiums earned	[1]	432,020	416,107	398,999
Operating segments | Insurance | Excess and surplus casualty
Segment Reporting Information [Line Items]
Net premiums earned	[1]	393,353	318,027	270,620
Operating segments | Insurance | Warranty and lenders solutions
Segment Reporting Information [Line Items]
Net premiums earned	[1]	127,222	153,958	114,687
Operating segments | Insurance | Other
Segment Reporting Information [Line Items]
Net premiums earned	[1]	438,409	365,210	301,262
Operating segments | Reinsurance
Segment Reporting Information [Line Items]
Net premiums earned		3,959,381	2,840,443	2,162,229
Net premiums written		4,923,976	3,254,374	2,457,370
Operating segments | Reinsurance | United States
Segment Reporting Information [Line Items]
Net premiums written	[1]	1,246,507	828,504	687,622
Operating segments | Reinsurance | Bermuda
Segment Reporting Information [Line Items]
Net premiums written	[1]	2,561,771	1,557,294	1,001,990
Operating segments | Reinsurance | Europe and other
Segment Reporting Information [Line Items]
Net premiums written	[1]	1,115,698	868,576	767,758
Operating segments | Reinsurance | Other specialty
Segment Reporting Information [Line Items]
Net premiums earned	[1]	1,377,880	818,801	626,409
Operating segments | Reinsurance | Property excluding property catastrophe
Segment Reporting Information [Line Items]
Net premiums earned	[1]	1,091,440	836,573	562,208
Operating segments | Reinsurance | Casualty
Segment Reporting Information [Line Items]
Net premiums earned	[1]	854,543	666,754	549,056
Operating segments | Reinsurance | Property catastrophe
Segment Reporting Information [Line Items]
Net premiums earned	[1]	366,991	280,738	237,736
Operating segments | Reinsurance | Marine and aviation
Segment Reporting Information [Line Items]
Net premiums earned	[1]	159,401	152,955	109,624
Operating segments | Reinsurance | Other
Segment Reporting Information [Line Items]
Net premiums earned	[1]	109,126	84,622	77,196
Operating segments | Mortgage
Segment Reporting Information [Line Items]
Net premiums earned		1,159,361	1,283,419	1,397,935
Net premiums written		1,132,571	1,261,068	1,279,850
Operating segments | Mortgage | United States
Segment Reporting Information [Line Items]
Net premiums earned		815,519	970,507	1,158,563
Net premiums written		780,256	914,477	1,021,950
Operating segments | Mortgage | Other geographic location
Segment Reporting Information [Line Items]
Net premiums earned		343,842	312,912	239,372
Net premiums written		352,315	346,591	257,900
Operating segments | Other
Segment Reporting Information [Line Items]
Net premiums earned		0	331,968	560,351
Net premiums written		0	354,702	537,589
Operating segments | Other | United States
Segment Reporting Information [Line Items]
Net premiums written	[1]	0	63,403	115,471
Operating segments | Other | Europe
Segment Reporting Information [Line Items]
Net premiums written	[1]	0	91,499	97,753
Operating segments | Other | Bermuda
Segment Reporting Information [Line Items]
Net premiums written	[1]	0	199,800	324,365
Operating segments | Other | Other specialty
Segment Reporting Information [Line Items]
Net premiums earned	[1]	0	118,356	186,717
Operating segments | Other | Property excluding property catastrophe
Segment Reporting Information [Line Items]
Net premiums earned	[1]	0	6,578	1,130
Operating segments | Other | Casualty
Segment Reporting Information [Line Items]
Net premiums earned	[1]	0	138,551	245,272
Operating segments | Other | Property catastrophe
Segment Reporting Information [Line Items]
Net premiums earned	[1]	0	15,235	23,037
Operating segments | Other | Marine and aviation
Segment Reporting Information [Line Items]
Net premiums earned	[1]	0	190	429
Operating segments | Other | Other
Segment Reporting Information [Line Items]
Net premiums earned	[1]	$ 0	$ 53,058	$ 103,766

[1] Segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions.

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Reserve for Losses and Loss Adjustment Expenses - Reconciliation of beginning and ending balances of losses and loss adjustment reserves (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Liability for Future Policy Benefits and Unpaid Claims and Claims Adjustment Expense [Abstract]
Reserve for losses and loss adjustment expenses at beginning of year		$ 17,757,156	$ 16,513,929	$ 13,891,842
Unpaid losses and loss adjustment expenses recoverable		5,599,231	4,314,855	4,082,650
Net reserve for losses and loss adjustment expenses at beginning of year		12,157,925	12,199,074	9,809,192
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year		5,798,528	4,940,987	4,851,051
Prior years		(771,011)	(356,184)	(161,452)
Total net incurred losses and loss adjustment expenses		5,027,517	4,584,803	4,689,599
Net losses and loss adjustment expense reserves of acquired business	[1]	0	104,176	0
Retroactive reinsurance transaction	[2]	0	(444,147)	182,210
Impact of deconsolidation of Somers		0	(1,460,611)	0
Foreign exchange (gains) losses and other		(290,376)	1,181	179,190
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year		(887,464)	(734,846)	(661,529)
Prior years		(2,254,484)	(2,091,705)	(1,999,588)
Total net paid losses and loss adjustment expenses		(3,141,948)	(2,826,551)	(2,661,117)
Net reserve for losses and loss adjustment expenses at end of year		13,753,118	12,157,925	12,199,074
Unpaid losses and loss adjustment expenses recoverable		6,278,825	5,599,231	4,314,855
Reserve for losses and loss adjustment expenses at end of year		$ 20,031,943	$ 17,757,156	$ 16,513,929

[1] Represents activity related to the Company’s acquisitions in the 2021 period.

[2] See ‘Retroactive Reinsurance Transactions’ section.

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Reserve for Losses and Loss Adjustment Expenses - Prior years reserve development (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 771,011	$ 356,184	$ 161,452
Operating segments | Insurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 25,300	$ 16,200	$ 7,800
Prior year reserve development (points)	0.60%	0.40%	0.30%
Operating segments | Insurance | Short-tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 55,300	$ 81,700	$ 33,600
Operating segments | Insurance | Short-tailed lines | Property Excluding Marine
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		38,900	21,600
Operating segments | Insurance | Short-tailed lines | Lenders products
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	37,400	26,700
Operating segments | Insurance | Short-tailed lines | Travel and Accident
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	14,800	16,200	8,400
Operating segments | Insurance | Medium-tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		(93,500)	(75,200)
Operating segments | Insurance | Medium-tailed lines | Programs
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)			(16,000)
Operating segments | Insurance | Medium-tailed lines | Professional liability
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(24,700)	(30,800)
Operating segments | Insurance | Medium-tailed lines | Surety
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)			(37,900)
Operating segments | Insurance | Medium-tailed lines | Contract binding
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(6,400)	(57,600)	(23,100)
Operating segments | Insurance | Medium-tailed lines | Marine
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	12,900
Operating segments | Insurance | Long-tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		28,100	49,400
Operating segments | Insurance | Long-tailed lines | Casualty
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(18,500)
Operating segments | Insurance | Long-tailed lines | Other business
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	21,500		38,800
Operating segments | Insurance | Long-tailed lines | Construction and national accounts
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(7,300)
Operating segments | Insurance | Long-tailed lines | Construction Product Line
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)			9,300
Operating segments | Insurance | Medium-tailed and long-tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(29,900)
Operating segments | Insurance | Short Tailed And Long Tailed Lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		109,800	83,000
Operating segments | Reinsurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 191,600	$ 178,800	$ 134,000
Prior year reserve development (points)	4.80%	6.30%	6.20%
Operating segments | Reinsurance | Short-tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		$ 175,500	$ 144,000
Operating segments | Reinsurance | Short-tailed lines | Property catastrophe and property other than property catastrophe
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)			87,700
Operating segments | Reinsurance | Short-tailed lines | Property catastrophe
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 24,000	(36,400)
Operating segments | Reinsurance | Short-tailed lines | Property excluding property catastrophe
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	109,400	88,600
Operating segments | Reinsurance | Short-tailed lines | Other specialty lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	35,000	123,300	53,600
Operating segments | Reinsurance | Medium-tailed lines | Marine and aviation
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	28,000
Operating segments | Reinsurance | Long-tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(4,600)	(5,300)	(21,900)
Operating segments | Reinsurance | Long-tailed lines | Casualty
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(4,600)
Operating segments | Reinsurance | Short Tailed And Medium Tailed Lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	196,200	184,100	155,900
Operating segments | Mortgage
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 554,100	$ 169,600	$ 19,000
Prior year reserve development (points)	47.80%	13.20%	1.40%
Operating segments | Mortgage | Primary mortgage business
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)			$ 16,200
Operating segments | Other
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		$ (8,400)	$ 700

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Short Duration Contracts - Claims development - Insurance (Details) $ in Thousands	Dec. 31, 2022 USD ($) claims	Dec. 31, 2021 USD ($)	Dec. 31, 2020 USD ($)	Dec. 31, 2019 USD ($)	Dec. 31, 2018 USD ($)	Dec. 31, 2017 USD ($)	Dec. 31, 2016 USD ($)	Dec. 31, 2015 USD ($)	Dec. 31, 2014 USD ($)	Dec. 31, 2013 USD ($)
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance	$ 13,445,271
Insurance | Property, energy, marine and aviation
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	2,279,988
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,547,766
All outstanding liabilities before 2013, net of reinsurance	18,239
Liabilities for losses and loss adjustment expenses, net of reinsurance	750,461
Insurance | Property, energy, marine and aviation | 2013
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	124,868	$ 125,813	$ 126,825	$ 128,157	$ 133,400	$ 134,473	$ 142,889	$ 148,622	$ 156,147	$ 158,548
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	124,402	124,381	124,227	122,894	125,014	121,779	119,649	110,432	84,680	32,216
Total of IBNR liabilities plus expected development on reported claims	$ 27
Cumulative number of reported claims | claims	3,982
Insurance | Property, energy, marine and aviation | 2014
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 133,605	134,803	134,895	134,192	132,166	136,050	147,248	145,679	148,104
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	122,792	122,165	115,253	98,423	87,681	84,061	77,764	53,632	25,849
Total of IBNR liabilities plus expected development on reported claims	$ 1,674
Cumulative number of reported claims | claims	3,557
Insurance | Property, energy, marine and aviation | 2015
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 90,816	91,833	91,770	97,789	102,449	103,921	109,769	112,299
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	87,564	87,260	86,190	87,870	86,196	76,282	64,900	23,561
Total of IBNR liabilities plus expected development on reported claims	$ 2,654
Cumulative number of reported claims | claims	4,244
Insurance | Property, energy, marine and aviation | 2016
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 87,618	92,108	95,989	100,003	105,184	100,843	104,002
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	87,232	90,808	94,570	97,089	98,303	83,218	24,684
Total of IBNR liabilities plus expected development on reported claims	$ 61
Cumulative number of reported claims | claims	5,704
Insurance | Property, energy, marine and aviation | 2017
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 225,298	231,199	230,413	235,924	246,264	280,686
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	217,764	215,874	211,688	195,512	139,849	30,215
Total of IBNR liabilities plus expected development on reported claims	$ 3,268
Cumulative number of reported claims | claims	6,287
Insurance | Property, energy, marine and aviation | 2018
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 170,411	170,057	173,693	186,030	180,981
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	149,663	142,838	134,858	102,285	30,026
Total of IBNR liabilities plus expected development on reported claims	$ 7,177
Cumulative number of reported claims | claims	5,048
Insurance | Property, energy, marine and aviation | 2019
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 161,156	165,477	178,564	179,056
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	139,141	133,911	105,380	26,130
Total of IBNR liabilities plus expected development on reported claims	$ 4,162
Cumulative number of reported claims | claims	5,942
Insurance | Property, energy, marine and aviation | 2020
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 335,747	329,362	359,394
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	251,055	194,487	55,619
Total of IBNR liabilities plus expected development on reported claims	$ 28,330
Cumulative number of reported claims | claims	8,546
Insurance | Property, energy, marine and aviation | 2021
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 428,719	426,870
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	267,677	90,423
Total of IBNR liabilities plus expected development on reported claims	$ 54,746
Cumulative number of reported claims | claims	7,566
Insurance | Property, energy, marine and aviation | 2022
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 521,750
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	100,476
Total of IBNR liabilities plus expected development on reported claims	$ 208,080
Cumulative number of reported claims | claims	8,965
Insurance | Third party occurrence business
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 4,677,656
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,755,958
All outstanding liabilities before 2013, net of reinsurance	263,297
Liabilities for losses and loss adjustment expenses, net of reinsurance	3,184,995
Insurance | Third party occurrence business | 2013
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	263,430	270,110	269,297	272,385	274,246	281,637	301,622	306,572	296,668	282,852
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	192,159	184,444	174,591	164,090	149,012	122,045	101,153	71,335	29,215	6,840
Total of IBNR liabilities plus expected development on reported claims	$ 43,148
Cumulative number of reported claims | claims	66,118
Insurance | Third party occurrence business | 2014
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 345,024	343,286	342,641	343,904	339,403	342,759	338,505	335,587	329,718
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	237,135	223,895	211,440	191,108	161,935	112,541	71,473	40,226	9,200
Total of IBNR liabilities plus expected development on reported claims	$ 60,263
Cumulative number of reported claims | claims	75,557
Insurance | Third party occurrence business | 2015
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 379,226	386,465	382,427	391,132	391,797	398,565	391,570	358,769
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	249,399	227,439	211,510	181,505	139,364	88,411	44,514	11,110
Total of IBNR liabilities plus expected development on reported claims	$ 75,540
Cumulative number of reported claims | claims	78,507
Insurance | Third party occurrence business | 2016
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 363,453	367,586	374,654	399,315	405,803	394,190	389,530
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	215,481	194,637	164,534	136,759	87,543	41,920	11,679
Total of IBNR liabilities plus expected development on reported claims	$ 93,800
Cumulative number of reported claims | claims	78,576
Insurance | Third party occurrence business | 2017
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 406,165	406,857	412,231	422,360	417,662	417,097
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	220,660	165,468	134,988	99,806	52,309	13,391
Total of IBNR liabilities plus expected development on reported claims	$ 114,603
Cumulative number of reported claims | claims	84,418
Insurance | Third party occurrence business | 2018
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 458,050	451,164	450,647	452,879	430,128
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	198,502	154,138	115,049	63,776	16,991
Total of IBNR liabilities plus expected development on reported claims	$ 156,700
Cumulative number of reported claims | claims	77,685
Insurance | Third party occurrence business | 2019
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 471,279	480,535	487,080	455,928
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	172,948	121,646	73,075	18,375
Total of IBNR liabilities plus expected development on reported claims	$ 195,283
Cumulative number of reported claims | claims	84,985
Insurance | Third party occurrence business | 2020
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 640,231	616,314	606,640
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	154,902	76,567	24,407
Total of IBNR liabilities plus expected development on reported claims	$ 309,019
Cumulative number of reported claims | claims	90,795
Insurance | Third party occurrence business | 2021
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 662,716	621,972
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	90,791	26,235
Total of IBNR liabilities plus expected development on reported claims	$ 431,302
Cumulative number of reported claims | claims	89,718
Insurance | Third party occurrence business | 2022
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 688,082
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	23,981
Total of IBNR liabilities plus expected development on reported claims	$ 614,366
Cumulative number of reported claims | claims	70,380
Insurance | Third party claims-made business
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 3,759,343
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,854,161
All outstanding liabilities before 2013, net of reinsurance	86,120
Liabilities for losses and loss adjustment expenses, net of reinsurance	1,991,302
Insurance | Third party claims-made business | 2013
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	281,584	273,607	271,156	281,642	290,852	294,372	320,177	324,044	320,266	301,608
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	253,570	246,813	245,423	238,730	216,984	197,861	179,261	137,857	87,386	19,007
Total of IBNR liabilities plus expected development on reported claims	$ 14,639
Cumulative number of reported claims | claims	14,953
Insurance | Third party claims-made business | 2014
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 296,153	287,573	291,498	297,248	281,271	278,556	298,541	279,410	264,273
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	260,333	249,307	243,137	229,314	207,447	172,722	129,409	63,288	13,814
Total of IBNR liabilities plus expected development on reported claims	$ 21,206
Cumulative number of reported claims | claims	15,482
Insurance | Third party claims-made business | 2015
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 266,758	267,725	252,263	255,207	259,830	276,256	277,358	258,740
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	220,871	216,892	193,105	174,084	126,431	100,030	52,007	9,059
Total of IBNR liabilities plus expected development on reported claims	$ 18,198
Cumulative number of reported claims | claims	14,392
Insurance | Third party claims-made business | 2016
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 329,534	326,960	321,764	314,412	308,080	291,258	274,996
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	256,705	242,300	205,478	158,127	127,203	68,157	10,537
Total of IBNR liabilities plus expected development on reported claims	$ 29,356
Cumulative number of reported claims | claims	15,083
Insurance | Third party claims-made business | 2017
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 316,673	323,128	308,172	311,724	285,738	270,272
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	232,508	195,788	143,064	112,975	67,529	9,281
Total of IBNR liabilities plus expected development on reported claims	$ 45,042
Cumulative number of reported claims | claims	15,198
Insurance | Third party claims-made business | 2018
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 347,449	336,106	319,646	314,112	272,543
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	208,063	158,389	118,105	68,244	12,241
Total of IBNR liabilities plus expected development on reported claims	$ 61,612
Cumulative number of reported claims | claims	15,934
Insurance | Third party claims-made business | 2019
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 322,178	317,363	317,312	289,128
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	154,630	122,046	65,286	12,373
Total of IBNR liabilities plus expected development on reported claims	$ 93,422
Cumulative number of reported claims | claims	15,858
Insurance | Third party claims-made business | 2020
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 423,375	413,156	383,497
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	151,750	87,248	17,070
Total of IBNR liabilities plus expected development on reported claims	$ 187,245
Cumulative number of reported claims | claims	15,438
Insurance | Third party claims-made business | 2021
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 517,975	514,676
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	90,487	23,253
Total of IBNR liabilities plus expected development on reported claims	$ 351,736
Cumulative number of reported claims | claims	15,751
Insurance | Third party claims-made business | 2022
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 657,664
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	25,244
Total of IBNR liabilities plus expected development on reported claims	$ 575,484
Cumulative number of reported claims | claims	18,190
Insurance | Multi-line and other specialty
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 4,849,348
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	3,655,902
All outstanding liabilities before 2013, net of reinsurance	22,275
Liabilities for losses and loss adjustment expenses, net of reinsurance	1,215,721
Insurance | Multi-line and other specialty | 2013
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	244,191	245,069	245,825	248,634	253,271	251,894	263,928	263,631	272,335	264,243
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	238,257	238,321	237,293	236,375	234,330	225,324	213,461	180,428	150,925	$ 86,680
Total of IBNR liabilities plus expected development on reported claims	$ 2,761
Cumulative number of reported claims | claims	86,371
Insurance | Multi-line and other specialty | 2014
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 310,977	309,061	310,051	313,221	317,197	318,268	318,453	325,705	301,548
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	295,896	294,630	293,131	291,727	281,195	267,079	234,267	196,899	$ 107,726
Total of IBNR liabilities plus expected development on reported claims	$ 3,968
Cumulative number of reported claims | claims	130,844
Insurance | Multi-line and other specialty | 2015
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 344,974	347,206	349,432	356,657	364,815	356,777	357,939	334,684
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	331,320	330,431	326,652	320,971	305,895	277,850	236,108	$ 138,153
Total of IBNR liabilities plus expected development on reported claims	$ 5,632
Cumulative number of reported claims | claims	170,579
Insurance | Multi-line and other specialty | 2016
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 408,716	408,004	409,987	416,108	427,829	430,976	408,686
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	390,350	385,314	379,305	362,823	341,789	304,743	$ 175,948
Total of IBNR liabilities plus expected development on reported claims	$ 8,616
Cumulative number of reported claims | claims	189,406
Insurance | Multi-line and other specialty | 2017
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 512,717	504,322	500,947	491,347	501,026	482,436
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	471,978	446,002	423,480	380,696	342,385	$ 181,102
Total of IBNR liabilities plus expected development on reported claims	$ 12,776
Cumulative number of reported claims | claims	229,570
Insurance | Multi-line and other specialty | 2018
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 564,693	565,116	562,848	564,563	512,406
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	508,649	479,824	442,643	389,047	$ 211,711
Total of IBNR liabilities plus expected development on reported claims	$ 21,722
Cumulative number of reported claims | claims	256,621
Insurance | Multi-line and other specialty | 2019
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 651,004	640,262	612,179	566,864
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	548,844	486,882	385,794	$ 211,970
Total of IBNR liabilities plus expected development on reported claims	$ 38,672
Cumulative number of reported claims | claims	250,441
Insurance | Multi-line and other specialty | 2020
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 515,016	569,123	618,340
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	358,967	309,106	$ 171,994
Total of IBNR liabilities plus expected development on reported claims	$ 87,261
Cumulative number of reported claims | claims	162,214
Insurance | Multi-line and other specialty | 2021
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 618,581	635,186
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	334,549	$ 156,992
Total of IBNR liabilities plus expected development on reported claims	$ 153,336
Cumulative number of reported claims | claims	113,165
Insurance | Multi-line and other specialty | 2022
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 678,479
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	177,092
Total of IBNR liabilities plus expected development on reported claims	$ 425,107
Cumulative number of reported claims | claims	89,859

