10-Q

UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C. 20549

FORM 10-Q

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

For the quarterly period ended June 30, 2022

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

Commission file number: 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 1/1000th interest in a 5.45% Series F preferred share	ACGLO	NASDAQ	Stock Market
Depositary shares, each representing a 1/1000th interest in a 4.55% Series G preferred share	ACGLN	NASDAQ	Stock Market

Indicate by check mark whether the registrant (1) has filed all reports required to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 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 is a shell company (as defined in Rule 12b-2 of the Exchange Act). Yes ☐ No ☑

As of July 29, 2022, there were 369,137,188 common shares, $0.0011 par value per share, of the registrant outstanding.

ARCH CAPITAL GROUP LTD.

INDEX TO FORM 10-Q

		Page No.
	PART I
	Financial Information	2
Item 1.	Consolidated Financial Statements	4
Item 2.	Management’s Discussion and Analysis of Financial Condition and Results of Operations	40
Item 3.	Quantitative and Qualitative Disclosures About Market Risk	65
Item 4.	Controls and Procedures	66
	PART II
	Other Information	66
Item 1.	Legal Proceedings	66
Item 1A.	Risk Factors	66
Item 2.	Unregistered Sales of Equity Securities and Use of Proceeds	67
Item 3.	Defaults Upon Senior Securities	67
Item 4.	Mine Safety Disclosures	67
Item 5.	Other Information	67
Item 6.	Exhibits	68
	Signatures	69

ARCH CAPITAL  1 2022 SECOND QUARTER FORM 10-Q

PART I. FINANCIAL INFORMATION

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 (the “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 disease (including COVID-19) on our business;

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

ARCH CAPITAL  2 2022 SECOND QUARTER FORM 10-Q

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

•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;

•changes in the method for determining the London Inter-bank Offered Rate (“LIBOR”) and the replacement of LIBOR with alternative benchmark rates;

•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 new guidance implementing the Tax Cuts and Jobs Act of 2017 and 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 our Annual Report on Form 10-K for the year ended December 31, 2021, as well as the other factors set forth in our 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  3 2022 SECOND QUARTER FORM 10-Q

ITEM 1. CONSOLIDATED FINANCIAL STATEMENTS

	Page No.
Report of Independent Registered Public Accounting Firm	5
Consolidated Balance Sheets
June 30, 2022 (unaudited) and December 31, 2021	6
Consolidated Statements of Income
For the three and six month periods ended June 30, 2022 and 2021 (unaudited)	7
Consolidated Statements of Comprehensive Income
For the three and six month periods ended June 30, 2022 and 2021 (unaudited)	8
Consolidated Statements of Changes in Shareholders’ Equity
For the three and six month periods ended June 30, 2022 and 2021 (unaudited)	9
Consolidated Statements of Cash Flows
For the six month periods ended June 30, 2022 and 2021 (unaudited)	10
Notes to Consolidated Financial Statements (unaudited)
Note 1 - Basis of Presentation and Recent Accounting Pronouncements	11
Note 2 - Share Transactions	11
Note 3 - Earnings Per Common Share	12
Note 4 - Segment Information	13
Note 5 - Reserve for Losses and Loss Adjustment Expenses	18
Note 6 - Allowance for Expected Credit Losses	20
Note 7 - Investment Information	22
Note 8 - Fair Value	28
Note 9 - Derivative Instruments	34
Note 10 - Commitments and Contingencies	35
Note 11 - Variable Interest Entities and Noncontrolling Interests	35
Note 12 - Other Comprehensive Income (Loss)	38
Note 13 - Income Taxes	39
Note 14 - Legal Proceedings	39
Note 15 - Transactions with Related Parties	39

ARCH CAPITAL  4 2022 SECOND QUARTER FORM 10-Q

Report of Independent Registered Public Accounting Firm

To the Board of Directors and Shareholders of Arch Capital Group Ltd.

Results of Review of Interim Financial Statements

We have reviewed the accompanying consolidated balance sheet of Arch Capital Group Ltd. and its subsidiaries (the “Company”) as of June 30, 2022, and the related consolidated statements of income, comprehensive income, and changes in shareholders’ equity for the three-month and six-month periods ended June 30, 2022 and 2021, and the consolidated statements of cash flows for the six-month periods ended June 30, 2022 and 2021, including the related notes (collectively referred to as the “interim financial statements”). Based on our reviews, we are not aware of any material modifications that should be made to the accompanying interim financial statements for them to be in conformity with accounting principles generally accepted in the United States of America.

We have previously audited, in accordance with the standards of the Public Company Accounting Oversight Board (United States) (PCAOB), the consolidated balance sheet of the Company as of December 31, 2021, and the related consolidated statements of income, comprehensive income, changes in shareholders’ equity, and cash flows for the year then ended (not presented herein), and in our report dated February 25, 2022, we expressed an unqualified opinion on those consolidated financial statements. In our opinion, the information set forth in the accompanying consolidated balance sheet as of December 31, 2021, is fairly stated, in all material respects, in relation to the consolidated balance sheet from which it has been derived.

Basis for Review Results

These interim financial statements are the responsibility of the Company’s management. We are a public accounting firm registered with the 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 review in accordance with the standards of the PCAOB. A review of interim financial information consists principally of applying analytical procedures and making inquiries of persons responsible for financial and accounting matters. It is substantially less in scope than an audit conducted in accordance with the standards of the PCAOB, the objective of which is the expression of an opinion regarding the financial statements taken as a whole. Accordingly, we do not express such an opinion.

/s/ PricewaterhouseCoopers LLP

New York, New York

August 3, 2022

ARCH CAPITAL  5 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONSOLIDATED BALANCE SHEETS

(U.S. dollars in thousands, except share data)

	(Unaudited)
	June 30, 2022		December 31, 2021
Assets
Investments:
Fixed maturities available for sale, at fair value (amortized cost: $18,816,372 and $17,973,823; net of allowance for credit losses: $58,410 and $2,883 )	$	17,585,029	$	17,998,109
Short-term investments available for sale, at fair value (amortized cost: $2,226,673 and $1,734,738; net of allowance for credit losses: $0 and $0)	2,227,874		1,734,716
Equity securities, at fair value	772,689		1,804,170
Other investments, at fair value	1,634,368		1,973,550
Investments accounted for using the equity method	3,496,341		3,077,611
Total investments	25,716,301		26,588,156
Cash	813,548		858,668
Accrued investment income	116,102		85,453
Investment in operating affiliates	967,603		1,135,655
Premiums receivable (net of allowance for credit losses: $38,170 and $39,958)	3,634,182		2,633,280
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $14,740 and $13,230)	5,938,511		5,880,735
Contractholder receivables (net of allowance for credit losses: $3,005 and $3,437)	1,758,018		1,828,691
Ceded unearned premiums	2,123,915		1,729,455
Deferred acquisition costs	1,069,845		901,841
Receivable for securities sold	157,329		60,179
Goodwill and intangible assets	868,014		944,983
Other assets	2,555,826		2,453,849
Total assets	$	45,719,194	$	45,100,945
Liabilities
Reserve for losses and loss adjustment expenses	$	18,194,324	$	17,757,156
Unearned premiums	7,145,297		6,011,942
Reinsurance balances payable	1,634,700		1,583,253
Contractholder payables	1,761,023		1,832,127
Collateral held for insured obligations	251,063		242,352
Senior notes	2,724,896		2,724,394
Payable for securities purchased	292,106		64,850
Other liabilities	1,289,760		1,329,742
Total liabilities	33,293,169		31,545,816
Commitments and Contingencies
Redeemable noncontrolling interests	8,459		9,233
Shareholders' Equity
Non-cumulative preferred shares	830,000		830,000
Common shares ($0.0011 par, shares issued: 586,887,791 and 583,289,850)	652		648
Additional paid-in capital	2,170,661		2,085,075
Retained earnings	15,035,644		14,455,868
Accumulated other comprehensive income (loss), net of deferred income tax	(1,258,265)		(64,600)
Common shares held in treasury, at cost (shares: 217,540,976 and 204,365,956)	(4,361,126)		(3,761,095)
Total shareholders' equity available to Arch	12,417,566		13,545,896
Total liabilities, noncontrolling interests and shareholders' equity	$	45,719,194	$	45,100,945

See Notes to Consolidated Financial Statements

ARCH CAPITAL 6 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONSOLIDATED STATEMENTS OF INCOME

(U.S. dollars in thousands, except share data)

	(Unaudited)				(Unaudited)
	Three Months Ended				Six Months Ended
	June 30,				June 30,
	2022		2021		2022		2021
Revenues
Net premiums earned	$	2,325,775	$	2,120,909	4,446,408		4,069,331
Net investment income	106,392		111,613		186,828		210,469
Net realized gains (losses)	(266,579)		202,907		(558,993)		345,368
Other underwriting income	2,970		5,529		8,867		11,639
Equity in net income (loss) of investment funds accounted for using the equity method	58,061		122,186		94,366		193,872
Other income (loss)	(11,777)		6,852		(20,802)		5,111
Total revenues	2,214,842		2,569,996		4,156,674		4,835,790
Expenses
Losses and loss adjustment expenses	1,102,656		1,159,831		2,103,491		2,362,931
Acquisition expenses	413,319		335,143		791,478		639,624
Other operating expenses	277,392		244,943		567,335		505,976
Corporate expenses	27,620		15,951		59,952		41,335
Amortization of intangible assets	27,207		15,286		54,374		29,688
Interest expense	32,795		35,700		65,503		74,046
Net foreign exchange (gains) losses	(87,775)		17,775		(91,620)		(2,288)
Total expenses	1,793,214		1,824,629		3,550,513		3,651,312
Income (loss) before income taxes and income (loss) from operating affiliates	421,628		745,367		606,161		1,184,478
Income tax expense	(22,323)		(51,179)		(33,942)		(90,039)
Income (loss) from operating affiliates	4,640		24,476		29,158		99,933
Net income (loss)	$	403,945	$	718,664	$	601,377	$	1,194,372
Net (income) loss attributable to noncontrolling interests	399		(43,178)		(1,233)		(80,730)
Net income (loss) available to Arch	404,344		675,486		600,144		1,113,642
Preferred dividends	(10,184)		(11,666)		(20,368)		(22,069)
Net income (loss) available to Arch common shareholders	$	394,160	$	663,820	$	579,776	$	1,091,573
Net income per common share and common share equivalent
Basic	$	1.07	$	1.67	$	1.56	$	2.73
Diluted	$	1.04	$	1.63	$	1.52	$	2.68
Weighted average common shares and common share equivalents outstanding
Basic	369,241,193		397,743,402		371,728,683		399,267,183
Diluted	377,952,988		406,485,994		380,905,512		407,687,680

See Notes to Consolidated Financial Statements

ARCH CAPITAL 7 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME

(U.S. dollars in thousands)

	(Unaudited)				(Unaudited)
	Three Months Ended				Six Months Ended
	June 30,				June 30,
	2022		2021		2022		2021
Comprehensive Income
Net income (loss)	$	403,945	$	718,664	$	601,377	$	1,194,372
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 period	(598,005)		78,571		(1,282,360)		(183,179)
Reclassification of net realized (gains) losses, included in net income (loss)	57,710		(60,547)		159,988		(57,850)
Foreign currency translation adjustments	(68,525)		6,205		(71,293)		(22,379)
Comprehensive income (loss)	(204,875)		742,893		(592,288)		930,964
Net (income) loss attributable to noncontrolling interests	399		(43,178)		(1,233)		(80,730)
Other comprehensive (income) loss attributable to noncontrolling interests	—		(10)		—		4,560
Comprehensive income (loss) available to Arch	$	(204,476)	$	699,705	$	(593,521)	$	854,794

See Notes to Consolidated Financial Statements

ARCH CAPITAL 8 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONSOLIDATED STATEMENTS OF CHANGES IN SHAREHOLDERS’ EQUITY

(U.S. dollars in thousands)

	(Unaudited)				(Unaudited)
	Three Months Ended				Six Months Ended
	June 30,				June 30,
	2022		2021		2022		2021
Non-cumulative preferred shares
Balance at beginning of period	$	830,000	$	780,000	$	830,000	$	780,000
Preferred shares issued	—		500,000		—		500,000
Balance at beginning and end of period	$	830,000	$	1,280,000	$	830,000	$	1,280,000
Common shares
Balance at beginning of period	651		645		648		643
Common shares issued, net	1		2		4		4
Balance at end of period	652		647		652		647
Additional paid-in capital
Balance at beginning of period	2,134,241		2,014,741		2,085,075		1,977,794
Amortization of share-based compensation	21,137		16,490		66,505		57,063
Issue costs on preferred shares	—		(14,179)		—		(14,179)
Other changes	15,283		11,867		19,081		8,241
Balance at end of period	2,170,661		2,028,919		2,170,661		2,028,919
Retained earnings
Balance at beginning of period	14,641,484		12,790,216		14,455,868		12,362,463
Net income (loss)	403,945		718,664		601,377		1,194,372
Net (income) loss attributable to noncontrolling interests	399		(43,178)		(1,233)		(80,730)
Preferred share dividends	(10,184)		(11,666)		(20,368)		(22,069)
Balance at end of period	15,035,644		13,454,036		15,035,644		13,454,036
Accumulated other comprehensive income (loss), net of deferred income tax
Balance at beginning of period	(649,445)		205,827		(64,600)		488,895
Unrealized appreciation (decline) in value of available-for-sale investments, net of deferred income tax:
Balance at beginning of period	(568,591)		246,711		13,486		501,295
Unrealized holding gains (losses) during period, net of reclassification adjustment	(540,295)		18,024		(1,122,372)		(241,029)
Unrealized holding gains (losses) during period attributable to noncontrolling interests	—		(33)		—		4,436
Balance at end of period	(1,108,886)		264,702		(1,108,886)		264,702
Foreign currency translation adjustments, net of deferred income tax:
Balance at beginning of period	(80,854)		(40,884)		(78,086)		(12,400)
Foreign currency translation adjustments	(68,525)		6,205		(71,293)		(22,379)
Foreign currency translation adjustments attributable to noncontrolling interests	—		25		—		125
Balance at end of period	(149,379)		(34,654)		(149,379)		(34,654)
Balance at end of period	(1,258,265)		230,048		(1,258,265)		230,048
Common shares held in treasury, at cost
Balance at beginning of period	(4,037,342)		(2,694,957)		(3,761,095)		(2,503,909)
Shares repurchased for treasury	(323,784)		(312,621)		(600,031)		(503,669)
Balance at end of period	(4,361,126)		(3,007,578)		(4,361,126)		(3,007,578)
Total shareholders’ equity available to Arch	12,417,566		13,986,072		12,417,566		13,986,072
Non-redeemable noncontrolling interests	—		918,874		—		918,874
Total shareholders’ equity	$	12,417,566	$	14,904,946	$	12,417,566	$	14,904,946

See Notes to Consolidated Financial Statements

ARCH CAPITAL 9 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONSOLIDATED STATEMENTS OF CASH FLOWS

(U.S. dollars in thousands)

	(Unaudited)
	Six Months Ended
	June 30,
	2022		2021
Operating Activities
Net income (loss)	$	601,377	$	1,194,372
Adjustments to reconcile net income (loss) to net cash provided by operating activities:
Net realized (gains) losses	555,273		(379,049)
Equity in net (income) or loss of investment funds accounted for using the equity method and other income or loss	43,815		(181,028)
Amortization of intangible assets	54,374		29,688
Share-based compensation	66,518		57,564
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable	634,482		948,505
Unearned premiums, net of ceded unearned premiums	872,371		838,650
Premiums receivable	(1,085,790)		(781,391)
Deferred acquisition costs	(173,911)		(214,893)
Reinsurance balances payable	72,095		331,461
Other items, net	(186,636)		(231,307)
Net cash provided by (used for) operating activities	1,453,968		1,612,572
Investing Activities
Purchases of fixed maturity investments	(9,705,957)		(23,554,384)
Purchases of equity securities	(655,573)		(620,774)
Purchases of other investments	(920,384)		(1,033,134)
Proceeds from sales of fixed maturity investments	8,078,968		23,130,388
Proceeds from sales of equity securities	1,490,212		542,290
Proceeds from sales, redemptions and maturities of other investments	863,333		772,549
Proceeds from redemptions and maturities of fixed maturity investments	444,073		805,836
Net settlements of derivative instruments	(44,838)		17,286
Net (purchases) sales of short-term investments	(439,992)		(378,086)
Change in cash collateral related to securities lending	—		(826)
Purchase of operating affiliate	—		(546,349)
Purchases of fixed assets	(23,830)		(23,585)
Other	98,386		(204,889)
Net cash provided by (used for) investing activities	(815,602)		(1,093,678)
Financing Activities
Proceeds from issuance of preferred shares, net	—		485,821
Purchases of common shares under share repurchase program	(575,676)		(485,315)
Proceeds from common shares issued, net	(4,065)		185
Change in cash collateral related to securities lending	—		826
Third party investment in non-redeemable noncontrolling interests	—		15,971
Dividends paid to redeemable noncontrolling interests	—		(1,907)
Other	(82,007)		27,639
Preferred dividends paid	(20,368)		(20,805)
Net cash provided by (used for) financing activities	(682,116)		22,415
Effects of exchange rate changes on foreign currency cash and restricted cash	(42,790)		(13,390)
Increase (decrease) in cash and restricted cash	(86,540)		527,919
Cash and restricted cash, beginning of year	1,314,771		1,290,544
Cash and restricted cash, end of period	$	1,228,231	$	1,818,463

See Notes to Consolidated Financial Statements

ARCH CAPITAL 10 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

1.    Basis of Presentation and Recent Accounting Pronouncements

General

Arch Capital Group Ltd. (“Arch Capital”) is a public 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. The Company’s consolidated financial statements through June 30, 2021 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 11.

Basis of Presentation

The interim consolidated financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America (“GAAP”). 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. In the opinion of management, the accompanying unaudited interim consolidated financial statements reflect all adjustments (consisting of normally recurring accruals) necessary for a fair statement of results on an interim basis. The results of any interim period are not necessarily indicative of the results for a full year or any future periods.

Certain information and footnote disclosures normally included in financial statements prepared in accordance with GAAP have been condensed or omitted; however, management believes that the disclosures are adequate to make the information presented not misleading. This report should be read in conjunction with the Company’s Annual Report on Form 10-K for the year ended December 31, 2021

(“2021 Form 10-K”), including the Company’s audited consolidated financial statements and related notes.

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, comprehensive income, shareholders’ equity or cash flows. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.

Recent Accounting Pronouncements

Recently Issued Accounting Standards Adopted

For information regarding additional accounting standards that the Company has not yet adopted, see note 3(s), “Significant Accounting Policies—Recent Accounting Pronouncements,” of the notes to consolidated financial statements in the Company’s 2021 Form 10-K.

2.    Share Transactions

Share Repurchases 

The board of directors of Arch Capital has authorized the investment in Arch Capital’s common shares through a share repurchase program. Since the inception of the share repurchase program, Arch Capital has repurchased 433.3 million common shares for an aggregate purchase price of $5.86 billion. For the six months ended June 30, 2022, Arch Capital repurchased 12.7 million shares under the share repurchase program with an aggregate purchase price of $575.7 million. At June 30, 2022, $606.6 million of share repurchases were available under the program, which may be effected from time to time in open market or privately negotiated transactions. 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.

The 2022 Long-Term Incentive and Share Award Plan (the“2022 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, will be 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 June 30, 2022, 9,000,000 shares are available for future issuance.

ARCH CAPITAL  11 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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 Company’s board of directors 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.

3.    Earnings Per Common Share

The following table sets forth the computation of basic and diluted earnings per common share:

	Three Months Ended				Six Months Ended
	June 30,				June 30,
	2022		2021		2022		2021
Numerator:
Net income (loss)	$	403,945	$	718,664	$	601,377	$	1,194,372
Amounts attributable to noncontrolling interests	399		(43,178)		(1,233)		(80,730)
Net income (loss) available to Arch	404,344		675,486		600,144		1,113,642
Preferred dividends	(10,184)		(11,666)		(20,368)		(22,069)
Net income (loss) available to Arch common shareholders	$	394,160	$	663,820	$	579,776	$	1,091,573
Denominator:
Weighted average common shares and common share equivalents outstanding — basic	369,241,193		397,743,402		371,728,683		399,267,183
Effect of dilutive common share equivalents:
Nonvested restricted shares	2,121,678		1,990,729		2,238,267		1,932,929
Stock options (1)	6,590,117		6,751,863		6,938,562		6,487,568
Weighted average common shares and common share equivalents outstanding — diluted	377,952,988		406,485,994		380,905,512		407,687,680
Earnings per common share:
Basic	$	1.07	$	1.67	$	1.56	$	2.73
Diluted	$	1.04	$	1.63	$	1.52	$	2.68

(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 the 2022 second quarter and 2021 second quarter, the number of stock options excluded were 773,163 and 1,974,849, respectively. For the six months ended June 30, 2022 and 2021, the number of stock options excluded were 778,724 and 2,395,749, respectively.

ARCH CAPITAL  12 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

4.    Segment Information

The Company classifies its businesses into three underwriting segments — insurance, reinsurance and mortgage — and two other 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, the 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; excess and surplus casualty; lenders products; professional lines; programs; property, energy, marine and aviation; travel, accident and health; and other (consisting of alternative markets, excess workers' compensation and surety business).

The reinsurance segment consists of the Company’s reinsurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include: casualty; marine and aviation; other specialty; property catastrophe; property excluding property catastrophe (losses on a single risk, both excess of loss and pro rata); and other (consisting of life reinsurance, casualty clash and other).

The mortgage segment includes the Company’s U.S. primary mortgage insurance business, investment and services related to U.S. credit-risk transfer (“CRT”) which are predominately with government sponsored enterprises (“GSE’s”) and international mortgage insurance and reinsurance operations. Arch Mortgage Insurance Company and United Guaranty Residential Insurance Company (combined “Arch MI U.S.”) are approved as eligible mortgage insurers by Federal National Mortgage Association (“Fannie Mae”) and Federal Home Loan Mortgage Corporation (“Freddie Mac”), each a GSE. Arch MI U.S. also includes Arch Mortgage Guaranty Company, which is not a GSE-approved entity.

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 11.

ARCH CAPITAL  13 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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:

	Three Months Ended
	June 30, 2022
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	1,705,167		$	1,793,398		$	371,896		$	3,869,727		$	—		$	3,869,727
Premiums ceded	(476,910)			(630,764)			(78,148)			(1,185,088)			—			(1,185,088)
Net premiums written	1,228,257			1,162,634			293,748			2,684,639			—			2,684,639
Change in unearned premiums	(126,113)			(234,635)			1,884			(358,864)			—			(358,864)
Net premiums earned	1,102,144			927,999			295,632			2,325,775			—			2,325,775
Other underwriting income (loss)	—			4,526			(1,556)			2,970			—			2,970
Losses and loss adjustment expenses	(629,759)			(537,578)			64,681			(1,102,656)			—			(1,102,656)
Acquisition expenses	(213,688)			(189,494)			(10,137)			(413,319)			—			(413,319)
Other operating expenses	(161,088)			(66,053)			(50,251)			(277,392)			—			(277,392)
Underwriting income (loss)	$	97,609		$	139,400		$	298,369		535,378			—			535,378
Net investment income										106,392			—			106,392
Net realized gains (losses)										(266,579)			—			(266,579)
Equity in net income (loss) of investment funds accounted for using the equity method										58,061			—			58,061
Other income (loss)										(11,777)			—			(11,777)
Corporate expenses (2)										(27,359)			—			(27,359)
Transaction costs and other (2)										(261)			—			(261)
Amortization of intangible assets										(27,207)			—			(27,207)
Interest expense										(32,795)			—			(32,795)
Net foreign exchange gains (losses)										87,775			—			87,775
Income (loss) before income taxes and income (loss) from operating affiliates										421,628			—			421,628
Income tax (expense) benefit										(22,323)			—			(22,323)
Income (loss) from operating affiliates										4,640			—			4,640
Net income (loss)										403,945			—			403,945
Amounts attributable to redeemable noncontrolling interests										399			—			399
Net income (loss) available to Arch										404,344			—			404,344
Preferred dividends										(10,184)			—			(10,184)
Net income (loss) available to Arch common shareholders										$	394,160		$	—		$	394,160
Underwriting Ratios
Loss ratio	57.1		%	57.9		%	(21.9)		%	47.4		%	—		%	47.4		%
Acquisition expense ratio	19.4		%	20.4		%	3.4		%	17.8		%	—		%	17.8		%
Other operating expense ratio	14.6		%	7.1		%	17.0		%	11.9		%	—		%	11.9		%
Combined ratio	91.1		%	85.4		%	(1.5)		%	77.1		%	—		%	77.1		%
Goodwill and intangible assets	$	236,661		$	166,437		$	464,916		$	868,014		$	—		$	868,014

(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 expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

ARCH CAPITAL  14 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

	Three Months Ended
	June 30, 2021
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	1,368,867		$	1,358,020		$	391,511		$	3,117,505		$	240,942		$	3,286,291
Premiums ceded	(405,312)			(433,288)			(55,665)			(893,372)			(65,551)			(886,767)
Net premiums written	963,555			924,732			335,846			2,224,133			175,391			2,399,524
Change in unearned premiums	(98,128)			(187,708)			(1,625)			(287,461)			8,846			(278,615)
Net premiums earned	865,427			737,024			334,221			1,936,672			184,237			2,120,909
Other underwriting income (loss)	—			1,053			4,148			5,201			328			5,529
Losses and loss adjustment expenses	(545,880)			(463,823)			(9,880)			(1,019,583)			(140,248)			(1,159,831)
Acquisition expenses	(136,852)			(133,585)			(30,117)			(300,554)			(34,589)			(335,143)
Other operating expenses	(133,342)			(44,695)			(48,312)			(226,349)			(18,594)			(244,943)
Underwriting income (loss)	$	49,353		$	95,974		$	250,060		395,387			(8,866)			386,521
Net investment income										89,430			22,183			111,613
Net realized gains (losses)										163,394			39,513			202,907
Equity in net income (loss) of investment funds accounted for using the equity method										122,186			—			122,186
Other income (loss)										6,852			—			6,852
Corporate expenses (2)										(17,175)			—			(17,175)
Transaction costs and other (2)										1,444			(220)			1,224
Amortization of intangible assets										(14,388)			(898)			(15,286)
Interest expense										(31,439)			(4,261)			(35,700)
Net foreign exchange gains (losses)										(17,892)			117			(17,775)
Income (loss) before income taxes and income (loss) from operating affiliates										697,799			47,568			745,367
Income tax (expense) benefit										(50,953)			(226)			(51,179)
Income (loss) from operating affiliates										24,476			—			24,476
Net income (loss)										671,322			47,342			718,664
Amounts attributable to redeemable noncontrolling interests										(580)			(981)			(1,561)
Amounts attributable to nonredeemable noncontrolling interests										—			(41,617)			(41,617)
Net income (loss) available to Arch										670,742			4,744			675,486
Preferred dividends										(11,666)			—			(11,666)
Net income (loss) available to Arch common shareholders										$	659,076		$	4,744		$	663,820
Underwriting Ratios
Loss ratio	63.1		%	62.9		%	3.0		%	52.6		%	76.1		%	54.7		%
Acquisition expense ratio	15.8		%	18.1		%	9.0		%	15.5		%	18.8		%	15.8		%
Other operating expense ratio	15.4		%	6.1		%	14.5		%	11.7		%	10.1		%	11.5		%
Combined ratio	94.3		%	87.1		%	26.5		%	79.8		%	105.0		%	82.0		%
Goodwill and intangible assets	$	270,262		$	16,168		$	370,405		$	656,835		$	10,318		$	667,153

(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 expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

ARCH CAPITAL  15 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

	Six Months Ended
	June 30, 2022
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	3,424,772		$	3,512,340		$	736,735		$	7,670,502		$	—		$	7,670,502
Premiums ceded	(989,619)			(1,210,582)			(154,867)			(2,351,723)			—			(2,351,723)
Net premiums written	2,435,153			2,301,758			581,868			5,318,779			—			5,318,779
Change in unearned premiums	(306,313)			(569,359)			3,301			(872,371)			—			(872,371)
Net premiums earned	2,128,840			1,732,399			585,169			4,446,408			—			4,446,408
Other underwriting income (loss)	—			5,362			3,505			8,867			—			8,867
Losses and loss adjustment expenses	(1,230,498)			(992,278)			119,285			(2,103,491)			—			(2,103,491)
Acquisition expenses	(409,338)			(361,490)			(20,650)			(791,478)			—			(791,478)
Other operating expenses	(327,913)			(135,829)			(103,593)			(567,335)			—			(567,335)
Underwriting income (loss)	$	161,091		$	248,164		$	583,716		$	992,971		$	—		$	992,971
Net investment income										186,828			—			186,828
Net realized gains (losses)										(558,993)			—			(558,993)
Equity in net income (loss) of investment funds accounted for using the equity method										94,366			—			94,366
Other income (loss)										(20,802)			—			(20,802)
Corporate expenses (2)										(59,294)			—			(59,294)
Transaction costs and other (2)										(658)			—			(658)
Amortization of intangible assets										(54,374)			—			(54,374)
Interest expense										(65,503)			—			(65,503)
Net foreign exchange gains (losses)										91,620			—			91,620
Income (loss) before income taxes and income (loss) from operating affiliates										606,161			—			606,161
Income tax (expense) benefit										(33,942)			—			(33,942)
Income (loss) from operating affiliates										29,158			—			29,158
Net income (loss)										601,377			—			601,377
Amounts attributable to redeemable noncontrolling interests										(1,233)			—			(1,233)
Net income (loss) available to Arch										600,144			—			600,144
Preferred dividends										(20,368)			—			(20,368)
Net income (loss) available to Arch common shareholders										$	579,776		$	—		$	579,776
Underwriting Ratios
Loss ratio	57.8		%	57.3		%	(20.4)		%	47.3		%	—		%	47.3		%
Acquisition expense ratio	19.2		%	20.9		%	3.5		%	17.8		%	—		%	17.8		%
Other operating expense ratio	15.4		%	7.8		%	17.7		%	12.8		%	—		%	12.8		%
Combined ratio	92.4		%	86.0		%	0.8		%	77.9		%	—		%	77.9		%

(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 expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

ARCH CAPITAL  16 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

	Six Months Ended
	June 30, 2021
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	2,784,753		$	2,829,080		$	782,757		$	6,394,798		$	457,465		$	6,683,497
Premiums ceded	(826,359)			(905,236)			(111,716)			(1,841,519)			(102,763)			(1,775,516)
Net premiums written	1,958,394			1,923,844			671,041			4,553,279			354,702			4,907,981
Change in unearned premiums	(273,493)			(541,920)			(503)			(815,916)			(22,734)			(838,650)
Net premiums earned	1,684,901			1,381,924			670,538			3,737,363			331,968			4,069,331
Other underwriting income (loss)	—			(145)			11,045			10,900			739			11,639
Losses and loss adjustment expenses	(1,081,627)			(948,693)			(73,569)			(2,103,889)			(259,042)			(2,362,931)
Acquisition expenses	(265,074)			(251,610)			(60,199)			(576,883)			(62,741)			(639,624)
Other operating expenses	(270,455)			(105,209)			(97,443)			(473,107)			(32,869)			(505,976)
Underwriting income (loss)	$	67,745		$	76,267		$	450,372		$	594,384		$	(21,945)		$	572,439
Net investment income										168,159			42,310			210,469
Net realized gains (losses)										264,730			80,638			345,368
Equity in net income (loss) of investment funds accounted for using the equity method										193,872			—			193,872
Other income (loss)										5,111			—			5,111
Corporate expenses (2)										(40,643)			—			(40,643)
Transaction costs and other (2)										243			(935)			(692)
Amortization of intangible assets										(28,790)			(898)			(29,688)
Interest expense										(65,636)			(8,410)			(74,046)
Net foreign exchange gains (losses)										3,613			(1,325)			2,288
Income (loss) before income taxes and income (loss) from operating affiliates										1,095,043			89,435			1,184,478
Income tax (expense) benefit										(89,805)			(234)			(90,039)
Income (loss) from operating affiliates										99,933			—			99,933
Net income (loss)										1,105,171			89,201			1,194,372
Amounts attributable to redeemable noncontrolling interests										(463)			(1,953)			(2,416)
Amounts attributable to nonredeemable noncontrolling interests										—			(78,314)			(78,314)
Net income (loss) available to Arch										1,104,708			8,934			1,113,642
Preferred dividends										(22,069)			—			(22,069)
Net income (loss) available to Arch common shareholders										$	1,082,639		$	8,934		$	1,091,573
Underwriting Ratios
Loss ratio	64.2		%	68.7		%	11.0		%	56.3		%	78.0		%	58.1		%
Acquisition expense ratio	15.7		%	18.2		%	9.0		%	15.4		%	18.9		%	15.7		%
Other operating expense ratio	16.1		%	7.6		%	14.5		%	12.7		%	9.9		%	12.4		%
Combined ratio	96.0		%	94.5		%	34.5		%	84.4		%	106.8		%	86.2		%

(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 expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

ARCH CAPITAL  17 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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:

	Three Months Ended				Six Months Ended
	June 30,				June 30,
	2022		2021		2022		2021
Reserve for losses and loss adjustment expenses at beginning of period	$	18,109,107	$	16,443,952	$	17,757,156	$	16,513,929
Unpaid losses and loss adjustment expenses recoverable	5,709,998		3,916,650		5,599,231		4,314,855
Net reserve for losses and loss adjustment expenses at beginning of period	12,399,109		12,527,302		12,157,925		12,199,074
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year	1,273,882		1,219,081		2,416,529		2,463,853
Prior years	(171,226)		(59,250)		(313,038)		(100,922)
Total net incurred losses and loss adjustment expenses	1,102,656		1,159,831		2,103,491		2,362,931
Retroactive reinsurance transactions (1)	—		—		—		(183,893)
Net foreign exchange (gains) losses and other	(248,655)		135,847		(281,295)		88,970
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year	(166,466)		(164,441)		(237,272)		(223,425)
Prior years	(578,668)		(607,911)		(1,234,873)		(1,193,029)
Total net paid losses and loss adjustment expenses	(745,134)		(772,352)		(1,472,145)		(1,416,454)
Net reserve for losses and loss adjustment expenses at end of period	12,507,976		13,050,628		12,507,976		13,050,628
Unpaid losses and loss adjustment expenses recoverable	5,686,348		4,146,020		5,686,348		4,146,020
Reserve for losses and loss adjustment expenses at end of period	$	18,194,324	$	17,196,648	$	18,194,324	$	17,196,648

(1)     During the 2021 first quarter, the Company entered into a reinsurance to close and other related agreements with Premia Managing Agency Limited (“Premia”), in connection with the 2018 and prior years of account related to the acquisition of Barbican Group Holdings Limited (“Barbican”).

Development on Prior Year Loss Reserves

2022 Second Quarter

During the 2022 second quarter, the Company recorded net favorable development on prior year loss reserves of $171.2 million, which consisted of $6.7 million from the insurance segment, $46.4 million from the reinsurance segment and $118.1 million from the mortgage segment.

The insurance segment’s net favorable development of $6.7 million, or 0.6 loss ratio points, for the 2022 second quarter consisted of $14.3 million of net favorable development in short-tailed lines and $7.5 million of net adverse development in medium-tailed and long-tailed lines. Net favorable development in short-tailed lines reflected $12.2 million of favorable development in lenders products, primarily from the 2021 accident year (i.e., the year in which a loss occurred). Net adverse development in medium-tailed lines included $6.3 million of adverse development in professional liability business, primarily from the 2018 and 2019 accident years, partially offset by favorable development in marine business of $2.6 million, primarily from the 2019 and prior accident years. Net adverse

development in long-tailed lines reflected $5.7 million related to executive assurance business, primarily from the 2013 and 2020 accident years.

The reinsurance segment’s net favorable development of $46.4 million, or 5.0 loss ratio points, for the 2022 second quarter consisted of $54.4 million of net favorable development in short-tailed and medium-tailed lines and $8.0 million of net adverse development in long-tailed lines. Net favorable development in short-tailed lines reflected $31.6 million of favorable development related to property other than property catastrophe business, primarily from 2016 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), $13.1 million of favorable development in other specialty business, primarily from the 2018 and 2021 underwriting year, and $6.3 million of favorable development related to property catastrophe business, primarily from the 2017 to 2021 underwriting years. Net favorable development in medium-tailed lines included $4.2 million in marine and aviation lines, across most underwriting years. Adverse development in long-tailed

ARCH CAPITAL  18 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

lines reflected an increase in casualty reserves, across several years, most notably the 2013 and 2021 underwriting years.

The mortgage segment’s net favorable development was $118.1 million, or 39.9 loss ratio points, for the 2022 second quarter, primarily related to the U.S. first lien portfolio from the 2020 accident year. The Company’s credit risk transfer, international, second lien and student loan business also contributed to the favorable development.

2021 Second Quarter

During the 2021 second quarter, the Company recorded net favorable development on prior year loss reserves of $59.3 million, which consisted of $4.0 million from the insurance segment, $20.5 million from the reinsurance segment and $43.1 million from the mortgage segment, partially offset by $8.3 million unfavorable from the ‘other’ segment.

The insurance segment’s net favorable development of $4.0 million, or 0.5 loss ratio points, for the 2021 second quarter consisted of $28.5 million of net favorable development in short-tailed and long-tailed lines and $24.5 million of net adverse development in medium-tailed lines. Net favorable development in short-tailed lines reflected $10.7 million of favorable development in lenders products, primarily from the 2020 accident year, $7.1 million of favorable development from property (excluding marine), primarily from the 2017, 2019 and 2020 accident years and $6.7 million of favorable development in travel and accident, primarily from the 2020 accident year. Net favorable development in long-tailed lines reflected $5.6 million of favorable development related to construction and national accounts, primarily from the 2016 to 2020 accident years. Net adverse development in medium-tailed lines included $20.1 million of adverse development in contract binding business, primarily from the 2014 to 2019 accident years.

The reinsurance segment’s net favorable development of $20.5 million, or 2.8 loss ratio points, for the 2021 second quarter consisted of $53.7 million of net favorable development in short-tailed and medium-tailed lines and $33.2 million of net adverse development in long-tailed lines. Net favorable development in short-tailed lines reflected $61.6 million of favorable development related to other specialty, primarily from the 2019 underwriting year, which was partially offset by $17.1 million of net adverse development related to property catastrophe, primarily from the 2020 underwriting year. Net favorable development of $4.0 million in medium-tailed lines reflected favorable development in marine and aviation, across most underwriting years. Net adverse development in long-tailed lines reflected $34.2 million of adverse development in casualty, primarily from the 2018 underwriting year.

The mortgage segment’s net favorable development was $43.1 million, or 12.9 loss ratio points, for the 2021 second quarter, with the largest contributor being reserve releases associated with the various vintage credit risk transfer contracts that were called by the GSEs. The net favorable development also included reserve releases in our international portfolio and subrogation recoveries on second lien and student loan business.

Six Months Ended June 30, 2022

During the six months ended June 30, 2022, the Company recorded net favorable development on prior year loss reserves of $313.0 million, which consisted of $14.0 million from the insurance segment, $78.9 million from the reinsurance segment and $220.2 million from the mortgage segment.

The insurance segment’s net favorable development of $14.0 million, or 0.7 loss ratio points, for the 2022 period consisted of $33.2 million of net favorable development in short-tailed and $19.2 million of net adverse development in medium and long-tailed lines. Net favorable development in short-tailed lines reflected $30.8 million of favorable development in lenders products, primarily from the 2021 accident year. Net adverse development in medium-tailed lines included $13.6 million of adverse development in professional liability business, primarily from the 2018 and 2019 accident years, and $6.1 million of adverse development in contract binding business, across most accident years, partially offset by $5.5 million of favorable development in marine business, across most accident years, and $5.2 million of favorable development in program business, primarily from the 2020 accident year. Net adverse development in long-tailed lines primarily reflected $7.6 million of adverse development related to construction and national accounts, primarily from the 2020 and 2021 accident year.