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Short Duration Contracts - Claims development - Reinsurance (Details) - USD ($) $ in Thousands	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017	Dec. 31, 2016	Dec. 31, 2015	Dec. 31, 2014	Dec. 31, 2013
Claims Development [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance	$ 13,445,271
Reinsurance | Casualty
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	3,179,551
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,155,014
All outstanding liabilities before 2013, net of reinsurance	299,288
Liabilities for losses and loss adjustment expenses, net of reinsurance	2,323,825
Reinsurance | Casualty | 2013
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	133,094	$ 133,687	$ 133,401	$ 129,120	$ 132,701	$ 134,204	$ 146,230	$ 152,392	$ 156,619	$ 163,425
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	87,485	81,167	76,141	70,289	62,751	54,323	42,861	22,886	9,822	2,421
Total of IBNR liabilities plus expected development on reported claims	26,542
Reinsurance | Casualty | 2014
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	231,175	230,944	234,293	233,922	224,105	227,485	214,724	217,991	212,923
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	152,586	143,929	133,263	113,596	90,530	63,214	40,651	15,973	3,885
Total of IBNR liabilities plus expected development on reported claims	33,255
Reinsurance | Casualty | 2015
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	247,419	245,756	242,554	235,637	231,473	224,385	216,759	217,343
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	151,119	136,138	119,096	95,988	70,523	46,933	20,208	4,440
Total of IBNR liabilities plus expected development on reported claims	44,753
Reinsurance | Casualty | 2016
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	268,079	264,475	264,573	257,214	242,089	221,004	208,192
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	155,584	131,341	112,818	86,362	51,494	25,626	5,720
Total of IBNR liabilities plus expected development on reported claims	46,122
Reinsurance | Casualty | 2017
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	310,858	304,194	293,381	267,173	251,827	262,894
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	163,243	136,489	112,474	63,922	30,316	6,417
Total of IBNR liabilities plus expected development on reported claims	52,415
Reinsurance | Casualty | 2018
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	293,320	281,852	276,802	284,405	270,621
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	154,173	128,728	106,443	31,240	7,576
Total of IBNR liabilities plus expected development on reported claims	56,325
Reinsurance | Casualty | 2019
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	372,669	361,549	334,755	325,359
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	129,766	96,593	57,568	15,798
Total of IBNR liabilities plus expected development on reported claims	93,310
Reinsurance | Casualty | 2020
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	349,831	367,595	378,668
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	90,156	50,383	17,646
Total of IBNR liabilities plus expected development on reported claims	169,909
Reinsurance | Casualty | 2021
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	431,165	434,187
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	53,264	14,633
Total of IBNR liabilities plus expected development on reported claims	292,696
Reinsurance | Casualty | 2022
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	541,941
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	17,638
Total of IBNR liabilities plus expected development on reported claims	482,552
Reinsurance | Property catastrophe
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	1,017,376
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	484,830
All outstanding liabilities before 2013, net of reinsurance	2,612
Liabilities for losses and loss adjustment expenses, net of reinsurance	535,158
Reinsurance | Property catastrophe | 2013
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	26,221	26,344	26,543	26,415	27,248	27,974	30,518	34,959	45,962	65,372
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	27,023	26,998	27,233	26,549	26,549	26,329	24,697	23,001	18,496	12,035
Total of IBNR liabilities plus expected development on reported claims	(138)
Reinsurance | Property catastrophe | 2014
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	19,045	19,004	19,229	19,326	20,026	21,764	24,500	29,801	43,800
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	18,592	18,629	18,550	18,421	18,244	18,679	17,902	19,544	13,619
Total of IBNR liabilities plus expected development on reported claims	(10)
Reinsurance | Property catastrophe | 2015
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	2,569	2,932	3,133	3,779	5,531	11,425	17,558	32,748
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,874	1,817	1,745	1,659	2,103	1,843	(2,109)	(3,141)
Total of IBNR liabilities plus expected development on reported claims	68
Reinsurance | Property catastrophe | 2016
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	5,181	5,987	6,886	9,190	12,749	16,582	23,224
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	2,594	2,433	2,086	2,932	1,870	1,759	(7,039)
Total of IBNR liabilities plus expected development on reported claims	877
Reinsurance | Property catastrophe | 2017
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	21,026	24,239	35,893	49,507	53,699	86,410
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	16,034	14,215	27,060	37,084	31,621	30,625
Total of IBNR liabilities plus expected development on reported claims	(803)
Reinsurance | Property catastrophe | 2018
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	10,722	19,831	33,425	52,001	73,041
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	(8,100)	(10,934)	18,253	7,344	27,424
Total of IBNR liabilities plus expected development on reported claims	3,039
Reinsurance | Property catastrophe | 2019
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	4,590	13,093	14,252	25,526
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	(11,472)	12,895	8,845	4,374
Total of IBNR liabilities plus expected development on reported claims	4,576
Reinsurance | Property catastrophe | 2020
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	326,262	322,680	260,244
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	200,510	152,075	52,592
Total of IBNR liabilities plus expected development on reported claims	33,413
Reinsurance | Property catastrophe | 2021
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	302,124	308,014
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	167,806	64,408
Total of IBNR liabilities plus expected development on reported claims	29,963
Reinsurance | Property catastrophe | 2022
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	299,636
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	69,969
Total of IBNR liabilities plus expected development on reported claims	73,474
Reinsurance | Property excluding property catastrophe
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	2,592,090
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,587,251
All outstanding liabilities before 2013, net of reinsurance	5,765
Liabilities for losses and loss adjustment expenses, net of reinsurance	1,010,604
Reinsurance | Property excluding property catastrophe | 2013
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	63,390	62,288	62,774	62,070	63,247	64,013	65,734	69,981	76,290	114,775
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	63,228	61,665	61,640	60,777	55,272	53,400	52,614	49,433	42,418	25,943
Total of IBNR liabilities plus expected development on reported claims	29
Reinsurance | Property excluding property catastrophe | 2014
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	79,307	80,348	81,812	83,476	87,768	90,031	98,263	116,331	142,092
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	77,894	77,728	78,029	78,067	77,687	76,060	71,144	62,414	23,342
Total of IBNR liabilities plus expected development on reported claims	443
Reinsurance | Property excluding property catastrophe | 2015
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	166,580	172,189	175,812	186,861	187,569	183,709	187,932	213,681
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	159,054	158,537	158,293	164,637	159,482	148,887	118,396	75,458
Total of IBNR liabilities plus expected development on reported claims	3,909
Reinsurance | Property excluding property catastrophe | 2016
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	128,941	135,116	138,216	134,362	136,367	144,323	174,506
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	114,432	113,300	111,039	103,202	97,918	94,121	33,236
Total of IBNR liabilities plus expected development on reported claims	6,208
Reinsurance | Property excluding property catastrophe | 2017
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	204,128	212,133	227,891	235,310	247,462	266,628
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	181,029	177,737	162,933	155,139	124,220	27,456
Total of IBNR liabilities plus expected development on reported claims	8,794
Reinsurance | Property excluding property catastrophe | 2018
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	201,429	211,852	234,794	238,876	222,932
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	174,778	166,598	151,632	107,172	29,654
Total of IBNR liabilities plus expected development on reported claims	7,370
Reinsurance | Property excluding property catastrophe | 2019
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	189,456	194,164	204,620	214,513
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	161,573	149,377	123,293	42,919
Total of IBNR liabilities plus expected development on reported claims	8,407
Reinsurance | Property excluding property catastrophe | 2020
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	319,097	338,712	366,726
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	242,844	207,061	100,927
Total of IBNR liabilities plus expected development on reported claims	36,912
Reinsurance | Property excluding property catastrophe | 2021
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	497,059	545,101
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	269,481	135,815
Total of IBNR liabilities plus expected development on reported claims	83,934
Reinsurance | Property excluding property catastrophe | 2022
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	742,703
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	142,938
Total of IBNR liabilities plus expected development on reported claims	360,528
Reinsurance | Marine and aviation
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	480,791
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	208,846
All outstanding liabilities before 2013, net of reinsurance	17,999
Liabilities for losses and loss adjustment expenses, net of reinsurance	289,944
Reinsurance | Marine and aviation | 2013
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	25,695	26,728	29,434	33,001	33,453	34,207	34,293	35,669	36,765	38,167
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	23,648	22,912	22,941	23,176	22,803	21,557	20,580	17,678	13,054	4,751
Total of IBNR liabilities plus expected development on reported claims	1,012
Reinsurance | Marine and aviation | 2014
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	18,511	21,651	21,698	22,919	23,302	25,297	26,995	28,757	30,566
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	17,084	15,729	15,650	14,794	14,368	12,209	11,335	7,795	4,005
Total of IBNR liabilities plus expected development on reported claims	800
Reinsurance | Marine and aviation | 2015
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	25,008	27,299	28,120	30,423	31,373	31,499	37,019	33,134
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	22,297	22,114	21,971	22,318	20,623	18,852	13,321	(6)
Total of IBNR liabilities plus expected development on reported claims	1,514
Reinsurance | Marine and aviation | 2016
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	11,952	14,896	16,834	19,122	23,448	22,625	27,258
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	7,028	6,656	5,764	3,169	445	(1,739)	(7,371)
Total of IBNR liabilities plus expected development on reported claims	4,080
Reinsurance | Marine and aviation | 2017
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	17,329	19,842	20,749	23,613	26,165	28,590
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	11,817	11,488	10,897	9,249	6,433	1,650
Total of IBNR liabilities plus expected development on reported claims	4,178
Reinsurance | Marine and aviation | 2018
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	21,052	24,192	24,058	25,680	27,613
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	13,923	13,332	11,021	6,817	1,993
Total of IBNR liabilities plus expected development on reported claims	3,738
Reinsurance | Marine and aviation | 2019
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	60,635	60,321	54,684	48,383
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	34,637	28,680	21,261	10,537
Total of IBNR liabilities plus expected development on reported claims	5,574
Reinsurance | Marine and aviation | 2020
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	79,338	75,695	82,716
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	42,203	26,129	9,096
Total of IBNR liabilities plus expected development on reported claims	28,621
Reinsurance | Marine and aviation | 2021
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	95,586	110,129
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	24,108	8,407
Total of IBNR liabilities plus expected development on reported claims	51,391
Reinsurance | Marine and aviation | 2022
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	125,685
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	12,101
Total of IBNR liabilities plus expected development on reported claims	99,917
Reinsurance | Other specialty
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	4,248,999
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	2,817,079
All outstanding liabilities before 2013, net of reinsurance	13,001
Liabilities for losses and loss adjustment expenses, net of reinsurance	1,444,921
Reinsurance | Other specialty | 2013
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	254,380	255,453	257,960	263,713	264,418	266,970	267,106	269,105	280,398	304,905
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	243,881	240,669	237,559	237,023	229,228	222,292	209,775	188,651	155,936	$ 81,609
Total of IBNR liabilities plus expected development on reported claims	4,327
Reinsurance | Other specialty | 2014
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	287,941	289,460	295,270	299,789	298,357	303,589	310,153	308,074	328,056
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	271,712	270,529	266,898	263,123	250,427	240,680	223,243	181,222	$ 92,743
Total of IBNR liabilities plus expected development on reported claims	6,034
Reinsurance | Other specialty | 2015
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	248,848	250,103	261,158	263,985	263,826	267,079	269,237	271,235
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	231,384	230,640	227,879	216,683	204,444	190,699	157,176	$ 80,453
Total of IBNR liabilities plus expected development on reported claims	6,340
Reinsurance | Other specialty | 2016
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	293,571	296,251	301,277	295,116	303,432	310,907	313,982
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	277,028	271,609	265,763	249,699	231,761	196,496	$ 103,649
Total of IBNR liabilities plus expected development on reported claims	8,371
Reinsurance | Other specialty | 2017
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	351,478	355,763	357,212	357,762	375,347	382,884
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	322,863	312,273	299,405	285,299	245,165	$ 130,150
Total of IBNR liabilities plus expected development on reported claims	22,234
Reinsurance | Other specialty | 2018
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	408,905	413,116	390,135	395,484	402,372
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	340,061	323,868	303,141	265,000	$ 124,996
Total of IBNR liabilities plus expected development on reported claims	32,668
Reinsurance | Other specialty | 2019
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	383,491	387,810	393,864	414,049
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	293,260	267,972	204,625	$ 116,762
Total of IBNR liabilities plus expected development on reported claims	38,889
Reinsurance | Other specialty | 2020
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	506,164	511,136	579,367
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	361,031	285,729	$ 129,621
Total of IBNR liabilities plus expected development on reported claims	57,946
Reinsurance | Other specialty | 2021
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	590,091	589,452
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	300,025	$ 146,503
Total of IBNR liabilities plus expected development on reported claims	148,264
Reinsurance | Other specialty | 2022
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	924,130
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	175,834
Total of IBNR liabilities plus expected development on reported claims	$ 601,334

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Short Duration Contracts - Claims development - Mortgage (Details) $ in Thousands	Dec. 31, 2022 USD ($) claims	Dec. 31, 2021 USD ($)	Dec. 31, 2020 USD ($)	Dec. 31, 2019 USD ($)	Dec. 31, 2018 USD ($)	Dec. 31, 2017 USD ($)	Dec. 31, 2016 USD ($)	Dec. 31, 2015 USD ($)	Dec. 31, 2014 USD ($)	Dec. 31, 2013 USD ($)
Claims Development [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance	$ 13,445,271
Mortgage
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	1,543,256
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,156,723
All outstanding liabilities before 2012, net of reinsurance	10,585
Liabilities for losses and loss adjustment expenses, net of reinsurance	397,118
Mortgage | 2013
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	390,299	$ 391,324	$ 391,062	$ 390,987	$ 393,149	$ 395,693	$ 405,809	$ 411,793	$ 419,668	$ 469,311
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	388,036	387,879	387,894	386,853	382,200	373,909	353,189	308,956	203,957	$ 41,447
Total of IBNR liabilities plus expected development on reported claims	$ 2
Cumulative number of paid claims | claims	9,474
Mortgage | 2014
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 260,554	262,829	262,682	261,091	265,992	266,027	279,434	297,151	316,095
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	257,232	256,875	256,285	254,175	247,038	233,879	201,925	129,159	$ 20,099
Total of IBNR liabilities plus expected development on reported claims	$ 4
Cumulative number of paid claims | claims	6,311
Mortgage | 2015
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 188,649	190,560	190,913	189,235	194,677	198,001	197,238	222,790
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	184,955	184,025	183,472	180,321	171,337	151,222	92,431	$ 16,159
Total of IBNR liabilities plus expected development on reported claims	$ 1
Cumulative number of paid claims | claims	4,573
Mortgage | 2016
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 137,415	141,657	142,392	140,608	148,715	170,532	183,556
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	132,387	131,717	131,161	127,286	113,357	72,201	$ 11,462
Total of IBNR liabilities plus expected development on reported claims	$ 0
Cumulative number of paid claims | claims	3,445
Mortgage | 2017
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 102,005	109,242	108,181	107,255	132,220	179,376
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	91,645	89,756	87,317	78,650	48,112	$ 8,622
Total of IBNR liabilities plus expected development on reported claims	$ (1)
Cumulative number of paid claims | claims	2,516
Mortgage | 2018
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 71,976	87,962	89,120	96,357	132,318
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	58,687	55,853	50,135	31,478	$ 3,966
Total of IBNR liabilities plus expected development on reported claims	$ (4)
Cumulative number of paid claims | claims	1,718
Mortgage | 2019
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 63,485	110,362	119,253	108,424
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	34,178	29,102	20,105	$ 2,899
Total of IBNR liabilities plus expected development on reported claims	$ 74
Cumulative number of paid claims | claims	1,002
Mortgage | 2020
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 78,334	373,533	420,003
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	7,740	4,144	$ 1,040
Total of IBNR liabilities plus expected development on reported claims	$ 476
Cumulative number of paid claims | claims	299
Mortgage | 2021
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 77,212	144,375
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,687	$ 469
Total of IBNR liabilities plus expected development on reported claims	$ 379
Cumulative number of paid claims | claims	72
Mortgage | 2022
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 173,327
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	176
Total of IBNR liabilities plus expected development on reported claims	$ 2,147
Cumulative number of paid claims | claims	7

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Short Duration Contracts - Percentage annual payout - all segments (Details)	Dec. 31, 2022
Insurance | Property, energy, marine and aviation
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	20.30%
Year Two	44.20%
Year Three	18.40%
Year Four	5.20%
Year Five	1.50%
Year Six	1.10%
Year Seven	2.00%
Year Eight	2.20%
Year Nine	0.30%
Year Ten	0.00%
Insurance | Third party occurrence business
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	3.40%
Year Two	9.30%
Year Three	11.80%
Year Four	11.20%
Year Five	9.70%
Year Six	9.70%
Year Seven	5.40%
Year Eight	4.50%
Year Nine	3.80%
Year Ten	2.90%
Insurance | Third party claims-made business
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	4.10%
Year Two	17.20%
Year Three	17.20%
Year Four	11.40%
Year Five	13.60%
Year Six	8.80%
Year Seven	6.40%
Year Eight	2.00%
Year Nine	2.10%
Year Ten	2.40%
Insurance | Multi-line and other specialty
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	34.30%
Year Two	28.90%
Year Three	10.90%
Year Four	8.80%
Year Five	4.50%
Year Six	3.10%
Year Seven	0.90%
Year Eight	0.40%
Year Nine	0.40%
Year Ten	0.00%
Reinsurance | Casualty
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	2.80%
Year Two	7.80%
Year Three	12.40%
Year Four	11.30%
Year Five	9.50%
Year Six	8.20%
Year Seven	7.50%
Year Eight	5.00%
Year Nine	3.80%
Year Ten	4.70%
Reinsurance | Property catastrophe
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	41.70%
Year Two	27.30%
Year Three	49.40%
Year Four	(115.60%)
Year Five	(10.70%)
Year Six	4.10%
Year Seven	1.70%
Year Eight	1.70%
Year Nine	(0.50%)
Year Ten	0.10%
Reinsurance | Property excluding property catastrophe
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	27.00%
Year Two	37.40%
Year Three	13.20%
Year Four	5.60%
Year Five	4.00%
Year Six	0.60%
Year Seven	2.40%
Year Eight	0.40%
Year Nine	0.10%
Year Ten	2.50%
Reinsurance | Marine and aviation
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	4.50%
Year Two	28.80%
Year Three	18.30%
Year Four	10.90%
Year Five	8.40%
Year Six	3.00%
Year Seven	2.40%
Year Eight	0.10%
Year Nine	3.60%
Year Ten	2.90%
Reinsurance | Other specialty
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	29.90%
Year Two	29.90%
Year Three	13.10%
Year Four	6.00%
Year Five	4.40%
Year Six	3.30%
Year Seven	1.80%
Year Eight	0.60%
Year Nine	0.80%
Year Ten	1.30%
Mortgage
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	5.60%
Year Two	30.90%
Year Three	23.80%
Year Four	9.80%
Year Five	4.00%
Year Six	1.80%
Year Seven	0.70%
Year Eight	0.30%
Year Nine	0.10%
Year Ten	0.00%

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Short Duration Contracts - Reconciliation of claims development to liability (Details) - USD ($) $ in Thousands		Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		$ 13,445,271
Unpaid losses and loss adjustment expenses recoverable		6,278,825	$ 5,599,231	$ 4,314,855	$ 4,082,650
Lines other than short duration		102,283
Discounting		(60,536)
Unallocated claims adjustment expenses		266,100
Total reconciling items		307,847
Reserve for losses and loss adjustment expenses		20,031,943	$ 17,757,156	$ 16,513,929	$ 13,891,842
Other short duration lines not included
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		301,222
Unpaid losses and loss adjustment expenses recoverable	[1]	560,642
Other short duration lines not included | Loss portfolio transfer
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Unpaid losses and loss adjustment expenses recoverable	[1]	280,200
Total for short duration lines
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Unpaid losses and loss adjustment expenses recoverable		6,278,825
Insurance | Property, energy, marine and aviation
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		750,461
Unpaid losses and loss adjustment expenses recoverable		423,740
Insurance | Third party occurrence business
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		3,184,995
Unpaid losses and loss adjustment expenses recoverable		1,761,871
Insurance | Third party claims-made business
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		1,991,302
Unpaid losses and loss adjustment expenses recoverable		995,921
Insurance | Multi-line and other specialty
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		1,215,721
Unpaid losses and loss adjustment expenses recoverable		173,051
Reinsurance | Casualty
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		2,323,825
Unpaid losses and loss adjustment expenses recoverable		684,663
Reinsurance | Property catastrophe
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		535,158
Unpaid losses and loss adjustment expenses recoverable		595,740
Reinsurance | Property excluding property catastrophe
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		1,010,604
Unpaid losses and loss adjustment expenses recoverable		206,867
Reinsurance | Marine and aviation
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		289,944
Unpaid losses and loss adjustment expenses recoverable		186,416
Reinsurance | Other specialty
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		1,444,921
Unpaid losses and loss adjustment expenses recoverable		656,130
Mortgage
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		397,118
Unpaid losses and loss adjustment expenses recoverable		37,531
Consolidating adjustments and eliminations
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Unpaid losses and loss adjustment expenses recoverable		$ (3,747)

[1] Includes unpaid loss and loss adjustment expenses recoverable of $280.2 million related to the loss portfolio transfer reinsurance agreements.

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Short Duration Contracts (Details)	12 Months Ended
	Dec. 31, 2022 USD ($)
Mortgage
Claims Development [Line Items]
Large claim size threshold	$ 250,000

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Allowance for Expected Credit Losses - Premiums receivable (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2022	Dec. 31, 2021
Credit Loss [Abstract]
Balance at beginning of period		$ 2,633,280	$ 2,064,586
Balance at end of period		3,624,777	2,633,280
Allowance for Expected Credit Losses
Balance at beginning of period		39,958	37,781
Change for provision of expected credit losses	[1]	(4,556)	2,177
Balance at end of period		35,402	39,958
Write-offs charged against the allowance		$ 11,400	$ 3,800

[1] Amounts deemed uncollectible are written-off in operating expenses. For the 2022 and 2021 periods, amounts written off totaled $11.4 million and $3.8 million, respectively.

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Allowance for Expected Credit Losses - Reinsurance recoverables (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021
Credit Loss [Abstract]
Balance at beginning of period	$ 5,880,735	$ 4,500,802
Balance at end of period	6,563,654	5,880,735
Allowance for Expected Credit Losses
Balance at beginning of period	13,230	11,636
Change for provision of expected credit losses	8,314	1,594
Balance at end of period	$ 21,544	$ 13,230

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Allowance for Expected Credit Losses - Ceded credit risk (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Concentration Risk [Line Items]
Reinsurance recoverable for paid and unpaid claims and claims adjustments		$ 6,563,654	$ 5,880,735	$ 4,500,802
Shareholders' equity | Reinsurer concentration risk | Largest balance due from any one carrier
Concentration Risk [Line Items]
Concentration risk percentage		9.00%	6.70%
AM Best "A-" Or Better Rating | Reinsurance recoverable | Reinsurer concentration risk
Concentration Risk [Line Items]
Concentration risk percentage		68.80%	69.70%
Rating Below A- | Reinsurance recoverable | Reinsurer concentration risk | All Other Carriers
Concentration Risk [Line Items]
Concentration risk percentage		0.10%	0.10%
No AM Best rating | Reinsurance recoverable | Reinsurer concentration risk | Reinsurance trusts or letters of credit
Concentration Risk [Line Items]
Concentration risk percentage		95.00%	91.00%
No AM Best rating | Reinsurance recoverable | Reinsurer concentration risk | All Other Carriers
Concentration Risk [Line Items]
Concentration risk percentage	[1]	31.10%	30.20%

[1] At December 31, 2022 and 2021 period, over 95% and 91% of such amount is collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other, respectively

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Allowance for Expected Credit Losses - Contractholder receivables (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021
Credit Loss [Abstract]
Balance at beginning of period	$ 1,828,691	$ 1,986,924
Balance at end of period	1,731,293	1,828,691
Allowance for Expected Credit Losses
Balance at beginning of period	3,437	8,638
Change for provision of expected credit losses	(746)	(5,201)
Balance at end of period	$ 2,691	$ 3,437

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Reinsurance - Effects of reinsurance (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Premiums Written
Direct	$ 8,540,787	$ 7,706,832	$ 6,553,910
Assumed	6,785,660	5,045,655	3,534,158
Ceded	(4,249,258)	(3,734,150)	(2,650,352)
Net premiums written	11,077,189	9,018,337	7,437,716
Premiums Earned
Direct	8,057,635	7,149,794	6,361,451
Assumed	5,767,738	4,333,873	3,213,873
Ceded	(4,147,296)	(3,401,369)	(2,583,389)
Net premiums earned	9,678,077	8,082,298	6,991,935
Losses and Loss Adjustment Expenses
Direct	3,990,768	4,266,758	4,392,392
Assumed	3,559,133	2,826,820	2,204,323
Ceded	(2,522,384)	(2,508,775)	(1,907,116)
Net	$ 5,027,517	$ 4,584,803	$ 4,689,599

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Reinsurance - Coverage and retention (Details) - Variable Interest Entity, Not Primary Beneficiary $ in Thousands	12 Months Ended
	Dec. 31, 2022 USD ($)
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	$ 7,270,589
Current Coverage	4,005,479
Remaining Retention, Net	$ 2,423,805
Amortization period	10 years
Bellemeade 2017-1 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	$ 368,114	[1]
Current Coverage	36,679	[1]
Remaining Retention, Net	142,461	[1]
Bellemeade 2018-1 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	374,460	[2]
Current Coverage	89,698	[2]
Remaining Retention, Net	143,592	[2]
Bellemeade 2018-3 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	506,110	[3]
Current Coverage	199,237	[3]
Remaining Retention, Net	152,861	[3]
Bellemeade 2019-1 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	341,790	[4]
Current Coverage	107,880	[4]
Remaining Retention, Net	118,908	[4]
Bellemeade 2019-2 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	621,022	[5]
Current Coverage	325,462	[5]
Remaining Retention, Net	191,550	[5]
Bellemeade 2019-3 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	700,920	[6]
Current Coverage	222,977	[6]
Remaining Retention, Net	208,931	[6]
Bellemeade 2019-4 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	577,267	[7]
Current Coverage	266,124	[7]
Remaining Retention, Net	142,564	[7]
Bellemeade 2020-2 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	449,167	[8]
Current Coverage	105,110	[8]
Remaining Retention, Net	237,709	[8]
Bellemeade 2020-2 Ltd | Funded By VIE
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	423,000
Bellemeade 2020-2 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	26,000
Bellemeade 2020-3 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	451,816	[9]
Current Coverage	250,971	[9]
Remaining Retention, Net	161,544	[9]
Bellemeade 2020-3 Ltd | Funded By VIE
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	418,000
Bellemeade 2020-3 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	34,000
Bellemeade 2020-4 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	337,013	[10]
Current Coverage	101,729	[10]
Remaining Retention, Net	138,131	[10]
Bellemeade 2020-4 Ltd | Funded By VIE
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	321,000
Bellemeade 2020-4 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	16,000
Bellemeade 2021-1 Ltd Member
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	643,577	[11]
Current Coverage	503,267	[11]
Remaining Retention, Net	153,525	[11]
Bellemeade 2021-1 Ltd Member | Funded By VIE
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	580,000
Bellemeade 2021-1 Ltd Member | Directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	64,000
Bellemeade 2021-2 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	616,017	[12]
Current Coverage	535,461	[12]
Remaining Retention, Net	138,524	[12]
Bellemeade 2021-2 Ltd | Funded By VIE
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	523,000
Bellemeade 2021-2 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	93,000
Bellemeade 2021-3 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	639,391	[13]
Current Coverage	616,959	[13]
Remaining Retention, Net	132,492	[13]
Bellemeade 2021-3 Ltd | Funded By VIE
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	508,000
Bellemeade 2021-3 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	131,000
Bellemeade 2022-01 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	316,760	[14]
Current Coverage	316,760	[14]
Remaining Retention, Net	143,577	[14]
Bellemeade 2022-01 Ltd | Funded By VIE
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	284,000
Bellemeade 2022-01 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	33,000
Bellemeade 2022-2 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	327,165	[15]
Current Coverage	327,165	[15]
Remaining Retention, Net	217,436	[15]
Bellemeade 2022-2 Ltd | Funded By VIE
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	201,000
Bellemeade 2022-2 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	$ 126,000

[1] Issued in October 2017, covering in-force policies issued between January 1, 2017 and June 30, 2017.

[2] Issued in April 2018, covering in-force policies issued between July 1, 2017 and December 31, 2017.

[3] Issued in October 2018, covering in-force policies issued between January 1, 2018 and June 30, 2018.

[4] Issued in March 2019, covering in-force policies primarily issued between 2005 to 2008 under United Guaranty Residential Insurance Company (“UGRIC”); as well as policies issued through 2015 under both UGRIC and Arch Mortgage Insurance Company.

[5] Issued in April 2019, covering in-force policies issued between July 1, 2018 and December 31, 2018.

[6] Issued in July 2019, covering in-force policies issued in 2016.

[7] Issued in October 2019, covering in-force policies issued between January 1, 2019 and June 30, 2019.

[8] Issued in September 2020, covering in-force policies issued between January 1, 2020 and May 31, 2020. $423 million was directly funded by Bellemeade 2020-2 Ltd. with an additional $26 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers

[9] Issued in November 2020, covering in-force policies issued between June 1, 2020 and August 31, 2020. $418 million was directly funded by Bellemeade 2020-3 Ltd. with an additional $34 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

[10] Issued in December 2020, covering in-force policies issued between July 1, 2019 and December 31, 2019. $321 million was directly funded by Bellemeade 2020-4 Ltd. with an additional $16 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers

[11] Issued in March 2021, covering in-force policies issued between September 1, 2020 and November 30, 2020. $580 million was directly funded by Bellemeade Re 2021-1 Ltd. with an additional $64 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

[12] Issued in June 2021, covering in-force policies issued between December 1, 2020 and March 31, 2021. $523 million was directly funded by Bellemeade Re 2021-2 Ltd. via insurance-linked notes, with an additional $93 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers

[13] Issued in September 2021, covering in-force policies issued between April 1, 2021 and June 30, 2021. $508 million was directly funded by Bellemeade Re 2021-3 Ltd. via insurance-linked notes, with an additional $131 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers

[14] Issued in January 2022, covering in-force policies issued between July 1, 2021 and November 30, 2021. $284 million was directly funded by Bellemeade Re 2022-1 Ltd. via insurance-linked notes, with an additional $33 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

[15] Issued in September 2022, covering in-force policies issued between November 1, 2021 and June 30, 2022. $201 million was directly funded by Bellemeade Re 2022-2 Ltd. via insurance-linked notes, with an additional $126 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers

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Investment Information - Summary of available for sale securities (Details) - USD ($) $ in Thousands	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Available for sale securities:
Estimated fair value	$ 21,014,451	$ 19,732,825
Gross Unrealized Gains	89,234	198,691
Gross Unrealized Losses	(1,648,287)	(171,544)
Allowance for Expected Credit Losses	(41,355)	(2,883)
Cost or Amortized Cost	22,614,859	19,708,561
Fixed maturities available for sale, at fair value
Available for sale securities:
Estimated fair value	19,682,789	17,998,109
Gross Unrealized Gains	88,680	198,123
Gross Unrealized Losses	(1,646,399)	(170,954)
Allowance for Expected Credit Losses	(41,355)	(2,883)	$ (2,397)
Cost or Amortized Cost	21,281,863	17,973,823
Fixed maturities available for sale, at fair value | Corporate bonds
Available for sale securities:
Estimated fair value	8,020,128	6,553,333
Gross Unrealized Gains	55,468	104,170
Gross Unrealized Losses	(781,353)	(69,194)
Allowance for Expected Credit Losses	(29,950)	(2,037)
Cost or Amortized Cost	8,775,963	6,520,394
Fixed maturities available for sale, at fair value | Mortgage backed securities
Available for sale securities:
Estimated fair value	795,391	408,477
Gross Unrealized Gains	4,933	2,825
Gross Unrealized Losses	(86,587)	(5,410)
Allowance for Expected Credit Losses	2	(48)
Cost or Amortized Cost	877,043	411,110
Fixed maturities available for sale, at fair value | Municipal bonds
Available for sale securities:
Estimated fair value	419,166	404,666
Gross Unrealized Gains	3,149	18,724
Gross Unrealized Losses	(33,360)	(1,409)
Allowance for Expected Credit Losses	(100)	(2)	(11)
Cost or Amortized Cost	449,477	387,353
Fixed maturities available for sale, at fair value | Commercial mortgage backed securities
Available for sale securities:
Estimated fair value	1,047,275	1,046,484
Gross Unrealized Gains	608	1,740
Gross Unrealized Losses	(57,667)	(3,117)
Allowance for Expected Credit Losses	(3,415)	(6)
Cost or Amortized Cost	1,107,749	1,047,867
Fixed maturities available for sale, at fair value | US government and government agencies
Available for sale securities:
Estimated fair value	5,161,193	4,772,764
Gross Unrealized Gains	14,891	10,076
Gross Unrealized Losses	(342,963)	(45,967)
Allowance for Expected Credit Losses	0	0
Cost or Amortized Cost	5,489,265	4,808,655
Fixed maturities available for sale, at fair value | Non-US government securities
Available for sale securities:
Estimated fair value	2,312,819	2,120,294
Gross Unrealized Gains	8,870	54,048
Gross Unrealized Losses	(237,846)	(34,749)
Allowance for Expected Credit Losses	(1,882)	(82)	$ 0
Cost or Amortized Cost	2,543,677	2,101,077
Fixed maturities available for sale, at fair value | Asset backed securities
Available for sale securities:
Estimated fair value	1,926,817	2,692,091
Gross Unrealized Gains	761	6,540
Gross Unrealized Losses	(106,623)	(11,108)
Allowance for Expected Credit Losses	(6,010)	(708)
Cost or Amortized Cost	2,038,689	2,697,367
Short-term investments
Available for sale securities:
Estimated fair value	1,331,662	1,734,716
Gross Unrealized Gains	554	568
Gross Unrealized Losses	(1,888)	(590)
Allowance for Expected Credit Losses	0	0
Cost or Amortized Cost	$ 1,332,996	$ 1,734,738