The reinsurance segment’s net favorable development of $78.9 million, or 4.6 loss ratio points, for the 2022 period consisted of $89.7 million of net favorable development from short-tailed and medium-tailed lines, partially offset by $10.9 million of net adverse development from long-tailed lines. Net favorable development of $74.9 million in short-tailed lines reflected $47.4 million of favorable development from property other than property catastrophe business, primarily from the 2015 to 2021 underwriting years,$18.0 million of favorable development from other specialty business, primarily from the 2016 and 2021 underwriting years, and $9.7 million from property catastrophe, primarily from the 2018 and 2019 underwriting years. Net favorable development in medium-tailed lines included $14.9 million in marine and aviation lines, across most underwriting years. Adverse development in long-tailed lines reflected an increase in casualty reserves, primarily from the 2021 underwriting year.

ARCH CAPITAL  19 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The mortgage segment’s net favorable development was $220.2 million, or 37.6 loss ratio points, for the 2022 period, with the largest contributor being reserve releases associated with the U.S. first lien portfolio from the 2020 accident year. The Company’s credit risk transfer, international, second lien and student loan business also contributed to the favorable development.

Six Months Ended June 30, 2021

During the six months ended June 30, 2021, the Company recorded net favorable development on prior year loss reserves of $100.9 million, which consisted of $8.1 million from the insurance segment, $47.3 million from the reinsurance segment, $54.0 million from the mortgage segment, partially offset by $8.4 million of adverse development from the ‘other’ segment.

The insurance segment’s net favorable development of $8.1 million, or 0.5 loss ratio points, for the 2021 period consisted of $53.5 million of net favorable development in short-tailed and long-tailed lines, partially offset by $45.4 million of net adverse development in medium-tailed lines. Net favorable development of $49.4 million in short-tailed lines reflected $21.6 million of favorable development from property (excluding marine), primarily from the 2018 to 2020 accident years, $18.6 million of favorable development in lenders products, primarily from the 2020 accident year and $9.3 million of favorable development in travel and accident, primarily from the 2020 accident year. Net favorable development of in long-tailed lines included favorable development primarily related to construction and national accounts, primarily in the 2016 to 2019 accident years. Net adverse development in medium-tailed lines reflected $20.1 million of adverse development in contract binding business, primarily in the 2014 to 2019 accident years, $12.6 million of adverse development on programs business, primarily from the 2016 to 2020 accident years, and $11.2 million of adverse development in professional liability business, primarily from the 2019 and 2020 accident years.

The reinsurance segment’s net favorable development of $47.3 million, or 3.4 loss ratio points, for the 2021 period consisted of $72.1 million of net favorable development from short-tailed and medium-tailed lines, partially offset by $24.8 million of net adverse development from long-tailed lines. Net favorable development of $67.2 million in short-tailed lines reflected $78.2 million of favorable development from other specialty lines, primarily from the 2019 underwriting year and $28.8 million of favorable development from property other than property catastrophe business, partially offset by adverse development of $39.6 million from property catastrophe, primarily from the 2020 underwriting year. Adverse development in long-tailed lines reflected an increase in reserves from casualty, primarily from the 2018 underwriting year.

The mortgage segment’s net favorable development was $54.0 million, or 8.1 loss ratio points, for the 2021 period, primarily driven by favorable development in the credit risk transfer and international portfolios. Subrogation recoveries on second lien and student loan business also contributed.

6.    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:

	Premium Receivables, Net of Allowance		Allowance for Expected Credit Losses
Three Months Ended June 30, 2022
Balance at beginning of period	$	3,223,504	$	39,073
Change for provision of expected credit losses (1)			(903)
Balance at end of period	$	3,634,182	$	38,170
Three Months Ended June 30, 2021
Balance at beginning of period	$	2,618,175	$	36,111
Change for provision of expected credit losses (1)			(132)
Balance at end of period	$	2,866,578	$	35,979
Six Months Ended June 30, 2022
Balance at beginning of period	$	2,633,280	$	39,958
Change for provision of expected credit losses (1)			(1,788)
Balance at end of period	$	3,634,182	$	38,170
Six Months Ended June 30, 2021
Balance at beginning of period	$	2,064,586	$	37,781
Change for provision of expected credit losses (1)			(1,802)
Balance at end of period	$	2,866,578	$	35,979

(1)Amounts deemed uncollectible are written-off in operating expenses. For the 2022 second quarter and 2021 second quarter, amounts written off were $3.3 million and $1.1 million, respectively. For the six months ended June 30, 2022 and 2021 period, amounts written off were $4.8 million and $1.2 million, respectively.

ARCH CAPITAL  20 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

Reinsurance Recoverables

The following table provides a roll forward of the allowance for expected credit losses of the Company’s reinsurance recoverables:

	Reinsurance Recoverables, Net of Allowance		Allowance for Expected Credit Losses
Three Months Ended June 30, 2022
Balance at beginning of period	$	5,941,000	$	18,483
Change for provision of expected credit losses			(3,743)
Balance at end of period	$	5,938,511	$	14,740
Three Months Ended June 30, 2021
Balance at beginning of period	$	4,041,076	$	10,872
Change for provision of expected credit losses			157
Balance at end of period	$	4,314,515	$	11,029
Six Months Ended June 30, 2022
Balance at beginning of period	$	5,880,735	$	13,230
Change for provision of expected credit losses			1,510
Balance at end of period	$	5,938,511	$	14,740
Six Months Ended June 30, 2021
Balance at beginning of period	$	4,500,802	$	11,636
Change for provision of expected credit losses			(607)
Balance at end of period	$	4,314,515	$	11,029

The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums):

	June 30,			December 31
	2022			2021
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	$	5,938,511		$	5,880,735
% due from carriers with A.M. Best rating of “A-” or better	69.3		%	69.7		%
% due from all other rated carriers	0.1		%	0.1		%
% due from all other carriers with no A.M. Best rating (1)	30.6		%	30.2		%
Largest balance due from any one carrier as % of total shareholders’ equity	7.8		%	6.7		%

(1)    At June 30, 2022 and December 31, 2021 over 93% and 91% of such amount were 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:

	Contract-holder Receivables, Net of Allowance		Allowance for Expected Credit Losses
Three Months Ended June 30, 2022
Balance at beginning of period	$	1,810,199	$	3,731
Change for provision of expected credit losses			(726)
Balance at end of period	$	1,758,018	$	3,005
Three Months Ended June 30, 2021
Balance at beginning of period	$	1,919,655	$	5,853
Change for provision of expected credit losses			(1,382)
Balance at end of period	1,882,948		$	4,471
Six Months Ended June 30, 2022
Balance at beginning of period	$	1,828,691	$	3,437
Change for provision of expected credit losses			(432)
Balance at end of period	$	1,758,018	$	3,005
Six Months Ended June 30, 2021
Balance at beginning of period	$	1,986,924	$	8,638
Change for provision of expected credit losses			(4,167)
Balance at end of period	1,882,948		$	4,471

ARCH CAPITAL  21 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

7.    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
June 30, 2022
Fixed maturities:
Corporate bonds	$	7,288,555	$	32,021	$	(655,664)	$	(38,494)	$	7,950,692
Mortgage backed securities	698,168		4,427		(55,898)		—		749,639
Municipal bonds	417,380		4,129		(18,936)		(298)		432,485
Commercial mortgage backed securities	1,023,088		1,533		(42,056)		(3,594)		1,067,205
U.S. government and government agencies	4,368,150		25,112		(240,786)		—		4,583,824
Non-U.S. government securities	2,181,943		16,175		(163,724)		(1,335)		2,330,827
Asset backed securities	1,607,745		1,001		(80,267)		(14,689)		1,701,700
Total	17,585,029		84,398		(1,257,331)		(58,410)		18,816,372
Short-term investments	2,227,874		2,458		(1,257)		—		2,226,673
Total	$	19,812,903	$	86,856	$	(1,258,588)	$	(58,410)	$	21,043,045
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  22 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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
June 30, 2022
Fixed maturities:
Corporate bonds	$	6,583,215	$	(580,235)	$	489,098	$	(75,429)	$	7,072,313	$	(655,664)
Mortgage backed securities	595,485		(46,415)		61,751		(9,483)		657,236		(55,898)
Municipal bonds	271,481		(17,908)		8,876		(1,028)		280,357		(18,936)
Commercial mortgage backed securities	973,212		(42,056)		—		—		973,212		(42,056)
U.S. government and government agencies	4,029,550		(235,510)		69,596		(5,276)		4,099,146		(240,786)
Non-U.S. government securities	1,929,278		(148,781)		103,969		(14,943)		2,033,247		(163,724)
Asset backed securities	1,292,087		(73,575)		136,119		(6,692)		1,428,206		(80,267)
Total	15,674,308		(1,144,480)		869,409		(112,851)		16,543,717		(1,257,331)
Short-term investments	505,798		(1,257)		—		—		505,798		(1,257)
Total	$	16,180,106	$	(1,145,737)	$	869,409	$	(112,851)	$	17,049,515	$	(1,258,588)
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 June 30, 2022, on a lot level basis, approximately 8,360 security lots out of a total of approximately 10,440 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 $5.7 million. 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  23 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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.

	June 30, 2022				December 31, 2021
Maturity	Estimated Fair Value		Amortized Cost		Estimated Fair Value		Amortized Cost
Due in one year or less	$	412,194	$	414,752	$	300,889	$	299,772
Due after one year through five years	9,423,547		9,927,876		8,355,255		8,339,387
Due after five years through 10 years	4,070,099		4,512,685		4,689,155		4,684,393
Due after 10 years	350,188		442,515		505,758		493,927
	14,256,028		15,297,828		13,851,057		13,817,479
Mortgage backed securities	698,168		749,639		408,477		411,110
Commercial mortgage backed securities	1,023,088		1,067,205		1,046,484		1,047,867
Asset backed securities	1,607,745		1,701,700		2,692,091		2,697,367
Total	$	17,585,029	$	18,816,372	$	17,998,109	$	17,973,823

Equity Securities, at Fair Value

At June 30, 2022, the Company held $0.8 billion of equity securities, at fair value, compared to $1.8 billion at December 31, 2021. Such holdings include publicly traded common stocks primarily in the consumer cyclical and non-cyclical, technology, communication and financial sectors and exchange-traded funds in fixed income, equity and other sectors.

Other Investments, at Fair Value

The following table summarizes the Company’s other investments and other investable assets:

	June 30, 2022		December 31, 2021
Fixed maturities	$	525,451	$	416,698
Other investments	1,054,771		1,432,553
Short-term investments	39,657		97,806
Equity securities	14,489		26,493
Total	$	1,634,368	$	1,973,550

The following table summarizes the Company’s other investments, as detailed in the previous table, by strategy:

	June 30, 2022		December 31, 2021
Lending	$	427,812	$	536,345
Investment grade fixed income	221,484		147,810
Term loan investments	152,277		484,950
Private equity	124,282		91,126
Energy	74,234		81,692
Credit related funds	54,682		70,278
Infrastructure	—		20,352
Total	$	1,054,771	$	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:

	June 30, 2022		December 31, 2021
Credit related funds	$	1,119,711	$	1,022,334
Private equity	646,904		436,042
Real estate	455,044		396,395
Lending	447,028		376,649
Equities	350,587		395,090
Infrastructure	231,816		230,070
Energy	115,514		119,141
Fixed income	129,737		101,890
Total	$	3,496,341	$	3,077,611

Certain of the Company’s other investments 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

ARCH CAPITAL  24 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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 has determined that it is not required to consolidate these investments because it is not the primary beneficiary of 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 line item:

	June 30, 2022		December 31, 2021
Investments accounted for using the equity method (1)	3,496,341		3,077,611
Investments accounted for using the fair value option (2)	128,826		170,595
Total	$	3,625,167	$	3,248,206

(1)    Aggregate unfunded commitments were $3.0 billion at June 30, 2022, compared to $2.6 billion at December 31, 2021.

(2)    Aggregate unfunded commitments were $21.7 million at June 30, 2022, compared to $18.8 million at December 31, 2021.

Net Investment Income

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

	June 30,
	2022		2021
Three Months Ended
Fixed maturities	$	105,342	$	88,625
Term loans	401		16,879
Equity securities	6,121		8,584
Short-term investments	4,120		1,138
Other (1)	7,583		19,950
Gross investment income	123,567		135,176
Investment expenses	(17,175)		(23,563)
Net investment income	$	106,392	$	111,613
Six Months Ended
Fixed maturities	$	187,395	$	179,251
Term loans	2,018		31,607
Equity securities	12,359		14,234
Short-term investments	6,695		1,745
Other (1)	18,042		34,305
Gross investment income	226,509		261,142
Investment expenses	(39,681)		(50,673)
Net investment income	$	186,828	$	210,469

(1)    Includes income distributions from investment funds and other items.

Net Realized Gains (Losses)

Net realized gains (losses), which include changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings were as follows:

	June 30,
	2022		2021
Three Months Ended
Available for sale securities:
Gross gains on investment sales	$	15,186	$	115,541
Gross losses on investment sales	(57,176)		(50,627)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	(39,255)		10,912
Other investments	(21,710)		60,884
Equity securities	(2,124)		5,492
Short-term investments	(2,008)		(104)
Equity securities, at fair value:
Net realized gains (losses) on sales during the period	16,879		33,570
Net unrealized gains (losses) on equity securities still held at reporting date	(106,375)		65,847
Allowance for credit losses:
Investments related	(25,026)		896
Underwriting related	842		1,381
Derivative instruments (1)	(45,684)		(51,109)
Other	(128)		10,224
Net realized gains (losses)	$	(266,579)	$	202,907
Six Months Ended
Available for sale securities:
Gross gains on investment sales	$	34,893	$	180,543
Gross losses on investment sales	(165,523)		(113,625)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	(69,844)		27,465
Other investments	(17,321)		107,739
Equity securities	(5,437)		7,557
Short-term investments	(2,157)		632
Equity securities, at fair value:
Net realized gains (losses) on sales during the period	82,090		71,419
Net unrealized gains (losses) on equity securities still held at reporting date	(282,570)		85,555
Allowance for credit losses:
Investments related	(56,748)		(752)
Underwriting related	(3,444)		6,649
Derivative instruments (1)	(69,395)		(14,993)
Other	(3,537)		(12,821)
Net realized gains (losses)	$	(558,993)	$	345,368

(1)    See note 9 for information on the Company’s derivative instruments.

ARCH CAPITAL  25 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

Equity in Net Income (Loss) of Investment Funds Accounted for Using the Equity Method

The Company recorded $58.1 million of equity in net income related to investment funds accounted for using the equity method in the 2022 second quarter, compared to income of $122.2 million for the 2021 second quarter and an income of $94.4 million for the six months ended June 30, 2022, compared to income of $193.9 million for six months ended June 30, 2021. 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). Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds.

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 of June 30, 2022, the Company owned approximately 29.86% of the issued shares of Coface, or 30.09% excluding treasury shares, with a carrying value of $536.0 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 June 30, 2022 the Company’s carrying value in Greysbridge was $309.6 million, compared to $375.7 million at December 31, 2021, which reflected the Company’s 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.

Income from operating affiliates for the 2022 second quarter was income of $4.6 million, compared to an income of $24.5 million, for the 2021 second quarter and income of $29.2 million for the six months ended June 30, 2022, compared to income of $99.9 million for six months ended June 30, 2021.

ARCH CAPITAL  26 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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:

	Structured Securities (1)		Municipal Bonds		Corporate Bonds		Total
Three Months Ended June 30, 2022
Balance at beginning of period	$	6,998	$	106	$	27,041	$	34,145
Additions for current-period provision for expected credit losses	4,788		252		13,466		18,506
Additions (reductions) for previously recognized expected credit losses	6,705		(60)		(205)		6,440
Reductions due to disposals	(208)		—		(473)		(681)
Balance at end of period	$	18,283	$	298	$	39,829	$	58,410
Three Months Ended June 30, 2021
Balance at beginning of period	$	1,207	$	2	$	2,621	$	3,830
Additions for current-period provision for expected credit losses	52		—		7		59
Additions (reductions) for previously recognized expected credit losses	(383)		4		(412)		(791)
Reductions due to disposals	(117)		—		(857)		(974)
Balance at end of period	$	759	$	6	$	1,359	$	2,124
Six Months Ended June 30, 2022
Balance at beginning of period	$	802	$	2	$	2,079	$	2,883
Additions for current-period provision for expected credit losses	10,778		347		38,616		49,741
Additions (reductions) for previously recognized expected credit losses	7,192		(51)		(220)		6,921
Reductions due to disposals	(489)		—		(646)		(1,135)
Balance at end of period	$	18,283	$	298	$	39,829	$	58,410
Six Months Ended June 30, 2021
Balance at beginning of period	$	1,490	$	11	$	896	$	2,397
Additions for current-period provision for expected credit losses	234		—		2,428		2,662
Additions (reductions) for previously recognized expected credit losses	(765)		(5)		(952)		(1,722)
Reductions due to disposals	(200)		—		(1,013)		(1,213)
Balance at end of period	$	759	$	6	$	1,359	$	2,124

(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

ARCH CAPITAL  27 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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. See note 18, “Commitments and Contingencies,” of the notes to consolidated financial statements in the Company’s 2021 Form 10-K.

The following table details the value of the Company’s restricted assets:

	June 30, 2022		December 31, 2021
Assets used for collateral or guarantees:
Affiliated transactions	$	4,193,561	$	4,223,955
Third party agreements	2,953,800		2,721,160
Deposits with U.S. regulatory authorities	781,024		798,100
Deposits with non-U.S. regulatory authorities	485,341		506,517
Total restricted assets	$	8,413,726	$	8,249,732

Reconciliation of Cash and Restricted Cash

The following table details reconciliation of cash and restricted cash within the Consolidated Balance Sheets:

	June 30, 2022		December 31, 2021
Cash	$	813,548	$	858,668
Restricted cash (included in ‘other assets’)	$	414,683	$	456,103
Cash and restricted cash	$	1,228,231	$	1,314,771

8.    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 average number of 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

ARCH CAPITAL  28 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

review, the Company will challenge any prices for a security or portfolio which are considered not to be representative of fair value. The Company did not adjust any of the prices obtained from the independent pricing sources at June 30, 2022.

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. Where quotes are unavailable, fair value is determined by the Investment Manager using quantitative and qualitative assessments such as internally modeled values. Of the $22.4 billion of financial assets and liabilities measured at fair value at June 30, 2022, approximately $10.9 million, or 0.0%, were priced using non-binding broker-dealer quotes or modeled valuations. 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 or modeled valuations.

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 a low level of transparency on the inputs used in the pricing process.

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. 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.

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. The pricing services also review prepayment speeds and other indicators, when applicable. As the significant inputs used in the pricing process for commercial mortgage-

ARCH CAPITAL  29 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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. The pricing services also review prepayment speeds and other indicators, when applicable. 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. Certain equity securities are included in Level 2 of the valuation hierarchy as the significant inputs used in the pricing process for such securities are observable market inputs. Other equity 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’s other investments 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. The fair values for certain of the Company’s other investments are determined using net asset values as advised by external fund managers. The net asset value is based on the fund manager’s valuation of the underlying holdings in accordance with the fund’s governing documents. 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. 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.

ARCH CAPITAL  30 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The following table presents the Company’s financial assets and liabilities measured at fair value by level at June 30, 2022:

			Estimated Fair Value Measurements 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	$	7,288,555	$	—	$	7,284,985	$	3,570
Mortgage backed securities	698,168		—		698,168		—
Municipal bonds	417,380		—		417,380		—
Commercial mortgage backed securities	1,023,088		—		1,023,088		—
U.S. government and government agencies	4,368,150		4,341,399		26,751		—
Non-U.S. government securities	2,181,943		—		2,181,943		—
Asset backed securities	1,607,745		—		1,604,878		2,867
Total	17,585,029		4,341,399		13,237,193		6,437
Short-term investments	2,227,874		2,049,235		178,639		—
Equity securities, at fair value	772,689		736,343		33,440		2,906
Derivative instruments (2)	122,033		—		122,033		—
Residential mortgage loans	3,929		—		3,929		—
Fair value option:
Corporate bonds	522,707		—		522,707		—
Non-U.S. government bonds	611		—		611		—
Asset backed securities	2,133		—		2,133		—
Short-term investments	39,657		886		38,771		—
Equity securities	14,489		10,097		—		4,392
Other investments	178,461		—		145,130		33,331
Other investments measured at net asset value (1)	876,310
Total	1,634,368		10,983		709,352		37,723
Total assets measured at fair value	$	22,345,922	$	7,137,960	$	14,284,586	$	47,066
Liabilities measured at fair value:
Other liabilities	$	(16,205)	$	—	$	—	$	(16,205)
Derivative instruments (2)	(75,147)		—		(75,147)		—
Total liabilities measured at fair value	$	(91,352)	$	—	$	(75,147)	$	(16,205)

(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 9.

ARCH CAPITAL  31 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2021:

			Estimated Fair Value Measurements 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
Short-term investments	1,734,716		1,052,822		681,894		—
Equity securities, at fair value	1,804,170		1,762,864		38,388		2,918
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		—
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:
Other 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 9.

ARCH CAPITAL  32 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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:

	Assets												Liabilities
s	Available For Sale				Fair Value Option						Fair Value
	Structured Securities (1)		Corporate Bonds		Corporate Bonds		Other Investments		Equity Securities		Equity Securities		Other Liabilities
Three Months Ended June 30, 2022
Balance at beginning of period	$	3,152	$	3,570	$	—	$	22,602	$	4,511	$	2,768	$	(17,591)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	(1)		—		—		27		(119)		(89)		(97)
Included in other comprehensive income	(85)		—		—		—		—		—		1,483
Purchases, issuances, sales and settlements
Purchases	—		—		—		10,702		—		227		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		—		—		—		—
Settlements	(199)		—		—		—		—		—		—
Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of period	$	2,867	$	3,570	$	—	$	33,331	$	4,392	$	2,906	$	(16,205)
Three Months Ended June 30, 2021
Balance at beginning of period	$	3,472	$	13	$	989	$	67,930	$	71,176	$	43,112	$	(465)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	12		—		9		633		2,502		922		(1)
Included in other comprehensive income	(57)		—		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		—		5,638		—		5,102		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(301)		—		—		—
Settlements	(3)		—		—		—		—		—		—
Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of period	$	3,424	$	13	$	998	$	73,900	$	73,678	$	49,136	$	(466)
Six Months Ended June 30, 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)	9		—		—		34		(356)		(236)		(195)
Included in other comprehensive income	(145)		—		—		—		—		—		950
Purchases, issuances, sales and settlements
Purchases	—		—		—		10,770		—		227		—
Issuances	—		—		—		—		—		—		—
Sales (3)	—		—		—		(2,471)		—		(3)		—
Settlements	(344)		—		—		(2,983)		—		—		—
Transfers in and/or out of Level 3	—		3,557		—		—		—		—		—
Balance at end of period	$	2,867	$	3,570	$	—	$	33,331	$	4,392	$	2,906	$	(16,205)
Six Months Ended June 30, 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)	(56)		—		13		881		4,690		1,826		(5)
Included in other comprehensive income	57		—		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		—		13,003		—		5,295		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(7,087)		—		—		—
Settlements	(3)		—		—		—		—		—		—
Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of period	$	3,424	$	13	$	998	$	73,900	$	73,678	$	49,136	$	(466)

(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

(2)    Gains or losses were included in net realized gains (losses).

ARCH CAPITAL  33 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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 June 30, 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 June 30, 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 $2.6 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 values of the senior notes are classified within Level 2.

9.    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)
June 30, 2022
Futures contracts	$	49,695	$	(22,561)	$	2,794,246
Foreign currency forward contracts	9,556		(18,884)		908,192
TBAs	—		—		—
Other	62,782		(33,702)		3,849,244
Total	$	122,033	$	(75,147)
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 June 30, 2022 or December 31, 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. Contractual close-out netting reduces derivatives credit exposure from gross to net exposure.

At June 30, 2022, asset derivatives and liability derivatives of $116.9 million and $75.1 million, respectively, 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 preceding table were not subject to a master netting agreement.

ARCH CAPITAL  34 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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	June 30,
hedging instruments:	2022		2021
Three Months Ended
Net realized gains (losses):
Futures contracts	$	(39,205)	$	(54,759)
Foreign currency forward contracts	(25,638)		1,295
TBAs	—		—
Other (1)	19,159		2,355
Total	$	(45,684)	$	(51,109)
Six Months Ended
Net realized gains (losses):
Futures contracts	$	(85,979)	$	(7,321)
Foreign currency forward contracts	(27,676)		(20,776)
TBAs	(51)		—
Other (1)	44,311		13,104
Total	$	(69,395)	$	(14,993)

(1)    Includes realized gains and losses on swaps, options and other derivatives contracts.

10.    Commitments and Contingencies

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 the existing credit agreement into a $925.0 million five-year credit 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 $1.3 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 June 30, 2022, the $425.0 million secured letter of credit facility, had $333.4 million of letters of credit outstanding and remaining capacity of $91.6 million. In

addition, certain of Arch Capital’s subsidiaries had outstanding secured and unsecured letters of credit through other facilities of $23.6 million and $290.0 million respectively, which were issued in the normal course of business.

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 $3.5 billion at June 30, 2022, compared to $3.0 billion at December 31, 2021.

Interest Paid

Interest paid on the Company’s senior notes and other borrowings were $64.6 million for the six months ended June 30, 2022, compared to $74.7 million for the 2021 period.

11.    Variable Interest Entities and Noncontrolling Interests

Somers

In March 2014, the Company invested $100.0 million and acquired approximately 11% of Somers’ outstanding common equity. Somers was considered a VIE and the Company concluded that it was the primary beneficiary of Somers, through June 30, 2021. As such, the results of Somers were included in the Company’s consolidated financial statements as of and for the periods ended June 30, 2021.

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 contemplated by the Merger Agreement and the related Greysbridge equity financing closed on July 1, 2021. In connection therewith and effective July 1, 2021, Somers became wholly owned by Greysbridge, and Greysbridge is now 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. Beginning in the 2021 third quarter, the Company classifies its investment as ‘investments in operating affiliates’ on the Company’s balance sheets and is accounted for under the equity method.

Somers generated $47.0 million of cash provided by operating activities, $96.3 million of cash provided by

ARCH CAPITAL  35 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

investing activities and $2.0 million of cash used for financing activities for the six months ended June 30, 2021.

Non-redeemable noncontrolling interests

Through June 30, 2021, the Company accounted for the portion of Somers’s common equity attributable to third party investors in the shareholders’ equity section of its consolidated balance sheets. The portion of Somers’s income or loss attributable to third party investors was recorded in the consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests.’

The following table sets forth activity in the non-redeemable noncontrolling interests:

	June 30,
	2021
Three Months Ended
Balance, beginning of period	$	876,864
Additional paid in capital attributable to noncontrolling interests	383
Amounts attributable to noncontrolling interests	41,617
Other comprehensive income (loss) attributable to noncontrolling interests	10
Balance, end of period	$	918,874
Six Months Ended
Balance, beginning of year	$	823,007
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 period	$	918,874

Redeemable noncontrolling interests

Through June 30, 2021, the Company accounted for redeemable noncontrolling interests in the mezzanine section of its consolidated balance sheets in accordance with applicable accounting guidance. Such redeemable noncontrolling interests primarily related to the Somers Preference Shares issued in late March 2014 with a par value of $0.01 per share and a liquidation preference of $25.00 per share. The Somers Preference Shares were issued at a discounted amount of $24.50 per share. Through June 30, 2021 preferred dividends, including the accretion of the discount and issuance costs, were included in ‘net (income) loss attributable to noncontrolling interests’ in the Company’s consolidated statements of income.

The following table sets forth activity in the redeemable non-controlling interests:

	June 30,
	2022		2021
Three Months Ended
Balance, beginning of period	$	9,763	$	57,670
Accretion of preference share issuance costs	—		23
Other	(1,304)		(160)
Balance, end of period	$	8,459	$	57,533
Six Months Ended
Balance, beginning of year	$	9,233	$	58,548
Accretion of preference share issuance costs	—		46
Other	(774)		(1,061)
Balance, end of period	$	8,459	$	57,533

The portion of income or loss attributable to third party investors, recorded in the Company’s consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests,’ are summarized in the table below:

	June 30,
	2022		2021
Three Months Ended
Amounts attributable to non-redeemable noncontrolling interests	$	—	$	(41,617)
Amounts attributable to redeemable noncontrolling interests	399		(1,561)
Net (income) loss attributable to noncontrolling interests	$	399	$	(43,178)
Six Months Ended
Amounts attributable to non-redeemable noncontrolling interests	$	—	$	(78,314)
Amounts attributable to redeemable noncontrolling interests	(1,233)		(2,416)
Net (income) loss attributable to noncontrolling interests	$	(1,233)	$	(80,730)

ARCH CAPITAL  36 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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.

			June 30, 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)	$	61,328	$	(68)	$	274	$	206	$	—	$	108,368	$	(159)	$	424	$	265
2018-1 Ltd. (Apr-18)	122,190		(342)		965		623		—		181,136		(528)		1,268		740
2018-3 Ltd. (Oct-18)	244,257		(566)		1,522		956		—		302,563		(1,018)		2,496		1,478
2019-1 Ltd. (Mar-19)	134,972		(127)		988		861		—		181,324		(380)		5,807		5,427
2019-2 Ltd. (Apr-19)	383,737		(426)		5,323		4,897		—		398,316		(515)		3,998		3,483
2019-3 Ltd. (Jul-19)	296,466		(282)		2,154		1,872		—		409,859		(584)		3,190		2,606
2019-4 Ltd. (Oct-19)	312,668		(306)		4,702		4,396		—		411,954		(462)		4,759		4,297
2020-2 Ltd. (Sep-20)	151,543		(58)		1,331		1,273		442		217,766		(177)		1,984		1,807
2020-3 Ltd. (Nov-20)	303,011		(26)		4,388		4,362		10,779		348,818		(128)		5,793		5,665
2020-4 Ltd. (Dec-20)	124,672		23		1,267		1,290		5,900		176,826		(50)		1,630		1,580
2021-1 Ltd. (Mar-21)	519,641		(1,006)		2,771		1,765		48,841		568,986		(303)		3,283		2,980
2021-2 Ltd. (Jun-21)	492,837		(577)		3,505		2,928		85,717		522,807		281		4,124		4,405
2021-3 Ltd. (Sep-21)	507,873		(1,082)		2,878		1,796		131,518		507,873		(411)		3,446		3,035
2022-1 Ltd. (Jan-22)	283,500		(282)		2,020		1,738		33,260
Total	$	3,938,695	$	(5,125)	$	34,088	$	28,963	$	316,457	$	4,336,596	$	(4,434)	$	42,202	$	37,768

(1) Coverage from a separate panel of reinsurers remaining at June 30, 2022.

ARCH CAPITAL  37 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

12.    Other Comprehensive Income (Loss)

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):

		Amounts Reclassified from AOCI
	Consolidated Statement of Income	Three Months Ended				Six Months Ended
Details About	Line Item That Includes	June 30,				June 30,
AOCI Components	Reclassification	2022		2021		2022		2021
Unrealized appreciation (decline) on available-for-sale investments
	Net realized gains (losses)	$	(41,990)	$	64,914	$	(130,630)	$	66,918
	Provision for credit losses	(25,026)		896		(56,748)		(751)
	Total before tax	(67,016)		65,810		(187,378)		66,167
	Income tax (expense) benefit	9,306		(5,263)		27,390		(8,317)
	Net of tax	$	(57,710)	$	60,547	$	(159,988)	$	57,850

	Before Tax Amount		Tax Expense (Benefit)		Net of Tax Amount
Three Months Ended June 30, 2022
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(676,048)	$	(78,043)	$	(598,005)
Less reclassification of net realized gains (losses) included in net income	(67,016)		(9,306)		(57,710)
Foreign currency translation adjustments	(68,562)		(37)		(68,525)
Other comprehensive income (loss)	$	(677,594)	$	(68,774)	$	(608,820)
Three Months Ended June 30, 2021
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	91,057	$	12,486	$	78,571
Less reclassification of net realized gains (losses) included in net income	65,810		5,263		60,547
Foreign currency translation adjustments	6,392		187		6,205
Other comprehensive income (loss)	$	31,639	$	7,410	$	24,229
Six Months Ended June 30, 2022
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(1,460,938)	$	(178,578)	$	(1,282,360)
Less reclassification of net realized gains (losses) included in net income	(187,378)		(27,390)		(159,988)
Foreign currency translation adjustments	(71,127)		166		(71,293)
Other comprehensive income (loss)	$	(1,344,687)	$	(151,022)	$	(1,193,665)
Six Months Ended June 30, 2021
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(203,303)	$	(20,124)	$	(183,179)
Less reclassification of net realized gains (losses) included in net income	66,167		8,317		57,850
Foreign currency translation adjustments	(22,023)		356		(22,379)
Other comprehensive income (loss)	$	(291,493)	$	(28,085)	$	(263,408)

ARCH CAPITAL  38 2022 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

13.    Income Taxes

The Company’s income tax provision on income before income taxes, including income (loss) from operating affiliates, resulted in an effective tax rate of 5.3% for the six months ended June 30, 2022, compared to 7.0% for the six months ended June 30, 2021.

The Company’s effective tax rate, which is based upon the expected annual effective tax rate, may fluctuate from period to period based on the relative mix of income or loss reported by jurisdiction and the varying tax rates in each jurisdiction.

The Company had a net deferred tax asset of $411.1 million at June 30, 2022, compared to a net deferred tax asset of $194.0 million at December 31, 2021. The change is primarily a result of market value fluctuations in the investment portfolio. In addition, the Company paid $128.6 million and $141.1 million of income taxes for the six months ended June 30, 2022 and 2021, respectively.

14.    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 June 30, 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.

15.    Transactions with Related Parties

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 June 30, 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 became owned 40% by the Company, 30% by certain funds managed by Kelso and 30% by certain funds managed by Warburg, the Company entered into certain reinsurance transactions with Somers. For the six months ended June 30, 2022, the Company ceded premiums written related to such transactions of $424.6 million (which includes reinsurance transactions in force 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 June 30, 2022, reinsurance recoverable on unpaid and paid losses from Somers was $964.7 million, with a reinsurance balance payable to Somers of $358.4 million. See note 11, “Variable Interest Entities and Noncontrolling Interests,” for information about Somers.

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 June 30, 2022, the Company owns $35.0 million in aggregate principal amount of Somers Group Holdings Ltd’s 6.5% senior notes, due July 2, 2029 and approximately 6.6% of Somers’s preference shares.

ARCH CAPITAL  39 2022 SECOND QUARTER FORM 10-Q

ITEM 2.     MANAGEMENT’S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS OF OPERATIONS

The following is a discussion and analysis of our financial condition and results of operations. This should be read in conjunction with our consolidated financial statements included in Item 1 of this report and also our Management’s Discussion and Analysis of Financial Condition and Results of Operations contained in our Annual Report on Form 10-K for the year ended December 31, 2021 (“2021 Form 10-K”). In addition, readers should review “Risk Factors” set forth in Item 1A of Part I of our 2021 Form 10-K and “ITEM 1A—Risk Factors” of this Form 10-Q. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.

Arch Capital Group Ltd. (“Arch Capital” and, together with its subsidiaries, “Arch”, “we”, “our” or “us”) is a publicly listed Bermuda exempted company with approximately $15.1 billion in capital at June 30, 2022 and, through operations in Bermuda, the United States, Europe, Canada, Australia and Hong Kong, writes insurance, reinsurance and mortgage insurance on a worldwide basis.

		Page No.
Current Outlook		41
Financial Measures		41
Comments on Non-GAAP Measures		43
Results of Operations		45
	Insurance Segment	45
	Reinsurance Segment	48
	Mortgage Segment	50
	Corporate Segment	53
Critical Accounting Policies, Estimates and Recent Accounting Pronouncements		54
Financial Condition		54
Liquidity		60
Capital Resources and Other		60

ARCH CAPITAL  40 2022 SECOND QUARTER FORM 10-Q

CURRENT OUTLOOK

Our objective for 2022 remains the same, to deliver long term value for our shareholders. We are committed to agile cycle management predicated by a focus on risk-adjusted returns, and this commitment has enabled us to accelerate our growth through the deployment of meaningful capacity to our clients. We continue to execute our cycle management strategy by actively allocating capital to the sectors where rates allow for returns that are substantially higher than our cost of capital, as demonstrated by the strong underwriting performance across each of our three segments.

Inflation continues to be a focus for our industry. We proactively analyze available data and incorporate emerging trends into our pricing and reserving. We believe that this discipline, coupled with increases in future investment returns and prudent reserving, mitigate inflation’s impact. For our mortgage operations, inflation mainly has a positive effect as it increases homeowner equity, which can potentially mitigate future losses.

The 2022 second quarter reflected growth across most property and casualty lines as we remain in a growth phase of the underwriting cycle. 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 time-tested strategy of protecting capital through soft markets and increasing our writings in hard markets gives us the best chance to generate superior risk adjusted returns over time. 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. Rate increases remain above the long-term loss cost trends and have spread to more lines than last year. In specialty 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. Our U.S. operations benefited from growth in professional liability, including cyber, as well as travel where we believe relative returns are attractive. Our specialty international insurance business, which includes our Lloyd's and U.K. regional businesses, delivered strong growth in the quarter with net premium written up 23%, primarily due to specialty, casualty and property.

In reinsurance, the emphasis remains on quota share treaties over excess of loss reinsurance. This strategy allows us to participate in the rate increases on primary insurance while improving the balance between risk and return. We remained disciplined in property catastrophe exposure and we will

deploy more capital to the line if expected returns improve meaningfully. The June 1 and July 1 renewals showed a property catastrophe market in transition and we are cautiously optimistic that this momentum could continue into the next year.

Our mortgage business continues to deliver the consistent underwriting results we projected when we began building it a decade ago. In our U.S. primary mortgage operations, delinquencies continue to trend to historically low levels, and cures on delinquent mortgages in our portfolio resulted in favorable prior year development in the quarter. The increase in mortgage interest rates is a steeper rise than we have seen in decades and have dramatically curtailed refinancing. Rising rates also mean that persistency is increasing, which allowed us to grow our U.S. primary mortgage insurance in force to an all-time high of $292 billion. This should result in a more stable base of premium income to help drive underwriting income in future periods. The credit quality of homebuyers remains excellent and we believe our portfolio is well positioned for a variety of economic scenarios. Outside of the U.S., we increased our writings in Australia as a result of our acquisition of Westpac’s LMI business in the 2021 third quarter.

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 $4.3 billion of aggregate reinsurance coverage at June 30, 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 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 $31.37 at June 30, 2022,

ARCH CAPITAL  41 2022 SECOND QUARTER FORM 10-Q

compared to $32.18 at March 31, 2022 and $32.02 at June 30, 2021. The 2.5% decrease in book value per share for the 2022 second quarter reflected negative total return on investments driven by rising interest rates on fixed maturities and mark-to-market impacts on our equity securities, which were partially offset by strong underwriting returns.

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 the average of beginning and ending common shareholders’ equity available to Arch during the period. After-tax operating income available to Arch common shareholders, a non-GAAP financial measure as defined in Regulation G, 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 investment funds 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 common shareholders. See “Comment on Non-GAAP Financial Measures.”