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Investment Information - Aging of available for sale securities in an unrealized loss position (Details) - USD ($) $ in Thousands	Dec. 31, 2022	Dec. 31, 2021
Available for sale securities:
Estimated Fair Value - Less than 12 Months	$ 12,975,400	$ 12,238,683
Gross Unrealized Losses - Less than 12 Months	(927,531)	(157,279)
Estimated Fair Value - 12 Months or More	5,671,580	297,357
Gross Unrealized Losses - 12 Months or More	(720,756)	(14,265)
Estimated Fair Value - Total	18,646,980	12,536,040
Gross Unrealized Losses - Total	(1,648,287)	(171,544)
Fixed maturities available for sale, at fair value
Available for sale securities:
Estimated Fair Value - Less than 12 Months	12,738,665	11,953,950
Gross Unrealized Losses - Less than 12 Months	(925,643)	(156,689)
Estimated Fair Value - 12 Months or More	5,671,580	297,357
Gross Unrealized Losses - 12 Months or More	(720,756)	(14,265)
Estimated Fair Value - Total	18,410,245	12,251,307
Gross Unrealized Losses - Total	(1,646,399)	(170,954)
Fixed maturities available for sale, at fair value | Corporate bonds
Available for sale securities:
Estimated Fair Value - Less than 12 Months	4,822,624	3,639,582
Gross Unrealized Losses - Less than 12 Months	(393,112)	(63,938)
Estimated Fair Value - 12 Months or More	2,559,399	98,867
Gross Unrealized Losses - 12 Months or More	(388,241)	(5,256)
Estimated Fair Value - Total	7,382,023	3,738,449
Gross Unrealized Losses - Total	(781,353)	(69,194)
Fixed maturities available for sale, at fair value | Mortgage backed securities
Available for sale securities:
Estimated Fair Value - Less than 12 Months	545,844	222,176
Gross Unrealized Losses - Less than 12 Months	(51,673)	(3,545)
Estimated Fair Value - 12 Months or More	154,154	46,809
Gross Unrealized Losses - 12 Months or More	(34,914)	(1,865)
Estimated Fair Value - Total	699,998	268,985
Gross Unrealized Losses - Total	(86,587)	(5,410)
Fixed maturities available for sale, at fair value | Municipal bonds
Available for sale securities:
Estimated Fair Value - Less than 12 Months	363,936	26,665
Gross Unrealized Losses - Less than 12 Months	(29,924)	(385)
Estimated Fair Value - 12 Months or More	16,282	16,361
Gross Unrealized Losses - 12 Months or More	(3,436)	(1,024)
Estimated Fair Value - Total	380,218	43,026
Gross Unrealized Losses - Total	(33,360)	(1,409)
Fixed maturities available for sale, at fair value | Commercial mortgage backed securities
Available for sale securities:
Estimated Fair Value - Less than 12 Months	598,392	675,603
Gross Unrealized Losses - Less than 12 Months	(34,899)	(2,805)
Estimated Fair Value - 12 Months or More	445,175	5,908
Gross Unrealized Losses - 12 Months or More	(22,768)	(312)
Estimated Fair Value - Total	1,043,567	681,511
Gross Unrealized Losses - Total	(57,667)	(3,117)
Fixed maturities available for sale, at fair value | US government and government agencies
Available for sale securities:
Estimated Fair Value - Less than 12 Months	3,556,676	4,211,621
Gross Unrealized Losses - Less than 12 Months	(197,259)	(44,180)
Estimated Fair Value - 12 Months or More	1,442,542	33,373
Gross Unrealized Losses - 12 Months or More	(145,704)	(1,787)
Estimated Fair Value - Total	4,999,218	4,244,994
Gross Unrealized Losses - Total	(342,963)	(45,967)
Fixed maturities available for sale, at fair value | Non-US government securities
Available for sale securities:
Estimated Fair Value - Less than 12 Months	1,702,973	1,511,301
Gross Unrealized Losses - Less than 12 Months	(153,587)	(31,983)
Estimated Fair Value - 12 Months or More	541,652	62,957
Gross Unrealized Losses - 12 Months or More	(84,259)	(2,766)
Estimated Fair Value - Total	2,244,625	1,574,258
Gross Unrealized Losses - Total	(237,846)	(34,749)
Fixed maturities available for sale, at fair value | Asset backed securities
Available for sale securities:
Estimated Fair Value - Less than 12 Months	1,148,220	1,667,002
Gross Unrealized Losses - Less than 12 Months	(65,189)	(9,853)
Estimated Fair Value - 12 Months or More	512,376	33,082
Gross Unrealized Losses - 12 Months or More	(41,434)	(1,255)
Estimated Fair Value - Total	1,660,596	1,700,084
Gross Unrealized Losses - Total	(106,623)	(11,108)
Short-term investments
Available for sale securities:
Estimated Fair Value - Less than 12 Months	236,735	284,733
Gross Unrealized Losses - Less than 12 Months	(1,888)	(590)
Estimated Fair Value - 12 Months or More	0	0
Gross Unrealized Losses - 12 Months or More	0	0
Estimated Fair Value - Total	236,735	284,733
Gross Unrealized Losses - Total	$ (1,888)	$ (590)

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Investment Information - Maturity profile of available for sale securities (Details) - USD ($) $ in Thousands	Dec. 31, 2022	Dec. 31, 2021
Estimated Fair Value:
Estimated fair value	$ 21,014,451	$ 19,732,825
Amortized Cost:
Amortized cost	22,614,859	19,708,561
Fixed maturities available for sale, at fair value
Estimated Fair Value:
Due in one year or less	510,669	300,889
Due after one year through five years	11,014,753	8,355,255
Due after five years through 10 years	3,984,497	4,689,155
Due after 10 years	403,387	505,758
Single maturity date	15,913,306	13,851,057
Estimated fair value	19,682,789	17,998,109
Amortized Cost:
Due in one year or less	536,962	299,772
Due after one year through five years	11,714,427	8,339,387
Due after five years through 10 years	4,527,447	4,684,393
Due after 10 years	479,546	493,927
Single maturity date	17,258,382	13,817,479
Amortized cost	21,281,863	17,973,823
Fixed maturities available for sale, at fair value | Mortgage backed securities
Estimated Fair Value:
Securities without single maturity date	795,391	408,477
Estimated fair value	795,391	408,477
Amortized Cost:
Securities without single maturity date	877,043	411,110
Amortized cost	877,043	411,110
Fixed maturities available for sale, at fair value | Commercial mortgage backed securities
Estimated Fair Value:
Securities without single maturity date	1,047,275	1,046,484
Estimated fair value	1,047,275	1,046,484
Amortized Cost:
Securities without single maturity date	1,107,749	1,047,867
Amortized cost	1,107,749	1,047,867
Fixed maturities available for sale, at fair value | Asset backed securities
Estimated Fair Value:
Securities without single maturity date	1,926,817	2,692,091
Estimated fair value	1,926,817	2,692,091
Amortized Cost:
Securities without single maturity date	2,038,689	2,697,367
Amortized cost	$ 2,038,689	$ 2,697,367

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Investment Information - Net investment Income (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Net investment income:
Gross investment income		$ 567,322	$ 477,123	$ 608,823
Investment expenses		(70,775)	(88,005)	(89,215)
Net investment income		496,547	389,118	519,608
Fixed maturities
Net investment income:
Gross investment income		468,659	330,061	412,481
Term loan investments
Net investment income:
Gross investment income		2,038	34,843	84,149
Equity securities
Net investment income:
Gross investment income		22,497	42,396	28,958
Short-term investments
Net investment income:
Gross investment income		29,519	6,928	10,840
Other
Net investment income:
Gross investment income	[1]	$ 44,609	$ 62,895	$ 72,395

[1] Includes income distributions from investment funds and other items

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Investment Information - Net realized gains and losses (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Net realized gains and losses:
Available for sale securities, gross gains on investment sales		$ 81,161	$ 313,886	$ 595,941
Available for sale securities, gross losses on investment sales		(317,150)	(156,791)	(117,282)
Equity securities at fair value, net realized gains (losses) on sales during the period		74,922	122,606	26,849
Equity securities at fair value, net unrealized gains (losses) on equity securities still held at reporting date		(267,927)	48,746	102,394
Allowance for credit losses - investment related		(43,909)	(2,100)	(3,597)
Allowance for credit losses - underwriting related		(13,274)	1,062	(10,007)
Derivative instruments		(75,023)	(32,390)	179,675
Other	[1]	(3,553)	(53,537)	3,575
Net realized gains (losses)		$ (662,734)	379,845	823,460
Derivative, Gain (Loss), Statement of Income or Comprehensive Income [Extensible Enumeration]		Net realized gains (losses)
Somers Holdings Ltd.
Net realized gains and losses:
Gain (loss) on deconsolidation			(33,100)
Fixed maturities
Net realized gains and losses:
Change in fair value of assets and liabilities accounted for using the fair value option		$ (70,951)	7,953	15,881
Other investments
Net realized gains and losses:
Change in fair value of assets and liabilities accounted for using the fair value option		(19,498)	116,781	13,656
Equity securities
Net realized gains and losses:
Change in fair value of assets and liabilities accounted for using the fair value option		(4,520)	13,028	14,629
Short-term investments
Net realized gains and losses:
Change in fair value of assets and liabilities accounted for using the fair value option		$ (3,012)	$ 601	$ 2,279

[1] 2021 period reflected $33.1 million of losses related to the Company’sdeconsolidation of Somers

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Investment Information - Other investments (Details) - USD ($) $ in Thousands	Dec. 31, 2022	Dec. 31, 2021
Fair Value, Option, Quantitative Disclosures [Line Items]
Other investments	$ 1,644,197	$ 1,973,550
Fixed maturities
Fair Value, Option, Quantitative Disclosures [Line Items]
Other investments	554,120	416,698
Other investments
Fair Value, Option, Quantitative Disclosures [Line Items]
Other investments	1,043,184	1,432,553
Short-term investments
Fair Value, Option, Quantitative Disclosures [Line Items]
Other investments	33,101	97,806
Equity securities
Fair Value, Option, Quantitative Disclosures [Line Items]
Other investments	$ 13,792	$ 26,493

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Investment Information - Other investments by strategy (Details) - USD ($) $ in Thousands	Dec. 31, 2022	Dec. 31, 2021
Schedule Of Other Investments [Line Items]
Other investments	$ 1,644,197	$ 1,973,550
Other investments
Schedule Of Other Investments [Line Items]
Other investments	1,043,184	1,432,553
Other investments | Lending
Schedule Of Other Investments [Line Items]
Other investments	405,871	536,345
Other investments | Investment grade fixed income
Schedule Of Other Investments [Line Items]
Other investments	271,143	147,810
Other investments | Term loan investments
Schedule Of Other Investments [Line Items]
Other investments	163,941	484,950
Other investments | Private equity
Schedule Of Other Investments [Line Items]
Other investments	123,266	91,126
Other investments | Energy
Schedule Of Other Investments [Line Items]
Other investments	22,627	81,692
Other investments | Credit related funds
Schedule Of Other Investments [Line Items]
Other investments	56,336	70,278
Other investments | Infrastructure
Schedule Of Other Investments [Line Items]
Other investments	$ 0	$ 20,352

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Investment Information - Equity method investments and investments in affiliates (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	$ 3,774,310	$ 3,077,611
Equity in net income (loss) of investment funds accounted for using the equity method	115,856	366,402	$ 146,693
Balance sheet:
Total assets	47,990,507	45,100,945	43,282,297
Total liabilities	35,069,605	31,545,816	29,294,856
Income statement:
Total revenues	9,614,808	9,249,980	8,508,509
Net income	1,482,423	2,239,462	1,465,711
Credit related funds
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	1,135,818	1,022,334
Private equity
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	916,534	436,042
Real estate
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	535,238	396,395
Lending
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	531,339	376,649
Infrastructure
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	245,246	230,070
Equity Funds
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	169,156	395,090
Fixed income
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	130,062	101,890
Energy
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	110,917	119,141
Equity Method Investment, Nonconsolidated Investee or Group of Investees [Member]
Balance sheet:
Invested assets	74,960,738	58,508,009
Total assets	88,062,991	69,648,905
Total liabilities	27,553,307	17,944,325
Net assets	60,509,684	51,704,580
Income statement:
Total revenues	12,305,082	11,785,949	5,762,098
Total expenses	5,374,047	3,238,606	1,656,029
Net income	$ 6,931,035	$ 8,547,343	$ 4,106,069

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Investment Information - Limited partnership interests (Details) - USD ($) $ in Thousands		Dec. 31, 2022	Dec. 31, 2021
Schedule of Equity Method Investments [Line Items]
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		$ 3,904,776	$ 3,248,206
Aggregate commitments		2,900,000	3,000,000
Equity method investments
Schedule of Equity Method Investments [Line Items]
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount	[1]	3,774,310	3,077,611
Aggregate commitments		2,600,000	2,600,000
Fair value option
Schedule of Equity Method Investments [Line Items]
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount	[2]	130,466	170,595
Aggregate commitments		$ 16,700	$ 18,800

[1] Aggregate unfunded commitments were $2.6 billion at December 31, 2022, consistent with $2.6 billion at December 31, 2021.

[2] Aggregate unfunded commitments were $16.7 million at December 31, 2022, compared to $18.8 million at December 31, 2021.

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Investment Information - Investments in operating affiliates (Details) € / shares in Units, $ / shares in Units, $ in Thousands, € in Millions	12 Months Ended
	Dec. 31, 2022 USD ($)	Dec. 31, 2021 USD ($)	Dec. 31, 2020 USD ($)	Dec. 31, 2021 EUR (€) € / shares	Jul. 01, 2021 $ / shares
Schedule of Equity Method Investments [Line Items]
Investment in operating affiliates	$ 964,604	$ 1,135,655
Income (loss) from operating affiliates	$ 73,891	$ 264,693	$ 16,766
Coface
Schedule of Equity Method Investments [Line Items]
Percentage ownership	29.90%	29.50%		29.50%
Investment in affiliate, price per share | € / shares				€ 9.95
Equity method investment, aggregate cost		$ 546,000		€ 453
Operating affiliate gain on acquisition		74,500
Operating affiliates , deferred gain on acquisition		36,000
Operating affiliates, deferred gain on acquisition, amortization period	5 years
Investment in operating affiliates	$ 562,900	630,500
Coface | Issued Shares Excluding Treasury Stock
Schedule of Equity Method Investments [Line Items]
Percentage ownership	30.10%
Greysbridge Holdings Ltd
Schedule of Equity Method Investments [Line Items]
Percentage ownership					40.00%
Investment in affiliate, price per share | $ / shares					$ 35.00
Equity method investment, aggregate cost		278,900
Operating affiliate gain on acquisition		95,700
Investment in operating affiliates	$ 305,600	375,700
Greysbridge Holdings Ltd | Kelso And Company
Schedule of Equity Method Investments [Line Items]
Percentage ownership					30.00%
Greysbridge Holdings Ltd | Warburg Pincus LLC
Schedule of Equity Method Investments [Line Items]
Percentage ownership					30.00%
Somers Holdings Ltd.
Schedule of Equity Method Investments [Line Items]
Gain (loss) on deconsolidation		$ (33,100)

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Investment Information - Allowance for expected credit losses (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2022	Dec. 31, 2021
Debt Securities, Available-for-sale, Allowance for Credit Loss [Line Items]
Balance at beginning of period		$ 2,883
Balance at end of period		41,355	$ 2,883
Fixed maturities
Debt Securities, Available-for-sale, Allowance for Credit Loss [Line Items]
Balance at beginning of period		2,883	2,397
Additions for current-period provision for expected credit losses		55,636	3,542
Additions (reductions) for previously recognized expected credit losses		(11,789)	(1,258)
Reductions due to disposals (2)		(5,375)	(1,798)	[1]
Balance at end of period		41,355	2,883
Fixed maturities | Structured securities
Debt Securities, Available-for-sale, Allowance for Credit Loss [Line Items]
Balance at beginning of period	[2]	802	1,490
Additions for current-period provision for expected credit losses	[2]	14,184	602
Additions (reductions) for previously recognized expected credit losses	[2]	(3,184)	(847)
Reductions due to disposals (2)	[2]	(2,379)	(443)	[1]
Balance at end of period	[2]	9,423	802
Fixed maturities | Municipal bonds
Debt Securities, Available-for-sale, Allowance for Credit Loss [Line Items]
Balance at beginning of period		2	11
Additions for current-period provision for expected credit losses		359	0
Additions (reductions) for previously recognized expected credit losses		(261)	(9)
Reductions due to disposals (2)		0	0	[1]
Balance at end of period		100	2
Fixed maturities | Non-US government securities
Debt Securities, Available-for-sale, Allowance for Credit Loss [Line Items]
Balance at beginning of period		82	0
Additions for current-period provision for expected credit losses		1,616	82
Additions (reductions) for previously recognized expected credit losses		275	0
Reductions due to disposals (2)		(91)	0	[1]
Balance at end of period		1,882	82
Fixed maturities | Corporate bonds
Debt Securities, Available-for-sale, Allowance for Credit Loss [Line Items]
Balance at beginning of period		1,997	896
Additions for current-period provision for expected credit losses		39,477	2,858
Additions (reductions) for previously recognized expected credit losses		(8,619)	(402)
Reductions due to disposals (2)		(2,905)	(1,355)	[1]
Balance at end of period		$ 29,950	$ 1,997

[1] Reduction for the 2021 periods primarily related to the Company’s deconsolidation of Somers.

[2] Includes asset backed securities, mortgage backed securities and commercial mortgage backed

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Investment Information - Restricted assets (Details) - USD ($) $ in Thousands		Dec. 31, 2022	Dec. 31, 2021
Restricted Assets [Line Items]
Restricted assets		$ 8,701,480	$ 8,249,732
Collateral or guarantees - affiliated transactions
Restricted Assets [Line Items]
Restricted assets		4,254,398	4,223,955
Collateral or guarantees - third party agreements
Restricted Assets [Line Items]
Restricted assets		2,632,892	2,289,631
Deposits with US regulatory authorities
Restricted Assets [Line Items]
Restricted assets		776,342	798,100
Deposits with non-US regulatory authorities
Restricted Assets [Line Items]
Restricted assets	[1]	$ 1,037,848	$ 938,046

[1] Primarily includes Funds at Lloyds, deposits with non-U.S. regulatory authorities and other restricted assets.