Our annualized net income return on average common equity was 13.3% for the 2022 second quarter, compared to 21.2% for the 2021 second quarter, and 9.5% for the six months ended June 30, 2022, compared to 17.4% for the 2021 period. Our Operating ROAE was 17.1% for the 2022 second quarter, compared to 13.0% for the 2021 second quarter, and 15.3% for the six months ended June 30, 2022, compared to 10.3% for the 2021 period. The 2022 periods reflected strong underwriting returns and a lower level of catastrophic activity, while the 2021 periods reflected lower underwriting returns due to an increased level of catastrophic activity and higher income from operating affiliates.

Total Return on Investments

Total return on investments includes investment income, equity in net income or loss of investment funds accounted for using the equity method, net realized gains and losses (excluding changes in the allowance for credit losses on non-investment related financial assets) and the change in unrealized gains and losses generated by Arch’s investment portfolio. Total return is calculated on a pre-tax basis and before investment expenses 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. The following table summarizes our total return compared to the benchmark return against which we measured our portfolio during the periods. See “Comment on Non-GAAP Financial Measures.”

	Arch Portfolio		Benchmark Return
Pre-tax total return (before investment expenses):
2022 Second Quarter	(3.02)	%	(5.37)	%
2021 Second Quarter	1.58	%	1.80	%
Six Months Ended June 30, 2022	(6.00)	%	(9.13)	%
Six Months Ended June 30, 2021	1.39	%	1.28	%

Total return for the 2022 periods reflected rising interest rates on fixed maturities and mark-to-market impacts on our equity securities. We continue to maintain a relative short duration on our portfolio of 2.94 years at June 30, 2022.

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 June 30, 2022, the benchmark return index had an average credit quality of “Aa3” by Moody’s Investors Service (“Moody’s”), and an estimated duration of 3.34 years.

ARCH CAPITAL  42 2022 SECOND QUARTER FORM 10-Q

The benchmark return index included weightings to the following indices:

	%
ICE BoAML 1-5 Year A - AAA U.S. Corporate Index	13.00	%
ICE BoAML 5-10 Year A - AAA U.S. Corporate Index	11.00
ICE BoAML 1-5 Year U.S. Treasury Index	11.00
MSCI ACWI Net Total Return USD Index	9.30
ICE BoAML 1-10 Year BBB U.S. Corporate Index	5.00
JPM CLOIE Investment Grade	5.00
S&P/LSTA Leveraged Loan Total Return Index	4.965
ICE BoAML U.S. Mortgage Backed Securities Index	4.00
ICE BoAML AAA US Fixed Rate CMBS	4.00
ICE BoAML 1-5 Year U.K. Gilt Index	4.00
ICE BoAML German Government 1-10 Year Index	3.50
ICE BoAML 0-3 Year U.S. Treasury Index	3.25
ICE BoAML 5-10 Year U.S. Treasury Index	3.00
ICE BoAML 1-10 Year U.S. Municipal Securities Index	3.00
Bloomberg Barclays ABS Aaa Index	3.00
ICE BoAML 1-5 Year Australia Government Index	2.75
ICE BoAML U.S. High Yield Constrained Index	2.50
ICE BoAML 1-5 Year Canada Government Index	2.00
ICE BofA CCC and Lower US High Yield Constrained Index	1.38
Bloomberg Barclays Global High Yield Index	1.38
S&P DJ Global ex-US Select Real Estate Securities Net Index	0.825
FTSE Nareit All Mortgage Capped Index Total Return USD	0.825
Bloomberg Barclays CMBS: Erisa Eligible Unhedged USD	0.825
ICE BoAML 15+ Year Canada Government Index	0.50
Total	100.00	%

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 investment funds 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 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 investment funds accounted for using the equity method, net foreign exchange gains or losses, transaction costs and other and loss on redemption of preferred shares 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 investment funds accounted for using the equity method and net foreign exchange gains or losses are an integral part of our operations, the decision to realize investment gains or losses, the recognition of the change in the carrying value of investments accounted for using the fair value option in net realized gains or losses, the recognition of net impairment losses, the recognition of equity in net income or loss of investment funds accounted for using the equity method and the recognition of foreign exchange gains or losses 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 our 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 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 investment funds 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 some of Arch’s preferred shares had no impact on shareholders' equity or cash flows. Due to these reasons, we exclude net realized gains or losses, equity in net income or loss of investment funds 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.

ARCH CAPITAL  43 2022 SECOND QUARTER FORM 10-Q

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 which 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. The ‘other’ segment includes the results of Somers through June 30, 2021. 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,” of the notes accompanying our consolidated financial statements, 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 through June 30, 2021, in accordance with Regulation G, is shown in note 4, “Segment Information” to our consolidated financial statements.

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 intangibles and, accordingly, investment income and other non-underwriting related items are not allocated to each underwriting segment. The ‘other’ segment includes the results of Somers through June 30, 2021.

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 Group Holdings Ltd. Somers Group Holdings Ltd. is the parent of Somers Re Ltd., a multi-line Bermuda reinsurance

company (together with Somers Group Holdings Ltd., “Somers”). Pursuant to GAAP, Somers was 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 contemplated by the Merger Agreement and the related Greysbridge equity financing closed on July 1, 2021. In connection therewith and effective July 1, 2021, Somers became wholly owned by Greysbridge, and Greysbridge became 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 11, “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 investment funds accounted for using the equity method, net realized gains and losses (excluding changes in the allowance for credit losses on non-investment related financial assets) and the change in unrealized gains and 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, and compares the return generated by our investment portfolio against benchmark returns during the periods.

ARCH CAPITAL  44 2022 SECOND QUARTER FORM 10-Q

RESULTS OF OPERATIONS

The following table summarizes our consolidated financial data, including a reconciliation of net income or loss available to Arch common shareholders to after-tax operating income or loss available to Arch common shareholders.

	Three Months Ended				Six Months Ended
	June 30,				June 30,
	2022		2021		2022		2021
Net income available to Arch common shareholders	$	394,160	$	663,820	$	579,776	$	1,091,573
Net realized (gains) losses	266,579		(167,438)		558,993		(272,989)
Equity in net (income) loss of investment funds accounted for using the equity method	(58,061)		(122,186)		(94,366)		(193,872)
Net foreign exchange (gains) losses	(87,797)		17,888		(91,652)		(3,444)
Transaction costs and other	261		(1,421)		658		(147)
Income tax expense (1)	(8,646)		16,553		(24,914)		25,864
After-tax operating income available to Arch common shareholders	$	506,496	$	407,216	$	928,495	$	646,985
Beginning common shareholders’ equity	$	12,089,589	$	12,316,472	$	12,715,896	$	12,325,886
Ending common shareholders’ equity	$	11,587,566	$	12,706,072	$	11,587,566	$	12,706,072
Average common shareholders’ equity	$	11,838,578	$	12,511,272	$	12,151,731	$	12,515,979
Annualized net income return on average common equity %	13.3		21.2		9.5		17.4
Annualized operating return on average common equity %	17.1		13.0		15.3		10.3

(1)    Income tax expense on net realized gains or losses, equity in net income or loss of investment funds 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.

Segment Information

We classify our businesses into three underwriting segments — insurance, reinsurance and mortgage — and two other 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, the 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:

	Three Months Ended June 30,
	2022			2021			%  Change
Gross premiums written	$	1,705,167		$	1,368,867		24.6
Premiums ceded	(476,910)			(405,312)
Net premiums written	1,228,257			963,555			27.5
Change in unearned premiums	(126,113)			(98,128)
Net premiums earned	1,102,144			865,427			27.4
Losses and loss adjustment expenses	(629,759)			(545,880)
Acquisition expenses	(213,688)			(136,852)
Other operating expenses	(161,088)			(133,342)
Underwriting income (loss)	$	97,609		$	49,353		97.8
Underwriting Ratios							% Point Change
Loss ratio	57.1		%	63.1		%	(6.0)
Acquisition expense ratio	19.4		%	15.8		%	3.6
Other operating expense ratio	14.6		%	15.4		%	(0.8)
Combined ratio	91.1		%	94.3		%	(3.2)

ARCH CAPITAL  45 2022 SECOND QUARTER FORM 10-Q

	Six Months Ended June 30,
	2022			2021			% Change
Gross premiums written	$	3,424,772		$	2,784,753		23.0
Premiums ceded	(989,619)			(826,359)
Net premiums written	2,435,153			1,958,394			24.3
Change in unearned premiums	(306,313)			(273,493)
Net premiums earned	2,128,840			1,684,901			26.3
Losses and loss adjustment expenses	(1,230,498)			(1,081,627)
Acquisition expenses	(409,338)			(265,074)
Other operating expenses	(327,913)			(270,455)
Underwriting income (loss)	$	161,091		$	67,745		137.8
Underwriting Ratios							% Point Change
Loss ratio	57.8		%	64.2		%	(6.4)
Acquisition expense ratio	19.2		%	15.7		%	3.5
Other operating expense ratio	15.4		%	16.1		%	(0.7)
Combined ratio	92.4		%	96.0		%	(3.6)

The insurance segment consists of our insurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include:

Construction and national accounts: primary and excess casualty coverages to middle and large accounts in the construction industry and a wide range of products for middle and large national accounts, specializing in loss sensitive primary casualty insurance programs (including large deductible, self-insured retention and retrospectively rated programs).

Excess and surplus casualty: primary and excess casualty insurance coverages, including middle market energy business, and contract binding, which primarily provides casualty coverage through a network of appointed agents to small and medium risks.

Lenders products: 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.

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 package policies, underwriting workers’ compensation and umbrella liability business in support of desirable package programs, targeting program managers with unique expertise and niche products offering general

liability, commercial automobile, inland marine and property business with minimal catastrophe exposure.

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, war, specie and liability. Aviation and standalone terrorism are also offered.

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.

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 and commercial surety coverages, including contract bonds (payment and performance bonds) primarily for medium and large contractors and commercial surety bonds for Fortune 1,000 companies and smaller transaction business programs.

Premiums Written.

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

	Three Months Ended June 30,
	2022			2021
	Amount		%	Amount		%
Professional lines	$	349,402	28.4	$	254,961	26.5
Property, energy, marine and aviation	258,765		21.1	207,762		21.6
Programs	163,339		13.3	149,373		15.5
Excess and surplus casualty	120,509		9.8	74,346		7.7
Travel, accident and health	105,970		8.6	71,071		7.4
Construction and national accounts	87,615		7.1	77,579		8.1
Lenders products	36,042		2.9	40,386		4.2
Other	106,615		8.7	88,077		9.1
Total	$	1,228,257	100.0	$	963,555	100.0

2022 Second Quarter versus 2021 Period. Gross premiums written by the insurance segment in the 2022 second quarter were 24.6% higher than in the 2021 second quarter, while net premiums written were 27.5% higher. The higher level of net premiums written reflected increases in most lines of business, due in part to rate increases, new business opportunities and growth in existing accounts.

ARCH CAPITAL  46 2022 SECOND QUARTER FORM 10-Q

	Six Months Ended June 30,
	2022			2021
	Amount		%	Amount		%
Professional lines	$	697,243	28.6	$	493,207	25.2
Property, energy, marine and aviation	468,986		19.3	378,260		19.3
Programs	292,740		12.0	307,774		15.7
Excess and surplus casualty	220,798		9.1	159,939		8.2
Travel, accident and health	271,302		11.1	163,377		8.3
Construction and national accounts	213,738		8.8	212,371		10.8
Lenders products	61,274		2.5	75,246		3.8
Other	209,072		8.6	168,220		8.6
Total	$	2,435,153	100.0	$	1,958,394	100.0

Six Months Ended June 30, 2022 versus 2021 period. Gross premiums written by the insurance segment for the six months ended June 30, 2022 were 23.0% higher than in the 2021 period, while net premiums written were 24.3% higher than in the 2021 period. 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:

	Three Months Ended June 30,
	2022			2021
	Amount		%	Amount		%
Professional lines	$	314,115	28.5	$	214,098	24.7
Property, energy, marine and aviation	192,410		17.5	167,716		19.4
Programs	148,681		13.5	118,974		13.7
Excess and surplus casualty	98,369		8.9	72,899		8.4
Travel, accident and health	130,185		11.8	62,610		7.2
Construction and national accounts	87,084		7.9	95,849		11.1
Lenders products	27,594		2.5	46,396		5.4
Other	103,706		9.4	86,885		10.0
Total	$	1,102,144	100.0	$	865,427	100.0

	Six Months Ended June 30,
	2022			2021
	Amount		%	Amount		%
Professional lines	$	603,928	28.4	$	413,769	24.6
Property, energy, marine and aviation	378,065		17.8	324,975		19.3
Programs	288,490		13.6	231,814		13.8
Excess and surplus casualty	189,130		8.9	148,266		8.8
Travel, accident and health	234,815		11.0	112,276		6.7
Construction and national accounts	173,232		8.1	198,520		11.8
Lenders products	58,182		2.7	86,477		5.1
Other	202,998		9.5	168,804		10.0
Total	$	2,128,840	100.0	$	1,684,901	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 reflect changes in net premiums written over the previous five quarters. Net premiums earned in the 2022 second quarter were 27.4% higher than in the 2021 second quarter. Net premiums earned for the six months ended June 30, 2022 were 26.3% higher than in the 2021 period.

Losses and Loss Adjustment Expenses.

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

	Three Months Ended				Six Months Ended
	June 30,				June 30,
	2022		2021		2022		2021
Current year	57.7	%	63.6	%	58.5	%	64.7	%
Prior period reserve development	(0.6)	%	(0.5)	%	(0.7)	%	(0.5)	%
Loss ratio	57.1	%	63.1	%	57.8	%	64.2	%

Current Year Loss Ratio.

2022 Second Quarter versus 2021 Period. The insurance segment’s current year loss ratio in the 2022 second quarter was 5.9 points lower than in the 2021 second quarter. The 2022 second quarter loss ratio reflected 1.2 points of current year catastrophic activity, compared to 3.2 points of catastrophic activity for the 2021 second quarter.

Six Months Ended June 30, 2022 versus 2021 Period. The insurance segment’s current year loss ratio for the six months ended June 30, 2022 was 6.2 points lower than in the 2021 period and reflected 2.1 points of current year catastrophic activity, primarily related to Russia’s invasion of Ukraine and other natural catastrophes, compared to 4.1 points in the 2021 period. The balance of the change in the 2022 loss ratios resulted, in part, from changes in mix of business.

ARCH CAPITAL  47 2022 SECOND QUARTER FORM 10-Q

Prior Period Reserve Development.

The insurance segment’s net favorable development was $6.7 million, or 0.6 points, for the 2022 second quarter, compared to $4.0 million, or 0.5 points, for the 2021 second quarter, and $14.0 million, or 0.7 points, for the six months ended June 30, 2022, compared to $8.1 million, or 0.5 points, for the 2021 period. See note 5, “Reserve for Losses and Loss Adjustment Expenses,” to our consolidated financial statements for information about the insurance segment’s prior year reserve development.

Underwriting Expenses.

2022 Second Quarter versus 2021 Period. The insurance segment’s underwriting expense ratio was 34.0% in the 2022 second quarter, compared to 31.2% in the 2021 second quarter. The increase in the 2022 second quarter was primarily due to higher gross commission ratios, growth in lines with higher acquisition costs, such as travel, and targeted personnel expansion to support our growth. This increase was partially offset by a higher level of net premiums earned.

Six Months Ended June 30, 2022 versus 2021 period. The insurance segment’s underwriting expense ratio was 34.6% for the six months ended June 30, 2022, compared to 31.8% for the 2021 period, 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:

	Three Months Ended June 30,
	2022			2021			%  Change
Gross premiums written	$	1,793,398		$	1,358,020		32.1
Premiums ceded	(630,764)			(433,288)
Net premiums written	1,162,634			924,732			25.7
Change in unearned premiums	(234,635)			(187,708)
Net premiums earned	927,999			737,024			25.9
Other underwriting income (loss)	4,526			1,053
Losses and loss adjustment expenses	(537,578)			(463,823)
Acquisition expenses	(189,494)			(133,585)
Other operating expenses	(66,053)			(44,695)
Underwriting income (loss)	$	139,400		$	95,974		45.2
Underwriting Ratios							% Point Change
Loss ratio	57.9		%	62.9		%	(5.0)
Acquisition expense ratio	20.4		%	18.1		%	2.3
Other operating expense ratio	7.1		%	6.1		%	1.0
Combined ratio	85.4		%	87.1		%	(1.7)

	Six Months Ended June 30,
	2022			2021			% Change
Gross premiums written	$	3,512,340		$	2,829,080		24.2
Premiums ceded	(1,210,582)			(905,236)
Net premiums written	2,301,758			1,923,844			19.6
Change in unearned premiums	(569,359)			(541,920)
Net premiums earned	1,732,399			1,381,924			25.4
Other underwriting income	5,362			(145)
Losses and loss adjustment expenses	(992,278)			(948,693)
Acquisition expenses	(361,490)			(251,610)
Other operating expenses	(135,829)			(105,209)
Underwriting income (loss)	$	248,164		$	76,267		225.4
Underwriting Ratios							% Point Change
Loss ratio	57.3		%	68.7		%	(11.4)
Acquisition expense ratio	20.9		%	18.2		%	2.7
Other operating expense ratio	7.8		%	7.6		%	0.2
Combined ratio	86.0		%	94.5		%	(8.5)

The reinsurance segment consists of our 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 or aggregation of losses from 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,

ARCH CAPITAL  48 2022 SECOND QUARTER FORM 10-Q

explosion, collapse, riot, vandalism, wind, tornado, flood and earthquake. Business is assumed on either a treaty basis 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.

Premiums Written.

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

	Three Months Ended June 30,
	2022			2021
	Amount		%	Amount		%
Other Specialty	$	434,710	37.4	$	296,325	32.0
Property excluding property catastrophe	299,042		25.7	249,101		26.9
Casualty	212,724		18.3	225,890		24.4
Property catastrophe	154,451		13.3	87,642		9.5
Marine and aviation	35,129		3.0	50,248		5.4
Other	26,578		2.3	15,526		1.7
Total	$	1,162,634	100.0	$	924,732	100.0

2022 Second Quarter versus 2021 Period. Gross premiums written by the reinsurance segment in the 2022 second quarter were 32.1% higher than in the 2021 second quarter, while net premiums written were 25.7% higher. The growth in net premiums written reflected increases in other specialty, property catastrophe and property excluding property catastrophe lines, primarily related to rate increases, new business opportunities and growth in existing accounts.

	Six Months Ended June 30,
	2022			2021
	Amount		%	Amount		%
Other Specialty	$	798,544	34.7	$	580,656	30.2
Property excluding property catastrophe	594,461		25.8	541,934		28.2
Casualty	479,179		20.8	444,146		23.1
Property catastrophe	283,422		12.3	204,849		10.6
Marine and aviation	86,946		3.8	111,886		5.8
Other	59,206		2.6	40,373		2.1
Total	$	2,301,758	100.0	$	1,923,844	100.0

Six Months Ended June 30, 2022 versus 2021 period. Gross premiums written by the reinsurance segment for the six months ended June 30, 2022 were 24.2% higher than in the 2021 period, while net premiums written were 19.6% higher than in the 2021 period. The increase in net premiums written reflected growth in other specialty, primarily due to new business and rate increases..

Net Premiums Earned.

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

	Three Months Ended June 30,
	2022			2021
	Amount		%	Amount		%
Other Specialty	$	284,321	30.6	$	211,817	28.7
Property excluding property catastrophe	266,545		28.7	202,780		27.5
Casualty	214,714		23.1	183,846		24.9
Property catastrophe	94,679		10.2	76,167		10.3
Marine and aviation	41,768		4.5	42,773		5.8
Other	25,972		2.8	19,641		2.7
Total	$	927,999	100.0	$	737,024	100.0

	Six Months Ended June 30,
	2022			2021
	Amount		%	Amount		%
Other Specialty	$	515,939	29.8	$	375,715	27.2
Property excluding property catastrophe	499,074		28.8	390,562		28.3
Casualty	412,572		23.8	332,877		24.1
Property catastrophe	171,755		9.9	164,178		11.9
Marine and aviation	83,960		4.8	82,881		6.0
Other	49,099		2.8	35,711		2.6
Total	$	1,732,399	100.0	$	1,381,924	100.0

Net 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. Net premiums earned by the reinsurance segment in the 2022 second quarter were 25.9% higher than in the 2021 second quarter, and reflect changes in net premiums written over the previous five quarters.

Other Underwriting Income (Loss).

Other underwriting income for the 2022 second quarter was $4.5 million, compared to $1.1 million for the 2021 second quarter, and $5.4 million for the six months ended June 30, 2022, compared to a loss of $0.1 million for the 2021 period.

Losses and Loss Adjustment Expenses.

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

	Three Months Ended				Six Months Ended
	June 30,				June 30,
	2022		2021		2022		2021
Current year	62.9	%	65.7	%	61.9	%	72.1	%
Prior period reserve development	(5.0)	%	(2.8)	%	(4.6)	%	(3.4)	%
Loss ratio	57.9	%	62.9	%	57.3	%	68.7	%

ARCH CAPITAL  49 2022 SECOND QUARTER FORM 10-Q

Current Year Loss Ratio.

2022 Second Quarter versus 2021 Period. The reinsurance segment’s current year loss ratio in the 2022 second quarter was 2.8 points lower than in the 2021 second quarter. The 2022 second quarter loss ratio reflected 7.5 points of current year catastrophic activity, primarily due to a series of natural events outside the U.S. The 2021 second quarter included 2.6 points of catastrophic activity, including winter storms Uri and Viola as well as other minor global events.

Six Months Ended June 30, 2022 versus 2021 Period. The reinsurance segment’s current year loss ratio for the six months ended June 30, 2022 was 10.2 points lower than in the 2021 period and reflected 7.0 points of current year catastrophic activity, primarily related to a series of natural events outside the U.S. and Russia’s invasion of Ukraine, compared to 12.9 points in the 2021 period.

Prior Period Reserve Development.

The reinsurance segment’s net favorable development was $46.4 million, or 5.0 points, for the 2022 second quarter, compared to $20.5 million, or 2.8 points, for the 2021 second quarter, and $78.9 million, or 4.6 points, for the six months ended June 30, 2022, compared to $47.3 million, or 3.4 points, for the 2021 period. See note 5, “Reserve for Losses and Loss Adjustment Expenses,” to our consolidated financial statements for information about the reinsurance segment’s prior year reserve development.

Underwriting Expenses.

2022 Second Quarter versus 2021 Period. The underwriting expense ratio for the reinsurance segment was 27.5% in the 2022 second quarter, compared to 24.2% in the 2021 second quarter, with the increase primarily resulting from growth in lines with higher acquisition costs and targeted personnel expansion to support our growth. This increase was partially offset by a higher level of net premiums earned.

Six Months Ended June 30, 2022 versus 2021 period. The underwriting expense ratio for the reinsurance segment was 28.7% for the six months ended June 30, 2022, compared to 25.8% for the 2021 period. The comparison of the underwriting expense ratios also reflected changes in the mix and type of business and a higher level of net premiums earned for the 2022 period.

Mortgage Segment 

Our mortgage operations include U.S. and international mortgage insurance and reinsurance operations as well as participation in GSE credit risk-sharing transactions.

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

	Three Months Ended June 30,
	2022			2021			% Change
Gross premiums written	$	371,896		$	391,511		(5.0)
Premiums ceded	(78,148)			(55,665)
Net premiums written	293,748			335,846			(12.5)
Change in unearned premiums	1,884			(1,625)
Net premiums earned	295,632			334,221			(11.5)
Other underwriting income	(1,556)			4,148
Losses and loss adjustment expenses	64,681			(9,880)
Acquisition expenses	(10,137)			(30,117)
Other operating expenses	(50,251)			(48,312)
Underwriting income	$	298,369		$	250,060		19.3
Underwriting Ratios							% Point Change
Loss ratio	(21.9)		%	3.0		%	(24.9)
Acquisition expense ratio	3.4		%	9.0		%	(5.6)
Other operating expense ratio	17.0		%	14.5		%	2.5
Combined ratio	(1.5)		%	26.5		%	(28.0)

	Six Months Ended June 30,
	2022			2021			% Change
Gross premiums written	$	736,735		$	782,757		(5.9)
Premiums ceded	(154,867)			(111,716)
Net premiums written	581,868			671,041			(13.3)
Change in unearned premiums	3,301			(503)
Net premiums earned	585,169			670,538			(12.7)
Other underwriting income	3,505			11,045
Losses and loss adjustment expenses	119,285			(73,569)
Acquisition expenses	(20,650)			(60,199)
Other operating expenses	(103,593)			(97,443)
Underwriting income	$	583,716		$	450,372		29.6
Underwriting Ratios							% Point Change
Loss ratio	(20.4)		%	11.0		%	(31.4)
Acquisition expense ratio	3.5		%	9.0		%	(5.5)
Other operating expense ratio	17.7		%	14.5		%	3.2
Combined ratio	0.8		%	34.5		%	(33.7)

ARCH CAPITAL  50 2022 SECOND QUARTER FORM 10-Q

Premiums Written.

The following tables set forth our mortgage segment’s net premiums written by underwriting location:

	Three Months Ended June 30,
	2022			2021
	Amount		%	Amount		%
Underwriting location:
United States	$	201,166	68.5	$	234,645	69.9
Other	92,582		31.5	101,201		30.1
Total	$	293,748	100.0	$	335,846	100.0

2022 Second Quarter versus 2021 Period. Gross premiums written by the mortgage segment in the 2022 second quarter were 5.0% lower than in the 2021 second quarter, while net premiums written were 12.5% lower. Net premiums written for the 2022 second quarter reflected a higher level of premiums ceded than in the 2021 second quarter.

	Six Months Ended June 30,
	2022			2021
	Amount		%	Amount		%
Underwriting location:
United States	$	402,316	69.1	$	482,174	71.9
Other	179,552		30.9	188,867		28.1
Total	$	581,868	100.0	$	671,041	100.0

Six Months Ended June 30, 2022 versus 2021 Period. Gross premiums written by the mortgage segment for the six months ended June 30, 2022 were 5.9% lower than in the 2021 period. The reduction in gross premiums written primarily reflected lower U.S. primary mortgage insurance single premium volume and a decrease in monthly premiums. Net premiums written for the six months ended June 30, 2022 were 13.3% lower than in the 2021 period and reflected a higher level of premiums ceded than in the 2021 period.

The persistency rate, which 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, was 71.3% for the Arch MI U.S. portfolio of mortgage insurance policies at June 30, 2022, reflecting a lower level of mortgage refinancing activity, compared to 62.4% at December 31, 2021.

The following tables provide details on the new insurance written (“NIW”) generated by Arch MI U.S. NIW represents the original principal balance of all loans that received coverage during the period.

(U.S. Dollars in millions)	Three Months Ended June 30,
	2022			2021
	Amount		%	Amount		%
Total new insurance written (NIW) (1)	$	23,499		$	28,372
Credit quality (FICO):
>=740	$	16,121	68.6	$	19,240	67.8
680-739	6,800		28.9	8,113		28.6
620-679	576		2.5	1,019		3.6
<620	2		—	—		—
Total	$	23,499	100.0	$	28,372	100.0
Loan-to-value (LTV):
95.01% and above	$	1,195	5.1	$	1,484	5.2
90.01% to 95.00%	13,290		56.6	13,936		49.1
85.01% to 90.00%	6,591		28.0	8,675		30.6
85.00% and below	2,423		10.3	4,277		15.1
Total	$	23,499	100.0	$	28,372	100.0
Monthly vs. single:
Monthly	$	22,872	97.3	$	26,725	94.2
Single	627		2.7	1,647		5.8
Total	$	23,499	100.0	$	28,372	100.0
Purchase vs. refinance:
Purchase	$	23,059	98.1	$	25,010	88.2
Refinance	440		1.9	3,362		11.8
Total	$	23,499	100.0	$	28,372	100.0

(1)Represents the original principal balance of all loans that received coverage during the period.

ARCH CAPITAL  51 2022 SECOND QUARTER FORM 10-Q

(U.S. Dollars in millions)	Six Months Ended June 30,
	2022			2021
	Amount		%	Amount		%
Total new insurance written (NIW) (1)	$	43,514		$	55,391
Credit quality (FICO):
>=740	$	29,273	67.3	$	37,058	66.9
680-739	13,054		30.0	16,531		29.8
620-679	1,182		2.7	1,802		3.3
<620	5		—	—		—
Total	$	43,514	100.0	$	55,391	100.0
Loan-to-value (LTV):
95.01% and above	$	2,291	5.3	$	3,092	5.6
90.01% to 95.00%	24,068		55.3	26,224		47.3
85.01% to 90.00%	12,324		28.3	16,987		30.7
85.01% and below	4,831		11.1	9,088		16.4
Total	$	43,514	100.0	$	55,391	100.0
Monthly vs. single:
Monthly	$	42,073	96.7	$	51,714	93.4
Single	1,441		3.3	3,677		6.6
Total	$	43,514	100.0	$	55,391	100.0
Purchase vs. refinance:
Purchase	$	42,216	97.0	$	45,515	82.2
Refinance	1,298		3.0	9,876		17.8
Total	$	43,514	100.0	$	55,391	100.0

Net Premiums Earned.

The following tables set forth our mortgage segment’s net premiums earned by underwriting location:

	Three Months Ended June 30,
	2022			2021
	Amount		%	Amount		%
Underwriting location:
United States	$	209,200	70.8	$	248,388	74.3
Other	86,432		29.2	85,833		25.7
Total	$	295,632	100.0	$	334,221	100.0

2022 Second Quarter versus 2021 Period. Net premiums earned for the 2022 second quarter were 11.5% lower than in the 2021 second quarter, and reflected a lower level of earnings from single premium policy terminations and a decline in monthly premiums.

	Six Months Ended June 30,
	2022			2021
	Amount		%	Amount		%
Underwriting location:
United States	$	418,725	71.6	$	510,938	76.2
Other	166,444		28.4	159,600		23.8
Total	$	585,169	100.0	$	670,538	100.0

Six Months Ended June 30, 2022 versus 2021 Period. For the six months ended June 30, 2022, net premiums earned were 12.7% lower than in the 2021 period, and reflected a lower level of earnings from single premium policy terminations and a decline in monthly premiums.

Other Underwriting Income (Loss).

Other underwriting income or loss, which is primarily related to GSE credit risk-sharing and our whole mortgage loan purchase and sell program was a loss of $1.6 million for the 2022 second quarter, compared to an income of $4.1 million for the 2021 second quarter.

Losses and Loss Adjustment Expenses.

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

	Three Months Ended				Six Months Ended
	June 30,				June 30,
	2022		2021		2022		2021
Current year	18.0	%	15.9	%	17.2	%	19.1	%
Prior period reserve development	(39.9)	%	(12.9)	%	(37.6)	%	(8.1)	%
Loss ratio	(21.9)	%	3.0	%	(20.4)	%	11.0	%

Current Year Loss Ratio.

2022 Second Quarter versus 2021 Period. The mortgage segment’s current year loss ratio was 2.1 points higher in the 2022 second quarter than in the 2021 second quarter. The higher current year loss ratio for the 2022 period reflected a lower level of net premiums earned in the U.S. primary mortgage insurance business.

Six Months Ended June 30, 2022 versus 2021 Period. The mortgage segment’s current year loss ratio was 1.9 points lower for the six months ended June 30, 2022 than for the 2021 period. The lower current year loss ratio for the 2022 period reflected lower delinquencies.

Prior Period Reserve Development.

The mortgage segment’s net favorable development was $118.1 million, or 39.9 points, for the 2022 second quarter, compared to $43.1 million, or 12.9 points, for the 2021 second quarter, and $220.2 million, or 37.6 points, for the six months ended June 30, 2022, compared to $54.0 million, or 8.1 points, for the 2021 period. See note 5, “Reserve for Losses and Loss Adjustment Expenses,” to our consolidated financial statements for information about the mortgage segment’s prior year reserve development.

Underwriting Expenses.

2022 Second Quarter versus 2021 Period. The underwriting expense ratio for the mortgage segment was 20.4% in the 2022 second quarter, compared to 23.5% in the 2021 second quarter, 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  52 2022 SECOND QUARTER FORM 10-Q

Six Months Ended June 30, 2022 versus 2021 period. The underwriting expense ratio for the mortgage segment was 21.2% for the six months ended June 30, 2022, compared to 23.5% for the 2021 period, 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.

Corporate Segment

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 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:

	Three Months Ended				Six Months Ended
	June 30,				June 30,
	2022		2021		2022		2021
Fixed maturities	$	105,342	$	77,709	$	187,395	$	156,726
Equity securities	6,121		8,282		12,359		13,932
Short-term investments	4,120		972		6,695		1,616
Other (1)	7,984		21,026		20,060		36,585
Gross investment income	123,567		107,989		226,509		208,859
Investment expenses (2)	(17,175)		(18,559)		(39,681)		(40,700)
Net investment income	$	106,392	$	89,430	$	186,828	168,159

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

(2)    Investment expenses were approximately 0.27% of average invested assets for the 2022 second quarter, compared to 0.30% for the 2021 second quarter, and 0.31% for the six months ended June 30, 2022, compared to 0.32% for the 2021 period.

The higher level of net investment income for the 2022 period, primarily related to higher yields available in the financial market. The pre-tax investment income yield, calculated based on amortized cost and on an annualized basis, was 1.76% for the 2022 second quarter, compared to 1.47% for the 2021 second quarter, and 1.54% for the six

months ended June 30, 2022, compared to 1.40% for the 2021 period.

Corporate Expenses.

Corporate expenses were $27.4 million for the 2022 second quarter, compared to $17.2 million for the 2021 second quarter, and $59.3 million for the six months ended June 30, 2022, compared to $40.6 million for the 2021 period. The increase in corporate expenses was primarily due to higher incentive compensation costs.

Other Income (Losses)

Other loss for the 2022 second quarter was $11.8 million, compared to income of $6.9 million for the 2021 second quarter, and a loss of $20.8 million for the six months ended June 30, 2022, compared to income of $5.1 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.

Transaction Costs and Other.

Transaction costs and other were $0.3 million for the 2022 second quarter, compared to a benefit of $1.4 million for the 2021 second quarter, and an expense of $0.7 million for the six months ended June 30, 2022, compared to a benefit of $0.2 million for the 2021 period. Amounts in the 2022 and 2021 periods reflect acquisitions activity for the respective periods.

Amortization of Intangible Assets.

Amortization of intangible assets for the 2022 second quarter was $27.2 million, compared to $14.4 million for the 2021 second quarter, and $54.4 million for the six months ended June 30, 2022, compared to $28.8 million for the 2021 period. Amounts in 2022 and 2021 period primarily attributed 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.

Interest Expense.

Interest expense was $32.8 million for the 2022 second quarter, compared to the $31.4 million for the 2021 second quarter, and $65.5 million for the six months ended June 30, 2022, consistent with $65.6 million for the 2021 period. Interest expense primarily reflects amounts related to our outstanding senior notes.

Net Realized Gains or Losses.

We recorded net realized losses of $266.6 million for the 2022 second quarter, which included $109.9 million of mark-to-market losses on equity securities, compared to net realized gains of $163.4 million for the 2021 second quarter, and net realized losses of $559.0 million for the six months ended June 30, 2022, compared to net realized gains of $264.7 million for the 2021 period. Currently, our portfolio is

ARCH CAPITAL  53 2022 SECOND QUARTER FORM 10-Q

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 and losses as the portfolio is adjusted and 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 7, “Investment Information—Net Realized Gains (Losses)” and note 7, “Investment Information—Allowance for Expected Credit Losses,” to our consolidated financial statements for additional information.

Equity in Net Income or Losses of Investment Funds Accounted for Using the Equity Method.

We recorded $58.1 million of equity in net income related to investment funds accounted for using the equity method in the 2022 second quarter, compared to $122.2 million for the 2021 second quarter, and $94.4 million for the six months ended June 30, 2022, compared to $193.9 million for the 2021 period. Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds. Investment funds accounted for using the equity method totaled $3.5 billion at June 30, 2022, compared to $3.1 billion at December 31, 2021. See note 7, “Investment Information—Investments Accounted For Using the Equity Method,” to our consolidated financial statements for additional information.

Net Foreign Exchange Gains or Losses.

Net foreign exchange gains for the 2022 second quarter were $87.8 million, compared to net foreign exchange losses for the 2021 second quarter of $17.9 million. Net foreign exchange gains for the six months ended June 30, 2022 were $91.6 million, compared to net foreign exchange gains for the 2021 period of $3.6 million. Amounts in both 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 (loss) before income taxes, including income (loss) from operating affiliates, resulted in an expense of 5.2% for the 2022 second quarter, compared to 7.1% for the 2021 second quarter, and 5.3% for the six months ended June 30, 2022, compared to 7.5% for the 2021 period. Our effective tax rate, which is based upon

the expected annual effective tax rate, may fluctuate from period to period based on the relative mix of income or loss reported by jurisdiction and the varying tax rates in each jurisdiction.

Income or Losses from Operating Affiliates.

Income from operating affiliates for 2022 second quarter was $4.6 million, compared to $24.5 million for the 2021 second quarter, and $29.2 million for the six months ended June 30, 2022, compared to $99.9 million for the 2021 period. Results for the 2021 period reflected a one-time gain of $74.5 million realized from our investment in Coface SA. See note 7, “Investment Information—Investments in Operating Affiliates,” to our consolidated financial statements for additional information.

CRITICAL ACCOUNTING POLICIES,

ESTIMATES AND RECENT ACCOUNTING PRONOUNCEMENTS

Critical accounting policies, estimates and recent accounting pronouncements are discussed in Management’s Discussion and Analysis of Financial Condition and Results of Operations contained in our 2021 Form 10-K, updated where applicable in the notes accompanying our consolidated financial statements, including note 1, “Basis of Presentation and Recent Accounting Pronouncements.”

FINANCIAL CONDITION

Investable Assets Held by Arch 

At June 30, 2022, approximately $18.0 billion, or 68.1%, of total investable assets held by Arch were internally managed, compared to $18.5 billion, or 67.3%, at December 31, 2021. See note 7, “Investment Information” to our consolidated financial statements for additional information.

	June 30, 2022,	December 31, 2021
Average effective duration (in years)	2.94	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 assigned by Standard & Poor’s Rating Services (“S&P”) and Moody’s Investors Service (“Moody’s”).

ARCH CAPITAL  54 2022 SECOND QUARTER FORM 10-Q

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
June 30, 2022
U.S. government and gov’t agencies (1)	$	4,892,483	27.0
AAA	3,352,551		18.5
AA	2,064,313		11.4
A	3,464,240		19.1
BBB	3,114,961		17.2
BB	551,876		3.0
B	367,275		2.0
Lower than B	4,742		—
Not rated	298,039		1.6
Total	$	18,110,480	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 residential 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
June 30, 2022
0-10%	$	12,462,902	$	(621,590)	49.4
10-20%	3,933,567		(586,383)		46.6
20-30%	138,629		(44,066)		3.5
Greater than 30%	8,619		(5,292)		0.4
Total	$	16,543,717	$	(1,257,331)	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 June 30, 2022, excluding guaranteed amounts and covered bonds:

	Estimated Fair Value		Credit Rating (1)
Bank of America Corporation	$	449,059	A-/A2
JPMorgan Chase & Co.	321,238		A-/A2
Citigroup Inc.	307,423		BBB+/A3
Morgan Stanley	284,134		A-/A1
The Goldman Sachs Group, Inc.	254,836		BBB+/A2
Wells Fargo & Company	250,140		BBB+/A1
Blackstone Inc.	169,489		BBB/Baa3
UBS Group AG	133,298		A/Aa3
Athene Global Funding	113,452		A+/NA
Dai-ichi Life Holdings, Inc.	112,215		AA-/A1
Total	$	2,395,284

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

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

	Agencies		Investment Grade		Below Investment Grade		Total
June 30, 2022
RMBS	$	505,253	$	152,348	$	40,567	$	698,168
CMBS	19,080		943,027		60,981		1,023,088
ABS	—		1,454,312		155,566		1,609,878
Total	$	524,333	$	2,549,687	$	257,114	$	3,331,134
December 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:

	June 30, 2022		December 31, 2021
Equities (1)	$	480,981	$	883,722
Exchange traded funds
Fixed income (2)	276,392		455,467
Equity and other (3)	29,805		491,474
Total	$	787,178	$	1,830,663

(1)Primarily in consumer non-cyclical, technology, communications, consumer cyclical and financial at June 30, 2022.

(2)Primarily in corporate at June 30, 2022.

(3)Primarily in large cap stocks, foreign equities, technology, healthcare and industrials at June 30, 2022.

For details on our other investments and other investable assets, see note 7, “Investment Information—Other Investments” to our consolidated financial statements.

ARCH CAPITAL  55 2022 SECOND QUARTER FORM 10-Q

For details on our investments accounted for using the equity method, see note 7, “Investment Information—Investments Accounted For Using the Equity Method,” to our consolidated financial statements.

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 9, “Derivative Instruments,” to our consolidated financial statements for additional disclosures related to 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 8, “Fair Value,” to our consolidated financial statements for a summary of our financial assets and liabilities measured at fair value, segregated by level in the fair value hierarchy.

Reinsurance

The effects of reinsurance on written and earned premiums and losses and loss adjustment expenses (“LAE”) with unaffiliated reinsurers were as follows:

	Three Months Ended				Six Months Ended
	June 30,				June 30,
	2022		2021		2022		2021
Premiums written:
Direct	$	2,124,594	$	1,909,893	$	4,255,903	$	3,802,138
Assumed	1,745,133		1,376,398		3,414,599		2,881,359
Ceded	(1,185,088)		(886,767)		(2,351,723)		(1,775,516)
Net	$	2,684,639	$	2,399,524	$	5,318,779	$	4,907,981
Premiums earned:
Direct	$	1,973,735	$	1,795,899	$	3,858,850	$	3,508,824
Assumed	1,339,749		1,091,968		2,512,553		2,039,582
Ceded	(987,709)		(766,958)		(1,924,995)		(1,479,075)
Net	$	2,325,775	$	2,120,909	$	4,446,408	$	4,069,331
Losses and LAE:
Direct	$	898,551	$	1,046,579	$	1,788,353	$	2,032,512
Assumed	637,285		554,256		1,291,546		1,221,567
Ceded	(433,180)		(441,004)		(976,408)		(891,148)
Net	$	1,102,656	$	1,159,831	$	2,103,491	$	2,362,931

See note 6, “Allowance for Expected Credit Losses,” to our consolidated financial statements for information about our reinsurance recoverables and related allowance for credit losses.

Bellemeade Re

We have entered into aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda (the “Bellemeade Agreements”). For the respective coverage periods, we 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. We will then retain losses in excess of the outstanding coverage limit. The aggregate excess of loss reinsurance coverage generally decreases over a ten-year period as the underlying covered mortgages amortize, unless provisional call options embedded within certain of the Bellemeade Agreements are executed or if pre-defined delinquency triggering events occur.

The following table summarizes the respective coverages and retentions at June 30, 2022:

Bellemeade Entities (Issue Date)	Initial Coverage at Issuance		Current Coverage		Remaining Retention, Net
2017-1 Ltd. (1)	$	368,114	$	61,328	$	134,231
2018-1 Ltd. (2)	374,460		122,190		134,417
2018-3 Ltd. (3)	506,110		244,257		140,403
2019-1 Ltd. (4)	341,790		134,972		100,485
2019-2 Ltd. (5)	621,022		383,737		177,021
2019-3 Ltd. (6)	700,920		296,466		198,510
2019-4 Ltd. (7)	577,267		312,668		131,922
2020-2 Ltd. (8)	449,167		151,985		231,059
2020-3 Ltd. (9)	451,816		313,790		160,325
2020-4 Ltd. (10)	337,013		130,572		137,414
2021-1 Ltd. (11)	643,577		568,482		155,403
2021-2 Ltd. (12)	616,017		578,554		143,190
2021-3 Ltd. (13)	639,391		639,391		140,170
2022-1 Ltd. (14)	316,760		316,760		153,915
Total	$	6,943,424	$	4,255,152	$	2,138,465

(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 2005-2008 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.

ARCH CAPITAL  56 2022 SECOND QUARTER FORM 10-Q

(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.

Reserve for Losses and Loss Adjustment Expenses 

We establish reserve for losses and loss adjustment expenses (“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.

At June 30, 2022 and December 31, 2021, our Loss Reserves, net of unpaid losses and loss adjustment expenses recoverable, by type and by operating segment were as follows:

	June 30, 2022		December 31, 2021
Insurance segment:
Case reserves	$	2,151,564	$	2,102,891
IBNR reserves	4,531,601		4,269,904
Total net reserves	6,683,165		6,372,795
Reinsurance segment:
Case reserves	1,730,929		1,733,571
Additional case reserves	400,013		426,531
IBNR reserves	2,851,212		2,656,527
Total net reserves	4,982,154		4,816,629
Mortgage segment:
Case reserves	576,874		741,897
IBNR reserves	265,783		226,604
Total net reserves	842,657		968,501
Total:
Case reserves	4,459,367		4,578,359
Additional case reserves	400,013		426,531
IBNR reserves	7,648,596		7,153,035
Total net reserves	$	12,507,976	$	12,157,925

At June 30, 2022 and December 31, 2021, the insurance segment’s Loss Reserves by major line of business, net of unpaid losses and loss adjustment expenses recoverable, were as follows:

	June 30, 2022		December 31, 2021
Insurance segment:
Professional lines	$	1,798,210	$	1,673,615
Construction and national accounts	1,528,805		1,490,206
Programs	830,573		793,187
Excess and surplus casualty	712,247		657,307
Property, energy, marine and aviation	606,472		599,093
Travel, accident and health	119,726		96,051
Lenders products	41,249		58,351
Other	1,045,883		1,004,985
Total net reserves	$	6,683,165	$	6,372,795

At June 30, 2022 and December 31, 2021, the reinsurance segment’s Loss Reserves by major line of business, net of unpaid losses and loss adjustment expenses recoverable, were as follows:

	June 30, 2022		December 31, 2021
Reinsurance segment:
Casualty	$	2,199,745	$	2,123,360
Other specialty	1,165,155		1,113,766
Property excluding property catastrophe	756,569		711,859
Property catastrophe	435,468		486,911
Marine and aviation	284,315		246,861
Other	140,902		133,872
Total net reserves	$	4,982,154	$	4,816,629

ARCH CAPITAL  57 2022 SECOND QUARTER FORM 10-Q

At June 30, 2022 and December 31, 2021, the mortgage segment’s Loss Reserves by major line of business, net of unpaid losses and loss adjustment expenses recoverable, were as follows:

	June 30, 2022		December 31, 2021
U.S. primary mortgage insurance (1)	$	608,947	$	710,708
U.S. credit risk transfer (CRT) and other	107,861		112,549
International mortgage insurance/ reinsurance	125,849		145,244
Total net reserves	$	842,657	$	968,501

(1)    At June 30, 2022, 33.7% of total net reserves represents 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.

Mortgage Operations Supplemental Information

The mortgage segment’s insurance in force (“IIF”) and risk in force (“RIF”) were as follows at June 30, 2022 and December 31, 2021:

(U.S. Dollars in millions)	June 30, 2022			December 31, 2021
	Amount		%	Amount		%
Insurance In Force (IIF) (1):
U.S. primary mortgage insurance	$	291,952	59.8	$	280,945	61.0
U.S. credit risk transfer (CRT) and other (2)	129,203		26.5	110,018		23.9
International mortgage insurance/reinsurance (3)	67,082		13.7	69,655		15.1
Total	$	488,237	100.0	$	460,618	100.0
Risk In Force (RIF) (4):
U.S. primary mortgage insurance	$	74,258	85.0	$	70,619	84.3
U.S. credit risk transfer (CRT) and other (2)	6,037		6.9	5,120		6.1
International mortgage insurance/reinsurance (3)	7,103		8.1	7,983		9.5
Total	$	87,398	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.

The IIF and RIF for our U.S. primary mortgage insurance business by policy year were as follows at June 30, 2022:

(U.S. Dollars in millions)	IIF			RIF			Delinquency
	Amount		%	Amount		%	Rate (1)
Policy year:
2012 and prior	$	10,972	3.8	$	2,620	3.5	8.15	%
2013	3,446		1.2	927		1.2	2.19	%
2014	4,129		1.4	1,135		1.5	2.74	%
2015	7,167		2.5	1,930		2.6	2.12	%
2016	11,866		4.1	3,179		4.3	2.52	%
2017	10,745		3.7	2,842		3.8	3.28	%
2018	11,494		3.9	2,926		3.9	4.04	%
2019	21,384		7.3	5,382		7.2	2.31	%
2020	73,516		25.2	18,332		24.7	0.84	%
2021	94,557		32.4	23,852		32.1	0.08	%
2022	42,676		14.6	11,133		15.0	0.50	%
Total	$	291,952	100.0	$	74,258	100.0	1.77	%

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

The IIF and RIF 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.

ARCH CAPITAL  58 2022 SECOND QUARTER FORM 10-Q

The following tables provide supplemental disclosures on risk in force for our U.S. primary mortgage insurance business at June 30, 2022 and December 31, 2021:

(U.S. Dollars in millions)	June 30, 2022				December 31, 2021
	Amount			%	Amount			%
Credit quality (FICO):
>=740	$	45,612		61.4	$	42,451		60.1
680-739	24,409			32.9	23,646			33.5
620-679	3,942			5.3	4,196			5.9
<620	295			0.4	326			0.5
Total	$	74,258		100.0	$	70,619		100.0
Weighted average FICO score	747				746
Loan-to-value (LTV):
95.01% and above	$	7,400		10.0	$	7,538		10.7
90.01% to 95.00%	41,951			56.5	38,829			55.0
85.01% to 90.00%	20,718			27.9	20,006			28.3
85.00% and below	4,189			5.6	4,246			6.0
Total	$	74,258		100.0	$	70,619		100.0
Weighted average LTV	92.8		%		92.8		%
Total RIF, net of external reinsurance	$	56,529			$	54,574

(U.S. Dollars in millions)	June 30, 2022			December 31, 2021
	Amount		%	Amount		%
Total RIF by State:
California	$	6,077	8.2	$	5,559	7.9
Texas	5,971		8.0	5,594		7.9
Florida	3,301		4.4	3,303		4.7
Georgia	3,109		4.2	2,902		4.1
North Carolina	3,075		4.1	2,921		4.1
Illinois	3,054		4.1	2,933		4.2
Minnesota	2,980		4.0	2,916		4.1
Massachusetts	2,684		3.6	2,537		3.6
Virginia	2,634		3.5	2,446		3.5
Michigan	2,558		3.4	2,492		3.5
Other	38,815		52.3	37,016		52.4
Total	$	74,258	100.0	$	70,619	100.0

The following table provides supplemental disclosures for our U.S. primary mortgage insurance business related to insured loans and loss metrics:

(U.S. Dollars in thousands, except policy, loan and claim count)	Six Months Ended
	June 30,
	2022			2021
Roll-forward of insured loans in default:
Beginning delinquent number of loans	27,645			52,234
New notices	16,813			18,415
Cures	(23,393)			(32,924)
Paid claims	(373)			(406)
Ending delinquent number of loans (1)	20,692			37,319
Ending number of policies in force (1)	1,168,147			1,199,918
Delinquency rate (1)	1.77		%	3.11		%
Losses:
Number of claims paid	373			406
Total paid claims	$	11,642		$	15,297
Average per claim	$	31.2		$	37.7
Severity (2)	75.2		%	81.0		%
Average case reserve per default (in thousands) (1)	$	30.3		$	19.5

(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 7.8 to 1 at June 30, 2022, compared to 8 to 1 at December 31, 2021.

Shareholders’ Equity and Book Value per Share

The following table presents the calculation of book value per share:

(U.S. dollars in thousands, except  share data)	June 30, 2022		December 31, 2021
Total shareholders’ equity available to Arch	$	12,417,566	$	13,545,896
Less preferred shareholders’ equity	830,000		830,000
Common shareholders’ equity available to Arch	$	11,587,566	$	12,715,896
Common shares and common share equivalents outstanding, net of treasury shares (1)	369,346,815		378,923,894
Book value per share	$	31.37	$	33.56

(1)Excludes the effects of 15,922,638 and 17,083,160 stock options and 564,448 and 729,636 restricted stock units outstanding at June 30, 2022 and December 31, 2021, respectively.

ARCH CAPITAL  59 2022 SECOND QUARTER FORM 10-Q

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.

For the six months ended June 30, 2022, Arch Capital received dividends of $689.9 million from Arch Reinsurance Ltd. (“Arch Re Bermuda”), our Bermuda based reinsurer and insurer which can pay approximately $3.1 billion to Arch Capital during the remainder of 2022 without providing an affidavit to the Bermuda Monetary Authority.

We expect that our liquidity needs, including our anticipated (re)insurance obligations and operating and capital expenditure needs, for the next twelve months, 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. On April 7, 2022 Arch Capital and certain of its subsidiaries amended the existing credit agreement. For details on our credit agreement, see note 10, “Commitments and Contingencies” to our consolidated financial statements.

Cash Flows

The following table summarizes our cash flows from operating, investing and financing activities.

	Six Months Ended
	June 30,
	2022		2021
Total cash provided by (used for):
Operating activities	$	1,453,968	$	1,565,718
Investing activities	(815,602)		(1,174,033)
Financing activities	(682,116)		8,352
Effects of exchange rate changes on foreign currency cash	(42,790)		(9,868)
Increase (decrease) in cash and restricted cash	$	(86,540)	$	390,169

•Cash provided by operating activities for the six months ended June 30, 2022 primarily reflected a higher level of expenses paid and higher premiums ceded to Somers than in the 2021 period.

•Cash used for investing activities for the six months ended June 30, 2022 was lower than in the 2021 period. Activity for the 2021 period reflected our $546.3 million purchase of 29.5% interest in Coface.

•Cash used for financing activities for the six months ended June 30, 2022 reflected $575.7 million of repurchases under our share repurchase program. Activity for the 2021 period, reflected $485.3 million of repurchases under our share repurchase program and $485.8 million issuance of preferred shares.

CAPITAL RESOURCES

The following table provides an analysis of our capital structure:

(U.S. dollars in thousands, except  share data)	June 30, 2022		Dec 31, 2021
Senior notes	$	2,724,896	$	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	11,587,566		12,715,896
Total	$	12,417,566	$	13,545,896
Total capital available to Arch	$	15,142,462	$	16,270,290
Debt to total capital (%)	18.0		16.7
Preferred to total capital (%)	5.5		5.1
Debt and preferred to total capital (%)	23.5		21.8

Arch MI U.S. is required to maintain compliance with the GSEs requirements, known as the Private Mortgage Insurer Eligibility Requirements or “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 June 30, 2022 with an estimated PMIER sufficiency ratio of 219%, compared to 197% at December 31, 2021.

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.

ARCH CAPITAL  60 2022 SECOND QUARTER FORM 10-Q

GUARANTOR INFORMATION

The below table provides a description of our senior notes payable at June 30, 2022:

	Interest		Principal		Carrying
Issuer/Due	(Fixed)		Amount		Amount
Arch Capital:
May 1, 2034	7.350	%	$	300,000	$	297,552
June 30, 2050	3.635	%	1,000,000		988,833
Arch-U.S.:
Nov. 1, 2043 (1)	5.144	%	500,000		495,125
Arch Finance:
Dec. 15, 2026 (1)	4.011	%	500,000		497,851
Dec. 15, 2046 (1)	5.031	%	450,000		445,535
Total			$	2,750,000	$	2,724,896

(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-U.S. and Arch Finance depend on their available cash resources, liquid investments and dividends or other distributions from their subsidiaries or affiliates to make payments, including the payment of debt service obligations and operating expenses they may incur.

The following tables present condensed financial information for Arch Capital (parent guarantor) and Arch-U.S. (subsidiary issuer):

	June 30, 2022
	Arch Capital		Arch-U.S.
Assets
Total investments	$	14,864	$	146,590
Cash	29,358		9,725
Investment in operating affiliates	5,867		—
Due from subsidiaries and affiliates	41		15
Other assets	7,674		29,119
Total assets	$	57,804	$	185,449
Liabilities
Senior notes	1,286,385		495,125
Due to subsidiaries and affiliates	—		501,816
Other liabilities	17,122		36,757
Total liabilities	$	1,303,507	$	1,033,698
Non-cumulative preferred shares	$	830,000	—

	December 31, 2021
	Arch Capital		Arch-U.S.
Assets
Total investments	$	2,038	$	137,124
Cash	16,317		18,392
Investment in operating affiliates	6,877		—
Due from subsidiaries and affiliates	—		26,000
Other assets	9,615		37,040
Total assets	$	34,847	$	218,556
Liabilities
Senior notes	1,286,208		495,063
Due to subsidiaries and affiliates	—		521,839
Other liabilities	24,767		47,410
Total liabilities	$	1,310,975	$	1,064,312
Non-cumulative preferred shares	$	830,000	—

	June 30, 2022
Six Months Ended	Arch Capital		Arch-U.S.
Revenues
Net investment income	$	744	$	154
Net realized gains (losses)	—		(338)
Equity in net income (loss) of investments accounted for using the equity method	—		5,651
Total revenues	744		5,467
Expenses
Corporate expenses	52,542		8,838
Interest expense	29,377		23,572
Total expenses	81,919		32,410
Income (loss) before income taxes and income (loss) from operating affiliates	(81,175)		(26,943)
Income tax (expense) benefit	—		5,453
Income (loss) from operating affiliates	(551)		—
Net income available to Arch	(81,726)		(21,490)
Preferred dividends	(20,368)		—
Net income (loss) available to Arch common shareholders	$	(102,094)	$	(21,490)

ARCH CAPITAL  61 2022 SECOND QUARTER FORM 10-Q

	December 31, 2021
Year Ended	Arch Capital		Arch-U.S.
Revenues
Net investment income	1,524		11,596
Net realized gains (losses)	—		72,437
Equity in net income (loss) of investments accounted for using the equity method	—		18,149
Total revenues	1,524		102,182
Expenses
Corporate expenses	71,818		5,875
Interest expense	58,741		47,292
Net foreign exchange (gains) losses	7		—
Total expenses	130,566		53,167
Income (loss) before income taxes and income (loss) from operating affiliates	(129,042)		49,015
Income tax (expense) benefit	—		(12,513)
Income (loss) from operating affiliates	(590)		—
Net income available to Arch	(129,632)		36,502
Preferred dividends	(48,343)		—
Loss on redemption of preferred shares	(15,101)		—
Net income (loss) available to Arch common shareholders	$	(193,076)	$	36,502

SHARE REPURCHASE PROGRAM

The board of directors of Arch Capital has authorized the investment in Arch Capital’s common shares through a share repurchase program. For the six months ended June 30, 2022, Arch Capital repurchased 12.7 million shares under the share repurchase program with an aggregate purchase price of $575.7 million. Since the inception of the share repurchase program through June 30, 2022, Arch Capital has repurchased 433.3 million common shares for an aggregate purchase price of $5.86 billion. At June 30, 2022, approximately $606.6 million of share repurchases were available under the program. 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. 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.

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. Man-made catastrophic events may include acts of war, acts of terrorism and political instability. 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.

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 July 1, 2022, our modeled peak zone catastrophe exposure was a windstorm affecting the Florida Tri-County, with a net probable maximum pre-tax loss of $888 million, followed by windstorms affecting the Gulf of Mexico and the Northeastern U.S. regions with net probable maximum pre-tax losses of $732 and $720 million, respectively. Our exposures to other perils, such as U.S. earthquake and international events, were less than the exposures arising from U.S. windstorms and hurricanes. As of July 1, 2022, our modeled peak zone earthquake exposure (San Francisco earthquake) represented approximately 69% of our peak zone catastrophe exposure, and our modeled peak zone international exposure (UK 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 tangible shareholders’ equity available to Arch. We reserve the right to change this threshold at any time. Based on in-force

ARCH CAPITAL  62 2022 SECOND QUARTER FORM 10-Q

exposure estimated as of July 1, 2022, our modeled RDS loss was approximately 9% 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. These factors include 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” and “Management’s Discussion and Analysis of Financial Condition and Results of Operations—Catastrophic Events and Severe Economic Events” in our 2021 Form 10-K.

MARKET SENSITIVE INSTRUMENTS AND RISK MANAGEMENT

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 June 30, 2022. Market risk represents the risk of changes in the fair value of a financial instrument and is comprised of several components, including liquidity, basis and price risks.

An analysis of material changes in market risk exposures at June 30, 2022 that affect the quantitative and qualitative disclosures presented in our 2021 Form 10-K (see section captioned “Management’s Discussion and Analysis of Financial Condition and Results of Operations—Market Sensitive Instruments and Risk Management”) were as follows: 

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 Fixed Income Securities:

(U.S. dollars in  billions)	Interest Rate Shift in Basis Points
	-100			-50			—		+50			+100
June 30, 2022
Total fair value	$	25.50		$	25.10		$	24.73	$	24.36		$	24.01
Change from base	3.1		%	1.5		%			(1.5)		%	(2.9)		%
Change in unrealized value	$	0.77		$	0.37				$	(0.37)		$	(0.72)
December 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.

ARCH CAPITAL  63 2022 SECOND QUARTER FORM 10-Q

The following table summarizes the effect that an immediate, parallel shift in credit spreads in a static interest rate environment would have had on our Fixed Income Securities:

(U.S. dollars in  billions)	Credit Spread Shift in Percentage Points
	-100			-50			—		+50			+100
June 30, 2022
Total fair value	$	25.86		$	25.29		$	24.73	$	24.17		$	23.60
Change from base	4.6		%	2.3		%			(2.3)		%	(4.6)		%
Change in unrealized value	$	1.13		$	0.56				$	(0.56)		$	(1.13)
December 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 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 June 30, 2022, our portfolio’s VaR was estimated to be 7.0% 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 June 30, 2022 and December 31, 2021, the fair value of our investments in equity securities and certain investments accounted for using the equity method with underlying equity strategies totaled $0.9 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 $85.1 million and $137.5 million at June 30, 2022 and December 31, 2021, respectively, and would have decreased book value per share by approximately $0.23 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 $85.1 million and $137.5 million at June 30, 2022 and December 31, 2021, respectively, and would have increased book value per share by approximately $0.23 and $0.36, respectively.

Investment-Related Derivatives. At June 30, 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 $6.5 billion, compared to $6.4 billion at December 31, 2021. If the underlying exposure of each investment-related derivative held at June 30, 2022 depreciated by 100 basis points, it would have resulted in a reduction in net income of approximately $65.4 million, and a decrease in book value per share of approximately $0.18 per share, compared to $63.8 million and $0.17 per share, respectively, on investment-related derivatives held at December 31, 2021. If the underlying exposure of each investment-related derivative held at June 30, 2022 appreciated by 100 basis points, it would have resulted in an increase in net income of approximately $65.4 million, and an increase in book value per share of approximately $0.18 per share, compared to $63.8 million and $0.17 per share, respectively, on investment-related derivatives held at December 31, 2021. See note 9, “Derivative Instruments,” to our consolidated financial statements for additional disclosures concerning derivatives.

For further discussion on investment activity, please refer to “Financial Condition—Investable Assets.”

ARCH CAPITAL  64 2022 SECOND QUARTER FORM 10-Q

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 9, “Derivative Instruments,” to our consolidated financial statements 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)	June 30, 2022		December 31, 2021
Net assets (liabilities), denominated in foreign currencies, excluding shareholders’ equity and derivatives	$	(1,108,727)	$	(825,371)
Shareholders’ equity denominated in foreign currencies (1)	1,037,758		1,095,706
Net foreign currency forward contracts outstanding (2)	74,250		15,151
Net exposures denominated in foreign currencies	$	3,281	$	285,486
Pre-tax impact of a hypothetical 10% appreciation of the U.S. Dollar against foreign currencies:
Shareholders’ equity	$	(328)	$	(28,549)
Book value per share	$	—	$	(0.08)
Pre-tax impact of a hypothetical 10% decline of the U.S. Dollar against foreign currencies:
Shareholders’ equity	$	328	$	28,549
Book value per share	$	—	$	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 we generally attempt to match the currency of our projected liabilities with investments in the same currencies, from time to time we may elect to over or underweight one or more currencies, which could increase our exposure to foreign currency fluctuations and increase the volatility of our 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 reserve 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 ultimately vary by the specific type of inflation affecting each line of business.

OTHER FINANCIAL INFORMATION

The consolidated financial statements as of June 30, 2022 have been reviewed by PricewaterhouseCoopers LLP, the registrant's independent public accountants, whose report is included as an exhibit to this filing. The report of PricewaterhouseCoopers LLP states that they did not audit and they do not express an opinion on that unaudited financial information. Accordingly, the degree of reliance on their report on such information should be restricted in light of the limited nature of the review procedures applied. PricewaterhouseCoopers LLP is not subject to the liability provisions of Section 11 of the Securities Act of 1933 for their report on the unaudited financial information because that report is not a "report" or a "part" of the registration statement prepared or certified by PricewaterhouseCoopers LLP within the meaning of Sections 7 and 11 of the Securities Act of 1933.

ITEM 3. 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 Operations,” which information is hereby incorporated by reference.

ARCH CAPITAL  65 2022 SECOND QUARTER FORM 10-Q

ITEM 4. CONTROLS AND PROCEDURES

Evaluation of Disclosure Controls and Procedures

In connection with the filing of this Form 10-Q, our management, including the Chief Executive Officer and Chief Financial Officer, conducted an evaluation, as of the end of the period covered by this report, 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 were effective as of the end of and during the period covered by this report with respect to information being recorded, processed, summarized and reported within time periods specified in the SEC’s rules and forms and with respect to timely communication to them and other members of management responsible for preparing periodic reports of all material information required to be disclosed in this report as it relates to Arch Capital and its consolidated subsidiaries.

We continue to enhance our operating procedures and internal controls 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.

Changes in Internal Controls Over Financial Reporting

There have been no changes in internal control over financial reporting that occurred during the quarter ended June 30, 2022 that have materially affected, or are reasonably likely to materially affect, internal control over financial reporting. We have not experienced any material impact to our internal controls over financial reporting.

PART II. OTHER INFORMATION

ITEM 1. 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 June 30, 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 1A. RISK FACTORS

There were no material changes from the risk factors previously disclosed in our Annual Report on Form 10-K for the year ended December 31, 2021.

ARCH CAPITAL  66 2022 SECOND QUARTER FORM 10-Q

ITEM 2. UNREGISTERED SALES OF EQUITY SECURITIES AND USE OF PROCEEDS

Issuer’s Repurchases of Equity Securities

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

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)
4/1/2022-4/30/2022	130,557	$	46.56	114,079	$	921,969
5/1/2022-5/31//2022	4,537,120	45.81		4,492,435	$	716,186
6/1/2022-6/30/2022	2,488,688	44.14		2,483,933	$	606,558
Total	7,156,365	$	45.24	7,090,447

(1)This column represents open market share repurchases, including an aggregate of 16,478, 44,685, and 4,755 shares repurchased by Arch Capital during April, May and June, respectively, other than through publicly announced plans or programs. We repurchased these shares from employees in order to facilitate the payment of withholding taxes on restricted shares granted and the exercise of stock appreciation rights, in each case at their fair 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)This column represents the remaining approximate dollar amount available at the end of each applicable period under Arch Capital’s $1.5 billion share repurchase authorization from October 8, 2021. Repurchases may be effected from time to time in open market or privately negotiated transactions through December 31, 2022.

ITEM 3. DEFAULTS UPON SENIOR SECURITIES

None.

ITEM 4. MINE SAFETY DISCLOSURES

Not applicable.

ITEM 5. OTHER INFORMATION

In accordance with Section 10a(i)(2) of the Securities and Exchange Act of 1934, as amended, we are responsible for disclosing non-audit services to be provided by our independent auditor, PricewaterhouseCoopers LLP, which are approved by the Audit Committee of our board of directors. During the 2022 second quarter, the Audit Committee approved engagements of PricewaterhouseCoopers LLP for permitted non-audit services, which consisted of tax consulting services, tax compliance services and other accounting consulting services.

ARCH CAPITAL  67 2022 SECOND QUARTER FORM 10-Q

ITEM 6. EXHIBITS

		Incorporated by Reference
Exhibit Number	Exhibit Description	Form	Original Number	Date Filed	Filed Herewith
10.1	Arch Capital Group Ltd. 2022 Long-Term Incentive and Share Award Plan	8-K	10.1	May 4, 2022
15	Accountants’ Awareness Letter (regarding unaudited interim financial information)				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.INS	XBRL Instance Document
101.SCH	XBRL Taxonomy Extension Schema Document
101.CAL	XBRL Taxonomy Extension Calculation Linkbase Document
101.DEF	XBRL Taxonomy Extension Definition Linkbase Document
101.LAB	XBRL Taxonomy Extension Label Linkbase Document
101.PRE	XBRL Taxonomy Extension Presentation Linkbase Document
104	Cover Page Interactive Data File (embedded within the Inline XBRL document)

ARCH CAPITAL  68 2022 SECOND QUARTER FORM 10-Q

SIGNATURES

Pursuant to the requirements 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)
	/s/ Marc Grandisson
Date: August 3, 2022	Marc Grandisson
	Chief Executive Officer (Principal Executive Officer)
	/s/ François Morin
Date: August 3, 2022	François Morin
	Executive Vice President, Chief Financial Officer (Principal Financial and Accounting Officer) and Treasurer

ARCH CAPITAL  69 2022 SECOND QUARTER FORM 10-Q

EX-15

Exhibit 15

August 3, 2022

Securities and Exchange Commission

100 F Street, N.E.

Washington, DC 20549

Commissioners:

We are aware that our report dated August 3, 2022, on our review of interim financial information of Arch Capital Group Ltd., which appears in this Quarterly Report on Form 10-Q, is incorporated by reference in the Registration Statements on Form S-3 (No. 333-250869) and in the Registration Statements on Form S-8 (Nos. 333-265285, 333-224783, 333-211193, 333-142835, 333-181308 and 333- 203993) of Arch Capital Group Ltd.

Very truly yours,

/s/ PricewaterhouseCoopers LLP

New York, New York

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 quarterly report on Form 10-Q 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 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 the audit committee of the 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:	August 3, 2022
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 quarterly report on Form 10-Q 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 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 the audit committee of the 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:	August 3, 2022
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 Quarterly Report of Arch Capital Group Ltd. (the “Company”) on Form 10-Q for the period ending June 30, 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) of the Securities Exchange Act of 1934; and

(2)    the information contained in such report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date:	August 3, 2022
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 Quarterly Report of Arch Capital Group Ltd. (the “Company”) on Form 10-Q for the period ending June 30, 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) of the Securities Exchange Act of 1934; and

(2)    the information contained in such report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date:	August 3, 2022
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 - shares	6 Months Ended
	Jun. 30, 2022	Jul. 29, 2022
Document and Entity Information [Abstract]
Document Type	10-Q
Document Quarterly Report	true
Document Period End Date	Jun. 30, 2022
Document Transition Report	false
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 Current Reporting Status	Yes
Entity Interactive Data Current	Yes
Entity Filer Category	Large Accelerated Filer
Entity Small Business	false
Entity Emerging Growth Company	false
Entity Shell Company	false
Entity Common Stock, Shares Outstanding		369,137,188
Document Fiscal Period Focus	Q2
Document Fiscal Year Focus	2022
Current Fiscal Year End Date	--12-31
Entity Central Index Key	0000947484
Amendment Flag	false
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 1/1000th 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 1/1000th interest in a 4.55% Series G preferred share
Trading Symbol	ACGLN
Security Exchange Name	NASDAQ

XML

Unaudited Consolidated Balance Sheets - USD ($) $ in Thousands	Jun. 30, 2022	Dec. 31, 2021
Investments:
Fixed maturities, available for sale, at fair value	$ 19,812,903	$ 19,732,825
Equity securities, at fair value	772,689	1,804,170
Other investments, at fair value	1,634,368	1,973,550
Investments accounted for using the equity method	3,496,341	3,077,611
Total investments	25,716,301	26,588,156
Cash	813,548	858,668
Accrued investment income	116,102	85,453
Investment in operating affiliates	967,603	1,135,655
Premiums receivable (net of allowance for credit losses: $38,170 and $39,958)	3,634,182	2,633,280
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $14,740 and $13,230)	5,938,511	5,880,735
Contractholder receivables (net of allowance for credit losses: $3,005 and $3,437)	1,758,018	1,828,691
Ceded unearned premiums	2,123,915	1,729,455
Deferred acquisition costs	1,069,845	901,841
Receivable for securities sold	157,329	60,179
Goodwill and intangible assets	868,014	944,983
Other assets	2,555,826	2,453,849
Total assets	45,719,194	45,100,945
Liabilities
Reserve for losses and loss adjustment expenses	18,194,324	17,757,156
Unearned premiums	7,145,297	6,011,942
Reinsurance balances payable	1,634,700	1,583,253
Contractholder payables	1,761,023	1,832,127
Collateral held for insured obligations	251,063	242,352
Senior notes	2,724,896	2,724,394
Payable for securities purchased	292,106	64,850
Other liabilities	1,289,760	1,329,742
Total liabilities	33,293,169	31,545,816
Commitments and Contingencies
Redeemable noncontrolling interests	8,459	9,233
Shareholders' Equity
Non-cumulative preferred shares	830,000	830,000
Common shares ($0.0011 par, shares issued: 586,887,791 and 583,289,850)	652	648
Additional paid-in capital	2,170,661	2,085,075
Retained earnings	15,035,644	14,455,868
Accumulated other comprehensive income (loss), net of deferred income tax	(1,258,265)	(64,600)
Common shares held in treasury, at cost (shares: 217,540,976 and 204,365,956)	(4,361,126)	(3,761,095)
Total shareholders' equity available to Arch	12,417,566	13,545,896
Total liabilities, noncontrolling interests and shareholders' equity	45,719,194	45,100,945
Fixed maturities available for sale, at fair value (amortized cost: $18,816,372 and $17,973,823; net of allowance for credit losses: $58,410 and $2,883 )
Investments:
Fixed maturities, available for sale, at fair value	17,585,029	17,998,109
Short-term investments available for sale, at fair value (amortized cost: $2,226,673 and $1,734,738; net of allowance for credit losses: $0 and $0)
Investments:
Fixed maturities, available for sale, at fair value	$ 2,227,874	$ 1,734,716

XML

Unaudited Consolidated Balance Sheets (Parentheticals) - USD ($) $ in Thousands	Jun. 30, 2022	Dec. 31, 2021
Available for sale securities, amortized cost	$ 21,043,045	$ 19,708,561
Allowance for credit losses on investments	58,410	2,883
Allowance for credit losses on premiums receivable	38,170	39,958
Allowance for credit losses on reinsurance recoverable	14,740	13,230
Allowance for credit losses on contractholder receivable	$ 3,005	$ 3,437
Common shares, par value per share	$ 0.0011	$ 0.0011
Common shares issued (shares)	586,887,791	583,289,850
Common shares held in treasury (shares)	217,540,976	204,365,956
Fixed maturities
Available for sale securities, amortized cost	$ 18,816,372	$ 17,973,823
Allowance for credit losses on investments	58,410	2,883
Short-term investments
Available for sale securities, amortized cost	2,226,673	1,734,738
Allowance for credit losses on investments	$ 0	$ 0

XML

Unaudited Consolidated Statements of Income - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Revenues
Net premiums earned	$ 2,325,775	$ 2,120,909	$ 4,446,408	$ 4,069,331
Net investment income	106,392	111,613	186,828	210,469
Net realized gains (losses)	(266,579)	202,907	(558,993)	345,368
Other underwriting income	2,970	5,529	8,867	11,639
Equity in net income (loss) of investment funds accounted for using the equity method	58,061	122,186	94,366	193,872
Other income (loss)	(11,777)	6,852	(20,802)	5,111
Total revenues	2,214,842	2,569,996	4,156,674	4,835,790
Expenses
Losses and loss adjustment expenses	1,102,656	1,159,831	2,103,491	2,362,931
Acquisition expenses	413,319	335,143	791,478	639,624
Other operating expenses	277,392	244,943	567,335	505,976
Corporate expenses	27,620	15,951	59,952	41,335
Amortization of intangible assets	27,207	15,286	54,374	29,688
Interest expense	32,795	35,700	65,503	74,046
Net foreign exchange (gains) losses	(87,775)	17,775	(91,620)	(2,288)
Total expenses	1,793,214	1,824,629	3,550,513	3,651,312
Income (loss) before income taxes and income (loss) from operating affiliates	421,628	745,367	606,161	1,184,478
Income tax expense	(22,323)	(51,179)	(33,942)	(90,039)
Income (loss) from operating affiliates	4,640	24,476	29,158	99,933
Net income (loss)	403,945	718,664	601,377	1,194,372
Net (income) loss attributable to noncontrolling interests	399	(43,178)	(1,233)	(80,730)
Net income (loss) available to Arch	404,344	675,486	600,144	1,113,642
Preferred dividends	(10,184)	(11,666)	(20,368)	(22,069)
Net income (loss) available to Arch common shareholders	$ 394,160	$ 663,820	$ 579,776	$ 1,091,573
Net income per common share and common share equivalent
Basic (per share)	$ 1.07	$ 1.67	$ 1.56	$ 2.73
Diluted (per share)	$ 1.04	$ 1.63	$ 1.52	$ 2.68
Weighted average common shares and common share equivalents outstanding
Basic (shares)	369,241,193	397,743,402	371,728,683	399,267,183
Diluted (shares)	377,952,988	406,485,994	380,905,512	407,687,680

XML

Unaudited Consolidated Statements of Comprehensive Income - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Comprehensive Income
Net income (loss)	$ 403,945	$ 718,664	$ 601,377	$ 1,194,372
Unrealized appreciation (decline) in value of available-for-sale investments:
Unrealized holding gains (losses) arising during period	(598,005)	78,571	(1,282,360)	(183,179)
Reclassification of net realized (gains) losses, included in net income (loss)	57,710	(60,547)	159,988	(57,850)
Foreign currency translation adjustments	(68,525)	6,205	(71,293)	(22,379)
Comprehensive income (loss)	(204,875)	742,893	(592,288)	930,964
Net (income) loss attributable to noncontrolling interests	399	(43,178)	(1,233)	(80,730)
Other comprehensive (income) loss attributable to noncontrolling interests	0	(10)	0	4,560
Comprehensive income (loss) available to Arch	$ (204,476)	$ 699,705	$ (593,521)	$ 854,794