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Investment Information - Cash and restricted cash (Details) - USD ($) $ in Thousands	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Disclosure Investment Information [Abstract]
Cash	$ 855,118	$ 858,668	$ 906,448
Restricted cash (included in ‘other assets’)	418,210	456,103	384,096
Cash and restricted cash	$ 1,273,328	$ 1,314,771	$ 1,290,544	$ 903,698

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Investment Information - Narrative (Details) $ in Thousands	12 Months Ended
	Dec. 31, 2022 USD ($) lots	Dec. 31, 2021 USD ($) lots
Continuous unrealized loss, qualitative disclosures:
Number of positions in an unrealized loss position (lots) | lots	9,810	4,700
Total number of positions (lots) | lots	12,590	10,240
Largest single loss | $	$ 7,200	$ 1,100
Equity securities, at fair value | $	$ 859,969	$ 1,804,170
Equity Method Investment, Financial Statement, Reported Amounts [Abstract]
Investments, time lag for reporting - low end of range	1 month
Investments, time lag for reporting - high end of range	3 months

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Fair Value - Fair Value Hierarchy (Details) - Recurring - USD ($) $ in Thousands		Dec. 31, 2022	Dec. 31, 2021
Quoted Prices in Active Markets for Identical Assets (Level 1)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		$ 7,186,000	$ 7,602,828
Liabilities measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Contingent consideration liability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Residential Mortgage
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities available for sale, at fair value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		5,144,467	4,744,517
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities available for sale, at fair value | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities available for sale, at fair value | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities available for sale, at fair value | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities available for sale, at fair value | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities available for sale, at fair value | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		5,144,467	4,744,517
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities available for sale, at fair value | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities available for sale, at fair value | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,197,304	1,052,822
Quoted Prices in Active Markets for Identical Assets (Level 1) | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		828,513	1,762,864
Quoted Prices in Active Markets for Identical Assets (Level 1) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		15,716	42,625
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		5,398	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		699	528
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		9,619	21,745
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Other investments fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	20,352
Significant Other Observable Inputs (Level 2)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		15,474,159	14,923,923
Liabilities measured at fair value		(75,961)	(54,224)
Significant Other Observable Inputs (Level 2) | Contingent consideration liability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		0	0
Significant Other Observable Inputs (Level 2) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(75,961)	(54,224)
Significant Other Observable Inputs (Level 2) | Residential Mortgage
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,283	49,847
Significant Other Observable Inputs (Level 2) | Fixed maturities available for sale, at fair value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		14,417,095	13,250,232
Significant Other Observable Inputs (Level 2) | Fixed maturities available for sale, at fair value | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		7,898,901	6,553,320
Significant Other Observable Inputs (Level 2) | Fixed maturities available for sale, at fair value | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		795,391	408,477
Significant Other Observable Inputs (Level 2) | Fixed maturities available for sale, at fair value | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		419,166	404,666
Significant Other Observable Inputs (Level 2) | Fixed maturities available for sale, at fair value | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,047,275	1,046,484
Significant Other Observable Inputs (Level 2) | Fixed maturities available for sale, at fair value | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		16,726	28,247
Significant Other Observable Inputs (Level 2) | Fixed maturities available for sale, at fair value | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,312,819	2,120,294
Significant Other Observable Inputs (Level 2) | Fixed maturities available for sale, at fair value | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,926,817	2,688,744
Significant Other Observable Inputs (Level 2) | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		134,358	681,894
Significant Other Observable Inputs (Level 2) | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		28,042	38,388
Significant Other Observable Inputs (Level 2) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		148,301	127,121
Significant Other Observable Inputs (Level 2) | Fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		744,080	776,441
Significant Other Observable Inputs (Level 2) | Fair value option | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		542,755	388,546
Significant Other Observable Inputs (Level 2) | Fair value option | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Other Observable Inputs (Level 2) | Fair value option | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		4,315	23,785
Significant Other Observable Inputs (Level 2) | Fair value option | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,652	4,367
Significant Other Observable Inputs (Level 2) | Fair value option | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		32,402	97,278
Significant Other Observable Inputs (Level 2) | Fair value option | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Other Observable Inputs (Level 2) | Fair value option | Other investments fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		162,956	262,465
Significant Unobservable Inputs (Level 3)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		162,073	39,007
Liabilities measured at fair value		(14,246)	(16,960)
Significant Unobservable Inputs (Level 3) | Contingent consideration liability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(14,246)	(16,960)
Significant Unobservable Inputs (Level 3) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Residential Mortgage
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fixed maturities available for sale, at fair value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		121,227	3,360
Significant Unobservable Inputs (Level 3) | Fixed maturities available for sale, at fair value | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		121,227	13
Significant Unobservable Inputs (Level 3) | Fixed maturities available for sale, at fair value | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fixed maturities available for sale, at fair value | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fixed maturities available for sale, at fair value | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fixed maturities available for sale, at fair value | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fixed maturities available for sale, at fair value | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fixed maturities available for sale, at fair value | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	3,347
Significant Unobservable Inputs (Level 3) | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		3,414	2,918
Significant Unobservable Inputs (Level 3) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		37,432	32,729
Significant Unobservable Inputs (Level 3) | Fair value option | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		4,173	4,748
Significant Unobservable Inputs (Level 3) | Fair value option | Other investments fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		33,259	27,981
Estimated Fair Value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		23,669,201	23,687,513
Liabilities measured at fair value		(90,207)	(71,184)
Estimated Fair Value | Contingent consideration liability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(14,246)	(16,960)
Estimated Fair Value | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(75,961)	(54,224)
Estimated Fair Value | Residential Mortgage
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,283	49,847
Estimated Fair Value | Fixed maturities available for sale, at fair value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		19,682,789	17,998,109
Estimated Fair Value | Fixed maturities available for sale, at fair value | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		8,020,128	6,553,333
Estimated Fair Value | Fixed maturities available for sale, at fair value | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		795,391	408,477
Estimated Fair Value | Fixed maturities available for sale, at fair value | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		419,166	404,666
Estimated Fair Value | Fixed maturities available for sale, at fair value | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,047,275	1,046,484
Estimated Fair Value | Fixed maturities available for sale, at fair value | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		5,161,193	4,772,764
Estimated Fair Value | Fixed maturities available for sale, at fair value | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,312,819	2,120,294
Estimated Fair Value | Fixed maturities available for sale, at fair value | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,926,817	2,692,091
Estimated Fair Value | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,331,662	1,734,716
Estimated Fair Value | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		859,969	1,804,170
Estimated Fair Value | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		148,301	127,121
Estimated Fair Value | Fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,644,197	1,973,550
Estimated Fair Value | Fair value option | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		542,755	388,546
Estimated Fair Value | Fair value option | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		5,398	0
Estimated Fair Value | Fair value option | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		4,315	23,785
Estimated Fair Value | Fair value option | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,652	4,367
Estimated Fair Value | Fair value option | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		33,101	97,806
Estimated Fair Value | Fair value option | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		13,792	26,493
Estimated Fair Value | Fair value option | Other investments fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		196,215	310,798
Estimated Fair Value | Fair value option | Other investments at net asset value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[1]	$ 846,969	$ 1,121,755

[1] In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.

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Fair Value - Rollforward of Level 3 assets and liabilities (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2022	Dec. 31, 2021
Contingent consideration liability
Level 3 liabilities rollforward
Balance at beginning of year		$ (16,960)	$ (461)
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	(364)	0
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		1,170	0
Purchases, issuances, sales and settlements
Purchases		0	(16,494)
Issuances		0	0
Sales		0	0	[2]
Settlements		1,908	(5)
Transfers in and/or out of Level 3		0	0
Balance at end of year		(14,246)	(16,960)
Equity securities
Level 3 assets rollforward
Balance at beginning of year		2,918	42,015
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	(470)	1,958
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0
Purchases, issuances, sales and settlements
Purchases		969	5,718
Issuances		0	0
Sales		(3)	(46,773)	[2]
Settlements		0	0
Transfers in and/or out of Level 3		0	0
Balance at end of year		3,414	2,918
Available for sale | Structured securities
Level 3 assets rollforward
Balance at beginning of year	[3]	3,347	3,426
Total gains or (losses) (realized/unrealized) - included in earnings	[1],[3]	(592)	(135)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income	[3]	(1)	133
Purchases, issuances, sales and settlements
Purchases	[3]	0	0
Issuances	[3]	0	0
Sales	[3]	(2,051)	0	[2]
Settlements	[3]	(703)	(77)
Transfers in and/or out of Level 3	[3]	0	0
Balance at end of year	[3]	0	3,347
Available for sale | Corporate bonds
Level 3 assets rollforward
Balance at beginning of year		13	13
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	352	0
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		(1,095)	0
Purchases, issuances, sales and settlements
Purchases		150,013	0
Issuances		0	0
Sales		(5,363)	0	[2]
Settlements		(26,250)	0
Transfers in and/or out of Level 3		3,557	0
Balance at end of year		121,227	13
Fair value option | Corporate bonds
Level 3 assets rollforward
Balance at beginning of year		0	985
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	0	13
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0
Purchases, issuances, sales and settlements
Purchases		0	0
Issuances		0	0
Sales		0	(998)	[2]
Settlements		0	0
Transfers in and/or out of Level 3		0	0
Balance at end of year		0	0
Fair value option | Other investments
Level 3 assets rollforward
Balance at beginning of year		27,981	67,103
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	(781)	868
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0
Purchases, issuances, sales and settlements
Purchases		12,381	13,213
Issuances		0	0
Sales		(3,339)	(53,203)	[2]
Settlements		(2,983)	0
Transfers in and/or out of Level 3		0	0
Balance at end of year		33,259	27,981
Fair value option | Equity securities
Level 3 assets rollforward
Balance at beginning of year		4,748	68,988
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	(575)	4,941
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0
Purchases, issuances, sales and settlements
Purchases		0	0
Issuances		0	0
Sales		0	(69,181)	[2]
Settlements		0	0
Transfers in and/or out of Level 3		0	0
Balance at end of year		$ 4,173	$ 4,748

[1] Gains or losses were included in net realized gains (losses).

[2] Sales for the 2021 period primarily relates to the Company’s deconsolidation of Somers

[3] Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities

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Fair Value - Narrative (Details) - USD ($) $ in Thousands	Dec. 31, 2022	Dec. 31, 2021
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Senior notes	$ 2,725,410	$ 2,724,394
Total assets and liabilities measured at fair value	23,800,000	23,800,000
Total assets and liabilities measured at fair value priced using non-binding broker quotes	$ 12,600	$ 7,700
Total assets and liabilities measured at fair value priced using non-binding broker quotes (percentage)	0.10%	0.00%
Unsecured debt | Senior Notes
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Senior notes	$ 2,700,000	$ 2,700,000
Estimated fair value of senior notes	$ 2,400,000	$ 3,300,000

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Derivative Instruments (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Derivative offsetting [Abstract]
Derivative assets subject to master netting agreements		$ 147,400	$ 122,300
Derivative liabilities subject to master netting agreements		73,200	53,900
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(75,023)	(32,390)	$ 179,675
Not Designated as Hedging Instrument
Derivative [Line Items]
Asset derivatives - fair value		148,301	127,121
Liability derivatives - fair value		(75,961)	(54,224)
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(75,023)	(32,390)	179,675
Not Designated as Hedging Instrument | Futures contracts
Derivative [Line Items]
Net derivatives - notional value	[1]	3,138,446	2,826,564
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(86,634)	(15,262)	114,987
Not Designated as Hedging Instrument | Futures contracts | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[2]	50,629	34,999
Not Designated as Hedging Instrument | Futures contracts | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[2]	(16,963)	(9,808)
Not Designated as Hedging Instrument | Foreign currency forward contracts
Derivative [Line Items]
Net derivatives - notional value	[1]	1,136,126	915,962
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		6,144	(39,755)	49,974
Not Designated as Hedging Instrument | Foreign currency forward contracts | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[2]	38,891	7,734
Not Designated as Hedging Instrument | Foreign currency forward contracts | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[2]	(35,446)	(11,390)
Not Designated as Hedging Instrument | TBAs
Derivative [Line Items]
Net derivatives - notional value	[1]		11,227
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(51)	(233)	1,129
Not Designated as Hedging Instrument | TBAs | Fixed maturities available for sale, at fair value
Derivative [Line Items]
Asset derivatives - fair value	[2]		11,227
Liability derivatives - fair value	[2]		0
Not Designated as Hedging Instrument | Other
Derivative [Line Items]
Net derivatives - notional value	[1]	3,591,793	3,736,773
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		5,518	22,860	$ 13,585
Not Designated as Hedging Instrument | Other | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[2]	58,781	73,161
Not Designated as Hedging Instrument | Other | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[2]	$ (23,552)	$ (33,026)

[1] Represents the absolute notional value of all outstanding contracts, consisting of long and short positions.

[2] The fair value of asset derivatives are included in ‘other assets’ and the fair value of liability derivatives are included in ‘other liabilities.’

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Variable Interest Entity and Noncontrolling Interests - Variable interest entity (Details) - USD ($) $ in Thousands	1 Months Ended
	Mar. 31, 2014	Jul. 01, 2021
Greysbridge Holdings Ltd
Variable Interest Entity [Line Items]
Percentage ownership		40.00%
Greysbridge Holdings Ltd | Kelso And Company
Variable Interest Entity [Line Items]
Percentage ownership		30.00%
Greysbridge Holdings Ltd | Warburg Pincus LLC
Variable Interest Entity [Line Items]
Percentage ownership		30.00%
Variable Interest Entity, Primary Beneficiary | Somers Holdings Ltd.
Variable Interest Entity [Line Items]
Initial investment contribution amount	$ 100,000
Variable Interest Entity, Primary Beneficiary | Common shares | Somers Holdings Ltd.
Variable Interest Entity [Line Items]
Number of shares acquired	2,500,000

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Variable Interest Entity and Noncontrolling Interests - Cash flows of variable interest entity (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Variable Interest Entity [Line Items]
Net Cash Provided by (Used in) Operating Activities	$ 3,815,227	$ 3,427,555	$ 2,886,505
Net cash used for investing activities	(3,102,055)	(2,139,732)	(3,043,226)
Net Cash Provided by (Used in) Financing Activities	(705,726)	(1,229,549)	521,278
Somers Holdings Ltd. | Variable Interest Entity, Primary Beneficiary
Variable Interest Entity [Line Items]
Net Cash Provided by (Used in) Operating Activities	0	46,991	181,736
Net cash used for investing activities	0	96,325	258,589
Net Cash Provided by (Used in) Financing Activities	$ 0	$ (2,042)	$ (335,776)

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Variable Interest Entity and Noncontrolling Interests - Non-redeemable noncontrolling interest (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Noncontrolling Interest [Line Items]
Non-redeemable noncontrolling interest, beginning of year	$ 0	$ 823,007
Amounts attributable to nonredeemable noncontrolling interests	0	(78,314)	$ (53,076)
Other comprehensive (income) loss attributable to noncontrolling interests	0	13,984	(9,062)
Non-redeemable noncontrolling interest, end of year	0	0	823,007
Somers Holdings Ltd. | Noncontrolling Interest
Noncontrolling Interest [Line Items]
Non-redeemable noncontrolling interest, beginning of year	0	823,007
Impact of deconsolidation of Somers	0	(918,874)
Additional paid in capital attributable to noncontrolling interests	0	22,113
Amounts attributable to nonredeemable noncontrolling interests	0	78,314
Other comprehensive (income) loss attributable to noncontrolling interests	0	(4,560)
Non-redeemable noncontrolling interest, end of year	$ 0	$ 0	$ 823,007

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Variable Interest Entity and Noncontrolling Interests - Redeemable noncontrolling interest (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Redeemable Noncontrolling Interest [Line Items]
Balance, beginning of year	$ 9,233	$ 58,548	$ 55,404
Impact of deconsolidation of Somers	0	(48,919)	0
Other	1,596	(396)	3,144
Balance, end of year	$ 10,829	$ 9,233	$ 58,548

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Variable Interest Entity and Noncontrolling Interests - Income or loss attributable to third party investors (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Noncontrolling Interest [Line Items]
Amounts attributable to non-redeemable noncontrolling interests	$ 0	$ (78,314)	$ (53,076)
Amounts attributable to redeemable noncontrolling interests	(5,490)	(4,299)	(7,114)
Net (income) loss attributable to noncontrolling interests	$ (5,490)	$ (82,613)	$ (60,190)

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Variable Interest Entity and Noncontrolling Interests - Other variable interest entity disclosures (Details) - USD ($) $ in Thousands		Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Variable Interest Entity [Line Items]
Total VIE Assets		$ 47,990,507	$ 45,100,945	$ 43,282,297
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		3,904,776	3,248,206
Variable Interest Entity, Not Primary Beneficiary
Variable Interest Entity [Line Items]
Total VIE Assets		3,594,884	4,336,596
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		1,776	(4,434)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		26,800	42,202
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		28,576	37,768
Remaining Coverage, Amount		410,593
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2017-1 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		36,679	108,368
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		(6)	(159)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		14	424
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		8	265
Remaining Coverage, Amount	[1]	0
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-1 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		89,698	181,136
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		(153)	(528)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		508	1,268
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		355	740
Remaining Coverage, Amount	[1]	0
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-3 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		199,237	302,563
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		(250)	(1,018)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		771	2,496
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		521	1,478
Remaining Coverage, Amount	[1]	0
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-1 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		107,880	181,324
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		(48)	(380)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		593	5,807
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		545	5,427
Remaining Coverage, Amount	[1]	0
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-2 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		325,462	398,316
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		(206)	(515)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		4,356	3,998
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		4,150	3,483
Remaining Coverage, Amount	[1]	0
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-3 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		222,977	409,859
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		(104)	(584)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		1,229	3,190
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		1,125	2,606
Remaining Coverage, Amount	[1]	0
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-4 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		266,124	411,954
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		(142)	(462)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		3,640	4,759
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		3,498	4,297
Remaining Coverage, Amount	[1]	0
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-2 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		105,110	217,766
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		(8)	(177)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		492	1,984
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		484	1,807
Remaining Coverage, Amount	[1]	0
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-3 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		243,891	348,818
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		53	(128)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		2,872	5,793
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		2,925	5,665
Remaining Coverage, Amount	[1]	7,079
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-4 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		97,563	176,826
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		32	(50)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		642	1,630
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		674	1,580
Remaining Coverage, Amount	[1]	4,165
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-1 Ltd Member
Variable Interest Entity [Line Items]
Total VIE Assets		467,469	568,986
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		239	(303)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		2,743	3,283
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		2,982	2,980
Remaining Coverage, Amount	[1]	35,798
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-2 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		458,362	522,807
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		581	281
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		2,855	4,124
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		3,436	4,405
Remaining Coverage, Amount	[1]	77,099
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-3 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		489,927	507,873
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		217	(411)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		2,704	3,446
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		2,921	$ 3,035
Remaining Coverage, Amount	[1]	127,032
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2022-01 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		283,500
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		399
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		1,765
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		2,164
Remaining Coverage, Amount	[1]	33,260
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2022-2 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		201,005
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		1,172
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		1,616
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		2,788
Remaining Coverage, Amount	[1]	$ 126,160

[1] Coverage from a separate panel of reinsurers remaining at December 31, 2022

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Other Comprehensive Income - Components of accumulated other comprehensive income (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	$ (64,600)	$ 488,895	$ 212,091
Other comprehensive income (loss) before reclassifications	(1,829,369)	(437,427)	702,991
Amounts reclassified from accumulated other comprehensive income	247,799	(116,068)	(426,187)
Net current period other comprehensive income (loss)	(1,581,570)	(553,495)	276,804
Ending balance	(1,646,170)	(64,600)	488,895
Unrealized Appreciation on Available-For-Sale Investments
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	13,486	501,295	258,486
Other comprehensive income (loss) before reclassifications	(1,772,649)	(371,741)	668,996
Amounts reclassified from accumulated other comprehensive income	247,799	(116,068)	(426,187)
Net current period other comprehensive income (loss)	(1,524,850)	(487,809)	242,809
Ending balance	(1,511,364)	13,486	501,295
Foreign Currency Translation Adjustments
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	(78,086)	(12,400)	(46,395)
Other comprehensive income (loss) before reclassifications	(56,720)	(65,686)	33,995
Amounts reclassified from accumulated other comprehensive income	0	0	0
Net current period other comprehensive income (loss)	(56,720)	(65,686)	33,995
Ending balance	$ (134,806)	$ (78,086)	$ (12,400)