XML

Unaudited Consolidated Statements of Changes in Shareholders' Equity - USD ($) $ in Thousands	Total	Non-cumulative preferred shares	Common shares	Additional paid-in capital	Retained earnings	Accumulated other comprehensive income (loss), net of deferred income tax	Unrealized appreciation (decline) in value of available-for-sale securities, 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 period at Dec. 31, 2020		$ 780,000	$ 643	$ 1,977,794	$ 12,362,463	$ 488,895	$ 501,295	$ (12,400)	$ (2,503,909)
Preferred shares issued		500,000
Common shares issued, net			4
Amortization of share-based compensation				57,063
Issue costs on preferred shares				(14,179)
Other changes				8,241
Net income (loss)	$ 1,194,372				1,194,372
Net (income) loss attributable to noncontrolling interests	(80,730)				(80,730)
Preferred share dividends	(22,069)				(22,069)
Unrealized holding gains (losses) during period, net of reclassification adjustment							(241,029)
Unrealized holding gains (losses) during period attributable to noncontrolling interests							4,436
Foreign currency translation adjustments	(22,379)							(22,379)
Foreign currency translation adjustments attributable to noncontrolling interests								125
Shares repurchased for treasury									(503,669)
Balance at end of period at Jun. 30, 2021	13,986,072	1,280,000	647	2,028,919	13,454,036	230,048	264,702	(34,654)	(3,007,578)
Non-redeemable noncontrolling interests, end of period at Jun. 30, 2021	918,874
Total shareholders’ equity at Jun. 30, 2021	14,904,946
Balance at beginning of period at Mar. 31, 2021		780,000	645	2,014,741	12,790,216	205,827	246,711	(40,884)	(2,694,957)
Preferred shares issued		500,000
Common shares issued, net			2
Amortization of share-based compensation				16,490
Issue costs on preferred shares				(14,179)
Other changes				11,867
Net income (loss)	718,664				718,664
Net (income) loss attributable to noncontrolling interests	(43,178)				(43,178)
Preferred share dividends	(11,666)				(11,666)
Unrealized holding gains (losses) during period, net of reclassification adjustment							18,024
Unrealized holding gains (losses) during period attributable to noncontrolling interests							(33)
Foreign currency translation adjustments	6,205							6,205
Foreign currency translation adjustments attributable to noncontrolling interests								25
Shares repurchased for treasury									(312,621)
Balance at end of period at Jun. 30, 2021	13,986,072	1,280,000	647	2,028,919	13,454,036	230,048	264,702	(34,654)	(3,007,578)
Non-redeemable noncontrolling interests, end of period at Jun. 30, 2021	918,874
Total shareholders’ equity at Jun. 30, 2021	14,904,946
Balance at beginning of period at Dec. 31, 2021	13,545,896	830,000	648	2,085,075	14,455,868	(64,600)	13,486	(78,086)	(3,761,095)
Preferred shares issued		0
Common shares issued, net			4
Amortization of share-based compensation				66,505
Issue costs on preferred shares				0
Other changes				19,081
Net income (loss)	601,377				601,377
Net (income) loss attributable to noncontrolling interests	(1,233)				(1,233)
Preferred share dividends	(20,368)				(20,368)
Unrealized holding gains (losses) during period, net of reclassification adjustment							(1,122,372)
Unrealized holding gains (losses) during period attributable to noncontrolling interests							0
Foreign currency translation adjustments	(71,293)							(71,293)
Foreign currency translation adjustments attributable to noncontrolling interests								0
Shares repurchased for treasury									(600,031)
Balance at end of period at Jun. 30, 2022	12,417,566	830,000	652	2,170,661	15,035,644	(1,258,265)	(1,108,886)	(149,379)	(4,361,126)
Non-redeemable noncontrolling interests, end of period at Jun. 30, 2022	0
Total shareholders’ equity at Jun. 30, 2022	12,417,566
Balance at beginning of period at Mar. 31, 2022		830,000	651	2,134,241	14,641,484	(649,445)	(568,591)	(80,854)	(4,037,342)
Preferred shares issued		0
Common shares issued, net			1
Amortization of share-based compensation				21,137
Issue costs on preferred shares				0
Other changes				15,283
Net income (loss)	403,945				403,945
Net (income) loss attributable to noncontrolling interests	399				399
Preferred share dividends	(10,184)				(10,184)
Unrealized holding gains (losses) during period, net of reclassification adjustment							(540,295)
Unrealized holding gains (losses) during period attributable to noncontrolling interests							0
Foreign currency translation adjustments	(68,525)							(68,525)
Foreign currency translation adjustments attributable to noncontrolling interests								0
Shares repurchased for treasury									(323,784)
Balance at end of period at Jun. 30, 2022	12,417,566	$ 830,000	$ 652	$ 2,170,661	$ 15,035,644	$ (1,258,265)	$ (1,108,886)	$ (149,379)	$ (4,361,126)
Non-redeemable noncontrolling interests, end of period at Jun. 30, 2022	0
Total shareholders’ equity at Jun. 30, 2022	$ 12,417,566

XML

Unaudited Consolidated Statements of Cash Flows - USD ($) $ in Thousands	6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021
Operating Activities
Net income (loss)	$ 601,377	$ 1,194,372
Adjustments to reconcile net income (loss) to net cash provided by operating activities:
Net realized (gains) losses	555,273	(379,049)
Equity in net (income) or loss of investment funds accounted for using the equity method and other income or loss	43,815	(181,028)
Amortization of intangible assets	54,374	29,688
Share-based compensation	66,518	57,564
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable	634,482	948,505
Unearned premiums, net of ceded unearned premiums	872,371	838,650
Premiums receivable	(1,085,790)	(781,391)
Deferred acquisition costs	(173,911)	(214,893)
Reinsurance balances payable	72,095	331,461
Other items, net	(186,636)	(231,307)
Net cash provided by (used for) operating activities	1,453,968	1,612,572
Investing Activities
Purchases of fixed maturity investments	(9,705,957)	(23,554,384)
Purchases of equity securities	(655,573)	(620,774)
Purchases of other investments	(920,384)	(1,033,134)
Proceeds from sales of fixed maturity investments	8,078,968	23,130,388
Proceeds from sales of equity securities	1,490,212	542,290
Proceeds from sales, redemptions and maturities of other investments	863,333	772,549
Proceeds from redemptions and maturities of fixed maturity investments	444,073	805,836
Net settlements of derivative instruments	(44,838)	17,286
Net (purchases) sales of short-term investments	(439,992)	(378,086)
Change in cash collateral related to securities lending	0	(826)
Purchase of operating affiliate	0	(546,349)
Purchases of fixed assets	(23,830)	(23,585)
Other	98,386	(204,889)
Net cash provided by (used for) investing activities	(815,602)	(1,093,678)
Financing Activities
Proceeds from issuance of preferred shares, net	0	485,821
Purchases of common shares under share repurchase program	(575,676)	(485,315)
Proceeds from common shares issued, net	(4,065)	185
Change in cash collateral related to securities lending	0	826
Third party investment in non-redeemable noncontrolling interests	0	15,971
Dividends paid to redeemable noncontrolling interests	0	(1,907)
Other	(82,007)	27,639
Preferred dividends paid	(20,368)	(20,805)
Net cash provided by (used for) financing activities	(682,116)	22,415
Effects of exchange rate changes on foreign currency cash and restricted cash	(42,790)	(13,390)
Increase (decrease) in cash and restricted cash	(86,540)	527,919
Cash and restricted cash, beginning of year	1,314,771	1,290,544
Cash and restricted cash, end of period	$ 1,228,231	$ 1,818,463

XML

Basis of Presentation and Recent Accounting Pronouncements

6 Months Ended

Jun. 30, 2022

Organization, Consolidation and Presentation of Financial Statements [Abstract]

Basis of Presentation and Recent Accounting Pronouncements

General

Arch Capital Group Ltd. (“Arch Capital”) is a public 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. The Company’s consolidated financial statements through June 30, 2021 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 11.

Basis of Presentation

The interim consolidated financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America (“GAAP”). 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. In the opinion of management, the accompanying unaudited interim consolidated financial statements reflect all adjustments (consisting of normally recurring accruals) necessary for a fair statement of results on an interim basis. The results of any interim period are not necessarily indicative of the results for a full year or any future periods.

Certain information and footnote disclosures normally included in financial statements prepared in accordance with GAAP have been condensed or omitted; however, management believes that the disclosures are adequate to make the information presented not misleading. This report should be read in conjunction with the Company’s Annual Report on Form 10-K for the year ended December 31, 2021

(“2021 Form 10-K”), including the Company’s audited consolidated financial statements and related notes.

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, comprehensive income, shareholders’ equity or cash flows. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.

Recent Accounting Pronouncements

Recently Issued Accounting Standards Adopted

For information regarding additional accounting standards that the Company has not yet adopted, see note 3(s), “Significant Accounting Policies—Recent Accounting Pronouncements,” of the notes to consolidated financial statements in the Company’s 2021 Form 10-K.

XML

Share Transactions

6 Months Ended

Jun. 30, 2022

Stockholders' Equity Note [Abstract]

Share Transactions

Share Repurchases 

The board of directors of Arch Capital has authorized the investment in Arch Capital’s common shares through a share repurchase program. Since the inception of the share repurchase program, Arch Capital has repurchased 433.3 million common shares for an aggregate purchase price of $5.86 billion. For the six months ended June 30, 2022, Arch Capital repurchased 12.7 million shares under the share repurchase program with an aggregate purchase price of $575.7 million. At June 30, 2022, $606.6 million of share repurchases were available under the program, which may be effected from time to time in open market or privately negotiated transactions. 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.

The 2022 Long-Term Incentive and Share Award Plan (the“2022 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, will be 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 June 30, 2022, 9,000,000 shares are available for future issuance.

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 Company’s board of directors 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.

XML

Earnings Per Common Share

6 Months Ended

Jun. 30, 2022

Earnings Per Share [Abstract]

Earnings Per Common Share

The following table sets forth the computation of basic and diluted earnings per common share:

	Three Months Ended				Six Months Ended
	June 30,				June 30,
	2022		2021		2022		2021
Numerator:
Net income (loss)	$	403,945	$	718,664	$	601,377	$	1,194,372
Amounts attributable to noncontrolling interests	399		(43,178)		(1,233)		(80,730)
Net income (loss) available to Arch	404,344		675,486		600,144		1,113,642
Preferred dividends	(10,184)		(11,666)		(20,368)		(22,069)
Net income (loss) available to Arch common shareholders	$	394,160	$	663,820	$	579,776	$	1,091,573
Denominator:
Weighted average common shares and common share equivalents outstanding — basic	369,241,193		397,743,402		371,728,683		399,267,183
Effect of dilutive common share equivalents:
Nonvested restricted shares	2,121,678		1,990,729		2,238,267		1,932,929
Stock options (1)	6,590,117		6,751,863		6,938,562		6,487,568
Weighted average common shares and common share equivalents outstanding — diluted	377,952,988		406,485,994		380,905,512		407,687,680
Earnings per common share:
Basic	$	1.07	$	1.67	$	1.56	$	2.73
Diluted	$	1.04	$	1.63	$	1.52	$	2.68

(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 the 2022 second quarter and 2021 second quarter, the number of stock options excluded were 773,163 and 1,974,849, respectively. For the six months ended June 30, 2022 and 2021, the number of stock options excluded were 778,724 and 2,395,749, respectively.

XML

Segment Information

6 Months Ended

Jun. 30, 2022

Segment Reporting [Abstract]

Segment Information

The Company classifies its businesses into three underwriting segments — insurance, reinsurance and mortgage — and two other 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, the 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; excess and surplus casualty; lenders products; professional lines; programs; property, energy, marine and aviation; travel, accident and health; and other (consisting of alternative markets, excess workers' compensation and surety business).

The reinsurance segment consists of the Company’s reinsurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include: casualty; marine and aviation; other specialty; property catastrophe; property excluding property catastrophe (losses on a single risk, both excess of loss and pro rata); and other (consisting of life reinsurance, casualty clash and other).

The mortgage segment includes the Company’s U.S. primary mortgage insurance business, investment and services related to U.S. credit-risk transfer (“CRT”) which are predominately with government sponsored enterprises (“GSE’s”) and international mortgage insurance and reinsurance operations. Arch Mortgage Insurance Company and United Guaranty Residential Insurance Company (combined “Arch MI U.S.”) are approved as eligible mortgage insurers by Federal National Mortgage Association (“Fannie Mae”) and Federal Home Loan Mortgage Corporation (“Freddie Mac”), each a GSE. Arch MI U.S. also includes Arch Mortgage Guaranty Company, which is not a GSE-approved entity.

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 11.

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:

	Three Months Ended
	June 30, 2022
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	1,705,167		$	1,793,398		$	371,896		$	3,869,727		$	—		$	3,869,727
Premiums ceded	(476,910)			(630,764)			(78,148)			(1,185,088)			—			(1,185,088)
Net premiums written	1,228,257			1,162,634			293,748			2,684,639			—			2,684,639
Change in unearned premiums	(126,113)			(234,635)			1,884			(358,864)			—			(358,864)
Net premiums earned	1,102,144			927,999			295,632			2,325,775			—			2,325,775
Other underwriting income (loss)	—			4,526			(1,556)			2,970			—			2,970
Losses and loss adjustment expenses	(629,759)			(537,578)			64,681			(1,102,656)			—			(1,102,656)
Acquisition expenses	(213,688)			(189,494)			(10,137)			(413,319)			—			(413,319)
Other operating expenses	(161,088)			(66,053)			(50,251)			(277,392)			—			(277,392)
Underwriting income (loss)	$	97,609		$	139,400		$	298,369		535,378			—			535,378
Net investment income										106,392			—			106,392
Net realized gains (losses)										(266,579)			—			(266,579)
Equity in net income (loss) of investment funds accounted for using the equity method										58,061			—			58,061
Other income (loss)										(11,777)			—			(11,777)
Corporate expenses (2)										(27,359)			—			(27,359)
Transaction costs and other (2)										(261)			—			(261)
Amortization of intangible assets										(27,207)			—			(27,207)
Interest expense										(32,795)			—			(32,795)
Net foreign exchange gains (losses)										87,775			—			87,775
Income (loss) before income taxes and income (loss) from operating affiliates										421,628			—			421,628
Income tax (expense) benefit										(22,323)			—			(22,323)
Income (loss) from operating affiliates										4,640			—			4,640
Net income (loss)										403,945			—			403,945
Amounts attributable to redeemable noncontrolling interests										399			—			399
Net income (loss) available to Arch										404,344			—			404,344
Preferred dividends										(10,184)			—			(10,184)
Net income (loss) available to Arch common shareholders										$	394,160		$	—		$	394,160
Underwriting Ratios
Loss ratio	57.1		%	57.9		%	(21.9)		%	47.4		%	—		%	47.4		%
Acquisition expense ratio	19.4		%	20.4		%	3.4		%	17.8		%	—		%	17.8		%
Other operating expense ratio	14.6		%	7.1		%	17.0		%	11.9		%	—		%	11.9		%
Combined ratio	91.1		%	85.4		%	(1.5)		%	77.1		%	—		%	77.1		%
Goodwill and intangible assets	$	236,661		$	166,437		$	464,916		$	868,014		$	—		$	868,014

(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 expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

	Three Months Ended
	June 30, 2021
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	1,368,867		$	1,358,020		$	391,511		$	3,117,505		$	240,942		$	3,286,291
Premiums ceded	(405,312)			(433,288)			(55,665)			(893,372)			(65,551)			(886,767)
Net premiums written	963,555			924,732			335,846			2,224,133			175,391			2,399,524
Change in unearned premiums	(98,128)			(187,708)			(1,625)			(287,461)			8,846			(278,615)
Net premiums earned	865,427			737,024			334,221			1,936,672			184,237			2,120,909
Other underwriting income (loss)	—			1,053			4,148			5,201			328			5,529
Losses and loss adjustment expenses	(545,880)			(463,823)			(9,880)			(1,019,583)			(140,248)			(1,159,831)
Acquisition expenses	(136,852)			(133,585)			(30,117)			(300,554)			(34,589)			(335,143)
Other operating expenses	(133,342)			(44,695)			(48,312)			(226,349)			(18,594)			(244,943)
Underwriting income (loss)	$	49,353		$	95,974		$	250,060		395,387			(8,866)			386,521
Net investment income										89,430			22,183			111,613
Net realized gains (losses)										163,394			39,513			202,907
Equity in net income (loss) of investment funds accounted for using the equity method										122,186			—			122,186
Other income (loss)										6,852			—			6,852
Corporate expenses (2)										(17,175)			—			(17,175)
Transaction costs and other (2)										1,444			(220)			1,224
Amortization of intangible assets										(14,388)			(898)			(15,286)
Interest expense										(31,439)			(4,261)			(35,700)
Net foreign exchange gains (losses)										(17,892)			117			(17,775)
Income (loss) before income taxes and income (loss) from operating affiliates										697,799			47,568			745,367
Income tax (expense) benefit										(50,953)			(226)			(51,179)
Income (loss) from operating affiliates										24,476			—			24,476
Net income (loss)										671,322			47,342			718,664
Amounts attributable to redeemable noncontrolling interests										(580)			(981)			(1,561)
Amounts attributable to nonredeemable noncontrolling interests										—			(41,617)			(41,617)
Net income (loss) available to Arch										670,742			4,744			675,486
Preferred dividends										(11,666)			—			(11,666)
Net income (loss) available to Arch common shareholders										$	659,076		$	4,744		$	663,820
Underwriting Ratios
Loss ratio	63.1		%	62.9		%	3.0		%	52.6		%	76.1		%	54.7		%
Acquisition expense ratio	15.8		%	18.1		%	9.0		%	15.5		%	18.8		%	15.8		%
Other operating expense ratio	15.4		%	6.1		%	14.5		%	11.7		%	10.1		%	11.5		%
Combined ratio	94.3		%	87.1		%	26.5		%	79.8		%	105.0		%	82.0		%
Goodwill and intangible assets	$	270,262		$	16,168		$	370,405		$	656,835		$	10,318		$	667,153

(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 expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

	Six Months Ended
	June 30, 2022
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	3,424,772		$	3,512,340		$	736,735		$	7,670,502		$	—		$	7,670,502
Premiums ceded	(989,619)			(1,210,582)			(154,867)			(2,351,723)			—			(2,351,723)
Net premiums written	2,435,153			2,301,758			581,868			5,318,779			—			5,318,779
Change in unearned premiums	(306,313)			(569,359)			3,301			(872,371)			—			(872,371)
Net premiums earned	2,128,840			1,732,399			585,169			4,446,408			—			4,446,408
Other underwriting income (loss)	—			5,362			3,505			8,867			—			8,867
Losses and loss adjustment expenses	(1,230,498)			(992,278)			119,285			(2,103,491)			—			(2,103,491)
Acquisition expenses	(409,338)			(361,490)			(20,650)			(791,478)			—			(791,478)
Other operating expenses	(327,913)			(135,829)			(103,593)			(567,335)			—			(567,335)
Underwriting income (loss)	$	161,091		$	248,164		$	583,716		$	992,971		$	—		$	992,971
Net investment income										186,828			—			186,828
Net realized gains (losses)										(558,993)			—			(558,993)
Equity in net income (loss) of investment funds accounted for using the equity method										94,366			—			94,366
Other income (loss)										(20,802)			—			(20,802)
Corporate expenses (2)										(59,294)			—			(59,294)
Transaction costs and other (2)										(658)			—			(658)
Amortization of intangible assets										(54,374)			—			(54,374)
Interest expense										(65,503)			—			(65,503)
Net foreign exchange gains (losses)										91,620			—			91,620
Income (loss) before income taxes and income (loss) from operating affiliates										606,161			—			606,161
Income tax (expense) benefit										(33,942)			—			(33,942)
Income (loss) from operating affiliates										29,158			—			29,158
Net income (loss)										601,377			—			601,377
Amounts attributable to redeemable noncontrolling interests										(1,233)			—			(1,233)
Net income (loss) available to Arch										600,144			—			600,144
Preferred dividends										(20,368)			—			(20,368)
Net income (loss) available to Arch common shareholders										$	579,776		$	—		$	579,776
Underwriting Ratios
Loss ratio	57.8		%	57.3		%	(20.4)		%	47.3		%	—		%	47.3		%
Acquisition expense ratio	19.2		%	20.9		%	3.5		%	17.8		%	—		%	17.8		%
Other operating expense ratio	15.4		%	7.8		%	17.7		%	12.8		%	—		%	12.8		%
Combined ratio	92.4		%	86.0		%	0.8		%	77.9		%	—		%	77.9		%

(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 expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

	Six Months Ended
	June 30, 2021
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	2,784,753		$	2,829,080		$	782,757		$	6,394,798		$	457,465		$	6,683,497
Premiums ceded	(826,359)			(905,236)			(111,716)			(1,841,519)			(102,763)			(1,775,516)
Net premiums written	1,958,394			1,923,844			671,041			4,553,279			354,702			4,907,981
Change in unearned premiums	(273,493)			(541,920)			(503)			(815,916)			(22,734)			(838,650)
Net premiums earned	1,684,901			1,381,924			670,538			3,737,363			331,968			4,069,331
Other underwriting income (loss)	—			(145)			11,045			10,900			739			11,639
Losses and loss adjustment expenses	(1,081,627)			(948,693)			(73,569)			(2,103,889)			(259,042)			(2,362,931)
Acquisition expenses	(265,074)			(251,610)			(60,199)			(576,883)			(62,741)			(639,624)
Other operating expenses	(270,455)			(105,209)			(97,443)			(473,107)			(32,869)			(505,976)
Underwriting income (loss)	$	67,745		$	76,267		$	450,372		$	594,384		$	(21,945)		$	572,439
Net investment income										168,159			42,310			210,469
Net realized gains (losses)										264,730			80,638			345,368
Equity in net income (loss) of investment funds accounted for using the equity method										193,872			—			193,872
Other income (loss)										5,111			—			5,111
Corporate expenses (2)										(40,643)			—			(40,643)
Transaction costs and other (2)										243			(935)			(692)
Amortization of intangible assets										(28,790)			(898)			(29,688)
Interest expense										(65,636)			(8,410)			(74,046)
Net foreign exchange gains (losses)										3,613			(1,325)			2,288
Income (loss) before income taxes and income (loss) from operating affiliates										1,095,043			89,435			1,184,478
Income tax (expense) benefit										(89,805)			(234)			(90,039)
Income (loss) from operating affiliates										99,933			—			99,933
Net income (loss)										1,105,171			89,201			1,194,372
Amounts attributable to redeemable noncontrolling interests										(463)			(1,953)			(2,416)
Amounts attributable to nonredeemable noncontrolling interests										—			(78,314)			(78,314)
Net income (loss) available to Arch										1,104,708			8,934			1,113,642
Preferred dividends										(22,069)			—			(22,069)
Net income (loss) available to Arch common shareholders										$	1,082,639		$	8,934		$	1,091,573
Underwriting Ratios
Loss ratio	64.2		%	68.7		%	11.0		%	56.3		%	78.0		%	58.1		%
Acquisition expense ratio	15.7		%	18.2		%	9.0		%	15.4		%	18.9		%	15.7		%
Other operating expense ratio	16.1		%	7.6		%	14.5		%	12.7		%	9.9		%	12.4		%
Combined ratio	96.0		%	94.5		%	34.5		%	84.4		%	106.8		%	86.2		%

(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 expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

XML

Reserve for Losses and Loss Adjustment Expenses

6 Months Ended

Jun. 30, 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:

	Three Months Ended				Six Months Ended
	June 30,				June 30,
	2022		2021		2022		2021
Reserve for losses and loss adjustment expenses at beginning of period	$	18,109,107	$	16,443,952	$	17,757,156	$	16,513,929
Unpaid losses and loss adjustment expenses recoverable	5,709,998		3,916,650		5,599,231		4,314,855
Net reserve for losses and loss adjustment expenses at beginning of period	12,399,109		12,527,302		12,157,925		12,199,074
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year	1,273,882		1,219,081		2,416,529		2,463,853
Prior years	(171,226)		(59,250)		(313,038)		(100,922)
Total net incurred losses and loss adjustment expenses	1,102,656		1,159,831		2,103,491		2,362,931
Retroactive reinsurance transactions (1)	—		—		—		(183,893)
Net foreign exchange (gains) losses and other	(248,655)		135,847		(281,295)		88,970
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year	(166,466)		(164,441)		(237,272)		(223,425)
Prior years	(578,668)		(607,911)		(1,234,873)		(1,193,029)
Total net paid losses and loss adjustment expenses	(745,134)		(772,352)		(1,472,145)		(1,416,454)
Net reserve for losses and loss adjustment expenses at end of period	12,507,976		13,050,628		12,507,976		13,050,628
Unpaid losses and loss adjustment expenses recoverable	5,686,348		4,146,020		5,686,348		4,146,020
Reserve for losses and loss adjustment expenses at end of period	$	18,194,324	$	17,196,648	$	18,194,324	$	17,196,648

(1)     During the 2021 first quarter, the Company entered into a reinsurance to close and other related agreements with Premia Managing Agency Limited (“Premia”), in connection with the 2018 and prior years of account related to the acquisition of Barbican Group Holdings Limited (“Barbican”).

Development on Prior Year Loss Reserves

2022 Second Quarter

During the 2022 second quarter, the Company recorded net favorable development on prior year loss reserves of $171.2 million, which consisted of $6.7 million from the insurance segment, $46.4 million from the reinsurance segment and $118.1 million from the mortgage segment.

The insurance segment’s net favorable development of $6.7 million, or 0.6 loss ratio points, for the 2022 second quarter consisted of $14.3 million of net favorable development in short-tailed lines and $7.5 million of net adverse development in medium-tailed and long-tailed lines. Net favorable development in short-tailed lines reflected $12.2 million of favorable development in lenders products, primarily from the 2021 accident year (i.e., the year in which a loss occurred). Net adverse development in medium-tailed lines included $6.3 million of adverse development in professional liability business, primarily from the 2018 and 2019 accident years, partially offset by favorable development in marine business of $2.6 million, primarily from the 2019 and prior accident years. Net adverse

development in long-tailed lines reflected $5.7 million related to executive assurance business, primarily from the 2013 and 2020 accident years.

The reinsurance segment’s net favorable development of $46.4 million, or 5.0 loss ratio points, for the 2022 second quarter consisted of $54.4 million of net favorable development in short-tailed and medium-tailed lines and $8.0 million of net adverse development in long-tailed lines. Net favorable development in short-tailed lines reflected $31.6 million of favorable development related to property other than property catastrophe business, primarily from 2016 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), $13.1 million of favorable development in other specialty business, primarily from the 2018 and 2021 underwriting year, and $6.3 million of favorable development related to property catastrophe business, primarily from the 2017 to 2021 underwriting years. Net favorable development in medium-tailed lines included $4.2 million in marine and aviation lines, across most underwriting years. Adverse development in long-tailed

lines reflected an increase in casualty reserves, across several years, most notably the 2013 and 2021 underwriting years.

The mortgage segment’s net favorable development was $118.1 million, or 39.9 loss ratio points, for the 2022 second quarter, primarily related to the U.S. first lien portfolio from the 2020 accident year. The Company’s credit risk transfer, international, second lien and student loan business also contributed to the favorable development.

2021 Second Quarter

During the 2021 second quarter, the Company recorded net favorable development on prior year loss reserves of $59.3 million, which consisted of $4.0 million from the insurance segment, $20.5 million from the reinsurance segment and $43.1 million from the mortgage segment, partially offset by $8.3 million unfavorable from the ‘other’ segment.

The insurance segment’s net favorable development of $4.0 million, or 0.5 loss ratio points, for the 2021 second quarter consisted of $28.5 million of net favorable development in short-tailed and long-tailed lines and $24.5 million of net adverse development in medium-tailed lines. Net favorable development in short-tailed lines reflected $10.7 million of favorable development in lenders products, primarily from the 2020 accident year, $7.1 million of favorable development from property (excluding marine), primarily from the 2017, 2019 and 2020 accident years and $6.7 million of favorable development in travel and accident, primarily from the 2020 accident year. Net favorable development in long-tailed lines reflected $5.6 million of favorable development related to construction and national accounts, primarily from the 2016 to 2020 accident years. Net adverse development in medium-tailed lines included $20.1 million of adverse development in contract binding business, primarily from the 2014 to 2019 accident years.

The reinsurance segment’s net favorable development of $20.5 million, or 2.8 loss ratio points, for the 2021 second quarter consisted of $53.7 million of net favorable development in short-tailed and medium-tailed lines and $33.2 million of net adverse development in long-tailed lines. Net favorable development in short-tailed lines reflected $61.6 million of favorable development related to other specialty, primarily from the 2019 underwriting year, which was partially offset by $17.1 million of net adverse development related to property catastrophe, primarily from the 2020 underwriting year. Net favorable development of $4.0 million in medium-tailed lines reflected favorable development in marine and aviation, across most underwriting years. Net adverse development in long-tailed lines reflected $34.2 million of adverse development in casualty, primarily from the 2018 underwriting year.

The mortgage segment’s net favorable development was $43.1 million, or 12.9 loss ratio points, for the 2021 second quarter, with the largest contributor being reserve releases associated with the various vintage credit risk transfer contracts that were called by the GSEs. The net favorable development also included reserve releases in our international portfolio and subrogation recoveries on second lien and student loan business.

Six Months Ended June 30, 2022

During the six months ended June 30, 2022, the Company recorded net favorable development on prior year loss reserves of $313.0 million, which consisted of $14.0 million from the insurance segment, $78.9 million from the reinsurance segment and $220.2 million from the mortgage segment.

The insurance segment’s net favorable development of $14.0 million, or 0.7 loss ratio points, for the 2022 period consisted of $33.2 million of net favorable development in short-tailed and $19.2 million of net adverse development in medium and long-tailed lines. Net favorable development in short-tailed lines reflected $30.8 million of favorable development in lenders products, primarily from the 2021 accident year. Net adverse development in medium-tailed lines included $13.6 million of adverse development in professional liability business, primarily from the 2018 and 2019 accident years, and $6.1 million of adverse development in contract binding business, across most accident years, partially offset by $5.5 million of favorable development in marine business, across most accident years, and $5.2 million of favorable development in program business, primarily from the 2020 accident year. Net adverse development in long-tailed lines primarily reflected $7.6 million of adverse development related to construction and national accounts, primarily from the 2020 and 2021 accident year.

The reinsurance segment’s net favorable development of $78.9 million, or 4.6 loss ratio points, for the 2022 period consisted of $89.7 million of net favorable development from short-tailed and medium-tailed lines, partially offset by $10.9 million of net adverse development from long-tailed lines. Net favorable development of $74.9 million in short-tailed lines reflected $47.4 million of favorable development from property other than property catastrophe business, primarily from the 2015 to 2021 underwriting years,$18.0 million of favorable development from other specialty business, primarily from the 2016 and 2021 underwriting years, and $9.7 million from property catastrophe, primarily from the 2018 and 2019 underwriting years. Net favorable development in medium-tailed lines included $14.9 million in marine and aviation lines, across most underwriting years. Adverse development in long-tailed lines reflected an increase in casualty reserves, primarily from the 2021 underwriting year.

The mortgage segment’s net favorable development was $220.2 million, or 37.6 loss ratio points, for the 2022 period, with the largest contributor being reserve releases associated with the U.S. first lien portfolio from the 2020 accident year. The Company’s credit risk transfer, international, second lien and student loan business also contributed to the favorable development.

Six Months Ended June 30, 2021

During the six months ended June 30, 2021, the Company recorded net favorable development on prior year loss reserves of $100.9 million, which consisted of $8.1 million from the insurance segment, $47.3 million from the reinsurance segment, $54.0 million from the mortgage segment, partially offset by $8.4 million of adverse development from the ‘other’ segment.

The insurance segment’s net favorable development of $8.1 million, or 0.5 loss ratio points, for the 2021 period consisted of $53.5 million of net favorable development in short-tailed and long-tailed lines, partially offset by $45.4 million of net adverse development in medium-tailed lines. Net favorable development of $49.4 million in short-tailed lines reflected $21.6 million of favorable development from property (excluding marine), primarily from the 2018 to 2020 accident years, $18.6 million of favorable development in lenders products, primarily from the 2020 accident year and $9.3 million of favorable development in travel and accident, primarily from the 2020 accident year. Net favorable development of in long-tailed lines included favorable development primarily related to construction and national accounts, primarily in the 2016 to 2019 accident years. Net adverse development in medium-tailed lines reflected $20.1 million of adverse development in contract binding business, primarily in the 2014 to 2019 accident years, $12.6 million of adverse development on programs business, primarily from the 2016 to 2020 accident years, and $11.2 million of adverse development in professional liability business, primarily from the 2019 and 2020 accident years.

The reinsurance segment’s net favorable development of $47.3 million, or 3.4 loss ratio points, for the 2021 period consisted of $72.1 million of net favorable development from short-tailed and medium-tailed lines, partially offset by $24.8 million of net adverse development from long-tailed lines. Net favorable development of $67.2 million in short-tailed lines reflected $78.2 million of favorable development from other specialty lines, primarily from the 2019 underwriting year and $28.8 million of favorable development from property other than property catastrophe business, partially offset by adverse development of $39.6 million from property catastrophe, primarily from the 2020 underwriting year. Adverse development in long-tailed lines reflected an increase in reserves from casualty, primarily from the 2018 underwriting year.

The mortgage segment’s net favorable development was $54.0 million, or 8.1 loss ratio points, for the 2021 period, primarily driven by favorable development in the credit risk transfer and international portfolios. Subrogation recoveries on second lien and student loan business also contributed.

XML

Allowance for Expected Credit Losses

6 Months Ended

Jun. 30, 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:

	Premium Receivables, Net of Allowance		Allowance for Expected Credit Losses
Three Months Ended June 30, 2022
Balance at beginning of period	$	3,223,504	$	39,073
Change for provision of expected credit losses (1)			(903)
Balance at end of period	$	3,634,182	$	38,170
Three Months Ended June 30, 2021
Balance at beginning of period	$	2,618,175	$	36,111
Change for provision of expected credit losses (1)			(132)
Balance at end of period	$	2,866,578	$	35,979
Six Months Ended June 30, 2022
Balance at beginning of period	$	2,633,280	$	39,958
Change for provision of expected credit losses (1)			(1,788)
Balance at end of period	$	3,634,182	$	38,170
Six Months Ended June 30, 2021
Balance at beginning of period	$	2,064,586	$	37,781
Change for provision of expected credit losses (1)			(1,802)
Balance at end of period	$	2,866,578	$	35,979

(1)Amounts deemed uncollectible are written-off in operating expenses. For the 2022 second quarter and 2021 second quarter, amounts written off were $3.3 million and $1.1 million, respectively. For the six months ended June 30, 2022 and 2021 period, amounts written off were $4.8 million and $1.2 million, respectively.

Reinsurance Recoverables

The following table provides a roll forward of the allowance for expected credit losses of the Company’s reinsurance recoverables:

	Reinsurance Recoverables, Net of Allowance		Allowance for Expected Credit Losses
Three Months Ended June 30, 2022
Balance at beginning of period	$	5,941,000	$	18,483
Change for provision of expected credit losses			(3,743)
Balance at end of period	$	5,938,511	$	14,740
Three Months Ended June 30, 2021
Balance at beginning of period	$	4,041,076	$	10,872
Change for provision of expected credit losses			157
Balance at end of period	$	4,314,515	$	11,029
Six Months Ended June 30, 2022
Balance at beginning of period	$	5,880,735	$	13,230
Change for provision of expected credit losses			1,510
Balance at end of period	$	5,938,511	$	14,740
Six Months Ended June 30, 2021
Balance at beginning of period	$	4,500,802	$	11,636
Change for provision of expected credit losses			(607)
Balance at end of period	$	4,314,515	$	11,029

The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums):

	June 30,			December 31
	2022			2021
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	$	5,938,511		$	5,880,735
% due from carriers with A.M. Best rating of “A-” or better	69.3		%	69.7		%
% due from all other rated carriers	0.1		%	0.1		%
% due from all other carriers with no A.M. Best rating (1)	30.6		%	30.2		%
Largest balance due from any one carrier as % of total shareholders’ equity	7.8		%	6.7		%

(1)    At June 30, 2022 and December 31, 2021 over 93% and 91% of such amount were 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:

	Contract-holder Receivables, Net of Allowance		Allowance for Expected Credit Losses
Three Months Ended June 30, 2022
Balance at beginning of period	$	1,810,199	$	3,731
Change for provision of expected credit losses			(726)
Balance at end of period	$	1,758,018	$	3,005
Three Months Ended June 30, 2021
Balance at beginning of period	$	1,919,655	$	5,853
Change for provision of expected credit losses			(1,382)
Balance at end of period	1,882,948		$	4,471
Six Months Ended June 30, 2022
Balance at beginning of period	$	1,828,691	$	3,437
Change for provision of expected credit losses			(432)
Balance at end of period	$	1,758,018	$	3,005
Six Months Ended June 30, 2021
Balance at beginning of period	$	1,986,924	$	8,638
Change for provision of expected credit losses			(4,167)
Balance at end of period	1,882,948		$	4,471

XML

Investment Information

6 Months Ended

Jun. 30, 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
June 30, 2022
Fixed maturities:
Corporate bonds	$	7,288,555	$	32,021	$	(655,664)	$	(38,494)	$	7,950,692
Mortgage backed securities	698,168		4,427		(55,898)		—		749,639
Municipal bonds	417,380		4,129		(18,936)		(298)		432,485
Commercial mortgage backed securities	1,023,088		1,533		(42,056)		(3,594)		1,067,205
U.S. government and government agencies	4,368,150		25,112		(240,786)		—		4,583,824
Non-U.S. government securities	2,181,943		16,175		(163,724)		(1,335)		2,330,827
Asset backed securities	1,607,745		1,001		(80,267)		(14,689)		1,701,700
Total	17,585,029		84,398		(1,257,331)		(58,410)		18,816,372
Short-term investments	2,227,874		2,458		(1,257)		—		2,226,673
Total	$	19,812,903	$	86,856	$	(1,258,588)	$	(58,410)	$	21,043,045
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
June 30, 2022
Fixed maturities:
Corporate bonds	$	6,583,215	$	(580,235)	$	489,098	$	(75,429)	$	7,072,313	$	(655,664)
Mortgage backed securities	595,485		(46,415)		61,751		(9,483)		657,236		(55,898)
Municipal bonds	271,481		(17,908)		8,876		(1,028)		280,357		(18,936)
Commercial mortgage backed securities	973,212		(42,056)		—		—		973,212		(42,056)
U.S. government and government agencies	4,029,550		(235,510)		69,596		(5,276)		4,099,146		(240,786)
Non-U.S. government securities	1,929,278		(148,781)		103,969		(14,943)		2,033,247		(163,724)
Asset backed securities	1,292,087		(73,575)		136,119		(6,692)		1,428,206		(80,267)
Total	15,674,308		(1,144,480)		869,409		(112,851)		16,543,717		(1,257,331)
Short-term investments	505,798		(1,257)		—		—		505,798		(1,257)
Total	$	16,180,106	$	(1,145,737)	$	869,409	$	(112,851)	$	17,049,515	$	(1,258,588)
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 June 30, 2022, on a lot level basis, approximately 8,360 security lots out of a total of approximately 10,440 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 $5.7 million. 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.

	June 30, 2022				December 31, 2021
Maturity	Estimated Fair Value		Amortized Cost		Estimated Fair Value		Amortized Cost
Due in one year or less	$	412,194	$	414,752	$	300,889	$	299,772
Due after one year through five years	9,423,547		9,927,876		8,355,255		8,339,387
Due after five years through 10 years	4,070,099		4,512,685		4,689,155		4,684,393
Due after 10 years	350,188		442,515		505,758		493,927
	14,256,028		15,297,828		13,851,057		13,817,479
Mortgage backed securities	698,168		749,639		408,477		411,110
Commercial mortgage backed securities	1,023,088		1,067,205		1,046,484		1,047,867
Asset backed securities	1,607,745		1,701,700		2,692,091		2,697,367
Total	$	17,585,029	$	18,816,372	$	17,998,109	$	17,973,823

Equity Securities, at Fair Value

At June 30, 2022, the Company held $0.8 billion of equity securities, at fair value, compared to $1.8 billion at December 31, 2021. Such holdings include publicly traded common stocks primarily in the consumer cyclical and non-cyclical, technology, communication and financial sectors and exchange-traded funds in fixed income, equity and other sectors.

Other Investments, at Fair Value

The following table summarizes the Company’s other investments and other investable assets:

	June 30, 2022		December 31, 2021
Fixed maturities	$	525,451	$	416,698
Other investments	1,054,771		1,432,553
Short-term investments	39,657		97,806
Equity securities	14,489		26,493
Total	$	1,634,368	$	1,973,550

The following table summarizes the Company’s other investments, as detailed in the previous table, by strategy:

	June 30, 2022		December 31, 2021
Lending	$	427,812	$	536,345
Investment grade fixed income	221,484		147,810
Term loan investments	152,277		484,950
Private equity	124,282		91,126
Energy	74,234		81,692
Credit related funds	54,682		70,278
Infrastructure	—		20,352
Total	$	1,054,771	$	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:

	June 30, 2022		December 31, 2021
Credit related funds	$	1,119,711	$	1,022,334
Private equity	646,904		436,042
Real estate	455,044		396,395
Lending	447,028		376,649
Equities	350,587		395,090
Infrastructure	231,816		230,070
Energy	115,514		119,141
Fixed income	129,737		101,890
Total	$	3,496,341	$	3,077,611

Certain of the Company’s other investments 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 has determined that it is not required to consolidate these investments because it is not the primary beneficiary of 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 line item:

	June 30, 2022		December 31, 2021
Investments accounted for using the equity method (1)	3,496,341		3,077,611
Investments accounted for using the fair value option (2)	128,826		170,595
Total	$	3,625,167	$	3,248,206

(1)    Aggregate unfunded commitments were $3.0 billion at June 30, 2022, compared to $2.6 billion at December 31, 2021.

(2)    Aggregate unfunded commitments were $21.7 million at June 30, 2022, compared to $18.8 million at December 31, 2021.

Net Investment Income

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

	June 30,
	2022		2021
Three Months Ended
Fixed maturities	$	105,342	$	88,625
Term loans	401		16,879
Equity securities	6,121		8,584
Short-term investments	4,120		1,138
Other (1)	7,583		19,950
Gross investment income	123,567		135,176
Investment expenses	(17,175)		(23,563)
Net investment income	$	106,392	$	111,613
Six Months Ended
Fixed maturities	$	187,395	$	179,251
Term loans	2,018		31,607
Equity securities	12,359		14,234
Short-term investments	6,695		1,745
Other (1)	18,042		34,305
Gross investment income	226,509		261,142
Investment expenses	(39,681)		(50,673)
Net investment income	$	186,828	$	210,469

(1)    Includes income distributions from investment funds and other items.

Net Realized Gains (Losses)

Net realized gains (losses), which include changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings were as follows:

	June 30,
	2022		2021
Three Months Ended
Available for sale securities:
Gross gains on investment sales	$	15,186	$	115,541
Gross losses on investment sales	(57,176)		(50,627)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	(39,255)		10,912
Other investments	(21,710)		60,884
Equity securities	(2,124)		5,492
Short-term investments	(2,008)		(104)
Equity securities, at fair value:
Net realized gains (losses) on sales during the period	16,879		33,570
Net unrealized gains (losses) on equity securities still held at reporting date	(106,375)		65,847
Allowance for credit losses:
Investments related	(25,026)		896
Underwriting related	842		1,381
Derivative instruments (1)	(45,684)		(51,109)
Other	(128)		10,224
Net realized gains (losses)	$	(266,579)	$	202,907
Six Months Ended
Available for sale securities:
Gross gains on investment sales	$	34,893	$	180,543
Gross losses on investment sales	(165,523)		(113,625)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	(69,844)		27,465
Other investments	(17,321)		107,739
Equity securities	(5,437)		7,557
Short-term investments	(2,157)		632
Equity securities, at fair value:
Net realized gains (losses) on sales during the period	82,090		71,419
Net unrealized gains (losses) on equity securities still held at reporting date	(282,570)		85,555
Allowance for credit losses:
Investments related	(56,748)		(752)
Underwriting related	(3,444)		6,649
Derivative instruments (1)	(69,395)		(14,993)
Other	(3,537)		(12,821)
Net realized gains (losses)	$	(558,993)	$	345,368

(1)    See note 9 for information on the Company’s derivative instruments.

Equity in Net Income (Loss) of Investment Funds Accounted for Using the Equity Method

The Company recorded $58.1 million of equity in net income related to investment funds accounted for using the equity method in the 2022 second quarter, compared to income of $122.2 million for the 2021 second quarter and an income of $94.4 million for the six months ended June 30, 2022, compared to income of $193.9 million for six months ended June 30, 2021. 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). Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds.

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 of June 30, 2022, the Company owned approximately 29.86% of the issued shares of Coface, or 30.09% excluding treasury shares, with a carrying value of $536.0 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 June 30, 2022 the Company’s carrying value in Greysbridge was $309.6 million, compared to $375.7 million at December 31, 2021, which reflected the Company’s 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.

Income from operating affiliates for the 2022 second quarter was income of $4.6 million, compared to an income of $24.5 million, for the 2021 second quarter and income of $29.2 million for the six months ended June 30, 2022, compared to income of $99.9 million for six months ended June 30, 2021.

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:

	Structured Securities (1)		Municipal Bonds		Corporate Bonds		Total
Three Months Ended June 30, 2022
Balance at beginning of period	$	6,998	$	106	$	27,041	$	34,145
Additions for current-period provision for expected credit losses	4,788		252		13,466		18,506
Additions (reductions) for previously recognized expected credit losses	6,705		(60)		(205)		6,440
Reductions due to disposals	(208)		—		(473)		(681)
Balance at end of period	$	18,283	$	298	$	39,829	$	58,410
Three Months Ended June 30, 2021
Balance at beginning of period	$	1,207	$	2	$	2,621	$	3,830
Additions for current-period provision for expected credit losses	52		—		7		59
Additions (reductions) for previously recognized expected credit losses	(383)		4		(412)		(791)
Reductions due to disposals	(117)		—		(857)		(974)
Balance at end of period	$	759	$	6	$	1,359	$	2,124
Six Months Ended June 30, 2022
Balance at beginning of period	$	802	$	2	$	2,079	$	2,883
Additions for current-period provision for expected credit losses	10,778		347		38,616		49,741
Additions (reductions) for previously recognized expected credit losses	7,192		(51)		(220)		6,921
Reductions due to disposals	(489)		—		(646)		(1,135)
Balance at end of period	$	18,283	$	298	$	39,829	$	58,410
Six Months Ended June 30, 2021
Balance at beginning of period	$	1,490	$	11	$	896	$	2,397
Additions for current-period provision for expected credit losses	234		—		2,428		2,662
Additions (reductions) for previously recognized expected credit losses	(765)		(5)		(952)		(1,722)
Reductions due to disposals	(200)		—		(1,013)		(1,213)
Balance at end of period	$	759	$	6	$	1,359	$	2,124

(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

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. See note 18, “Commitments and Contingencies,” of the notes to consolidated financial statements in the Company’s 2021 Form 10-K.

The following table details the value of the Company’s restricted assets:

	June 30, 2022		December 31, 2021
Assets used for collateral or guarantees:
Affiliated transactions	$	4,193,561	$	4,223,955
Third party agreements	2,953,800		2,721,160
Deposits with U.S. regulatory authorities	781,024		798,100
Deposits with non-U.S. regulatory authorities	485,341		506,517
Total restricted assets	$	8,413,726	$	8,249,732

Reconciliation of Cash and Restricted Cash

The following table details reconciliation of cash and restricted cash within the Consolidated Balance Sheets:

	June 30, 2022		December 31, 2021
Cash	$	813,548	$	858,668
Restricted cash (included in ‘other assets’)	$	414,683	$	456,103
Cash and restricted cash	$	1,228,231	$	1,314,771

XML

Fair Value

6 Months Ended

Jun. 30, 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 average number of 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. The Company did not adjust any of the prices obtained from the independent pricing sources at June 30, 2022.

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. Where quotes are unavailable, fair value is determined by the Investment Manager using quantitative and qualitative assessments such as internally modeled values. Of the $22.4 billion of financial assets and liabilities measured at fair value at June 30, 2022, approximately $10.9 million, or 0.0%, were priced using non-binding broker-dealer quotes or modeled valuations. 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 or modeled valuations.

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 a low level of transparency on the inputs used in the pricing process.

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. 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.

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. The pricing services also review prepayment speeds and other indicators, when applicable. 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. The pricing services also review prepayment speeds and other indicators, when applicable. 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. Certain equity securities are included in Level 2 of the valuation hierarchy as the significant inputs used in the pricing process for such securities are observable market inputs. Other equity 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’s other investments 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. The fair values for certain of the Company’s other investments are determined using net asset values as advised by external fund managers. The net asset value is based on the fund manager’s valuation of the underlying holdings in accordance with the fund’s governing documents. 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. 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 June 30, 2022:

			Estimated Fair Value Measurements 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	$	7,288,555	$	—	$	7,284,985	$	3,570
Mortgage backed securities	698,168		—		698,168		—
Municipal bonds	417,380		—		417,380		—
Commercial mortgage backed securities	1,023,088		—		1,023,088		—
U.S. government and government agencies	4,368,150		4,341,399		26,751		—
Non-U.S. government securities	2,181,943		—		2,181,943		—
Asset backed securities	1,607,745		—		1,604,878		2,867
Total	17,585,029		4,341,399		13,237,193		6,437
Short-term investments	2,227,874		2,049,235		178,639		—
Equity securities, at fair value	772,689		736,343		33,440		2,906
Derivative instruments (2)	122,033		—		122,033		—
Residential mortgage loans	3,929		—		3,929		—
Fair value option:
Corporate bonds	522,707		—		522,707		—
Non-U.S. government bonds	611		—		611		—
Asset backed securities	2,133		—		2,133		—
Short-term investments	39,657		886		38,771		—
Equity securities	14,489		10,097		—		4,392
Other investments	178,461		—		145,130		33,331
Other investments measured at net asset value (1)	876,310
Total	1,634,368		10,983		709,352		37,723
Total assets measured at fair value	$	22,345,922	$	7,137,960	$	14,284,586	$	47,066
Liabilities measured at fair value:
Other liabilities	$	(16,205)	$	—	$	—	$	(16,205)
Derivative instruments (2)	(75,147)		—		(75,147)		—
Total liabilities measured at fair value	$	(91,352)	$	—	$	(75,147)	$	(16,205)

(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 9.

The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2021:

			Estimated Fair Value Measurements 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
Short-term investments	1,734,716		1,052,822		681,894		—
Equity securities, at fair value	1,804,170		1,762,864		38,388		2,918
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		—
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:
Other 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 9.

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:

	Assets												Liabilities
s	Available For Sale				Fair Value Option						Fair Value
	Structured Securities (1)		Corporate Bonds		Corporate Bonds		Other Investments		Equity Securities		Equity Securities		Other Liabilities
Three Months Ended June 30, 2022
Balance at beginning of period	$	3,152	$	3,570	$	—	$	22,602	$	4,511	$	2,768	$	(17,591)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	(1)		—		—		27		(119)		(89)		(97)
Included in other comprehensive income	(85)		—		—		—		—		—		1,483
Purchases, issuances, sales and settlements
Purchases	—		—		—		10,702		—		227		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		—		—		—		—
Settlements	(199)		—		—		—		—		—		—
Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of period	$	2,867	$	3,570	$	—	$	33,331	$	4,392	$	2,906	$	(16,205)
Three Months Ended June 30, 2021
Balance at beginning of period	$	3,472	$	13	$	989	$	67,930	$	71,176	$	43,112	$	(465)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	12		—		9		633		2,502		922		(1)
Included in other comprehensive income	(57)		—		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		—		5,638		—		5,102		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(301)		—		—		—
Settlements	(3)		—		—		—		—		—		—
Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of period	$	3,424	$	13	$	998	$	73,900	$	73,678	$	49,136	$	(466)
Six Months Ended June 30, 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)	9		—		—		34		(356)		(236)		(195)
Included in other comprehensive income	(145)		—		—		—		—		—		950
Purchases, issuances, sales and settlements
Purchases	—		—		—		10,770		—		227		—
Issuances	—		—		—		—		—		—		—
Sales (3)	—		—		—		(2,471)		—		(3)		—
Settlements	(344)		—		—		(2,983)		—		—		—
Transfers in and/or out of Level 3	—		3,557		—		—		—		—		—
Balance at end of period	$	2,867	$	3,570	$	—	$	33,331	$	4,392	$	2,906	$	(16,205)
Six Months Ended June 30, 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)	(56)		—		13		881		4,690		1,826		(5)
Included in other comprehensive income	57		—		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		—		13,003		—		5,295		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(7,087)		—		—		—
Settlements	(3)		—		—		—		—		—		—
Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of period	$	3,424	$	13	$	998	$	73,900	$	73,678	$	49,136	$	(466)

(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

(2)    Gains or losses were included in net realized gains (losses).

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 June 30, 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 June 30, 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 $2.6 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 values of the senior notes are classified within Level 2.

XML

Derivative Instruments

6 Months Ended

Jun. 30, 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)
June 30, 2022
Futures contracts	$	49,695	$	(22,561)	$	2,794,246
Foreign currency forward contracts	9,556		(18,884)		908,192
TBAs	—		—		—
Other	62,782		(33,702)		3,849,244
Total	$	122,033	$	(75,147)
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 June 30, 2022 or December 31, 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. Contractual close-out netting reduces derivatives credit exposure from gross to net exposure.

At June 30, 2022, asset derivatives and liability derivatives of $116.9 million and $75.1 million, respectively, 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 preceding table 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	June 30,
hedging instruments:	2022		2021
Three Months Ended
Net realized gains (losses):
Futures contracts	$	(39,205)	$	(54,759)
Foreign currency forward contracts	(25,638)		1,295
TBAs	—		—
Other (1)	19,159		2,355
Total	$	(45,684)	$	(51,109)
Six Months Ended
Net realized gains (losses):
Futures contracts	$	(85,979)	$	(7,321)
Foreign currency forward contracts	(27,676)		(20,776)
TBAs	(51)		—
Other (1)	44,311		13,104
Total	$	(69,395)	$	(14,993)

(1)    Includes realized gains and losses on swaps, options and other derivatives contracts.

XML

Commitments and Contingencies

6 Months Ended

Jun. 30, 2022

Commitments and Contingencies Disclosure [Abstract]

Commitments and Contingencies

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 $3.5 billion at June 30, 2022, compared to $3.0 billion at December 31, 2021.

Interest Paid

Interest paid on the Company’s senior notes and other borrowings were $64.6 million for the six months ended June 30, 2022, compared to $74.7 million for the 2021 period

XML

Variable Interest Entities and Noncontrolling Interests

6 Months Ended

Jun. 30, 2022

Noncontrolling Interest [Abstract]

Variable Interest Entity and Noncontrolling Interests

Somers

In March 2014, the Company invested $100.0 million and acquired approximately 11% of Somers’ outstanding common equity. Somers was considered a VIE and the Company concluded that it was the primary beneficiary of Somers, through June 30, 2021. As such, the results of Somers were included in the Company’s consolidated financial statements as of and for the periods ended June 30, 2021.

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 contemplated by the Merger Agreement and the related Greysbridge equity financing closed on July 1, 2021. In connection therewith and effective July 1, 2021, Somers became wholly owned by Greysbridge, and Greysbridge is now 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. Beginning in the 2021 third quarter, the Company classifies its investment as ‘investments in operating affiliates’ on the Company’s balance sheets and is accounted for under the equity method.

Somers generated $47.0 million of cash provided by operating activities, $96.3 million of cash provided by

investing activities and $2.0 million of cash used for financing activities for the six months ended June 30, 2021.

Non-redeemable noncontrolling interests

Through June 30, 2021, the Company accounted for the portion of Somers’s common equity attributable to third party investors in the shareholders’ equity section of its consolidated balance sheets. The portion of Somers’s income or loss attributable to third party investors was recorded in the consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests.’

The following table sets forth activity in the non-redeemable noncontrolling interests:

	June 30,
	2021
Three Months Ended
Balance, beginning of period	$	876,864
Additional paid in capital attributable to noncontrolling interests	383
Amounts attributable to noncontrolling interests	41,617
Other comprehensive income (loss) attributable to noncontrolling interests	10
Balance, end of period	$	918,874
Six Months Ended
Balance, beginning of year	$	823,007
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 period	$	918,874

Redeemable noncontrolling interests

Through June 30, 2021, the Company accounted for redeemable noncontrolling interests in the mezzanine section of its consolidated balance sheets in accordance with applicable accounting guidance. Such redeemable noncontrolling interests primarily related to the Somers Preference Shares issued in late March 2014 with a par value of $0.01 per share and a liquidation preference of $25.00 per share. The Somers Preference Shares were issued at a discounted amount of $24.50 per share. Through June 30, 2021 preferred dividends, including the accretion of the discount and issuance costs, were included in ‘net (income) loss attributable to noncontrolling interests’ in the Company’s consolidated statements of income.

The following table sets forth activity in the redeemable non-controlling interests:

	June 30,
	2022		2021
Three Months Ended
Balance, beginning of period	$	9,763	$	57,670
Accretion of preference share issuance costs	—		23
Other	(1,304)		(160)
Balance, end of period	$	8,459	$	57,533
Six Months Ended
Balance, beginning of year	$	9,233	$	58,548
Accretion of preference share issuance costs	—		46
Other	(774)		(1,061)
Balance, end of period	$	8,459	$	57,533

The portion of income or loss attributable to third party investors, recorded in the Company’s consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests,’ are summarized in the table below:

	June 30,
	2022		2021
Three Months Ended
Amounts attributable to non-redeemable noncontrolling interests	$	—	$	(41,617)
Amounts attributable to redeemable noncontrolling interests	399		(1,561)
Net (income) loss attributable to noncontrolling interests	$	399	$	(43,178)
Six Months Ended
Amounts attributable to non-redeemable noncontrolling interests	$	—	$	(78,314)
Amounts attributable to redeemable noncontrolling interests	(1,233)		(2,416)
Net (income) loss attributable to noncontrolling interests	$	(1,233)	$	(80,730)

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.

			June 30, 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)	$	61,328	$	(68)	$	274	$	206	$	—	$	108,368	$	(159)	$	424	$	265
2018-1 Ltd. (Apr-18)	122,190		(342)		965		623		—		181,136		(528)		1,268		740
2018-3 Ltd. (Oct-18)	244,257		(566)		1,522		956		—		302,563		(1,018)		2,496		1,478
2019-1 Ltd. (Mar-19)	134,972		(127)		988		861		—		181,324		(380)		5,807		5,427
2019-2 Ltd. (Apr-19)	383,737		(426)		5,323		4,897		—		398,316		(515)		3,998		3,483
2019-3 Ltd. (Jul-19)	296,466		(282)		2,154		1,872		—		409,859		(584)		3,190		2,606
2019-4 Ltd. (Oct-19)	312,668		(306)		4,702		4,396		—		411,954		(462)		4,759		4,297
2020-2 Ltd. (Sep-20)	151,543		(58)		1,331		1,273		442		217,766		(177)		1,984		1,807
2020-3 Ltd. (Nov-20)	303,011		(26)		4,388		4,362		10,779		348,818		(128)		5,793		5,665
2020-4 Ltd. (Dec-20)	124,672		23		1,267		1,290		5,900		176,826		(50)		1,630		1,580
2021-1 Ltd. (Mar-21)	519,641		(1,006)		2,771		1,765		48,841		568,986		(303)		3,283		2,980
2021-2 Ltd. (Jun-21)	492,837		(577)		3,505		2,928		85,717		522,807		281		4,124		4,405
2021-3 Ltd. (Sep-21)	507,873		(1,082)		2,878		1,796		131,518		507,873		(411)		3,446		3,035
2022-1 Ltd. (Jan-22)	283,500		(282)		2,020		1,738		33,260
Total	$	3,938,695	$	(5,125)	$	34,088	$	28,963	$	316,457	$	4,336,596	$	(4,434)	$	42,202	$	37,768

(1) Coverage from a separate panel of reinsurers remaining at June 30, 2022.

XML

Other Comprehensive Income (Loss)

6 Months Ended

Jun. 30, 2022

Comprehensive Income Note Disclosure [Abstract]

Other Comprehensive Income (Loss)

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):

		Amounts Reclassified from AOCI
	Consolidated Statement of Income	Three Months Ended				Six Months Ended
Details About	Line Item That Includes	June 30,				June 30,
AOCI Components	Reclassification	2022		2021		2022		2021
Unrealized appreciation (decline) on available-for-sale investments
	Net realized gains (losses)	$	(41,990)	$	64,914	$	(130,630)	$	66,918
	Provision for credit losses	(25,026)		896		(56,748)		(751)
	Total before tax	(67,016)		65,810		(187,378)		66,167
	Income tax (expense) benefit	9,306		(5,263)		27,390		(8,317)
	Net of tax	$	(57,710)	$	60,547	$	(159,988)	$	57,850

	Before Tax Amount		Tax Expense (Benefit)		Net of Tax Amount
Three Months Ended June 30, 2022
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(676,048)	$	(78,043)	$	(598,005)
Less reclassification of net realized gains (losses) included in net income	(67,016)		(9,306)		(57,710)
Foreign currency translation adjustments	(68,562)		(37)		(68,525)
Other comprehensive income (loss)	$	(677,594)	$	(68,774)	$	(608,820)
Three Months Ended June 30, 2021
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	91,057	$	12,486	$	78,571
Less reclassification of net realized gains (losses) included in net income	65,810		5,263		60,547
Foreign currency translation adjustments	6,392		187		6,205
Other comprehensive income (loss)	$	31,639	$	7,410	$	24,229
Six Months Ended June 30, 2022
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(1,460,938)	$	(178,578)	$	(1,282,360)
Less reclassification of net realized gains (losses) included in net income	(187,378)		(27,390)		(159,988)
Foreign currency translation adjustments	(71,127)		166		(71,293)
Other comprehensive income (loss)	$	(1,344,687)	$	(151,022)	$	(1,193,665)
Six Months Ended June 30, 2021
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(203,303)	$	(20,124)	$	(183,179)
Less reclassification of net realized gains (losses) included in net income	66,167		8,317		57,850
Foreign currency translation adjustments	(22,023)		356		(22,379)
Other comprehensive income (loss)	$	(291,493)	$	(28,085)	$	(263,408)

XML

Income Taxes

6 Months Ended

Jun. 30, 2022

Income Tax Disclosure [Abstract]

Income Taxes

The Company’s income tax provision on income before income taxes, including income (loss) from operating affiliates, resulted in an effective tax rate of 5.3% for the six months ended June 30, 2022, compared to 7.0% for the six months ended June 30, 2021.

The Company’s effective tax rate, which is based upon the expected annual effective tax rate, may fluctuate from period to period based on the relative mix of income or loss reported by jurisdiction and the varying tax rates in each jurisdiction.

The Company had a net deferred tax asset of $411.1 million at June 30, 2022, compared to a net deferred tax asset of $194.0 million at December 31, 2021. The change is primarily a result of market value fluctuations in the investment portfolio. In addition, the Company paid $128.6 million and $141.1 million of income taxes for the six months ended June 30, 2022 and 2021, respectively.

XML

Legal Proceedings	6 Months Ended
	Jun. 30, 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 June 30, 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.

XML

Transactions With Related Parties

6 Months Ended

Jun. 30, 2022

Related Party Transactions [Abstract]

Transactions with related parties

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 June 30, 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 became owned 40% by the Company, 30% by certain funds managed by Kelso and 30% by certain funds managed by Warburg, the Company entered into certain reinsurance transactions with Somers. For the six months ended June 30, 2022, the Company ceded premiums written related to such transactions of $424.6 million (which includes reinsurance transactions in force 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 June 30, 2022, reinsurance recoverable on unpaid and paid losses from Somers was $964.7 million, with a reinsurance balance payable to Somers of $358.4 million. See note 11, “Variable Interest Entities and Noncontrolling Interests,” for information about Somers.

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 June 30, 2022, the Company owns $35.0 million in aggregate principal amount of Somers Group Holdings Ltd’s 6.5% senior notes, due July 2, 2029 and approximately 6.6% of Somers’s preference shares.

XML

Basis of Presentation and Recent Accounting Pronouncements (Policies)	6 Months Ended
	Jun. 30, 2022
Organization, Consolidation and Presentation of Financial Statements [Abstract]
Basis of accounting	The interim consolidated financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America (“GAAP”). 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. In the opinion of management, the accompanying unaudited interim consolidated financial statements reflect all adjustments (consisting of normally recurring accruals) necessary for a fair statement of results on an interim basis. The results of any interim period are not necessarily indicative of the results for a full year or any future periods.
Reclassification of prior periods	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, comprehensive income, shareholders’ equity or cash flows.
Recent accounting pronouncements	For information regarding additional accounting standards that the Company has not yet adopted, see note 3(s), “Significant Accounting Policies—Recent Accounting Pronouncements,” of the notes to consolidated financial statements in the Company’s 2021 Form 10-K

XML

Earnings Per Common Share (Tables)

6 Months Ended

Jun. 30, 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:

	Three Months Ended				Six Months Ended
	June 30,				June 30,
	2022		2021		2022		2021
Numerator:
Net income (loss)	$	403,945	$	718,664	$	601,377	$	1,194,372
Amounts attributable to noncontrolling interests	399		(43,178)		(1,233)		(80,730)
Net income (loss) available to Arch	404,344		675,486		600,144		1,113,642
Preferred dividends	(10,184)		(11,666)		(20,368)		(22,069)
Net income (loss) available to Arch common shareholders	$	394,160	$	663,820	$	579,776	$	1,091,573
Denominator:
Weighted average common shares and common share equivalents outstanding — basic	369,241,193		397,743,402		371,728,683		399,267,183
Effect of dilutive common share equivalents:
Nonvested restricted shares	2,121,678		1,990,729		2,238,267		1,932,929
Stock options (1)	6,590,117		6,751,863		6,938,562		6,487,568
Weighted average common shares and common share equivalents outstanding — diluted	377,952,988		406,485,994		380,905,512		407,687,680
Earnings per common share:
Basic	$	1.07	$	1.67	$	1.56	$	2.73
Diluted	$	1.04	$	1.63	$	1.52	$	2.68

(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 the 2022 second quarter and 2021 second quarter, the number of stock options excluded were 773,163 and 1,974,849, respectively. For the six months ended June 30, 2022 and 2021, the number of stock options excluded were 778,724 and 2,395,749, respectively.

XML

Segment Information (Tables)

6 Months Ended

Jun. 30, 2022

Segment Reporting [Abstract]

Analysis of underwriting income or loss by segment and reconciliation to net income 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:

	Three Months Ended
	June 30, 2022
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	1,705,167		$	1,793,398		$	371,896		$	3,869,727		$	—		$	3,869,727
Premiums ceded	(476,910)			(630,764)			(78,148)			(1,185,088)			—			(1,185,088)
Net premiums written	1,228,257			1,162,634			293,748			2,684,639			—			2,684,639
Change in unearned premiums	(126,113)			(234,635)			1,884			(358,864)			—			(358,864)
Net premiums earned	1,102,144			927,999			295,632			2,325,775			—			2,325,775
Other underwriting income (loss)	—			4,526			(1,556)			2,970			—			2,970
Losses and loss adjustment expenses	(629,759)			(537,578)			64,681			(1,102,656)			—			(1,102,656)
Acquisition expenses	(213,688)			(189,494)			(10,137)			(413,319)			—			(413,319)
Other operating expenses	(161,088)			(66,053)			(50,251)			(277,392)			—			(277,392)
Underwriting income (loss)	$	97,609		$	139,400		$	298,369		535,378			—			535,378
Net investment income										106,392			—			106,392
Net realized gains (losses)										(266,579)			—			(266,579)
Equity in net income (loss) of investment funds accounted for using the equity method										58,061			—			58,061
Other income (loss)										(11,777)			—			(11,777)
Corporate expenses (2)										(27,359)			—			(27,359)
Transaction costs and other (2)										(261)			—			(261)
Amortization of intangible assets										(27,207)			—			(27,207)
Interest expense										(32,795)			—			(32,795)
Net foreign exchange gains (losses)										87,775			—			87,775
Income (loss) before income taxes and income (loss) from operating affiliates										421,628			—			421,628
Income tax (expense) benefit										(22,323)			—			(22,323)
Income (loss) from operating affiliates										4,640			—			4,640
Net income (loss)										403,945			—			403,945
Amounts attributable to redeemable noncontrolling interests										399			—			399
Net income (loss) available to Arch										404,344			—			404,344
Preferred dividends										(10,184)			—			(10,184)
Net income (loss) available to Arch common shareholders										$	394,160		$	—		$	394,160
Underwriting Ratios
Loss ratio	57.1		%	57.9		%	(21.9)		%	47.4		%	—		%	47.4		%
Acquisition expense ratio	19.4		%	20.4		%	3.4		%	17.8		%	—		%	17.8		%
Other operating expense ratio	14.6		%	7.1		%	17.0		%	11.9		%	—		%	11.9		%
Combined ratio	91.1		%	85.4		%	(1.5)		%	77.1		%	—		%	77.1		%
Goodwill and intangible assets	$	236,661		$	166,437		$	464,916		$	868,014		$	—		$	868,014

(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 expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

	Three Months Ended
	June 30, 2021
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	1,368,867		$	1,358,020		$	391,511		$	3,117,505		$	240,942		$	3,286,291
Premiums ceded	(405,312)			(433,288)			(55,665)			(893,372)			(65,551)			(886,767)
Net premiums written	963,555			924,732			335,846			2,224,133			175,391			2,399,524
Change in unearned premiums	(98,128)			(187,708)			(1,625)			(287,461)			8,846			(278,615)
Net premiums earned	865,427			737,024			334,221			1,936,672			184,237			2,120,909
Other underwriting income (loss)	—			1,053			4,148			5,201			328			5,529
Losses and loss adjustment expenses	(545,880)			(463,823)			(9,880)			(1,019,583)			(140,248)			(1,159,831)
Acquisition expenses	(136,852)			(133,585)			(30,117)			(300,554)			(34,589)			(335,143)
Other operating expenses	(133,342)			(44,695)			(48,312)			(226,349)			(18,594)			(244,943)
Underwriting income (loss)	$	49,353		$	95,974		$	250,060		395,387			(8,866)			386,521
Net investment income										89,430			22,183			111,613
Net realized gains (losses)										163,394			39,513			202,907
Equity in net income (loss) of investment funds accounted for using the equity method										122,186			—			122,186
Other income (loss)										6,852			—			6,852
Corporate expenses (2)										(17,175)			—			(17,175)
Transaction costs and other (2)										1,444			(220)			1,224
Amortization of intangible assets										(14,388)			(898)			(15,286)
Interest expense										(31,439)			(4,261)			(35,700)
Net foreign exchange gains (losses)										(17,892)			117			(17,775)
Income (loss) before income taxes and income (loss) from operating affiliates										697,799			47,568			745,367
Income tax (expense) benefit										(50,953)			(226)			(51,179)
Income (loss) from operating affiliates										24,476			—			24,476
Net income (loss)										671,322			47,342			718,664
Amounts attributable to redeemable noncontrolling interests										(580)			(981)			(1,561)
Amounts attributable to nonredeemable noncontrolling interests										—			(41,617)			(41,617)
Net income (loss) available to Arch										670,742			4,744			675,486
Preferred dividends										(11,666)			—			(11,666)
Net income (loss) available to Arch common shareholders										$	659,076		$	4,744		$	663,820
Underwriting Ratios
Loss ratio	63.1		%	62.9		%	3.0		%	52.6		%	76.1		%	54.7		%
Acquisition expense ratio	15.8		%	18.1		%	9.0		%	15.5		%	18.8		%	15.8		%
Other operating expense ratio	15.4		%	6.1		%	14.5		%	11.7		%	10.1		%	11.5		%
Combined ratio	94.3		%	87.1		%	26.5		%	79.8		%	105.0		%	82.0		%
Goodwill and intangible assets	$	270,262		$	16,168		$	370,405		$	656,835		$	10,318		$	667,153

(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 expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

	Six Months Ended
	June 30, 2022
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	3,424,772		$	3,512,340		$	736,735		$	7,670,502		$	—		$	7,670,502
Premiums ceded	(989,619)			(1,210,582)			(154,867)			(2,351,723)			—			(2,351,723)
Net premiums written	2,435,153			2,301,758			581,868			5,318,779			—			5,318,779
Change in unearned premiums	(306,313)			(569,359)			3,301			(872,371)			—			(872,371)
Net premiums earned	2,128,840			1,732,399			585,169			4,446,408			—			4,446,408
Other underwriting income (loss)	—			5,362			3,505			8,867			—			8,867
Losses and loss adjustment expenses	(1,230,498)			(992,278)			119,285			(2,103,491)			—			(2,103,491)
Acquisition expenses	(409,338)			(361,490)			(20,650)			(791,478)			—			(791,478)
Other operating expenses	(327,913)			(135,829)			(103,593)			(567,335)			—			(567,335)
Underwriting income (loss)	$	161,091		$	248,164		$	583,716		$	992,971		$	—		$	992,971
Net investment income										186,828			—			186,828
Net realized gains (losses)										(558,993)			—			(558,993)
Equity in net income (loss) of investment funds accounted for using the equity method										94,366			—			94,366
Other income (loss)										(20,802)			—			(20,802)
Corporate expenses (2)										(59,294)			—			(59,294)
Transaction costs and other (2)										(658)			—			(658)
Amortization of intangible assets										(54,374)			—			(54,374)
Interest expense										(65,503)			—			(65,503)
Net foreign exchange gains (losses)										91,620			—			91,620
Income (loss) before income taxes and income (loss) from operating affiliates										606,161			—			606,161
Income tax (expense) benefit										(33,942)			—			(33,942)
Income (loss) from operating affiliates										29,158			—			29,158
Net income (loss)										601,377			—			601,377
Amounts attributable to redeemable noncontrolling interests										(1,233)			—			(1,233)
Net income (loss) available to Arch										600,144			—			600,144
Preferred dividends										(20,368)			—			(20,368)
Net income (loss) available to Arch common shareholders										$	579,776		$	—		$	579,776
Underwriting Ratios
Loss ratio	57.8		%	57.3		%	(20.4)		%	47.3		%	—		%	47.3		%
Acquisition expense ratio	19.2		%	20.9		%	3.5		%	17.8		%	—		%	17.8		%
Other operating expense ratio	15.4		%	7.8		%	17.7		%	12.8		%	—		%	12.8		%
Combined ratio	92.4		%	86.0		%	0.8		%	77.9		%	—		%	77.9		%

(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 expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

	Six Months Ended
	June 30, 2021
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	2,784,753		$	2,829,080		$	782,757		$	6,394,798		$	457,465		$	6,683,497
Premiums ceded	(826,359)			(905,236)			(111,716)			(1,841,519)			(102,763)			(1,775,516)
Net premiums written	1,958,394			1,923,844			671,041			4,553,279			354,702			4,907,981
Change in unearned premiums	(273,493)			(541,920)			(503)			(815,916)			(22,734)			(838,650)
Net premiums earned	1,684,901			1,381,924			670,538			3,737,363			331,968			4,069,331
Other underwriting income (loss)	—			(145)			11,045			10,900			739			11,639
Losses and loss adjustment expenses	(1,081,627)			(948,693)			(73,569)			(2,103,889)			(259,042)			(2,362,931)
Acquisition expenses	(265,074)			(251,610)			(60,199)			(576,883)			(62,741)			(639,624)
Other operating expenses	(270,455)			(105,209)			(97,443)			(473,107)			(32,869)			(505,976)
Underwriting income (loss)	$	67,745		$	76,267		$	450,372		$	594,384		$	(21,945)		$	572,439
Net investment income										168,159			42,310			210,469
Net realized gains (losses)										264,730			80,638			345,368
Equity in net income (loss) of investment funds accounted for using the equity method										193,872			—			193,872
Other income (loss)										5,111			—			5,111
Corporate expenses (2)										(40,643)			—			(40,643)
Transaction costs and other (2)										243			(935)			(692)
Amortization of intangible assets										(28,790)			(898)			(29,688)
Interest expense										(65,636)			(8,410)			(74,046)
Net foreign exchange gains (losses)										3,613			(1,325)			2,288
Income (loss) before income taxes and income (loss) from operating affiliates										1,095,043			89,435			1,184,478
Income tax (expense) benefit										(89,805)			(234)			(90,039)
Income (loss) from operating affiliates										99,933			—			99,933
Net income (loss)										1,105,171			89,201			1,194,372
Amounts attributable to redeemable noncontrolling interests										(463)			(1,953)			(2,416)
Amounts attributable to nonredeemable noncontrolling interests										—			(78,314)			(78,314)
Net income (loss) available to Arch										1,104,708			8,934			1,113,642
Preferred dividends										(22,069)			—			(22,069)
Net income (loss) available to Arch common shareholders										$	1,082,639		$	8,934		$	1,091,573
Underwriting Ratios
Loss ratio	64.2		%	68.7		%	11.0		%	56.3		%	78.0		%	58.1		%
Acquisition expense ratio	15.7		%	18.2		%	9.0		%	15.4		%	18.9		%	15.7		%
Other operating expense ratio	16.1		%	7.6		%	14.5		%	12.7		%	9.9		%	12.4		%
Combined ratio	96.0		%	94.5		%	34.5		%	84.4		%	106.8		%	86.2		%

(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 expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

XML

Reserve for Losses and Loss Adjustment Expenses (Tables)

6 Months Ended

Jun. 30, 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:

	Three Months Ended				Six Months Ended
	June 30,				June 30,
	2022		2021		2022		2021
Reserve for losses and loss adjustment expenses at beginning of period	$	18,109,107	$	16,443,952	$	17,757,156	$	16,513,929
Unpaid losses and loss adjustment expenses recoverable	5,709,998		3,916,650		5,599,231		4,314,855
Net reserve for losses and loss adjustment expenses at beginning of period	12,399,109		12,527,302		12,157,925		12,199,074
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year	1,273,882		1,219,081		2,416,529		2,463,853
Prior years	(171,226)		(59,250)		(313,038)		(100,922)
Total net incurred losses and loss adjustment expenses	1,102,656		1,159,831		2,103,491		2,362,931
Retroactive reinsurance transactions (1)	—		—		—		(183,893)
Net foreign exchange (gains) losses and other	(248,655)		135,847		(281,295)		88,970
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year	(166,466)		(164,441)		(237,272)		(223,425)
Prior years	(578,668)		(607,911)		(1,234,873)		(1,193,029)
Total net paid losses and loss adjustment expenses	(745,134)		(772,352)		(1,472,145)		(1,416,454)
Net reserve for losses and loss adjustment expenses at end of period	12,507,976		13,050,628		12,507,976		13,050,628
Unpaid losses and loss adjustment expenses recoverable	5,686,348		4,146,020		5,686,348		4,146,020
Reserve for losses and loss adjustment expenses at end of period	$	18,194,324	$	17,196,648	$	18,194,324	$	17,196,648

(1)     During the 2021 first quarter, the Company entered into a reinsurance to close and other related agreements with Premia Managing Agency Limited (“Premia”), in connection with the 2018 and prior years of account related to the acquisition of Barbican Group Holdings Limited (“Barbican”).

XML

Allowance for Expected Credit Losses (Tables)

6 Months Ended

Jun. 30, 2022

Credit Loss [Abstract]

Premiums receivable

The following table provides a roll forward of the allowance for expected credit losses of the Company’s premium receivables:

	Premium Receivables, Net of Allowance		Allowance for Expected Credit Losses
Three Months Ended June 30, 2022
Balance at beginning of period	$	3,223,504	$	39,073
Change for provision of expected credit losses (1)			(903)
Balance at end of period	$	3,634,182	$	38,170
Three Months Ended June 30, 2021
Balance at beginning of period	$	2,618,175	$	36,111
Change for provision of expected credit losses (1)			(132)
Balance at end of period	$	2,866,578	$	35,979
Six Months Ended June 30, 2022
Balance at beginning of period	$	2,633,280	$	39,958
Change for provision of expected credit losses (1)			(1,788)
Balance at end of period	$	3,634,182	$	38,170
Six Months Ended June 30, 2021
Balance at beginning of period	$	2,064,586	$	37,781
Change for provision of expected credit losses (1)			(1,802)
Balance at end of period	$	2,866,578	$	35,979

(1)Amounts deemed uncollectible are written-off in operating expenses. For the 2022 second quarter and 2021 second quarter, amounts written off were $3.3 million and $1.1 million, respectively. For the six months ended June 30, 2022 and 2021 period, amounts written off were $4.8 million and $1.2 million, respectively.