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Other Comprehensive Income - Amounts reclassified from accumulated other comprehensive income (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Reclassification out of Accumulated Other Comprehensive Income [Line Items]
Provision for credit losses	$ (43,909)	$ (2,100)	$ (3,597)
Other-than-temporary impairment losses	0	0
Other-than-temporary impairment losses			(533)
Income (loss) before income taxes	1,562,384	2,368,042	1,577,549
Income tax (expense) benefit	(79,961)	(128,582)	(111,838)
Net of tax	1,476,933	2,156,849	1,405,521
Reclassification out of accumulated other comprehensive income | Unrealized Appreciation on Available-For-Sale Investments
Reclassification out of Accumulated Other Comprehensive Income [Line Items]
Net realized gains (losses)	(235,989)	157,095	478,659
Provision for credit losses	(43,909)	(2,099)	(3,597)
Other-than-temporary impairment losses	0	0
Other-than-temporary impairment losses			(533)
Income (loss) before income taxes	(279,898)	154,996	474,529
Income tax (expense) benefit	32,099	(38,928)	(48,342)
Net of tax	$ (247,799)	$ 116,068	$ 426,187

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Other Comprehensive Income - Tax effects on components of other comprehensive income (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Before tax amount:
Unrealized holding gains (losses) arising during period, before tax	$ (2,010,443)	$ (406,774)	$ 754,572
Less reclassification of net realized gains (losses) included in net income, before tax	(279,898)	154,996	474,529
Foreign currency translation adjustments, before tax	(56,554)	(64,423)	33,706
Other comprehensive income (loss), before tax	(1,787,099)	(626,193)	313,749
Tax expense (benefit):
Unrealized holding gains (losses) arising during period, tax	(237,794)	(19,845)	75,855
Less reclassification of net realized gains (losses) included in net income, tax	(32,099)	38,928	48,342
Foreign currency translation adjustments, tax	166	59	370
Other comprehensive income (loss), tax	(205,529)	(58,714)	27,883
Net of tax amount:
Unrealized holding gains (losses) arising during period, net of tax	(1,772,649)	(386,929)	678,717
Less reclassification of net realized gains (losses) included in net income, net of tax	(247,799)	116,068	426,187
Foreign currency translation adjustments, net of tax	(56,720)	(64,482)	33,336
Net current period other comprehensive income (loss)	$ (1,581,570)	$ (567,479)	$ 285,866

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Earnings Per Common Share (Details) - USD ($) $ / shares in Units, $ in Thousands		12 Months Ended
		Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Numerator:
Net income		$ 1,482,423	$ 2,239,462	$ 1,465,711
Net (income) loss attributable to noncontrolling interests		(5,490)	(82,613)	(60,190)
Net income available to Arch		1,476,933	2,156,849	1,405,521
Preferred share dividends		(40,736)	(48,343)	(41,612)
Loss on redemption of preferred shares		0	(15,101)	0
Net income available to Arch common shareholders		$ 1,436,197	$ 2,093,405	$ 1,363,909
Denominator:
Weighted average common shares outstanding		368,612,197	391,748,715	403,062,179
Effect of dilutive common share equivalents:
Nonvested restricted shares		2,103,036	1,996,524	1,682,309
Stock options	[1]	6,894,534	6,600,697	5,514,967
Weighted average common shares and common share equivalents outstanding — diluted		377,609,767	400,345,936	410,259,455
Earnings per common share:
Basic (per share)		$ 3.90	$ 5.34	$ 3.38
Diluted (per share)		$ 3.80	$ 5.23	$ 3.32
Stock Options
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Antidilutive securities excluded from computation of earnings per common share (shares)		798,053	2,398,608	2,249,821

[1] Certain stock options were not included in the computation of diluted earnings per share where the exercise price of the stock options exceeded the average market price and would have been anti-dilutive or where, when applying the treasury stock method to in-the-money options, the sum of the proceeds, including unrecognized compensation, exceeded the average market price and would have been anti-dilutive. For 2022, 2021 and 2020, the number of stock options excluded were 798,053, 2,398,608 and 2,249,821, respectively.

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Income Taxes - Components of income tax (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Current expense (benefit):
United States	$ 195,588	$ 284,274	$ 181,571
Non-U.S.	5,628	11,259	16,091
Current Income Tax Expense (Benefit)	201,216	295,533	197,662
Deferred expense (benefit):
United States	(96,599)	(123,261)	(89,170)
Non-U.S.	(24,656)	(43,690)	3,346
Deferred Income Tax Expense (Benefit)	(121,255)	(166,951)	(85,824)
Income tax expense (benefit)	$ 79,961	$ 128,582	$ 111,838

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Income Taxes - Income before taxes by jurisdiction (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Income Tax Disclosure [Line Items]
Income (loss) before income taxes	$ 1,562,384	$ 2,368,042	$ 1,577,549
Bermuda
Income Tax Disclosure [Line Items]
Income (loss) before income taxes	985,828	1,518,616	1,114,117
United States
Income Tax Disclosure [Line Items]
Income (loss) before income taxes	400,865	643,239	409,893
Other
Income Tax Disclosure [Line Items]
Income (loss) before income taxes	$ 175,691	$ 206,187	$ 53,539

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Income Taxes - Statutory tax rate by jurisdiction (Details)	12 Months Ended
	Dec. 31, 2022
Bermuda
Income Tax Disclosure [Line Items]
Statutory tax rate (percentage)	0.00%
United States
Income Tax Disclosure [Line Items]
Statutory tax rate (percentage)	21.00%
United Kingdom
Income Tax Disclosure [Line Items]
Statutory tax rate (percentage)	19.00%
Ireland
Income Tax Disclosure [Line Items]
Statutory tax rate (percentage)	12.50%
Denmark
Income Tax Disclosure [Line Items]
Statutory tax rate (percentage)	22.00%
Canada
Income Tax Disclosure [Line Items]
Statutory tax rate (percentage)	26.50%
Gibraltar
Income Tax Disclosure [Line Items]
Statutory tax rate (percentage)	12.50%
Australia
Income Tax Disclosure [Line Items]
Statutory tax rate (percentage)	30.00%
Hong Kong
Income Tax Disclosure [Line Items]
Statutory tax rate (percentage)	16.50%
Netherlands
Income Tax Disclosure [Line Items]
Statutory tax rate (percentage)	25.80%

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Income Taxes - Reconciliation of effective tax rate (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Income Tax Disclosure [Abstract]
Expected income tax expense (benefit) computed on pre-tax income at weighted average income tax rate	$ 110,337	$ 158,269	$ 111,947
Addition (reduction) in income tax expense (benefit) resulting from:
Investment income	(12,762)	(23,572)	(1,824)
State taxes, net of U.S. federal tax benefit	10,650	20,978	5,027
Dividend withholding taxes	10,559	12,211	7,105
Change in valuation allowance	(22,726)	(40,425)	13,190
Base eroding tax	7,694	0	0
Share based compensation	(9,159)	(5,339)	(2,533)
Tax credits	(9,736)	0	0
Intercompany loan write-off	(3,544)	0	(22,083)
Other	(1,352)	6,460	1,009
Income tax expense	$ 79,961	$ 128,582	$ 111,838

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Income Taxes - Components of deferred tax assets and liabilities (Details) - USD ($) $ in Thousands	Dec. 31, 2022	Dec. 31, 2021
Deferred income tax assets:
Net operating loss	$ 76,665	$ 87,960
Discounting of net loss reserves	77,556	72,001
Net unearned premium reserve	96,581	75,483
Compensation liabilities	55,269	28,062
Foreign tax credit carryforward	16,738	20,058
Bad debt reserves	17,365	10,252
Depreciation and amortization	141,409	115,041
Lease liability	26,681	21,453
Net unrealized decline of investments	192,949	0
Lloyds year of account deferral	1,385	0
Other, net	14,450	703
Deferred tax assets before valuation allowance	717,048	431,013
Valuation allowance	(6,968)	(43,953)
Deferred tax assets net of valuation allowance	710,080	387,060
Deferred income tax liabilities:
Deposit accounting liability	(2,658)	(1,578)
Goodwill and intangibles	(38,905)	(70,549)
Lloyds year of account deferral	0	(12,514)
Contingency reserve	(43,870)	(49,486)
Deferred policy acquisition costs	(63,708)	(25,612)
Investment related	(9,225)	(7,492)
Net unrealized appreciation of investments	0	(8,377)
Right-of-use asset	(20,781)	(17,406)
Total deferred tax liabilities	(179,147)	(193,014)
Net deferred income tax assets	$ 530,933	$ 194,046

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Income Taxes - Operating loss carryfowards and tax credits (Details) - USD ($) $ in Thousands		Dec. 31, 2022	Dec. 31, 2021
Operating Loss Carryforwards [Line Items]
Foreign tax credit carryforward		$ 16,738	$ 20,058
United Kingdom
Operating Loss Carryforwards [Line Items]
Operating loss carryforwards		198,571
Foreign tax credit carryforward		13,907
Ireland
Operating Loss Carryforwards [Line Items]
Operating loss carryforwards		61,685
Australia
Operating Loss Carryforwards [Line Items]
Operating loss carryforwards		32,333
Hong Kong
Operating Loss Carryforwards [Line Items]
Operating loss carryforwards		28,080
Netherlands
Operating Loss Carryforwards [Line Items]
Operating loss carryforwards		60
United States
Operating Loss Carryforwards [Line Items]
Operating loss carryforwards	[1]	23,766
Operating loss carryforward, portion subject to utilization limits		7,000
Operating loss carryforward, annual utilization limit		600
AMT credit carryforward		$ 2,830

[1] On January 30, 2014, the Company’s U.S. mortgage operations underwent an ownership change for U.S. federal income tax purposes as a result of the Company’s acquisition of the CMG Entities. As a result of this ownership change, a limitation has been imposed upon the utilization of approximately $7.0 million of the Company’s existing U.S. net operating loss carryforwards. Utilization is limited to approximately $0.6 million per year in accordance with Section 382 of the Internal Revenue Code of 1986 as amended (“the Code”).

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Income Taxes - Unrecognized tax benefits (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021
Reconciliation of beginning and ending amount of unrecognized tax benefits
Balance at beginning of year	$ 2,008	$ 2,008
Additions based on tax positions related to the current year	0	0
Additions for tax positions of prior years	0	0
Reductions for tax positions of prior years	0	0
Settlements	0	0
Balance at end of year	$ 2,008	$ 2,008

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Income Taxes - Summary of open tax years by major jurisdiction (Details)	12 Months Ended
	Dec. 31, 2022
United States | Minimum
Income Tax Contingency [Line Items]
Open tax year	2015
United States | Maximum
Income Tax Contingency [Line Items]
Open tax year	2022
United Kingdom | Minimum
Income Tax Contingency [Line Items]
Open tax year	2020
United Kingdom | Maximum
Income Tax Contingency [Line Items]
Open tax year	2022
Ireland | Minimum
Income Tax Contingency [Line Items]
Open tax year	2018
Ireland | Maximum
Income Tax Contingency [Line Items]
Open tax year	2022
Canada | Minimum
Income Tax Contingency [Line Items]
Open tax year	2018
Canada | Maximum
Income Tax Contingency [Line Items]
Open tax year	2022
Switzerland | Minimum
Income Tax Contingency [Line Items]
Open tax year	2018
Switzerland | Maximum
Income Tax Contingency [Line Items]
Open tax year	2022
Denmark | Minimum
Income Tax Contingency [Line Items]
Open tax year	2018
Denmark | Maximum
Income Tax Contingency [Line Items]
Open tax year	2022
Australia | Minimum
Income Tax Contingency [Line Items]
Open tax year	2018
Australia | Maximum
Income Tax Contingency [Line Items]
Open tax year	2022

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Income Taxes - Narrative (Details) - USD ($) $ in Millions	Dec. 31, 2022	Dec. 31, 2021
Operating Loss Carryforwards [Line Items]
Current income taxes payable	$ 40.6
Other assets | T&L Bonds
Operating Loss Carryforwards [Line Items]
US mortgage guaranty tax and loss bonds	$ 12.4	$ 31.6

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Transactions with Related Parties (Details)	12 Months Ended
	Dec. 31, 2022 USD ($) director	Dec. 31, 2021 USD ($)	Dec. 31, 2020 USD ($)	Dec. 31, 2017 USD ($)	Jan. 01, 2024	Jul. 01, 2021	Jan. 01, 2021 USD ($)	Dec. 31, 2019 USD ($)
Related Party Transaction [Line Items]
Purchases of other investments	$ 1,720,457,000	$ 1,859,096,000	$ 1,808,727,000
Net reserves	13,753,118,000	12,157,925,000	12,199,074,000					$ 9,809,192,000
Reinsurance recoverable for paid and unpaid claims and claims adjustments	6,563,654,000	5,880,735,000	4,500,802,000
Ceded premiums written	4,249,258,000	3,734,150,000	2,650,352,000
Reinsurance balances payable	1,529,919,000	1,583,253,000
Net premiums written	11,077,189,000	9,018,337,000	7,437,716,000
Net premiums earned	$ 9,678,077,000	8,082,298,000	$ 6,991,935,000
Forecast
Related Party Transaction [Line Items]
Put Call Right To Sell Purchase Shares					33.30%
Greysbridge Holdings Ltd
Related Party Transaction [Line Items]
Percentage ownership						40.00%
Kelso And Company | Greysbridge Holdings Ltd
Related Party Transaction [Line Items]
Percentage ownership						30.00%
Premia Holdings Ltd
Related Party Transaction [Line Items]
Number of directors | director	7
Warburg Pincus LLC | Greysbridge Holdings Ltd
Related Party Transaction [Line Items]
Percentage ownership						30.00%
Arch Re Bermuda And Affiliates | Premia Holdings Ltd
Related Party Transaction [Line Items]
Number of directors | director	2
Equity Method Investee | Premia Holdings Ltd
Related Party Transaction [Line Items]
Percentage ownership				25.00%
Quota share agreement percentage	25.00%
Purchases of other investments				$ 100,000,000
Net premiums written	$ 121,100,000	40,400,000
Net premiums earned	119,900,000	40,400,000
Funds Held under Reinsurance Agreements, Asset	118,700,000	53,500,000
Equity Method Investee | Barbican
Related Party Transaction [Line Items]
Net reserves							$ 380,000,000
Reinsurance recoverable for paid and unpaid claims and claims adjustments	0	0
Funds held liability	0	0
Equity Method Investee | Somers Holdings Ltd.
Related Party Transaction [Line Items]
Reinsurance recoverable for paid and unpaid claims and claims adjustments	1,200,000,000	902,800,000
Reinsurance balances payable	413,800,000	258,400,000
Senior notes	$ 35,000,000
Preferred shares, dividend rate (as a percent)	6.50%
Net premiums written	$ 519,400,000	$ 379,100,000

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Leases - Additional information regarding leases (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Lessee, Lease, Description [Line Items]
Operating lease costs		$ 33,571	$ 31,691
Sublease Income	[1]	(988)	0
Cash payments included in the measurement of lease liabilities reported in operating cash flows		26,051	32,094
Right-of-use assets obtained in exchange for new lease liabilities		42,841	22,686
Right-of-use assets	[2]	123,083	106,836
Operating lease liability	[2]	$ 151,890	$ 126,711
Weighted average discount rate		4.20%	3.90%
Weighted average remaining lease term		6 years 7 months 6 days	5 years 10 months 24 days
Balance sheet location of right of use asset		Other assets	Other assets
Balance sheet location of operating lease liability		Other liabilities	Other liabilities
Lease, Cost		$ 38,900	$ 39,100	$ 37,400
Maximum
Lessee, Lease, Description [Line Items]
Operating lease term		10 years

[1] The sublease income primarily relates to office property in Raleigh, North Carolina.

[2] The right-of-use assets are included in ‘other assets’ while the operating lease liability is included in ‘other liabilities.’

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Leases - Contractual maturities (Details) - USD ($) $ in Thousands		Dec. 31, 2022	Dec. 31, 2021
Contractual maturities of operating lease liabilities
2023		$ 31,861
2024		30,091
2025		24,651
2026		21,939
2027		17,859
2028 and thereafter		48,522
Total undiscounted lease liability		174,923
Less: present value adjustment		(23,033)
Operating lease liability	[1]	$ 151,890	$ 126,711

[1] The right-of-use assets are included in ‘other assets’ while the operating lease liability is included in ‘other liabilities.’

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Commitments and Contingencies - Concentrations of credit risk (Details)	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Customer concentration risk | Gross written premiums
Concentration Risk [Line Items]
Concentration risk, threshold	10.00%
Customer concentration risk | Gross written premiums | Marsh & McLennan Companies and its subsidiaries
Concentration Risk [Line Items]
Concentration risk percentage	17.30%	18.30%	13.30%
Customer concentration risk | Gross written premiums | AON Corporation and its subsidiaries
Concentration Risk [Line Items]
Concentration risk percentage	13.80%	12.20%	12.00%
Credit concentration risk | Shareholders' equity
Concentration Risk [Line Items]
Concentration risk, threshold	10.00%

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Commitments and Contingencies - Other commitments (Details) - USD ($) $ in Millions	Dec. 31, 2022	Dec. 31, 2021
Commitments and Contingencies Disclosure [Abstract]
Investment commitments	$ 2,900.0	$ 3,000.0
Estimated purchase commitments, primarily related to software and computerized systems	$ 150.1	$ 114.1

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Debt and Financing Arrangements - Schedule of senior notes outstanding (Details) - USD ($) $ in Thousands		Dec. 31, 2022	Dec. 31, 2021
Debt Instrument [Line Items]
Carrying amount		$ 2,725,410	$ 2,724,394
Senior Notes
Debt Instrument [Line Items]
Principal amount		2,750,000
Carrying amount		$ 2,725,410	2,724,394
Senior Notes | 7.350% senior notes due 2034
Debt Instrument [Line Items]
Stated interest rate (percentage)	[1]	7.35%
Principal amount	[1]	$ 300,000
Carrying amount		$ 297,618	297,488
Senior Notes | 5.144% senior notes due 2043
Debt Instrument [Line Items]
Stated interest rate (percentage)	[2]	5.144%
Principal amount	[2]	$ 500,000
Carrying amount		$ 495,188	495,063
Senior Notes | 4.011% senior notes due 2026
Debt Instrument [Line Items]
Stated interest rate (percentage)	[3]	4.011%
Principal amount	[3]	$ 500,000
Carrying amount		$ 498,073	497,633
Senior Notes | 5.031% senior notes due 2046
Debt Instrument [Line Items]
Stated interest rate (percentage)	[4]	5.031%
Principal amount	[4]	$ 450,000
Carrying amount		$ 445,582	445,490
Senior Notes | 3.635% senior notes due 2050
Debt Instrument [Line Items]
Stated interest rate (percentage)	[5]	3.635%
Principal amount	[5]	$ 1,000,000
Carrying amount		$ 988,949	$ 988,720

[1] Senior notes of Arch Capital issued on May 4, 2004 and due May 1, 2034 (“2034 notes”).

[2] Senior notes of Arch-U.S., a wholly-owned subsidiary of Arch Capital, issued on December 13, 2013 and due November 1, 2043 (“2043 notes”), fully and unconditionally guaranteed by Arch Capital.

[3] Senior notes of Arch Capital Finance LLC (“Arch Finance”), a wholly-owned finance subsidiary of Arch Capital, issued on December 8, 2016 and due December 15, 2026 (“2026 notes”), fully and unconditionally guaranteed by Arch Capital.

[4] Senior notes of Arch Finance issued on December 8, 2016 and due December 15, 2046 (“2046 notes”), fully and unconditionally guaranteed by Arch Capital

[5] Senior notes of Arch Capital issued on June 30, 2020 and due June 30, 2050 (“2050 notes”).

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Debt and Financing Arrangements - Letter of Credit and Revolving Credit Facilities (Details) - USD ($) $ in Thousands	Dec. 31, 2022	Apr. 07, 2022	Dec. 31, 2021
Line of Credit Facility [Line Items]
Advances from Federal Home Loan Banks	$ 0		$ 80,000
Investments pledged as security for FHLB advances			80,200
Credit Facility
Line of Credit Facility [Line Items]
Maximum borrowing capacity		$ 925,000
Optional increased capacity	1,250,000
Credit Facility | Asset Pledged as Collateral | Letter of Credit
Line of Credit Facility [Line Items]
Financial Instruments, Owned, at Fair Value	465,200
Secured letter of credit facility
Line of Credit Facility [Line Items]
Maximum borrowing capacity	425,000
Remaining capacity	101,900
Outstanding borrowings	323,100
Unsecured revolving loan and letter of credit facility
Line of Credit Facility [Line Items]
Maximum borrowing capacity	500,000
Remaining capacity	500,000
Outstanding borrowings	0		$ 0
Other Arch Capital Subsidiaries | Secured letter of credit facility
Line of Credit Facility [Line Items]
Outstanding borrowings	24,600
Other Arch Capital Subsidiaries | Unsecured revolving loan and letter of credit facility
Line of Credit Facility [Line Items]
Outstanding borrowings	$ 400,000

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Goodwill and Intangible Assets - Analysis of goodwill and intangible assets (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Goodwill
Goodwill, beginning of year	$ 344,865	$ 314,629
Goodwill, acquisitions	8,389	31,677
Goodwill, foreign currency translation adjustment	(11,181)	(1,441)
Goodwill, end of year	342,073	344,865	$ 314,629
Intangible assets (indefinite life)
Intangible assets with an indefinite life, beginning of year	71,357	79,219
Intangible assets with an indefinite life, acquisitions	0	0
Indefinite lived intangible assets, impact of deconsolidation of Somers		(7,650)
Intangible assets with an indefinite life, foreign currency translation adjustment	(2,576)	(212)
Intangible assets with an indefinite life, end of year	68,781	71,357	79,219
Intangible assets (finite life)
Intangible assets with a finite life, beginning of year	528,761	299,015
Intangible assets with a finite life, acquisitions	0	318,459
Intangible assets with a finite life, amortization	(106,200)	(82,955)	(69,031)
Intangible assets with a finite life, foreign currency translation adjustment	(29,126)	(5,758)
Intangible assets with a finite life, end of year	393,435	528,761	299,015
Total
Goodwill and intangible assets, beginning of year	944,983	692,863
Goodwill and intangible assets, acquisitions	8,389	350,136
Indefinite Lived and Finite Lived Intangible Assets Decrease Due To Deconsolidation		(7,650)
Goodwill and intangible assets, foreign currency movements and other adjustments	(42,883)	(7,411)
Goodwill and intangible assets, end of year	804,289	944,983	692,863
Goodwill and intangible assets, gross balance	1,523,775
Intangible assets with a finite life, accumulated amortization	(678,020)	(571,839)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	(41,466)	1,436
Goodwill and intangible assets	804,289	944,983	$ 692,863
Goodwill
Goodwill
Goodwill, end of year	342,073
Total
Goodwill and intangible assets, beginning of year	344,865
Goodwill and intangible assets, end of year	342,073	344,865
Goodwill, gross balance	351,231
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	(9,158)	2,023
Goodwill and intangible assets	342,073	$ 344,865
Intangible assets with an indefinite life
Intangible assets (indefinite life)
Intangible assets with an indefinite life, end of year	68,781
Total
Indefinite-lived intangible assets, gross balance	70,246
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	(1,465)
Intangible assets with a finite life
Intangible assets (finite life)
Intangible assets with a finite life, end of year	393,435
Total
Intangible assets with a finite life, gross balance	1,102,298
Intangible assets with a finite life, accumulated amortization	(678,020)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	$ (30,843)

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Goodwill and Intangible Assets - Summary of intangible assets by major class (Details) - USD ($) $ in Thousands	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	$ 1,523,775	$ 1,515,386
Intangible assets with a finite life, accumulated amortization	(678,020)	(571,839)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	(41,466)	1,436
Goodwill and intangible assets	804,289	944,983	$ 692,863
Intangible liability - unfavorable service contract
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	(9,533)	(9,533)
Intangible assets with a finite life, accumulated amortization	9,533	9,435
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	0	0
Goodwill and intangible assets	0	(98)
Intangible assets with a finite life
Schedule of Goodwill And Intangible Assets [Line Items]
Intangible assets with a finite life, accumulated amortization	(678,020)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	(30,843)
Intangible assets with a finite life | Acquired insurance contracts
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	451,505	451,505
Intangible assets with a finite life, accumulated amortization	(426,202)	(409,592)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	339	339
Goodwill and intangible assets	25,642	42,252
Intangible assets with a finite life | Operating platform
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	52,674	52,674
Intangible assets with a finite life, accumulated amortization	(50,302)	(48,838)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	2	56
Goodwill and intangible assets	2,374	3,892
Intangible assets with a finite life | Distribution relationships
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	602,518	602,518
Intangible assets with a finite life, accumulated amortization	(207,908)	(120,302)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	(31,110)	(2,207)
Goodwill and intangible assets	363,500	480,009
Intangible assets with a finite life | Other
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	5,134	5,134
Intangible assets with a finite life, accumulated amortization	(3,141)	(2,542)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	(74)	114
Goodwill and intangible assets	1,919	2,706
Goodwill
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	351,231	342,842
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	(9,158)	2,023
Goodwill and intangible assets	342,073	344,865
Intangible assets with an indefinite life
Schedule of Goodwill And Intangible Assets [Line Items]
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	(1,465)
Intangible assets with an indefinite life | Insurance licenses
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	48,331	48,331
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	0	0
Goodwill and intangible assets	48,331	48,331
Intangible assets with an indefinite life | Syndicate capacity
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	21,915	21,915
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	(1,465)	1,111
Goodwill and intangible assets	$ 20,450	$ 23,026

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Goodwill and Intangible Assets - Future amortization expense (Details) - USD ($) $ in Thousands	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Goodwill and Intangible Assets Disclosure [Abstract]
2023	$ 91,605
2024	73,366
2025	41,060
2026	32,091
2027	29,268
2028 and thereafter	126,045
Finite-Lived Intangible Assets, Net	$ 393,435	$ 528,761	$ 299,015

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Goodwill and Intangible Assets - Narrative (Details)	12 Months Ended
	Dec. 31, 2022
Minimum
Finite-Lived Intangible Assets [Line Items]
Remaining useful lives of intangible assets	1 year
Maximum
Finite-Lived Intangible Assets [Line Items]
Remaining useful lives of intangible assets	14 years

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Shareholders' Equity - Roll-forward of changes in issued and outstanding common shares (Details) - $ / shares		12 Months Ended
		Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Common Shares:
Shares issued, beginning of year		583,289,850	579,000,841	574,617,195
Shares issued	[1]	3,517,399	2,669,229	2,646,164
Restricted shares issued, net of cancellations		1,443,513	1,619,780	1,737,482
Shares issued, end of year		588,250,762	583,289,850	579,000,841
Common shares held in treasury, end of year		(217,904,765)	(204,365,956)	(172,280,199)
Common shares outstanding, end of year		370,345,997	378,923,894	406,720,642
Authorized and Issued:
Common shares authorized		1,800,000,000
Common shares, par value per share		$ 0.0011	$ 0.0011
Preferred shares authorized		50,000,000
Preferred shares, par value per share		$ 0.01

[1] Includes shares issued from the exercise of stock options and stock appreciation rights, the vesting of restricted share units and shares issued from the employee share purchase plan.

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Shareholders' Equity - Share repurchase program (Details) - USD ($) $ / shares in Units, $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Class of Stock [Line Items]
Aggregate cost of shares repurchased	$ 585,823	$ 1,234,294	$ 83,472
Number of shares repurchased (shares)	12,891,405	31,486,830	2,850,102
Average price per share repurchased	$ 45.44	$ 39.20	$ 29.29
Common shares held in treasury (shares)	217,904,765	204,365,956	172,280,199
Common shares held in treasury, at cost	$ 4,377,920	$ 3,761,095
Common shares
Class of Stock [Line Items]
Remaining share repurchase authorization	$ 1,000,000
Cumulative number of shares acquired since inception of share repurchase program	433,600,000
Aggregate purchase price of shares acquired since inception of share repurchase program	$ 5,900,000

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Shareholders' Equity - Preferred shares (Details) - USD ($) $ / shares in Units, shares in Millions, $ in Millions		1 Months Ended				4 Months Ended
	Jan. 01, 2018	Sep. 30, 2021	Jun. 30, 2021	Nov. 30, 2017	Aug. 31, 2017	Nov. 30, 2017	Dec. 31, 2022	Jun. 30, 2022
Class of Stock [Line Items]
Preferred shares, par value per share							$ 0.01
Series C Preferred Shares
Class of Stock [Line Items]
Preferred shares, dividend rate (as a percent)	6.75%
Series E preferred shares
Class of Stock [Line Items]
Preferred shares, dividend rate (as a percent)		5.25%
Preferred shares, redemption price per share		$ 25
Series F Preferred Shares
Class of Stock [Line Items]
Preferred shares issued				$ 100	$ 230	$ 330
Preferred shares, dividend rate (as a percent)						5.45%
Preferred shares, par value per share				$ 0.01		$ 0.01
Liquidation preference per share				25,000		25,000
Preferred shares, redemption price per share				$ 25,000		$ 25,000
Series F depositary share equivalent
Class of Stock [Line Items]
Preference shares, number of shares issued				13.2		13.2
Proportionate interest of preference shares, per depositary share				0.10%		0.10%
Liquidation preference per share				$ 25		$ 25
Preferred shares, redemption price per share				$ 25		$ 25
Series G Preferred Stock
Class of Stock [Line Items]
Preferred shares issued			$ 500
Preferred shares, dividend rate (as a percent)			4.55%
Preferred shares, par value per share			$ 0.01
Liquidation preference per share			25,000
Preferred shares, redemption price per share			$ 25,000
Series G depositary share equivalent
Class of Stock [Line Items]
Preference shares, number of shares issued			20.0
Proportionate interest of preference shares, per depositary share								0.10%
Liquidation preference per share			$ 25
Preferred shares, redemption price per share			$ 25

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Share-Based Compensation - Long Term Incentive Plan (Details) - shares	Dec. 31, 2022	May 04, 2022	May 06, 2016
2022 Long Term Incentive and Share Award Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of shares reserved for issuance		9,000,000
Number of shares authorized for incentive stock options		6,000,000
Shares available for issuance	9,000,000
2018 Long Term Incentive and Share Award Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of shares reserved for issuance	34,500,000
Shares available for issuance	4,577,991
2015 Long Term Incentive And Share Award Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of shares reserved for issuance	12,900,000
Shares available for issuance	504,872
2007 Employee Share Purchase Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares available for issuance	1,041,837		4,689,777

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Share-Based Compensation - Valuation assumptions (Details)	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Share-Based Payment Arrangement [Abstract]
Dividend yield	0.00%	0.00%	0.00%
Expected volatility	24.00%	24.20%	16.60%
Risk free interest rate	2.00%	1.00%	1.20%
Expected option life	6 years	6 years	6 years

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Share-Based Compensation - Stock option activity (Details) - Stock Options $ / shares in Units, $ in Thousands	12 Months Ended
	Dec. 31, 2022 USD ($) $ / shares shares
Number of Options / SARs
Outstanding, beginning of year (in shares) | shares	17,083,160
Granted (in shares) | shares	784,963
Exercised (in shares) | shares	(3,412,371)
Forfeited or expired (in shares) | shares	(34,851)
Outstanding, end of year (in shares) | shares	14,420,901
Exercisable, end of year (in shares) | shares	12,433,470
Weighted Average Exercise Price
Outstanding, beginning of year, weighted average exercise price | $ / shares	$ 25.06
Granted, weighted average exercise price | $ / shares	47.46
Exercised, weighted average exercise price | $ / shares	16.91
Forfeited or expired, weighted average exercise price | $ / shares	39.96
Outstanding, end of year, weighted average exercise price | $ / shares	28.17
Exercisable, end of year, weighted average exercise price | $ / shares	$ 26.20
Weighted average contractual term, outstanding, end of year	4 years 4 months 13 days
Weighted average contractual term, exercisable, end of year	3 years 9 months 7 days
Aggregate intrinsic value, outstanding, end of year | $	$ 499,051
Aggregate intrinsic value, exercisable, end of year | $	$ 454,769

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Share-Based Compensation - Options additional information (Details) - USD ($) $ / shares in Units, $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period	3 years
Options and SARs
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period	3 years
Proceeds from stock options exercised	$ 17,200
Tax benefit from exercise of stock options and SARs	$ 8,700
Weighted average grant date fair value	$ 13.26	$ 9.22	$ 8.14
Aggregate intrinsic value of options exercised	$ 113,409	$ 47,074	$ 59,723

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Share-Based Compensation - Restricted common shares and restricted stock units activity (Details)	12 Months Ended
	Dec. 31, 2022 $ / shares shares
Restricted Common Shares
Unvested Shares:
Unvested balance, beginning of year (in shares) | shares	2,070,837
Restricted shares and restricted unit awards granted | shares	914,694
Vested (in shares) | shares	(744,096)
Forfeited (in shares) | shares	(75,881)
Unvested balance, end of year (in shares) | shares	2,165,554
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year, weighted average grant date fair value | $ / shares	$ 36.35
Weighted average grant date fair value | $ / shares	47.45
Vested, weighted average grant date fair value | $ / shares	38.21
Forfeited, weighted average grant date fair value | $ / shares	41.13
Unvested balance, end of year, weighted average grant date fair value | $ / shares	$ 40.23
Restricted Unit Awards
Unvested Shares:
Unvested balance, beginning of year (in shares) | shares	699,866
Restricted shares and restricted unit awards granted | shares	174,699
Vested (in shares) | shares	(330,144)
Forfeited (in shares) | shares	(27,128)
Unvested balance, end of year (in shares) | shares	517,293
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year, weighted average grant date fair value | $ / shares	$ 33.29
Weighted average grant date fair value | $ / shares	47.50
Vested, weighted average grant date fair value | $ / shares	34.38
Forfeited, weighted average grant date fair value | $ / shares	37.51
Unvested balance, end of year, weighted average grant date fair value | $ / shares	$ 37.17

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Share-Based Compensation - Restricted stock additional information (Details) - USD ($) $ / shares in Units, $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period	3 years
Restricted Common Shares And Restricted Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period	3 years
Restricted shares and restricted unit awards granted	1,089,393	1,261,773	1,535,330
Weighted average grant date fair value	$ 47.45	$ 36.12	$ 37.55
Aggregate fair value of vested restricted share and unit awards	$ 78,129	$ 65,477	$ 39,703
Aggregate intrinsic value of restricted units outstanding	$ 32,500

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Share-Based Compensation - Performance shares and performance units activity (Details)	12 Months Ended
	Dec. 31, 2022 $ / shares shares
Performance Shares
Unvested Shares:
Unvested balance, beginning of year (in shares) | shares	1,861,760
Performance shares and units granted | shares	669,742
Performance shares, performance adjustment | shares	(54,904)	[1],[2]
Vested (in shares) | shares	(583,544)
Forfeited (in shares) | shares	(10,138)
Unvested balance, end of year (in shares) | shares	1,882,916
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year, weighted average grant date fair value | $ / shares	$ 38.93
Weighted average grant date fair value | $ / shares	49.91
Performance shares, performance adjustment, weighted average grant date fair value | $ / shares	36.07	[1],[2]
Vested, weighted average grant date fair value | $ / shares	36.07
Forfeited, weighted average grant date fair value | $ / shares	49.91
Unvested balance, end of year, weighted average grant date fair value | $ / shares	$ 43.75
Performance Units
Unvested Shares:
Unvested balance, beginning of year (in shares) | shares	29,770
Performance shares and units granted | shares	21,030
Performance shares, performance adjustment | shares	8,921	[1],[2]
Vested (in shares) | shares	(19,695)
Forfeited (in shares) | shares	(316)
Unvested balance, end of year (in shares) | shares	39,710
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year, weighted average grant date fair value | $ / shares	$ 38.71
Weighted average grant date fair value | $ / shares	49.91
Performance shares, performance adjustment, weighted average grant date fair value | $ / shares	35.83	[1],[2]
Vested, weighted average grant date fair value | $ / shares	35.83
Forfeited, weighted average grant date fair value | $ / shares	49.91
Unvested balance, end of year, weighted average grant date fair value | $ / shares	$ 45.33

[1] The performance adjustment represents the change in PSUs, which vested following the end of the performance period. The performance units were granted at the target level of achievement

[2] The performance adjustment represents the difference between the number of performance shares granted and earned, which vested following the end of the performance period. The performance shares were granted at the maximum level of achievement.