Reinsurance recoverables

The following table provides a roll forward of the allowance for expected credit losses of the Company’s reinsurance recoverables:

	Reinsurance Recoverables, Net of Allowance		Allowance for Expected Credit Losses
Three Months Ended June 30, 2022
Balance at beginning of period	$	5,941,000	$	18,483
Change for provision of expected credit losses			(3,743)
Balance at end of period	$	5,938,511	$	14,740
Three Months Ended June 30, 2021
Balance at beginning of period	$	4,041,076	$	10,872
Change for provision of expected credit losses			157
Balance at end of period	$	4,314,515	$	11,029
Six Months Ended June 30, 2022
Balance at beginning of period	$	5,880,735	$	13,230
Change for provision of expected credit losses			1,510
Balance at end of period	$	5,938,511	$	14,740
Six Months Ended June 30, 2021
Balance at beginning of period	$	4,500,802	$	11,636
Change for provision of expected credit losses			(607)
Balance at end of period	$	4,314,515	$	11,029

Ceded credit risk

The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums):

	June 30,			December 31
	2022			2021
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	$	5,938,511		$	5,880,735
% due from carriers with A.M. Best rating of “A-” or better	69.3		%	69.7		%
% due from all other rated carriers	0.1		%	0.1		%
% due from all other carriers with no A.M. Best rating (1)	30.6		%	30.2		%
Largest balance due from any one carrier as % of total shareholders’ equity	7.8		%	6.7		%

(1)    At June 30, 2022 and December 31, 2021 over 93% and 91% of such amount were 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:

	Contract-holder Receivables, Net of Allowance		Allowance for Expected Credit Losses
Three Months Ended June 30, 2022
Balance at beginning of period	$	1,810,199	$	3,731
Change for provision of expected credit losses			(726)
Balance at end of period	$	1,758,018	$	3,005
Three Months Ended June 30, 2021
Balance at beginning of period	$	1,919,655	$	5,853
Change for provision of expected credit losses			(1,382)
Balance at end of period	1,882,948		$	4,471
Six Months Ended June 30, 2022
Balance at beginning of period	$	1,828,691	$	3,437
Change for provision of expected credit losses			(432)
Balance at end of period	$	1,758,018	$	3,005
Six Months Ended June 30, 2021
Balance at beginning of period	$	1,986,924	$	8,638
Change for provision of expected credit losses			(4,167)
Balance at end of period	1,882,948		$	4,471

XML

Investment Information (Tables)

6 Months Ended

Jun. 30, 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
June 30, 2022
Fixed maturities:
Corporate bonds	$	7,288,555	$	32,021	$	(655,664)	$	(38,494)	$	7,950,692
Mortgage backed securities	698,168		4,427		(55,898)		—		749,639
Municipal bonds	417,380		4,129		(18,936)		(298)		432,485
Commercial mortgage backed securities	1,023,088		1,533		(42,056)		(3,594)		1,067,205
U.S. government and government agencies	4,368,150		25,112		(240,786)		—		4,583,824
Non-U.S. government securities	2,181,943		16,175		(163,724)		(1,335)		2,330,827
Asset backed securities	1,607,745		1,001		(80,267)		(14,689)		1,701,700
Total	17,585,029		84,398		(1,257,331)		(58,410)		18,816,372
Short-term investments	2,227,874		2,458		(1,257)		—		2,226,673
Total	$	19,812,903	$	86,856	$	(1,258,588)	$	(58,410)	$	21,043,045
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
June 30, 2022
Fixed maturities:
Corporate bonds	$	6,583,215	$	(580,235)	$	489,098	$	(75,429)	$	7,072,313	$	(655,664)
Mortgage backed securities	595,485		(46,415)		61,751		(9,483)		657,236		(55,898)
Municipal bonds	271,481		(17,908)		8,876		(1,028)		280,357		(18,936)
Commercial mortgage backed securities	973,212		(42,056)		—		—		973,212		(42,056)
U.S. government and government agencies	4,029,550		(235,510)		69,596		(5,276)		4,099,146		(240,786)
Non-U.S. government securities	1,929,278		(148,781)		103,969		(14,943)		2,033,247		(163,724)
Asset backed securities	1,292,087		(73,575)		136,119		(6,692)		1,428,206		(80,267)
Total	15,674,308		(1,144,480)		869,409		(112,851)		16,543,717		(1,257,331)
Short-term investments	505,798		(1,257)		—		—		505,798		(1,257)
Total	$	16,180,106	$	(1,145,737)	$	869,409	$	(112,851)	$	17,049,515	$	(1,258,588)
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

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.

	June 30, 2022				December 31, 2021
Maturity	Estimated Fair Value		Amortized Cost		Estimated Fair Value		Amortized Cost
Due in one year or less	$	412,194	$	414,752	$	300,889	$	299,772
Due after one year through five years	9,423,547		9,927,876		8,355,255		8,339,387
Due after five years through 10 years	4,070,099		4,512,685		4,689,155		4,684,393
Due after 10 years	350,188		442,515		505,758		493,927
	14,256,028		15,297,828		13,851,057		13,817,479
Mortgage backed securities	698,168		749,639		408,477		411,110
Commercial mortgage backed securities	1,023,088		1,067,205		1,046,484		1,047,867
Asset backed securities	1,607,745		1,701,700		2,692,091		2,697,367
Total	$	17,585,029	$	18,816,372	$	17,998,109	$	17,973,823

Summary of other investments and other investable assets

The following table summarizes the Company’s other investments and other investable assets:

	June 30, 2022		December 31, 2021
Fixed maturities	$	525,451	$	416,698
Other investments	1,054,771		1,432,553
Short-term investments	39,657		97,806
Equity securities	14,489		26,493
Total	$	1,634,368	$	1,973,550

The following table summarizes the Company’s other investments, as detailed in the previous table, by strategy:

	June 30, 2022		December 31, 2021
Lending	$	427,812	$	536,345
Investment grade fixed income	221,484		147,810
Term loan investments	152,277		484,950
Private equity	124,282		91,126
Energy	74,234		81,692
Credit related funds	54,682		70,278
Infrastructure	—		20,352
Total	$	1,054,771	$	1,432,553

Summary of investments accounted for using equity method

The following table summarizes the Company’s investments accounted for using the equity method, by strategy:

	June 30, 2022		December 31, 2021
Credit related funds	$	1,119,711	$	1,022,334
Private equity	646,904		436,042
Real estate	455,044		396,395
Lending	447,028		376,649
Equities	350,587		395,090
Infrastructure	231,816		230,070
Energy	115,514		119,141
Fixed income	129,737		101,890
Total	$	3,496,341	$	3,077,611

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 line item:

	June 30, 2022		December 31, 2021
Investments accounted for using the equity method (1)	3,496,341		3,077,611
Investments accounted for using the fair value option (2)	128,826		170,595
Total	$	3,625,167	$	3,248,206

(1)    Aggregate unfunded commitments were $3.0 billion at June 30, 2022, compared to $2.6 billion at December 31, 2021.

(2)    Aggregate unfunded commitments were $21.7 million at June 30, 2022, compared to $18.8 million at December 31, 2021.

Components of net investment income

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

	June 30,
	2022		2021
Three Months Ended
Fixed maturities	$	105,342	$	88,625
Term loans	401		16,879
Equity securities	6,121		8,584
Short-term investments	4,120		1,138
Other (1)	7,583		19,950
Gross investment income	123,567		135,176
Investment expenses	(17,175)		(23,563)
Net investment income	$	106,392	$	111,613
Six Months Ended
Fixed maturities	$	187,395	$	179,251
Term loans	2,018		31,607
Equity securities	12,359		14,234
Short-term investments	6,695		1,745
Other (1)	18,042		34,305
Gross investment income	226,509		261,142
Investment expenses	(39,681)		(50,673)
Net investment income	$	186,828	$	210,469

(1)    Includes income distributions from investment funds and other items.

Summary of net realized gains (losses), including change in allowance for credit losses on financial assets and net impairment losses recognized in earnings

Net realized gains (losses), which include changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings were as follows:

	June 30,
	2022		2021
Three Months Ended
Available for sale securities:
Gross gains on investment sales	$	15,186	$	115,541
Gross losses on investment sales	(57,176)		(50,627)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	(39,255)		10,912
Other investments	(21,710)		60,884
Equity securities	(2,124)		5,492
Short-term investments	(2,008)		(104)
Equity securities, at fair value:
Net realized gains (losses) on sales during the period	16,879		33,570
Net unrealized gains (losses) on equity securities still held at reporting date	(106,375)		65,847
Allowance for credit losses:
Investments related	(25,026)		896
Underwriting related	842		1,381
Derivative instruments (1)	(45,684)		(51,109)
Other	(128)		10,224
Net realized gains (losses)	$	(266,579)	$	202,907
Six Months Ended
Available for sale securities:
Gross gains on investment sales	$	34,893	$	180,543
Gross losses on investment sales	(165,523)		(113,625)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	(69,844)		27,465
Other investments	(17,321)		107,739
Equity securities	(5,437)		7,557
Short-term investments	(2,157)		632
Equity securities, at fair value:
Net realized gains (losses) on sales during the period	82,090		71,419
Net unrealized gains (losses) on equity securities still held at reporting date	(282,570)		85,555
Allowance for credit losses:
Investments related	(56,748)		(752)
Underwriting related	(3,444)		6,649
Derivative instruments (1)	(69,395)		(14,993)
Other	(3,537)		(12,821)
Net realized gains (losses)	$	(558,993)	$	345,368

(1)    See note 9 for information on the Company’s derivative instruments.

Rollforward 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:

	Structured Securities (1)		Municipal Bonds		Corporate Bonds		Total
Three Months Ended June 30, 2022
Balance at beginning of period	$	6,998	$	106	$	27,041	$	34,145
Additions for current-period provision for expected credit losses	4,788		252		13,466		18,506
Additions (reductions) for previously recognized expected credit losses	6,705		(60)		(205)		6,440
Reductions due to disposals	(208)		—		(473)		(681)
Balance at end of period	$	18,283	$	298	$	39,829	$	58,410
Three Months Ended June 30, 2021
Balance at beginning of period	$	1,207	$	2	$	2,621	$	3,830
Additions for current-period provision for expected credit losses	52		—		7		59
Additions (reductions) for previously recognized expected credit losses	(383)		4		(412)		(791)
Reductions due to disposals	(117)		—		(857)		(974)
Balance at end of period	$	759	$	6	$	1,359	$	2,124
Six Months Ended June 30, 2022
Balance at beginning of period	$	802	$	2	$	2,079	$	2,883
Additions for current-period provision for expected credit losses	10,778		347		38,616		49,741
Additions (reductions) for previously recognized expected credit losses	7,192		(51)		(220)		6,921
Reductions due to disposals	(489)		—		(646)		(1,135)
Balance at end of period	$	18,283	$	298	$	39,829	$	58,410
Six Months Ended June 30, 2021
Balance at beginning of period	$	1,490	$	11	$	896	$	2,397
Additions for current-period provision for expected credit losses	234		—		2,428		2,662
Additions (reductions) for previously recognized expected credit losses	(765)		(5)		(952)		(1,722)
Reductions due to disposals	(200)		—		(1,013)		(1,213)
Balance at end of period	$	759	$	6	$	1,359	$	2,124

(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

Summary of restricted assets

The following table details the value of the Company’s restricted assets:

	June 30, 2022		December 31, 2021
Assets used for collateral or guarantees:
Affiliated transactions	$	4,193,561	$	4,223,955
Third party agreements	2,953,800		2,721,160
Deposits with U.S. regulatory authorities	781,024		798,100
Deposits with non-U.S. regulatory authorities	485,341		506,517
Total restricted assets	$	8,413,726	$	8,249,732

Reconciliation of cash and restricted cash

The following table details reconciliation of cash and restricted cash within the Consolidated Balance Sheets:

	June 30, 2022		December 31, 2021
Cash	$	813,548	$	858,668
Restricted cash (included in ‘other assets’)	$	414,683	$	456,103
Cash and restricted cash	$	1,228,231	$	1,314,771

XML

Fair Value (Tables)

6 Months Ended

Jun. 30, 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 June 30, 2022:

			Estimated Fair Value Measurements 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	$	7,288,555	$	—	$	7,284,985	$	3,570
Mortgage backed securities	698,168		—		698,168		—
Municipal bonds	417,380		—		417,380		—
Commercial mortgage backed securities	1,023,088		—		1,023,088		—
U.S. government and government agencies	4,368,150		4,341,399		26,751		—
Non-U.S. government securities	2,181,943		—		2,181,943		—
Asset backed securities	1,607,745		—		1,604,878		2,867
Total	17,585,029		4,341,399		13,237,193		6,437
Short-term investments	2,227,874		2,049,235		178,639		—
Equity securities, at fair value	772,689		736,343		33,440		2,906
Derivative instruments (2)	122,033		—		122,033		—
Residential mortgage loans	3,929		—		3,929		—
Fair value option:
Corporate bonds	522,707		—		522,707		—
Non-U.S. government bonds	611		—		611		—
Asset backed securities	2,133		—		2,133		—
Short-term investments	39,657		886		38,771		—
Equity securities	14,489		10,097		—		4,392
Other investments	178,461		—		145,130		33,331
Other investments measured at net asset value (1)	876,310
Total	1,634,368		10,983		709,352		37,723
Total assets measured at fair value	$	22,345,922	$	7,137,960	$	14,284,586	$	47,066
Liabilities measured at fair value:
Other liabilities	$	(16,205)	$	—	$	—	$	(16,205)
Derivative instruments (2)	(75,147)		—		(75,147)		—
Total liabilities measured at fair value	$	(91,352)	$	—	$	(75,147)	$	(16,205)

(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 9.

The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2021:

			Estimated Fair Value Measurements 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
Short-term investments	1,734,716		1,052,822		681,894		—
Equity securities, at fair value	1,804,170		1,762,864		38,388		2,918
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		—
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:
Other 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 9.

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:

	Assets												Liabilities
s	Available For Sale				Fair Value Option						Fair Value
	Structured Securities (1)		Corporate Bonds		Corporate Bonds		Other Investments		Equity Securities		Equity Securities		Other Liabilities
Three Months Ended June 30, 2022
Balance at beginning of period	$	3,152	$	3,570	$	—	$	22,602	$	4,511	$	2,768	$	(17,591)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	(1)		—		—		27		(119)		(89)		(97)
Included in other comprehensive income	(85)		—		—		—		—		—		1,483
Purchases, issuances, sales and settlements
Purchases	—		—		—		10,702		—		227		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		—		—		—		—
Settlements	(199)		—		—		—		—		—		—
Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of period	$	2,867	$	3,570	$	—	$	33,331	$	4,392	$	2,906	$	(16,205)
Three Months Ended June 30, 2021
Balance at beginning of period	$	3,472	$	13	$	989	$	67,930	$	71,176	$	43,112	$	(465)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	12		—		9		633		2,502		922		(1)
Included in other comprehensive income	(57)		—		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		—		5,638		—		5,102		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(301)		—		—		—
Settlements	(3)		—		—		—		—		—		—
Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of period	$	3,424	$	13	$	998	$	73,900	$	73,678	$	49,136	$	(466)
Six Months Ended June 30, 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)	9		—		—		34		(356)		(236)		(195)
Included in other comprehensive income	(145)		—		—		—		—		—		950
Purchases, issuances, sales and settlements
Purchases	—		—		—		10,770		—		227		—
Issuances	—		—		—		—		—		—		—
Sales (3)	—		—		—		(2,471)		—		(3)		—
Settlements	(344)		—		—		(2,983)		—		—		—
Transfers in and/or out of Level 3	—		3,557		—		—		—		—		—
Balance at end of period	$	2,867	$	3,570	$	—	$	33,331	$	4,392	$	2,906	$	(16,205)
Six Months Ended June 30, 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)	(56)		—		13		881		4,690		1,826		(5)
Included in other comprehensive income	57		—		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		—		13,003		—		5,295		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(7,087)		—		—		—
Settlements	(3)		—		—		—		—		—		—
Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of period	$	3,424	$	13	$	998	$	73,900	$	73,678	$	49,136	$	(466)

(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

(2)    Gains or losses were included in net realized gains (losses).

XML

Derivative Instruments (Tables)

6 Months Ended

Jun. 30, 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)
June 30, 2022
Futures contracts	$	49,695	$	(22,561)	$	2,794,246
Foreign currency forward contracts	9,556		(18,884)		908,192
TBAs	—		—		—
Other	62,782		(33,702)		3,849,244
Total	$	122,033	$	(75,147)
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	June 30,
hedging instruments:	2022		2021
Three Months Ended
Net realized gains (losses):
Futures contracts	$	(39,205)	$	(54,759)
Foreign currency forward contracts	(25,638)		1,295
TBAs	—		—
Other (1)	19,159		2,355
Total	$	(45,684)	$	(51,109)
Six Months Ended
Net realized gains (losses):
Futures contracts	$	(85,979)	$	(7,321)
Foreign currency forward contracts	(27,676)		(20,776)
TBAs	(51)		—
Other (1)	44,311		13,104
Total	$	(69,395)	$	(14,993)

(1)    Includes realized gains and losses on swaps, options and other derivatives contracts.

XML

Variable Interest Entities and Noncontrolling Interests (Tables)

6 Months Ended

Jun. 30, 2022

Noncontrolling Interest [Abstract]

Activity in non-redeemable noncontrolling interests

The following table sets forth activity in the non-redeemable noncontrolling interests:

	June 30,
	2021
Three Months Ended
Balance, beginning of period	$	876,864
Additional paid in capital attributable to noncontrolling interests	383
Amounts attributable to noncontrolling interests	41,617
Other comprehensive income (loss) attributable to noncontrolling interests	10
Balance, end of period	$	918,874
Six Months Ended
Balance, beginning of year	$	823,007
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 period	$	918,874

Activity in redeemable noncontrolling interests

The following table sets forth activity in the redeemable non-controlling interests:

	June 30,
	2022		2021
Three Months Ended
Balance, beginning of period	$	9,763	$	57,670
Accretion of preference share issuance costs	—		23
Other	(1,304)		(160)
Balance, end of period	$	8,459	$	57,533
Six Months Ended
Balance, beginning of year	$	9,233	$	58,548
Accretion of preference share issuance costs	—		46
Other	(774)		(1,061)
Balance, end of period	$	8,459	$	57,533

Portion of income or loss attributable to third party investors

The portion of income or loss attributable to third party investors, recorded in the Company’s consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests,’ are summarized in the table below:

	June 30,
	2022		2021
Three Months Ended
Amounts attributable to non-redeemable noncontrolling interests	$	—	$	(41,617)
Amounts attributable to redeemable noncontrolling interests	399		(1,561)
Net (income) loss attributable to noncontrolling interests	$	399	$	(43,178)
Six Months Ended
Amounts attributable to non-redeemable noncontrolling interests	$	—	$	(78,314)
Amounts attributable to redeemable noncontrolling interests	(1,233)		(2,416)
Net (income) loss attributable to noncontrolling interests	$	(1,233)	$	(80,730)

Total assets and maximum exposure to loss associated with VIEs

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.

			June 30, 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)	$	61,328	$	(68)	$	274	$	206	$	—	$	108,368	$	(159)	$	424	$	265
2018-1 Ltd. (Apr-18)	122,190		(342)		965		623		—		181,136		(528)		1,268		740
2018-3 Ltd. (Oct-18)	244,257		(566)		1,522		956		—		302,563		(1,018)		2,496		1,478
2019-1 Ltd. (Mar-19)	134,972		(127)		988		861		—		181,324		(380)		5,807		5,427
2019-2 Ltd. (Apr-19)	383,737		(426)		5,323		4,897		—		398,316		(515)		3,998		3,483
2019-3 Ltd. (Jul-19)	296,466		(282)		2,154		1,872		—		409,859		(584)		3,190		2,606
2019-4 Ltd. (Oct-19)	312,668		(306)		4,702		4,396		—		411,954		(462)		4,759		4,297
2020-2 Ltd. (Sep-20)	151,543		(58)		1,331		1,273		442		217,766		(177)		1,984		1,807
2020-3 Ltd. (Nov-20)	303,011		(26)		4,388		4,362		10,779		348,818		(128)		5,793		5,665
2020-4 Ltd. (Dec-20)	124,672		23		1,267		1,290		5,900		176,826		(50)		1,630		1,580
2021-1 Ltd. (Mar-21)	519,641		(1,006)		2,771		1,765		48,841		568,986		(303)		3,283		2,980
2021-2 Ltd. (Jun-21)	492,837		(577)		3,505		2,928		85,717		522,807		281		4,124		4,405
2021-3 Ltd. (Sep-21)	507,873		(1,082)		2,878		1,796		131,518		507,873		(411)		3,446		3,035
2022-1 Ltd. (Jan-22)	283,500		(282)		2,020		1,738		33,260
Total	$	3,938,695	$	(5,125)	$	34,088	$	28,963	$	316,457	$	4,336,596	$	(4,434)	$	42,202	$	37,768

(1) Coverage from a separate panel of reinsurers remaining at June 30, 2022.

XML

Other Comprehensive Income (Loss) (Tables)

6 Months Ended

Jun. 30, 2022

Comprehensive Income Note Disclosure [Abstract]

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):

		Amounts Reclassified from AOCI
	Consolidated Statement of Income	Three Months Ended				Six Months Ended
Details About	Line Item That Includes	June 30,				June 30,
AOCI Components	Reclassification	2022		2021		2022		2021
Unrealized appreciation (decline) on available-for-sale investments
	Net realized gains (losses)	$	(41,990)	$	64,914	$	(130,630)	$	66,918
	Provision for credit losses	(25,026)		896		(56,748)		(751)
	Total before tax	(67,016)		65,810		(187,378)		66,167
	Income tax (expense) benefit	9,306		(5,263)		27,390		(8,317)
	Net of tax	$	(57,710)	$	60,547	$	(159,988)	$	57,850

Schedule of comprehensive income (loss)

	Before Tax Amount		Tax Expense (Benefit)		Net of Tax Amount
Three Months Ended June 30, 2022
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(676,048)	$	(78,043)	$	(598,005)
Less reclassification of net realized gains (losses) included in net income	(67,016)		(9,306)		(57,710)
Foreign currency translation adjustments	(68,562)		(37)		(68,525)
Other comprehensive income (loss)	$	(677,594)	$	(68,774)	$	(608,820)
Three Months Ended June 30, 2021
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	91,057	$	12,486	$	78,571
Less reclassification of net realized gains (losses) included in net income	65,810		5,263		60,547
Foreign currency translation adjustments	6,392		187		6,205
Other comprehensive income (loss)	$	31,639	$	7,410	$	24,229
Six Months Ended June 30, 2022
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(1,460,938)	$	(178,578)	$	(1,282,360)
Less reclassification of net realized gains (losses) included in net income	(187,378)		(27,390)		(159,988)
Foreign currency translation adjustments	(71,127)		166		(71,293)
Other comprehensive income (loss)	$	(1,344,687)	$	(151,022)	$	(1,193,665)
Six Months Ended June 30, 2021
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(203,303)	$	(20,124)	$	(183,179)
Less reclassification of net realized gains (losses) included in net income	66,167		8,317		57,850
Foreign currency translation adjustments	(22,023)		356		(22,379)
Other comprehensive income (loss)	$	(291,493)	$	(28,085)	$	(263,408)

XML

Basis of Presentation and Recent Accounting Pronouncements (Details)	Jul. 01, 2021
Greysbridge Holdings Ltd | Warburg Pincus LLC
Schedule of Equity Method Investments [Line Items]
Percentage ownership	30.00%
Greysbridge Holdings Ltd | Kelso And Company
Schedule of Equity Method Investments [Line Items]
Percentage ownership	30.00%
Greysbridge Holdings Ltd
Schedule of Equity Method Investments [Line Items]
Percentage ownership	40.00%

XML

Share Transactions - Share repurchases (Details) - Common shares shares in Millions, $ in Millions	6 Months Ended
	Jun. 30, 2022 USD ($) shares
Class of Stock [Line Items]
Cumulative number of shares acquired since inception of share repurchase program | shares	433.3
Aggregate purchase price of shares acquired since inception of share repurchase program	$ 5,860.0
Treasury stock, shares acquired (shares) | shares	12.7
Shares repurchased for treasury	$ 575.7
Remaining authorized repurchase amount	$ 606.6

XML

Share Transactions - Long-Term Incentive and Share Award Plan (Details) - 2022 Long-term incentive and share award plan - shares	Jun. 30, 2022	May 04, 2022
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of shares authorized (in shares)		9,000,000
Number of shares available for future issuance (in shares)	9,000,000
Stock options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of shares authorized (in shares)		6,000,000

XML

Share Transactions - Issuance of preferred shares (Details) - USD ($) $ / shares in Units, $ in Thousands, shares in Millions	1 Months Ended	6 Months Ended
	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Class of Stock [Line Items]
Proceeds from issuance of preferred shares, net		$ 0	$ 485,821
Depositary Series G Preferred Stock
Class of Stock [Line Items]
Preferred shares issued	$ 500,000
Preferred shares, dividend rate (as a percent)	4.55%
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 G Depositary Share Equivalent
Class of Stock [Line Items]
Preferred shares issued	$ 500,000
Preference shares, number of shares issued	20.0
Liquidation preference per share	$ 25		25
Preferred shares, redemption price per share	$ 25		$ 25
Proportionate interest of preference shares (per depositary share)	0.10%		0.10%

XML

Earnings Per Common Share (Details) - USD ($) $ / shares in Units, $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Numerator:
Net income (loss)		$ 403,945	$ 718,664	$ 601,377	$ 1,194,372
Amounts attributable to noncontrolling interests		399	(43,178)	(1,233)	(80,730)
Net income available to Arch		404,344	675,486	600,144	1,113,642
Preferred dividends		(10,184)	(11,666)	(20,368)	(22,069)
Net income (loss) available to Arch common shareholders		$ 394,160	$ 663,820	$ 579,776	$ 1,091,573
Denominator:
Weighted average common shares outstanding — basic		369,241,193	397,743,402	371,728,683	399,267,183
Effect of dilutive common share equivalents:
Nonvested restricted shares		2,121,678	1,990,729	2,238,267	1,932,929
Stock options	[1]	6,590,117	6,751,863	6,938,562	6,487,568
Weighted average common shares and common share equivalents outstanding — diluted		377,952,988	406,485,994	380,905,512	407,687,680
Earnings per common share:
Basic (per share)		$ 1.07	$ 1.67	$ 1.56	$ 2.73
Diluted (per share)		$ 1.04	$ 1.63	$ 1.52	$ 2.68
Stock options
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Antidilutive securities excluded from computation of earnings per common share (shares)		773,163	1,974,849	778,724	2,395,749

[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 the 2022 second quarter and 2021 second quarter, the number of stock options excluded were 773,163 and 1,974,849, respectively. For the six months ended June 30, 2022 and 2021, the number of stock options excluded were 778,724 and 2,395,749, respectively.

XML

Segment Information - Summary of underwriting income or loss by segment (Details) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2022 USD ($)	Jun. 30, 2021 USD ($)	Jun. 30, 2022 USD ($) segment	Jun. 30, 2021 USD ($)	Dec. 31, 2021 USD ($)
Segment Reporting Information [Line Items]
Gross premiums written		$ 3,869,727	$ 3,286,291	$ 7,670,502	$ 6,683,497
Premiums ceded		(1,185,088)	(886,767)	(2,351,723)	(1,775,516)
Net premiums written		2,684,639	2,399,524	5,318,779	4,907,981
Change in unearned premiums		(358,864)	(278,615)	(872,371)	(838,650)
Net premiums earned		2,325,775	2,120,909	4,446,408	4,069,331
Other underwriting income (loss)		2,970	5,529	8,867	11,639
Losses and loss adjustment expenses		(1,102,656)	(1,159,831)	(2,103,491)	(2,362,931)
Acquisition expenses		(413,319)	(335,143)	(791,478)	(639,624)
Other operating expenses		(277,392)	(244,943)	(567,335)	(505,976)
Underwriting income (loss)		535,378	386,521	992,971	572,439
Net investment income		106,392	111,613	186,828	210,469
Net realized gains (losses)		(266,579)	202,907	(558,993)	345,368
Equity in net income (loss) of investment funds accounted for using the equity method		58,061	122,186	94,366	193,872
Other income (loss)		(11,777)	6,852	(20,802)	5,111
Corporate expenses		(27,359)	(17,175)	(59,294)	(40,643)
Transaction costs and other		(261)	1,224	(658)	(692)
Amortization of intangible assets		(27,207)	(15,286)	(54,374)	(29,688)
Interest expense		(32,795)	(35,700)	(65,503)	(74,046)
Net foreign exchange gains (losses)		87,775	(17,775)	91,620	2,288
Income (loss) before income taxes and income (loss) from operating affiliates		421,628	745,367	606,161	1,184,478
Income tax expense (benefit)		(22,323)	(51,179)	(33,942)	(90,039)
Income (loss) from operating affiliates		4,640	24,476	29,158	99,933
Net income (loss)		403,945	718,664	601,377	1,194,372
Amounts attributable to redeemable noncontrolling interests		399	(1,561)	(1,233)	(2,416)
Amounts attributable to non-redeemable noncontrolling interests		0	(41,617)	0	(78,314)
Net income (loss) available to Arch		404,344	675,486	600,144	1,113,642
Preferred dividends		(10,184)	(11,666)	(20,368)	(22,069)
Net income (loss) available to Arch common shareholders		$ 394,160	$ 663,820	$ 579,776	$ 1,091,573
Underwriting Ratios
Loss ratio		47.40%	54.70%	47.30%	58.10%
Acquisition expense ratio		17.80%	15.80%	17.80%	15.70%
Other operating expense ratio		11.90%	11.50%	12.80%	12.40%
Combined ratio		77.10%	82.00%	77.90%	86.20%
Goodwill and intangible assets		$ 868,014	$ 667,153	$ 868,014	$ 667,153	$ 944,983
Operating segments | Underwriting Segments
Segment Reporting Information [Line Items]
Number of segments | segment				3
Gross premiums written	[1]	3,869,727	3,117,505	$ 7,670,502	6,394,798
Premiums ceded		(1,185,088)	(893,372)	(2,351,723)	(1,841,519)
Net premiums written		2,684,639	2,224,133	5,318,779	4,553,279
Change in unearned premiums		(358,864)	(287,461)	(872,371)	(815,916)
Net premiums earned		2,325,775	1,936,672	4,446,408	3,737,363
Other underwriting income (loss)		2,970	5,201	8,867	10,900
Losses and loss adjustment expenses		(1,102,656)	(1,019,583)	(2,103,491)	(2,103,889)
Acquisition expenses		(413,319)	(300,554)	(791,478)	(576,883)
Other operating expenses		(277,392)	(226,349)	(567,335)	(473,107)
Underwriting income (loss)		535,378	395,387	992,971	594,384
Net investment income		106,392	89,430	186,828	168,159
Net realized gains (losses)		(266,579)	163,394	(558,993)	264,730
Equity in net income (loss) of investment funds accounted for using the equity method		58,061	122,186	94,366	193,872
Other income (loss)		(11,777)	6,852	(20,802)	5,111
Corporate expenses	[2]	(27,359)	(17,175)	(59,294)	(40,643)
Transaction costs and other	[2]	(261)	1,444	(658)	243
Amortization of intangible assets		(27,207)	(14,388)	(54,374)	(28,790)
Interest expense		(32,795)	(31,439)	(65,503)	(65,636)
Net foreign exchange gains (losses)		87,775	(17,892)	91,620	3,613
Income (loss) before income taxes and income (loss) from operating affiliates		421,628	697,799	606,161	1,095,043
Income tax expense (benefit)		(22,323)	(50,953)	(33,942)	(89,805)
Income (loss) from operating affiliates		4,640	24,476	29,158	99,933
Net income (loss)		403,945	671,322	601,377	1,105,171
Amounts attributable to redeemable noncontrolling interests		399	(580)	(1,233)	(463)
Amounts attributable to non-redeemable noncontrolling interests			0		0
Net income (loss) available to Arch		404,344	670,742	600,144	1,104,708
Preferred dividends		(10,184)	(11,666)	(20,368)	(22,069)
Net income (loss) available to Arch common shareholders		$ 394,160	$ 659,076	$ 579,776	$ 1,082,639
Underwriting Ratios
Loss ratio		47.40%	52.60%	47.30%	56.30%
Acquisition expense ratio		17.80%	15.50%	17.80%	15.40%
Other operating expense ratio		11.90%	11.70%	12.80%	12.70%
Combined ratio		77.10%	79.80%	77.90%	84.40%
Goodwill and intangible assets		$ 868,014	$ 656,835	$ 868,014	$ 656,835
Operating segments | Insurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	1,705,167	1,368,867	3,424,772	2,784,753
Premiums ceded		(476,910)	(405,312)	(989,619)	(826,359)
Net premiums written		1,228,257	963,555	2,435,153	1,958,394
Change in unearned premiums		(126,113)	(98,128)	(306,313)	(273,493)
Net premiums earned		1,102,144	865,427	2,128,840	1,684,901
Other underwriting income (loss)		0	0	0	0
Losses and loss adjustment expenses		(629,759)	(545,880)	(1,230,498)	(1,081,627)
Acquisition expenses		(213,688)	(136,852)	(409,338)	(265,074)
Other operating expenses		(161,088)	(133,342)	(327,913)	(270,455)
Underwriting income (loss)		$ 97,609	$ 49,353	$ 161,091	$ 67,745
Underwriting Ratios
Loss ratio		57.10%	63.10%	57.80%	64.20%
Acquisition expense ratio		19.40%	15.80%	19.20%	15.70%
Other operating expense ratio		14.60%	15.40%	15.40%	16.10%
Combined ratio		91.10%	94.30%	92.40%	96.00%
Goodwill and intangible assets		$ 236,661	$ 270,262	$ 236,661	$ 270,262
Operating segments | Reinsurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	1,793,398	1,358,020	3,512,340	2,829,080
Premiums ceded		(630,764)	(433,288)	(1,210,582)	(905,236)
Net premiums written		1,162,634	924,732	2,301,758	1,923,844
Change in unearned premiums		(234,635)	(187,708)	(569,359)	(541,920)
Net premiums earned		927,999	737,024	1,732,399	1,381,924
Other underwriting income (loss)		4,526	1,053	5,362	(145)
Losses and loss adjustment expenses		(537,578)	(463,823)	(992,278)	(948,693)
Acquisition expenses		(189,494)	(133,585)	(361,490)	(251,610)
Other operating expenses		(66,053)	(44,695)	(135,829)	(105,209)
Underwriting income (loss)		$ 139,400	$ 95,974	$ 248,164	$ 76,267
Underwriting Ratios
Loss ratio		57.90%	62.90%	57.30%	68.70%
Acquisition expense ratio		20.40%	18.10%	20.90%	18.20%
Other operating expense ratio		7.10%	6.10%	7.80%	7.60%
Combined ratio		85.40%	87.10%	86.00%	94.50%
Goodwill and intangible assets		$ 166,437	$ 16,168	$ 166,437	$ 16,168
Operating segments | Mortgage
Segment Reporting Information [Line Items]
Gross premiums written	[1]	371,896	391,511	736,735	782,757
Premiums ceded		(78,148)	(55,665)	(154,867)	(111,716)
Net premiums written		293,748	335,846	581,868	671,041
Change in unearned premiums		1,884	(1,625)	3,301	(503)
Net premiums earned		295,632	334,221	585,169	670,538
Other underwriting income (loss)		(1,556)	4,148	3,505	11,045
Losses and loss adjustment expenses		64,681	(9,880)	119,285	(73,569)
Acquisition expenses		(10,137)	(30,117)	(20,650)	(60,199)
Other operating expenses		(50,251)	(48,312)	(103,593)	(97,443)
Underwriting income (loss)		$ 298,369	$ 250,060	$ 583,716	$ 450,372
Underwriting Ratios
Loss ratio		(21.90%)	3.00%	(20.40%)	11.00%
Acquisition expense ratio		3.40%	9.00%	3.50%	9.00%
Other operating expense ratio		17.00%	14.50%	17.70%	14.50%
Combined ratio		(1.50%)	26.50%	0.80%	34.50%
Goodwill and intangible assets		$ 464,916	$ 370,405	$ 464,916	$ 370,405
Operating segments | Corporate and Other Segments
Segment Reporting Information [Line Items]
Number of segments | segment				2
Gross premiums written	[1]	0	240,942	$ 0	457,465
Premiums ceded		0	(65,551)	0	(102,763)
Net premiums written		0	175,391	0	354,702
Change in unearned premiums		0	8,846	0	(22,734)
Net premiums earned		0	184,237	0	331,968
Other underwriting income (loss)		0	328	0	739
Losses and loss adjustment expenses		0	(140,248)	0	(259,042)
Acquisition expenses		0	(34,589)	0	(62,741)
Other operating expenses		0	(18,594)	0	(32,869)
Underwriting income (loss)		0	(8,866)	0	(21,945)
Net investment income		0	22,183	0	42,310
Net realized gains (losses)		0	39,513	0	80,638
Equity in net income (loss) of investment funds accounted for using the equity method		0	0	0	0
Other income (loss)		0	0	0	0
Corporate expenses	[2]	0	0	0	0
Transaction costs and other	[2]	0	(220)	0	(935)
Amortization of intangible assets		0	(898)	0	(898)
Interest expense		0	(4,261)	0	(8,410)
Net foreign exchange gains (losses)		0	117	0	(1,325)
Income (loss) before income taxes and income (loss) from operating affiliates		0	47,568	0	89,435
Income tax expense (benefit)		0	(226)	0	(234)
Income (loss) from operating affiliates		0	0	0	0
Net income (loss)		0	47,342	0	89,201
Amounts attributable to redeemable noncontrolling interests		0	(981)	0	(1,953)
Amounts attributable to non-redeemable noncontrolling interests			(41,617)		(78,314)
Net income (loss) available to Arch		0	4,744	0	8,934
Preferred dividends		0	0	0	0
Net income (loss) available to Arch common shareholders		$ 0	$ 4,744	$ 0	$ 8,934
Underwriting Ratios
Loss ratio		0.00%	76.10%	0.00%	78.00%
Acquisition expense ratio		0.00%	18.80%	0.00%	18.90%
Other operating expense ratio		0.00%	10.10%	0.00%	9.90%
Combined ratio		0.00%	105.00%	0.00%	106.80%
Goodwill and intangible assets		$ 0	$ 10,318	$ 0	$ 10,318

[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 expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

XML

Reserve for Losses and Loss Adjustment Expenses - Reconciliation of beginning and ending balances of losses and loss adjustment reserves (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Liability for Future Policy Benefits and Unpaid Claims and Claims Adjustment Expense [Abstract]
Reserve for losses and loss adjustment expenses at beginning of period		$ 18,109,107	$ 16,443,952	$ 17,757,156	$ 16,513,929
Unpaid losses and loss adjustment expenses recoverable		5,709,998	3,916,650	5,599,231	4,314,855
Net reserve for losses and loss adjustment expenses at beginning of period		12,399,109	12,527,302	12,157,925	12,199,074
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year		1,273,882	1,219,081	2,416,529	2,463,853
Prior years		(171,226)	(59,250)	(313,038)	(100,922)
Total net incurred losses and loss adjustment expenses		1,102,656	1,159,831	2,103,491	2,362,931
Retroactive reinsurance transaction	[1]	0	0	0	(183,893)
Net foreign exchange (gains) losses and other		(248,655)	135,847	(281,295)	88,970
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year		(166,466)	(164,441)	(237,272)	(223,425)
Prior years		(578,668)	(607,911)	(1,234,873)	(1,193,029)
Total net paid losses and loss adjustment expenses		(745,134)	(772,352)	(1,472,145)	(1,416,454)
Net reserve for losses and loss adjustment expenses at end of period		12,507,976	13,050,628	12,507,976	13,050,628
Unpaid losses and loss adjustment expenses recoverable		5,686,348	4,146,020	5,686,348	4,146,020
Reserve for losses and loss adjustment expenses at end of period		$ 18,194,324	$ 17,196,648	$ 18,194,324	$ 17,196,648

[1] During the 2021 first quarter, the Company entered into a reinsurance to close and other related agreements with Premia Managing Agency Limited (“Premia”), in connection with the 2018 and prior years of account related to the acquisition of Barbican Group Holdings Limited (“Barbican”).