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Share-Based Compensation - Performance shares and units additional information (Details) - $ / shares	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period	3 years
Expected volatility	24.00%	24.20%	16.60%
Risk free interest rate	2.00%	1.00%	1.20%
Performance Common Shares and Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period	3 years
Expected volatility	38.10%	37.50%	18.10%
Risk free interest rate	1.70%	0.30%	1.10%
Performance shares and units granted	690,772	685,104	557,204
Weighted average grant date fair value	$ 49.91	$ 37.38	$ 44.17
Performance Common Shares and Units | Minimum
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Payout percentage	0.00%
Performance Common Shares and Units | Maximum
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Payout percentage	200.00%

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Share-Based Compensation - Share-based compensation expense (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share based compensation expense	$ 87,672	$ 86,580	$ 69,892
Share based compensation expense, net of tax	76,526	75,667	60,345
Options and SARs
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share based compensation expense	11,891	12,316	11,744
Share based compensation expense, net of tax	10,726	10,927	10,388
Restricted Common Shares And Restricted Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share based compensation expense	50,278	46,817	41,284
Share based compensation expense, net of tax	42,346	39,349	34,599
Performance Awards
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share based compensation expense	21,510	23,696	14,729
Share based compensation expense, net of tax	19,794	21,920	13,380
Employee Share Purchase Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share based compensation expense	3,993	3,751	2,135
Share based compensation expense, net of tax	$ 3,660	$ 3,471	$ 1,978

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Share-Based Compensation - Unrecognized compensation cost and period for recognition (Details) $ in Millions	12 Months Ended
	Dec. 31, 2022 USD ($)
Stock Options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unrecognized compensation cost related to unvested awards	$ 6,357
Weighted average recognition period (years)	9 months
Restricted Common Shares And Restricted Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unrecognized compensation cost related to unvested awards	$ 42,096
Weighted average recognition period (years)	1 year
Performance Common Shares and Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unrecognized compensation cost related to unvested awards	$ 7,520
Weighted average recognition period (years)	5 months 23 days

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Retirement Plans (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Retirement Benefits [Abstract]
Defined contribution plan, expense	$ 67.0	$ 60.4	$ 52.0

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Statutory Information - Summary of statutory capital, surplus and net income (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Bermuda
Statutory Accounting Practices [Line Items]
Actual statutory capital and surplus	[1]	$ 19,546,128	$ 17,528,510
Required statutory capital and surplus	[1]	6,449,878	5,661,301
Statutory net income (loss)		1,729,925	2,370,746	$ 1,579,889
Ireland
Statutory Accounting Practices [Line Items]
Actual statutory capital and surplus	[1]	968,443	958,200
Required statutory capital and surplus	[1]	815,194	794,933
Statutory net income (loss)		(52,757)	25,191	18,397
United States
Statutory Accounting Practices [Line Items]
Actual statutory capital and surplus	[1]	6,194,954	5,600,652
Required statutory capital and surplus	[1]	1,748,543	1,717,646
Statutory net income (loss)		219,524	345,790	143,271
United Kingdom
Statutory Accounting Practices [Line Items]
Actual statutory capital and surplus	[1]	1,018,092	902,002
Required statutory capital and surplus	[1]	543,104	563,164
Statutory net income (loss)		56,818	35,286	4,078
Canada
Statutory Accounting Practices [Line Items]
Actual statutory capital and surplus	[1]	68,637	70,063
Required statutory capital and surplus	[1]	47,825	42,513
Statutory net income (loss)		9,215	6,985	(1,049)
Australia
Statutory Accounting Practices [Line Items]
Actual statutory capital and surplus	[1]	284,998	283,693
Required statutory capital and surplus	[1]	175,885	214,022
Statutory net income (loss)		$ 38,538	$ 11,874	$ (8,601)

[1] Such amounts include ownership interests in affiliated insurance and reinsurance subsidiaries.

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Statutory Information - Narrative (Details) $ in Millions	12 Months Ended
	Dec. 31, 2022 USD ($) subsidiary
Ireland
Statutory Accounting Practices [Line Items]
Number Of Subsidiaries | subsidiary	3
Mortgage | North Carolina or Wisconsin
Statutory Accounting Practices [Line Items]
Required contingency loss reserve as a percentage of net earned premiums	50.00%
Withdrawal restriction period	10 years
Withdrawal restriction period, with prior approval	35.00%
Maximum risk to capital ratio	2500.00%
United Guaranty Residential Insurance Company [Member] | North Carolina
Statutory Accounting Practices [Line Items]
Dividends available for payment in 2022, total	$ 156.5
Arch Re US | United States
Statutory Accounting Practices [Line Items]
Dividends available for payment in 2022, total	$ 255.4
Arch Re Bermuda | Bermuda
Statutory Accounting Practices [Line Items]
Dividends, percentage permitted	25.00%
Dividend required notice period	7 days
Dividends available for payment in 2022 without prior regulatory approval	$ 3,700.0

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Schedule II - Condensed Financial Information of Registrant - Balance Sheet (Details) - USD ($) $ / shares in Units, $ in Thousands	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Assets
Total investments	$ 27,292,927	$ 26,588,156
Cash	855,118	858,668	$ 906,448
Investment in operating affiliates	964,604	1,135,655
Other assets	2,919,605	2,453,849
Total assets	47,990,507	45,100,945	43,282,297
Liabilities
Senior notes	2,725,410	2,724,394
Other liabilities	1,367,068	1,329,742
Total liabilities	35,069,605	31,545,816	29,294,856
Shareholders’ Equity
Non-cumulative preferred shares	830,000	830,000
Common shares ($0.0011 par, shares issued: 588,250,762 and 583,289,850)	654	648
Additional paid-in capital	2,211,444	2,085,075
Retained earnings	15,892,065	14,455,868
Accumulated other comprehensive income (loss), net of deferred income tax	(1,646,170)	(64,600)	488,895	$ 212,091
Common shares held in treasury, at cost (shares: 217,904,765 and 204,365,956)	(4,377,920)	(3,761,095)
Total shareholders' equity	12,910,073	13,545,896	$ 13,105,886
Total liabilities and shareholders' equity	$ 47,990,507	$ 45,100,945
Parenthetical information:
Common shares, par value per share	$ 0.0011	$ 0.0011
Common shares issued (shares)	588,250,762	583,289,850	579,000,841	574,617,195
Common shares held in treasury (shares)	217,904,765	204,365,956	172,280,199
Parent Company
Assets
Total investments	$ 7,282	$ 2,038
Cash	11,393	16,317
Investment in subsidiaries	14,191,188	14,822,024
Investment in operating affiliates	5,259	6,877
Due from Affiliates	1,554	11
Other assets	17,203	9,604
Total assets	14,233,879	14,856,871
Liabilities
Senior notes	1,286,567	1,286,208
Other liabilities	37,239	24,767
Total liabilities	1,323,806	1,310,975
Shareholders’ Equity
Non-cumulative preferred shares	830,000	830,000
Common shares ($0.0011 par, shares issued: 588,250,762 and 583,289,850)	654	648
Additional paid-in capital	2,211,444	2,085,075
Retained earnings	15,892,065	14,455,868
Accumulated other comprehensive income (loss), net of deferred income tax	(1,646,170)	(64,600)
Common shares held in treasury, at cost (shares: 217,904,765 and 204,365,956)	(4,377,920)	(3,761,095)
Total shareholders' equity	12,910,073	13,545,896
Total liabilities and shareholders' equity	$ 14,233,879	$ 14,856,871
Parenthetical information:
Common shares, par value per share	$ 0.0011	$ 0.0011
Common shares issued (shares)	588,250,762	583,289,850
Common shares held in treasury (shares)	217,904,765	204,365,956

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Schedule II - Condensed Financial Information of Registrant - Statement of Income (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Revenues
Net investment income	$ 496,547	$ 389,118	$ 519,608
Net realized gains (losses)	(662,734)	379,845	823,460
Total revenues	9,614,808	9,249,980	8,508,509
Expenses
Corporate expenses	95,482	79,157	81,988
Interest expense	130,266	139,470	143,456
Net foreign exchange losses (gains)	(100,905)	(41,529)	83,634
Total expenses	8,126,315	7,146,629	6,947,726
Income (loss) from operating affiliates	73,891	264,693	16,766
Net income available to Arch	1,476,933	2,156,849	1,405,521
Preferred share dividends	(40,736)	(48,343)	(41,612)
Loss on redemption of preferred shares	0	(15,101)	0
Net income available to Arch common shareholders	1,436,197	2,093,405	1,363,909
Parent
Revenues
Net investment income	2,058	1,524	53
Net realized gains (losses)	29	0	(2,110)
Total revenues	2,087	1,524	(2,057)
Expenses
Corporate expenses	85,997	71,818	65,566
Interest expense	58,759	58,741	40,445
Net foreign exchange losses (gains)	(1)	7	3
Total expenses	144,755	130,566	106,014
Income (loss) before income taxes	(142,668)	(129,042)	(108,071)
Income (loss) from operating affiliates	(1,047)	(590)	(437)
Income (loss) before equity in net income of subsidiaries	(143,715)	(129,632)	(108,508)
Equity in net income of subsidiaries	1,592,929	2,286,481	1,514,029
Net income available to Arch	1,449,214	2,156,849	1,405,521
Preferred share dividends	(40,736)	(48,343)	(41,612)
Loss on redemption of preferred shares	0	(15,101)	0
Net income available to Arch common shareholders	$ 1,408,478	$ 2,093,405	$ 1,363,909

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Schedule II - Condensed Financial Information of Registrant - Statement of Cash Flows (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Operating Activities:
Net Cash Provided by (Used in) Operating Activities	$ 3,815,227	$ 3,427,555	$ 2,886,505
Investing Activities:
Net (purchases) sales of short-term investments	467,249	165,272	(1,029,681)
Purchases of fixed assets	(51,672)	(41,394)	(39,872)
Other	125,405	(523,864)	(62,197)
Net cash used for investing activities	(3,102,055)	(2,139,732)	(3,043,226)
Financing Activities:
Purchases of common shares under share repurchase program	(585,823)	(1,234,294)	(83,472)
Proceeds from common shares issued, net	6,660	6,418	1,876
Proceeds from issuance of preferred shares, net	0	485,821	0
Redemption of preferred shares	0	(450,000)	0
Proceeds from borrowings	0	0	1,018,793
Preferred dividends paid	(40,736)	(48,280)	(41,612)
Net Cash Provided by (Used in) Financing Activities	(705,726)	(1,229,549)	521,278
Increase (decrease) in cash and restricted cash	(41,443)	24,227	386,846
Cash and restricted cash, beginning of year	1,314,771	1,290,544	903,698
Cash and restricted cash, end of year	1,273,328	1,314,771	1,290,544
Parent
Operating Activities:
Net Cash Provided by (Used in) Operating Activities	621,307	1,727,529	124,751
Investing Activities:
Net (purchases) sales of short-term investments	(4,838)	(1,866)	(130)
Capital contributed to subsidiaries	0	(487,161)	(988,975)
Purchases of fixed assets	(22)	(783)	(15)
Other	(1,462)	0	0
Net cash used for investing activities	(6,322)	(489,810)	(989,120)
Financing Activities:
Purchases of common shares under share repurchase program	(585,823)	(1,234,294)	(83,472)
Proceeds from common shares issued, net	6,660	6,418	1,876
Proceeds from issuance of preferred shares, net	0	485,821	0
Redemption of preferred shares	0	(450,000)	0
Proceeds from borrowings	0	0	988,393
Preferred dividends paid	(40,736)	(48,280)	(41,612)
Net Cash Provided by (Used in) Financing Activities	(619,899)	(1,240,335)	865,185
Increase (decrease) in cash and restricted cash	(4,914)	(2,616)	816
Cash and restricted cash, beginning of year	16,344	18,960	18,144
Cash and restricted cash, end of year	$ 11,430	$ 16,344	$ 18,960

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Schedule III - Supplementary Insurance Information (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
SEC Schedule, 12-16, Insurance Companies, Supplementary Insurance Information [Line Items]
Deferred Acquisition Costs		$ 1,263,870	$ 901,841	$ 790,708
Reserves for Losses and Loss Adjustment Expenses		20,031,943	17,757,156	16,513,928
Unearned Premiums		7,337,002	6,011,942	4,838,965
Net Premiums Earned		9,678,077	8,082,298	6,991,935
Net Losses and Loss Adjustment Expenses Incurred		5,027,517	4,584,803	4,689,599
Amortization of Deferred Acquisition Costs		1,739,580	1,303,178	1,004,842
Other Operating Expenses	[1]	1,128,175	998,595	875,176
Net Premiums Written		11,077,189	9,018,337	7,437,716
Operating segments | Insurance
SEC Schedule, 12-16, Insurance Companies, Supplementary Insurance Information [Line Items]
Deferred Acquisition Costs		301,398	378,265	254,833
Reserves for Losses and Loss Adjustment Expenses		11,017,327	9,810,622	8,989,930
Unearned Premiums		3,381,810	2,937,664	2,334,225
Net Premiums Earned		4,559,335	3,626,468	2,871,420
Net Losses and Loss Adjustment Expenses Incurred		2,782,945	2,344,365	2,092,453
Amortization of Deferred Acquisition Costs		885,866	606,265	418,483
Other Operating Expenses	[1]	665,472	558,906	489,153
Net Premiums Written		5,020,642	4,148,193	3,162,907
Operating segments | Reinsurance
SEC Schedule, 12-16, Insurance Companies, Supplementary Insurance Information [Line Items]
Deferred Acquisition Costs		992,339	424,390	278,422
Reserves for Losses and Loss Adjustment Expenses		8,305,854	6,878,721	5,027,742
Unearned Premiums		3,206,284	2,263,264	1,356,983
Net Premiums Earned		3,959,381	2,840,443	2,162,229
Net Losses and Loss Adjustment Expenses Incurred		2,568,843	1,924,719	1,628,320
Amortization of Deferred Acquisition Costs		813,555	536,754	354,048
Other Operating Expenses	[1]	267,531	212,810	168,011
Net Premiums Written		4,923,976	3,254,374	2,457,370
Operating segments | Mortgage
SEC Schedule, 12-16, Insurance Companies, Supplementary Insurance Information [Line Items]
Deferred Acquisition Costs		(29,867)	99,186	203,748
Reserves for Losses and Loss Adjustment Expenses		708,762	1,067,813	976,673
Unearned Premiums		748,908	811,014	740,043
Net Premiums Earned		1,159,361	1,283,419	1,397,935
Net Losses and Loss Adjustment Expenses Incurred		(324,271)	56,677	528,344
Amortization of Deferred Acquisition Costs		40,159	97,418	134,240
Other Operating Expenses	[1]	195,172	194,010	162,202
Net Premiums Written		1,132,571	1,261,068	1,279,850
Operating segments | Other
SEC Schedule, 12-16, Insurance Companies, Supplementary Insurance Information [Line Items]
Deferred Acquisition Costs				53,705
Reserves for Losses and Loss Adjustment Expenses				1,519,583
Unearned Premiums				407,714
Net Premiums Earned			331,968	560,351
Net Losses and Loss Adjustment Expenses Incurred			259,042	440,482
Amortization of Deferred Acquisition Costs			62,741	98,071
Other Operating Expenses	[1]		32,869	55,810
Net Premiums Written			$ 354,702	$ 537,589

[1] Certain other operating expenses relate to the Company’s corporate segment. Such amounts are not reflected in the table above. See note 4, “Segment Information,” to our consolidated financial statements in Item 8 for information related to the corporate segment.

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Schedule IV - Reinsurance (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2022	Dec. 31, 2021		Dec. 31, 2020
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Gross Amount		$ 8,540,787	$ 7,706,832		$ 6,553,910
Ceded to other Companies		(4,249,258)	(3,734,150)		(2,650,352)
Assumed From Other Companies		6,785,660	5,045,655		3,534,158
Net Amount		$ 11,077,189	$ 9,018,337		$ 7,437,716
Percentage of Amount Assumed to Net		61.30%	55.90%		47.50%
Operating segments | Insurance
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Gross Amount		$ 6,889,358	$ 5,833,873		$ 4,659,416
Ceded to other Companies	[1]	(1,910,222)	(1,719,541)		(1,525,655)
Assumed From Other Companies	[1]	41,506	33,861		29,146
Net Amount		$ 5,020,642	$ 4,148,193		$ 3,162,907
Percentage of Amount Assumed to Net		0.80%	0.80%		0.90%
Operating segments | Reinsurance
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Gross Amount		$ 395,063	$ 408,520		$ 305,435
Ceded to other Companies	[1]	(2,024,462)	(1,839,556)		(1,014,716)
Assumed From Other Companies	[1]	6,553,375	4,685,410		3,166,651
Net Amount		$ 4,923,976	$ 3,254,374		$ 2,457,370
Percentage of Amount Assumed to Net		133.10%	144.00%		128.90%
Operating segments | Mortgage
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Gross Amount		$ 1,256,366	$ 1,213,333		$ 1,192,316
Ceded to other Companies	[1]	(322,400)	(246,757)		(194,149)
Assumed From Other Companies	[1]	198,605	294,492		281,683
Net Amount		$ 1,132,571	$ 1,261,068		$ 1,279,850
Percentage of Amount Assumed to Net		17.50%	23.40%		22.00%
Operating segments | Other
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Gross Amount			$ 251,106		$ 396,743
Ceded to other Companies		$ 0	(102,763)	[1]	(190,957)	[1]
Assumed From Other Companies	[1]		206,359		331,803
Net Amount		$ 0	$ 354,702		$ 537,589
Percentage of Amount Assumed to Net			58.20%		61.70%

[1] Certain amounts included in the gross premiums written of each segment are related to intersegment transactions and are included in the gross premiums written of each segment. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

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Schedule VI - Supplementary Information For Property and Casualty Insurance Underwriters (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
SEC Schedule, 12-18, Supplemental Information, Property-Casualty Insurance Underwriters [Line Items]
Net Losses and Loss Adjustment Expenses Incurred Related to Current Year	$ 5,798,528	$ 4,940,987	$ 4,851,051
Net Losses and Loss Adjustment Expenses Incurred Related to Prior Years	(771,011)	(356,184)	(161,452)
Consolidated Subsidiaries
SEC Schedule, 12-18, Supplemental Information, Property-Casualty Insurance Underwriters [Line Items]
Deferred Acquisition Costs	1,263,870	901,841	790,708
Reserves for Losses and Loss Adjustment Expenses	20,031,943	17,757,156	16,513,929
Discount, if any, deducted in Column C	60,536	55,575	23,326
Unearned Premiums	7,337,002	6,011,942	4,838,965
Net Premiums Earned	9,678,077	8,082,298	6,991,935
Net investment income	496,547	389,118	519,608
Net Losses and Loss Adjustment Expenses Incurred Related to Current Year	5,798,528	4,940,987	4,851,051
Net Losses and Loss Adjustment Expenses Incurred Related to Prior Years	(771,011)	(356,184)	(161,452)
Amortization of Deferred Acquisition Costs	1,739,580	1,303,178	1,004,842
Net Paid Losses and Loss Adjustment Expenses	3,141,948	2,826,551	2,661,117
Net Premiums Written	$ 11,077,189	$ 9,018,337	$ 7,437,716