XML

Reserve for Losses and Loss Adjustment Expenses - Prior year development (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 171,226	$ 59,250	$ 313,038	$ 100,922
Operating segments | Insurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 6,700	$ 4,000	$ 14,000	$ 8,100
Percentage of prior year development	0.60%	0.50%	0.70%	0.50%
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)	$ 14,300		$ 33,200	$ 49,400
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)		$ 7,100		21,600
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)		6,700		9,300
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)	12,200	10,700	30,800	18,600
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)		(24,500)		(45,400)
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)			5,200	(12,600)
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)	(6,300)		(13,600)	(11,200)
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)		(20,100)	(6,100)	(20,100)
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)	2,600		5,500
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)		5,600	(7,600)
Operating segments | Insurance | Long tailed lines | Executive assurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(5,700)
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)	(7,500)		(19,200)
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)		28,500		53,500
Operating segments | Reinsurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 46,400	$ 20,500	$ 78,900	$ 47,300
Percentage of prior year development	5.00%	2.80%	4.60%	3.40%
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)			$ 74,900	$ 67,200
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)	$ 6,300	$ (17,100)	9,700	(39,600)
Operating segments | Reinsurance | Short tailed lines | 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)	31,600		47,400	28,800
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)	13,100	61,600	18,000	78,200
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)	4,200	4,000	14,900
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)	(8,000)	(33,200)	(10,900)	(24,800)
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)		(34,200)
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)	54,400	53,700	89,700	72,100
Operating segments | Mortgage
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 118,100	$ 43,100	$ 220,200	$ 54,000
Percentage of prior year development	39.90%	12.90%	37.60%	8.10%
Operating segments | Other
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		$ (8,300)		$ (8,400)

XML

Allowance for Expected Credit Losses - Premiums receivable (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Credit Loss [Abstract]
Balance at beginning of period		$ 3,223,504	$ 2,618,175	$ 2,633,280	$ 2,064,586
Balance at end of period		3,634,182	2,866,578	3,634,182	2,866,578
Allowance for Expected Credit Losses
Balance at beginning of period		39,073	36,111	39,958	37,781
Change for provision of expected credit losses	[1]	(903)	(132)	(1,788)	(1,802)
Balance at end of period		38,170	35,979	38,170	35,979
Write-offs charged against the allowance		$ 3,300	$ 1,100	$ 4,800	$ 1,200

[1] Amounts deemed uncollectible are written-off in operating expenses. For the 2022 second quarter and 2021 second quarter, amounts written off were $3.3 million and $1.1 million, respectively. For the six months ended June 30, 2022 and 2021 period, amounts written off were $4.8 million and $1.2 million, respectively.

XML

Allowance for Expected Credit Losses - Reinsurance recoverables (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Credit Loss [Abstract]
Balance at beginning of period	$ 5,941,000	$ 4,041,076	$ 5,880,735	$ 4,500,802
Balance at end of period	5,938,511	4,314,515	5,938,511	4,314,515
Allowance for Expected Credit Losses
Balance at beginning of period	18,483	10,872	13,230	11,636
Change for provision of expected credit losses	(3,743)	157	1,510	(607)
Balance at end of period	$ 14,740	$ 11,029	$ 14,740	$ 11,029

XML

Allowance for Expected Credit Losses - Ceded credit risk (Details) - USD ($) $ in Thousands		6 Months Ended	12 Months Ended
		Jun. 30, 2022	Dec. 31, 2021	Mar. 31, 2022	Jun. 30, 2021	Mar. 31, 2021	Dec. 31, 2020
Ceded Credit Risk [Line Items]
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses		$ 5,938,511	$ 5,880,735	$ 5,941,000	$ 4,314,515	$ 4,041,076	$ 4,500,802
Reinsurance recoverable | Reinsurer concentration risk | AM Best A minus Or Better Rating
Ceded Credit Risk [Line Items]
Concentration risk percentage		69.30%	69.70%
Reinsurance recoverable | Reinsurer concentration risk | AM Best Rating Below A Minus | All Other Carriers
Ceded Credit Risk [Line Items]
Concentration risk percentage		0.10%	0.10%
Reinsurance recoverable | Reinsurer concentration risk | Not Rated | All Other Carriers
Ceded Credit Risk [Line Items]
Concentration risk percentage	[1]	30.60%	30.20%
Reinsurance recoverable | Reinsurer concentration risk | Not Rated | Reinsurance trusts or letters of credit
Ceded Credit Risk [Line Items]
Concentration risk percentage		93.00%	91.00%
Stockholders' equity | Reinsurer concentration risk | Largest Balance Due From Any One Carrier
Ceded Credit Risk [Line Items]
Concentration risk percentage		7.80%	6.70%

[1] At June 30, 2022 and December 31, 2021 over 93% and 91% of such amount were collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other, respectively

XML

Allowance for Expected Credit Losses - Contractholder receivables (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Credit Loss [Abstract]
Balance at beginning of period	$ 1,810,199	$ 1,919,655	$ 1,828,691	$ 1,986,924
Balance at end of period	1,758,018	1,882,948	1,758,018	1,882,948
Allowance for Expected Credit Losses
Balance at beginning of period	3,731	5,853	3,437	8,638
Change for provision of expected credit losses	(726)	(1,382)	(432)	(4,167)
Balance at end of period	$ 3,005	$ 4,471	$ 3,005	$ 4,471

XML

Investment Information - Summary of available for sale securities (Details) - USD ($) $ in Thousands	Jun. 30, 2022	Mar. 31, 2022	Dec. 31, 2021	Jun. 30, 2021	Mar. 31, 2021	Dec. 31, 2020
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	$ 19,812,903		$ 19,732,825
Gross Unrealized Gains	86,856		198,691
Gross Unrealized Losses	(1,258,588)		(171,544)
Allowance for Expected Credit Losses	(58,410)	$ (34,145)	(2,883)	$ (2,124)	$ (3,830)	$ (2,397)
Cost or Amortized Cost	21,043,045		19,708,561
Municipal bonds
Debt Securities, Available-for-sale [Line Items]
Allowance for Expected Credit Losses	(298)	$ (106)	(2)	$ (6)	$ (2)	$ (11)
Fixed maturities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	17,585,029		17,998,109
Gross Unrealized Gains	84,398		198,123
Gross Unrealized Losses	(1,257,331)		(170,954)
Allowance for Expected Credit Losses	(58,410)		(2,883)
Cost or Amortized Cost	18,816,372		17,973,823
Fixed maturities | Corporate bonds
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	7,288,555		6,553,333
Gross Unrealized Gains	32,021		104,170
Gross Unrealized Losses	(655,664)		(69,194)
Allowance for Expected Credit Losses	(38,494)		(2,037)
Cost or Amortized Cost	7,950,692		6,520,394
Fixed maturities | Mortgage backed securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	698,168		408,477
Gross Unrealized Gains	4,427		2,825
Gross Unrealized Losses	(55,898)		(5,410)
Allowance for Expected Credit Losses	0		(48)
Cost or Amortized Cost	749,639		411,110
Fixed maturities | Municipal bonds
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	417,380		404,666
Gross Unrealized Gains	4,129		18,724
Gross Unrealized Losses	(18,936)		(1,409)
Allowance for Expected Credit Losses	(298)		(2)
Cost or Amortized Cost	432,485		387,353
Fixed maturities | Commercial mortgage backed securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	1,023,088		1,046,484
Gross Unrealized Gains	1,533		1,740
Gross Unrealized Losses	(42,056)		(3,117)
Allowance for Expected Credit Losses	(3,594)		(6)
Cost or Amortized Cost	1,067,205		1,047,867
Fixed maturities | US government and government agencies
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	4,368,150		4,772,764
Gross Unrealized Gains	25,112		10,076
Gross Unrealized Losses	(240,786)		(45,967)
Allowance for Expected Credit Losses	0		0
Cost or Amortized Cost	4,583,824		4,808,655
Fixed maturities | Non-US government securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	2,181,943		2,120,294
Gross Unrealized Gains	16,175		54,048
Gross Unrealized Losses	(163,724)		(34,749)
Allowance for Expected Credit Losses	(1,335)		(82)
Cost or Amortized Cost	2,330,827		2,101,077
Fixed maturities | Asset backed securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	1,607,745		2,692,091
Gross Unrealized Gains	1,001		6,540
Gross Unrealized Losses	(80,267)		(11,108)
Allowance for Expected Credit Losses	(14,689)		(708)
Cost or Amortized Cost	1,701,700		2,697,367
Short-term investments
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	2,227,874		1,734,716
Gross Unrealized Gains	2,458		568
Gross Unrealized Losses	(1,257)		(590)
Allowance for Expected Credit Losses	0		0
Cost or Amortized Cost	$ 2,226,673		$ 1,734,738

XML

Investment Information - Aging of available for sale securities in an unrealized loss position (Details) - USD ($) $ in Thousands	Jun. 30, 2022	Dec. 31, 2021
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	$ 16,180,106	$ 12,238,683
Estimated Fair Value - 12 Months or More	869,409	297,357
Estimated Fair Value	17,049,515	12,536,040
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(1,145,737)	(157,279)
Gross Unrealized Losses - 12 Months or More	(112,851)	(14,265)
Gross Unrealized Losses	(1,258,588)	(171,544)
Fixed maturities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	15,674,308	11,953,950
Estimated Fair Value - 12 Months or More	869,409	297,357
Estimated Fair Value	16,543,717	12,251,307
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(1,144,480)	(156,689)
Gross Unrealized Losses - 12 Months or More	(112,851)	(14,265)
Gross Unrealized Losses	(1,257,331)	(170,954)
Fixed maturities | Corporate bonds
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	6,583,215	3,639,582
Estimated Fair Value - 12 Months or More	489,098	98,867
Estimated Fair Value	7,072,313	3,738,449
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(580,235)	(63,938)
Gross Unrealized Losses - 12 Months or More	(75,429)	(5,256)
Gross Unrealized Losses	(655,664)	(69,194)
Fixed maturities | Mortgage backed securities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	595,485	222,176
Estimated Fair Value - 12 Months or More	61,751	46,809
Estimated Fair Value	657,236	268,985
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(46,415)	(3,545)
Gross Unrealized Losses - 12 Months or More	(9,483)	(1,865)
Gross Unrealized Losses	(55,898)	(5,410)
Fixed maturities | Municipal bonds
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	271,481	26,665
Estimated Fair Value - 12 Months or More	8,876	16,361
Estimated Fair Value	280,357	43,026
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(17,908)	(385)
Gross Unrealized Losses - 12 Months or More	(1,028)	(1,024)
Gross Unrealized Losses	(18,936)	(1,409)
Fixed maturities | Commercial mortgage backed securities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	973,212	675,603
Estimated Fair Value - 12 Months or More	0	5,908
Estimated Fair Value	973,212	681,511
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(42,056)	(2,805)
Gross Unrealized Losses - 12 Months or More	0	(312)
Gross Unrealized Losses	(42,056)	(3,117)
Fixed maturities | US government and government agencies
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	4,029,550	4,211,621
Estimated Fair Value - 12 Months or More	69,596	33,373
Estimated Fair Value	4,099,146	4,244,994
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(235,510)	(44,180)
Gross Unrealized Losses - 12 Months or More	(5,276)	(1,787)
Gross Unrealized Losses	(240,786)	(45,967)
Fixed maturities | Non-US government securities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	1,929,278	1,511,301
Estimated Fair Value - 12 Months or More	103,969	62,957
Estimated Fair Value	2,033,247	1,574,258
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(148,781)	(31,983)
Gross Unrealized Losses - 12 Months or More	(14,943)	(2,766)
Gross Unrealized Losses	(163,724)	(34,749)
Fixed maturities | Asset backed securities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	1,292,087	1,667,002
Estimated Fair Value - 12 Months or More	136,119	33,082
Estimated Fair Value	1,428,206	1,700,084
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(73,575)	(9,853)
Gross Unrealized Losses - 12 Months or More	(6,692)	(1,255)
Gross Unrealized Losses	(80,267)	(11,108)
Short-term investments
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	505,798	284,733
Estimated Fair Value - 12 Months or More	0	0
Estimated Fair Value	505,798	284,733
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(1,257)	(590)
Gross Unrealized Losses - 12 Months or More	0	0
Gross Unrealized Losses	$ (1,257)	$ (590)

XML

Investment Information - Maturity profile of available for sale securities) (Details) - USD ($) $ in Thousands	Jun. 30, 2022	Dec. 31, 2021
Estimated Fair Value
Estimated Fair Value	$ 19,812,903	$ 19,732,825
Amortized Cost
Cost or Amortized Cost	21,043,045	19,708,561
Fixed maturities
Estimated Fair Value
Due in one year or less	412,194	300,889
Due after one year through five years	9,423,547	8,355,255
Due after five years through 10 years	4,070,099	4,689,155
Due after 10 years	350,188	505,758
Single maturity date	14,256,028	13,851,057
Estimated Fair Value	17,585,029	17,998,109
Amortized Cost
Due in one year or less	414,752	299,772
Due after one year through five years	9,927,876	8,339,387
Due after five years through 10 years	4,512,685	4,684,393
Due after 10 years	442,515	493,927
Single maturity date	15,297,828	13,817,479
Cost or Amortized Cost	18,816,372	17,973,823
Fixed maturities | Mortgage backed securities
Estimated Fair Value
Securities without single maturity date	698,168	408,477
Estimated Fair Value	698,168	408,477
Amortized Cost
Securities without single maturity date	749,639	411,110
Cost or Amortized Cost	749,639	411,110
Fixed maturities | Commercial mortgage backed securities
Estimated Fair Value
Securities without single maturity date	1,023,088	1,046,484
Estimated Fair Value	1,023,088	1,046,484
Amortized Cost
Securities without single maturity date	1,067,205	1,047,867
Cost or Amortized Cost	1,067,205	1,047,867
Fixed maturities | Asset backed securities
Estimated Fair Value
Securities without single maturity date	1,607,745	2,692,091
Estimated Fair Value	1,607,745	2,692,091
Amortized Cost
Securities without single maturity date	1,701,700	2,697,367
Cost or Amortized Cost	$ 1,701,700	$ 2,697,367

XML

Investment Information - Other investments (Details) - USD ($) $ in Thousands	Jun. 30, 2022	Dec. 31, 2021
Schedule Of Other Investments [Line Items]
Other investments, at fair value	$ 1,634,368	$ 1,973,550
Fixed maturities
Schedule Of Other Investments [Line Items]
Other investments, at fair value	525,451	416,698
Other investments
Schedule Of Other Investments [Line Items]
Other investments, at fair value	1,054,771	1,432,553
Other investments | Lending
Schedule Of Other Investments [Line Items]
Other investments, at fair value	427,812	536,345
Other investments | Investment grade fixed income
Schedule Of Other Investments [Line Items]
Other investments, at fair value	221,484	147,810
Other investments | Term loan investments
Schedule Of Other Investments [Line Items]
Other investments, at fair value	152,277	484,950
Other investments | Private equity
Schedule Of Other Investments [Line Items]
Other investments, at fair value	124,282	91,126
Other investments | Energy
Schedule Of Other Investments [Line Items]
Other investments, at fair value	74,234	81,692
Other investments | Credit related funds
Schedule Of Other Investments [Line Items]
Other investments, at fair value	54,682	70,278
Other investments | Infrastructure
Schedule Of Other Investments [Line Items]
Other investments, at fair value	0	20,352
Short-term investments
Schedule Of Other Investments [Line Items]
Other investments, at fair value	39,657	97,806
Equity securities
Schedule Of Other Investments [Line Items]
Other investments, at fair value	$ 14,489	$ 26,493

XML

Investment Information - Equity method investments (Details) - USD ($) $ in Thousands	Jun. 30, 2022	Dec. 31, 2021
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	$ 3,496,341	$ 3,077,611
Credit related funds
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	1,119,711	1,022,334
Private equity
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	646,904	436,042
Real estate
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	455,044	396,395
Lending
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	447,028	376,649
Equity securities
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	350,587	395,090
Infrastructure
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	231,816	230,070
Energy
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	115,514	119,141
Fixed income
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	$ 129,737	$ 101,890

XML

Investment Information - Limited partnership interests (Details) - USD ($) $ in Thousands		Jun. 30, 2022	Dec. 31, 2021
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss		$ 3,625,167	$ 3,248,206
Aggregate unfunded commitments		3,500,000	3,000,000
Equity method investments
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss	[1]	3,496,341	3,077,611
Aggregate unfunded commitments		3,000,000	2,600,000
Fair value option
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss	[2]	128,826	170,595
Aggregate unfunded commitments		$ 21,700	$ 18,800

[1] Aggregate unfunded commitments were $3.0 billion at June 30, 2022, compared to $2.6 billion at December 31, 2021.

[2] Aggregate unfunded commitments were $21.7 million at June 30, 2022, compared to $18.8 million at December 31, 2021.

XML

Investment Information - Net investment income (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Net investment income:
Gross investment income		$ 123,567	$ 135,176	$ 226,509	$ 261,142
Investment expenses		(17,175)	(23,563)	(39,681)	(50,673)
Net investment income		106,392	111,613	186,828	210,469
Fixed maturities
Net investment income:
Gross investment income		105,342	88,625	187,395	179,251
Term loans
Net investment income:
Gross investment income		401	16,879	2,018	31,607
Equity securities
Net investment income:
Gross investment income		6,121	8,584	12,359	14,234
Short-term investments
Net investment income:
Gross investment income		4,120	1,138	6,695	1,745
Other
Net investment income:
Gross investment income	[1]	$ 7,583	$ 19,950	$ 18,042	$ 34,305

[1] Includes income distributions from investment funds and other items.

XML

Investment Information - Net realized gains and losses (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Available for sale securities:
Available for sale securities, gross gains on investment sales		$ 15,186	$ 115,541	$ 34,893	$ 180,543
Available for sale securities, gross losses on investment sales		(57,176)	(50,627)	(165,523)	(113,625)
Equity securities, at fair value:
Net realized gains (losses) on sales during the period		16,879	33,570	82,090	71,419
Net unrealized gains (losses) on equity securities still held at reporting date		(106,375)	65,847	(282,570)	85,555
Allowance for credit losses:
Allowance for credit losses - investments related		(25,026)	896	(56,748)	(752)
Allowance for credit losses - underwriting related		842	1,381	(3,444)	6,649
Derivative instruments	[1]	(45,684)	(51,109)	(69,395)	(14,993)
Other		(128)	10,224	(3,537)	(12,821)
Net realized gains (losses)		(266,579)	202,907	(558,993)	345,368
Fixed maturities
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		(39,255)	10,912	(69,844)	27,465
Other investments
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		(21,710)	60,884	(17,321)	107,739
Equity securities
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		(2,124)	5,492	(5,437)	7,557
Short-term investments
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		$ (2,008)	$ (104)	$ (2,157)	$ 632

[1] See note 9 for information on the Company’s derivative instruments.

XML

Investment Information - Investment in operating affiliates (Details) € / shares in Units, $ / shares in Units, $ in Thousands, € in Millions	3 Months Ended		6 Months Ended		12 Months Ended
	Jun. 30, 2022 USD ($)	Jun. 30, 2021 USD ($)	Jun. 30, 2022 USD ($)	Jun. 30, 2021 USD ($)	Dec. 31, 2021 USD ($)	Dec. 31, 2021 EUR (€) € / shares	Jul. 01, 2021 $ / shares
Schedule of Equity Method Investments [Line Items]
Time lag for reporting			3 months
Investment in operating affiliates	$ 967,603		$ 967,603		$ 1,135,655
Income (loss) from operating affiliates	$ 4,640	$ 24,476	$ 29,158	$ 99,933
Coface
Schedule of Equity Method Investments [Line Items]
Percentage ownership	29.86%		29.86%		29.50%	29.50%
Investment in affiliate, price per share | € / shares						€ 9.95
Operating affiliate, aggregate cost					$ 546,000	€ 453
Investment in operating affiliates	$ 536,000		$ 536,000		630,500
Operating affiliate, gain on acquisition					74,500
Greysbridge Holdings Ltd
Schedule of Equity Method Investments [Line Items]
Percentage ownership							40.00%
Investment in affiliate, price per share | $ / shares							$ 35.00
Operating affiliate, aggregate cost					278,900
Investment in operating affiliates	$ 309,600		$ 309,600		375,700
Operating affiliate, gain on acquisition					$ 95,700
Issued Shares Excluding Treasury Stock | Coface
Schedule of Equity Method Investments [Line Items]
Percentage ownership	30.09%		30.09%
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%

XML

Investment Information - Allowance for expected credit losses (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Allowance for expected credit losses
Balance at beginning of period		$ 34,145	$ 3,830	$ 2,883	$ 2,397
Additions for current-period provision for expected credit losses		18,506	59	49,741	2,662
Additions (reductions) for previously recognized expected credit losses		6,440	(791)	6,921	(1,722)
Reductions due to disposals		(681)	(974)	(1,135)	(1,213)
Balance at end of period		58,410	2,124	58,410	2,124
Structured securities
Allowance for expected credit losses
Balance at beginning of period	[1]	6,998	1,207	802	1,490
Additions for current-period provision for expected credit losses	[1]	4,788	52	10,778	234
Additions (reductions) for previously recognized expected credit losses	[1]	6,705	(383)	7,192	(765)
Reductions due to disposals	[1]	(208)	(117)	(489)	(200)
Balance at end of period	[1]	18,283	759	18,283	759
Municipal bonds
Allowance for expected credit losses
Balance at beginning of period		106	2	2	11
Additions for current-period provision for expected credit losses		252	0	347	0
Additions (reductions) for previously recognized expected credit losses		(60)	4	(51)	(5)
Reductions due to disposals		0	0	0	0
Balance at end of period		298	6	298	6
Corporate bonds
Allowance for expected credit losses
Balance at beginning of period		27,041	2,621	2,079	896
Additions for current-period provision for expected credit losses		13,466	7	38,616	2,428
Additions (reductions) for previously recognized expected credit losses		(205)	(412)	(220)	(952)
Reductions due to disposals		(473)	(857)	(646)	(1,013)
Balance at end of period		$ 39,829	$ 1,359	$ 39,829	$ 1,359

[1] Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

XML

Investment Information - Restricted assets (Details) - USD ($) $ in Thousands	Jun. 30, 2022	Dec. 31, 2021
Restricted Assets [Line Items]
Restricted assets	$ 8,413,726	$ 8,249,732
Collateral or guarantees - affiliated transactions
Restricted Assets [Line Items]
Restricted assets	4,193,561	4,223,955
Collateral or guarantees - third party agreements
Restricted Assets [Line Items]
Restricted assets	2,953,800	2,721,160
Deposits with US regulatory authorities
Restricted Assets [Line Items]
Restricted assets	781,024	798,100
Deposits with non-US regulatory authorities
Restricted Assets [Line Items]
Restricted assets	$ 485,341	$ 506,517

XML

Investment Information - Cash and restricted cash (Details) - USD ($) $ in Thousands	Jun. 30, 2022	Dec. 31, 2021	Jun. 30, 2021	Dec. 31, 2020
Disclosure Investment Information [Abstract]
Cash	$ 813,548	$ 858,668
Restricted cash (included in ‘other assets’)	414,683	456,103
Cash and restricted cash	$ 1,228,231	$ 1,314,771	$ 1,818,463	$ 1,290,544

XML

Investment Information - Narrative (Details) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2022 USD ($) lots	Jun. 30, 2021 USD ($)	Jun. 30, 2022 USD ($) lots	Jun. 30, 2021 USD ($)	Dec. 31, 2021 USD ($) lots
Continuous unrealized loss, qualitative disclosures:
Number of positions in an unrealized loss position (lots) | lots	8,360		8,360		4,700
Total number of positions (lots) | lots	10,440		10,440		10,240
Largest single loss	$ 5,700		$ 5,700		$ 1,100
Narrative items:
Equity securities, at fair value	772,689		772,689		$ 1,804,170
Equity in net (loss) income of investment funds accounted for using the equity method	$ 58,061	$ 122,186	$ 94,366	$ 193,872
Time lag for reporting			3 months
Minimum
Narrative items:
Time lag for reporting			1 month
Maximum
Narrative items:
Time lag for reporting			3 months

XML

Fair Value - Fair Value Hierarchy (Details) - Recurring - USD ($) $ in Thousands		Jun. 30, 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		$ 7,137,960	$ 7,602,828
Liabilities measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Other liabilities
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 loans
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
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		4,341,399	4,744,517
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | 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 | 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 | 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 | 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 | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		4,341,399	4,744,517
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | 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 | 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		2,049,235	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		736,343	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		10,983	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 | 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		886	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		10,097	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		14,284,586	14,923,923
Liabilities measured at fair value		(75,147)	(54,224)
Significant Other Observable Inputs (Level 2) | Other liabilities
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		(75,147)	(54,224)
Significant Other Observable Inputs (Level 2) | Residential mortgage loans
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		3,929	49,847
Significant Other Observable Inputs (Level 2) | Fixed maturities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		13,237,193	13,250,232
Significant Other Observable Inputs (Level 2) | Fixed maturities | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		7,284,985	6,553,320
Significant Other Observable Inputs (Level 2) | Fixed maturities | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		698,168	408,477
Significant Other Observable Inputs (Level 2) | Fixed maturities | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		417,380	404,666
Significant Other Observable Inputs (Level 2) | Fixed maturities | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,023,088	1,046,484
Significant Other Observable Inputs (Level 2) | Fixed maturities | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		26,751	28,247
Significant Other Observable Inputs (Level 2) | Fixed maturities | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,181,943	2,120,294
Significant Other Observable Inputs (Level 2) | Fixed maturities | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,604,878	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		178,639	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		33,440	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		122,033	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		709,352	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		522,707	388,546
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		611	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		2,133	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		38,771	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		145,130	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		47,066	39,007
Liabilities measured at fair value		(16,205)	(16,960)
Significant Unobservable Inputs (Level 3) | Other liabilities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(16,205)	(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 loans
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
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		6,437	3,360
Significant Unobservable Inputs (Level 3) | Fixed maturities | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		3,570	13
Significant Unobservable Inputs (Level 3) | Fixed maturities | 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 | 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 | 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 | 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 | 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 | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,867	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		2,906	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		37,723	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 | 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		4,392	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		33,331	27,981
Estimated Fair Value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		22,345,922	23,687,513
Liabilities measured at fair value		(91,352)	(71,184)
Estimated Fair Value | Other liabilities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(16,205)	(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		(75,147)	(54,224)
Estimated Fair Value | Residential mortgage loans
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		3,929	49,847
Estimated Fair Value | Fixed maturities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		17,585,029	17,998,109
Estimated Fair Value | Fixed maturities | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		7,288,555	6,553,333
Estimated Fair Value | Fixed maturities | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		698,168	408,477
Estimated Fair Value | Fixed maturities | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		417,380	404,666
Estimated Fair Value | Fixed maturities | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,023,088	1,046,484
Estimated Fair Value | Fixed maturities | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		4,368,150	4,772,764
Estimated Fair Value | Fixed maturities | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,181,943	2,120,294
Estimated Fair Value | Fixed maturities | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,607,745	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		2,227,874	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		772,689	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		122,033	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		1,634,368	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		522,707	388,546
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		611	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		2,133	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		39,657	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		14,489	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		178,461	310,798
Estimated Fair Value | Fair value option | Other investments measured at net asset value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[1]	$ 876,310	$ 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.

XML

Fair Value - Rollforward of Level 3 assets and liabilities (Details) - Recurring - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Other liabilities
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		$ (17,591)	$ (465)	$ (16,960)	$ (461)
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	(97)	(1)	(195)	(5)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		1,483	0	950	0
Purchases, issuances, sales and settlements
Purchases		0	0	0	0
Issuances		0	0	0	0
Sales		0	0	0	0
Settlements		0	0	0	0
Transfers in and/or out of Level 3		0	0	0	0
Balance at end of period		(16,205)	(466)	(16,205)	(466)
Available for sale | Structured securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period	[2]	3,152	3,472	3,347	3,426
Total gains or (losses) (realized/unrealized) - included in earnings	[1],[2]	(1)	12	9	(56)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income	[2]	(85)	(57)	(145)	57
Purchases, issuances, sales and settlements
Purchases	[2]	0	0	0	0
Issuances	[2]	0	0	0	0
Sales	[2]	0	0	0	0
Settlements	[2]	(199)	(3)	(344)	(3)
Transfers in and/or out of Level 3	[2]	0	0	0	0
Balance at end of period	[2]	2,867	3,424	2,867	3,424
Available for sale | Corporate bonds
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		3,570	13	13	13
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	0	0	0	0
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0	0	0
Purchases, issuances, sales and settlements
Purchases		0	0	0	0
Issuances		0	0	0	0
Sales		0	0	0	0
Settlements		0	0	0	0
Transfers in and/or out of Level 3		0	0	3,557	0
Balance at end of period		3,570	13	3,570	13
Fair value option | Corporate bonds
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		0	989	0	985
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	0	9	0	13
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0	0	0
Purchases, issuances, sales and settlements
Purchases		0	0	0	0
Issuances		0	0	0	0
Sales		0	0	0	0
Settlements		0	0	0	0
Transfers in and/or out of Level 3		0	0	0	0
Balance at end of period		0	998	0	998
Fair value option | Other investments
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		22,602	67,930	27,981	67,103
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	27	633	34	881
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0	0	0
Purchases, issuances, sales and settlements
Purchases		10,702	5,638	10,770	13,003
Issuances		0	0	0	0
Sales		0	(301)	(2,471)	(7,087)
Settlements		0	0	(2,983)	0
Transfers in and/or out of Level 3		0	0	0	0
Balance at end of period		33,331	73,900	33,331	73,900
Fair value option | Equity securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		4,511	71,176	4,748	68,988
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	(119)	2,502	(356)	4,690
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0	0	0
Purchases, issuances, sales and settlements
Purchases		0	0	0	0
Issuances		0	0	0	0
Sales		0	0	0	0
Settlements		0	0	0	0
Transfers in and/or out of Level 3		0	0	0	0
Balance at end of period		4,392	73,678	4,392	73,678
Equity securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		2,768	43,112	2,918	42,015
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	(89)	922	(236)	1,826
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0	0	0
Purchases, issuances, sales and settlements
Purchases		227	5,102	227	5,295
Issuances		0	0	0	0
Sales		0	0	(3)	0
Settlements		0	0	0	0
Transfers in and/or out of Level 3		0	0	0	0
Balance at end of period		$ 2,906	$ 49,136	$ 2,906	$ 49,136

[1] Gains or losses were included in net realized gains (losses).

[2] Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

XML

Fair Value - Narrative (Details) - USD ($) $ in Thousands	Jun. 30, 2022	Dec. 31, 2021
Fair Value Disclosures [Abstract]
Total assets and liabilities measured at fair value	$ 22,400,000	$ 23,800,000
Total assets and liabilities measured at fair value priced using non-binding broker quotes	$ 10,900	$ 7,700
Total assets and liabilities measured at fair value priced using non-binding broker quotes (percentage)	0.00%	0.00%
Senior notes	$ 2,724,896	$ 2,724,394
Estimated fair value of senior notes	$ 2,600,000	$ 3,300,000

XML

Derivative Instruments - Fair value and notional amount of derivatives (Details) - USD ($) $ in Thousands		Jun. 30, 2022	Dec. 31, 2021
Derivative offsetting
Derivative assets subject to master netting agreements		$ 116,900	$ 122,300
Derivative liabilities subject to master netting agreements		75,100	53,900
Not designated as hedging instrument
Derivative [Line Items]
Asset derivatives - fair value		122,033	127,121
Liability derivatives - fair value		(75,147)	(54,224)
Not designated as hedging instrument | Futures contracts
Derivative [Line Items]
Net derivatives - notional value	[1]	2,794,246	2,826,564
Not designated as hedging instrument | Futures contracts | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[2]	49,695	34,999
Not designated as hedging instrument | Futures contracts | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[2]	(22,561)	(9,808)
Not designated as hedging instrument | Foreign currency forward contracts
Derivative [Line Items]
Net derivatives - notional value	[1]	908,192	915,962
Not designated as hedging instrument | Foreign currency forward contracts | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[2]	9,556	7,734
Not designated as hedging instrument | Foreign currency forward contracts | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[2]	(18,884)	(11,390)
Not designated as hedging instrument | TBAs
Derivative [Line Items]
Net derivatives - notional value	[1]	0	11,227
Not designated as hedging instrument | TBAs | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[2]	0	11,227
Not designated as hedging instrument | TBAs | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[2]	0	0
Not designated as hedging instrument | Other
Derivative [Line Items]
Net derivatives - notional value	[1]	3,849,244	3,736,773
Not designated as hedging instrument | Other | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[2]	62,782	73,161
Not designated as hedging instrument | Other | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[2]	$ (33,702)	$ (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.’

XML

Derivative Instruments - Summary of net realized gains (losses) recorded in the consolidated statements of income (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments	[1]	$ (45,684)	$ (51,109)	$ (69,395)	$ (14,993)
Not designated as hedging instrument
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(45,684)	(51,109)	(69,395)	(14,993)
Not designated as hedging instrument | Futures contracts
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(39,205)	(54,759)	(85,979)	(7,321)
Not designated as hedging instrument | Foreign currency forward contracts
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(25,638)	1,295	(27,676)	(20,776)
Not designated as hedging instrument | TBAs
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		0	0	(51)	0
Not designated as hedging instrument | Other
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments	[2]	$ 19,159	$ 2,355	$ 44,311	$ 13,104

[1] See note 9 for information on the Company’s derivative instruments.

[2] Includes realized gains and losses on swaps, options and other derivatives contracts

XML

Commitments and Contingencies (Details) - USD ($) $ in Millions		6 Months Ended
	Apr. 07, 2022	Jun. 30, 2022	Jun. 30, 2021	Dec. 31, 2021
Commitments and Contingencies Disclosure [Abstract]
Investment commitments		$ 3,500.0		$ 3,000.0
Interest paid on senior notes and other borrowings		64.6	$ 74.7
Credit Agreement
Line of Credit Facility [Line Items]
Maximum borrowing capacity	$ 925.0
Credit facility term	5 years
Optional increased capacity	$ 1,300.0
Secured Facility
Line of Credit Facility [Line Items]
Maximum borrowing capacity	425.0	425.0
Revolving credit agreement borrowings		333.4
Remaining capacity		91.6
Unsecured Facility
Line of Credit Facility [Line Items]
Maximum borrowing capacity	$ 500.0
Secured Letters of Credit | Barbican Group Holdings Limited
Line of Credit Facility [Line Items]
Revolving credit agreement borrowings		23.6
Unsecured Letters of Credit | Barbican Group Holdings Limited
Line of Credit Facility [Line Items]
Revolving credit agreement borrowings		$ 290.0

XML

Variable Interest Entities and Noncontrolling Interests - Variable interest entity (Details) - USD ($) $ in Thousands	1 Months Ended	6 Months Ended
	Mar. 31, 2014	Jun. 30, 2022	Jun. 30, 2021	Jul. 01, 2021
Variable Interest Entity [Line Items]
Net cash provided by (used for) operating activities		$ 1,453,968	$ 1,612,572
Net cash provided by (used for) investing activities		(815,602)	(1,093,678)
Net cash (used for) provided by financing activities		$ (682,116)	22,415
Greysbridge Holdings Ltd
Variable Interest Entity [Line Items]
Percentage ownership				40.00%
Kelso And Company | Greysbridge Holdings Ltd
Variable Interest Entity [Line Items]
Percentage ownership				30.00%
Warburg Pincus LLC | Greysbridge Holdings Ltd
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
Ownership percentage	11.00%
Net cash provided by (used for) operating activities			47,000
Net cash provided by (used for) investing activities			96,300
Net cash (used for) provided by financing activities			$ (2,000)

XML

Variable Interest Entities and Noncontrolling Interests - Non-redeemable noncontrolling interests (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Noncontrolling Interest [Line Items]
Amounts attributable to noncontrolling interests	$ 0	$ 41,617	$ 0	$ 78,314
Other comprehensive (income) loss attributable to noncontrolling interests	0	10	0	(4,560)
Non-redeemable noncontrolling interests, end of period	$ 0	918,874	$ 0	918,874
Somers Holdings Ltd
Noncontrolling Interest [Line Items]
Non-redeemable noncontrolling interests, beginning of period		876,864		823,007
Additional paid in capital attributable to noncontrolling interests		383		22,113
Amounts attributable to noncontrolling interests		41,617		78,314
Other comprehensive (income) loss attributable to noncontrolling interests		10		(4,560)
Non-redeemable noncontrolling interests, end of period		$ 918,874		$ 918,874

XML

Variable Interest Entities and Noncontrolling Interests - Redeemable noncontrolling interests (Details) - USD ($) $ / shares in Units, $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021	Mar. 31, 2014
Redeemable Noncontrolling Interest [Line Items]
Redeemable noncontrolling interests, beginning of period			$ 9,233
Redeemable noncontrolling interests, end of period	$ 8,459		8,459
Somers Holdings Ltd
Redeemable Noncontrolling Interest [Line Items]
Redeemable noncontrolling interests, beginning of period	9,763	$ 57,670	9,233	$ 58,548
Accretion of preference share issuance costs	0	23	0	46
Other	(1,304)	(160)	(774)	(1,061)
Redeemable noncontrolling interests, end of period	$ 8,459	$ 57,533	$ 8,459	$ 57,533
Cumulative redeemable preference shares | Somers Holdings Ltd
Redeemable Noncontrolling Interest [Line Items]
Par value per share					$ 0.01
Liquidation preference per share					25.00
Issue price per share					$ 24.50

XML

Variable Interest Entities and Noncontrolling Interests - Income or loss attributable to third party investors (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Noncontrolling Interest [Abstract]
Amounts attributable to non-redeemable noncontrolling interests	$ 0	$ (41,617)	$ 0	$ (78,314)
Amounts attributable to redeemable noncontrolling interests	399	(1,561)	(1,233)	(2,416)
Net (income) loss attributable to noncontrolling interests	$ 399	$ (43,178)	$ (1,233)	$ (80,730)

XML

Variable Interest Entities and Noncontrolling Interests - Other variable interest entity disclosures (Details) - USD ($) $ in Thousands		Jun. 30, 2022	Dec. 31, 2021
Variable Interest Entity [Line Items]
Total VIE Assets		$ 45,719,194	$ 45,100,945
Maximum Exposure to Loss, Total		3,625,167	3,248,206
Variable Interest Entity, Not Primary Beneficiary
Variable Interest Entity [Line Items]
Total VIE Assets		3,938,695	4,336,596
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(5,125)	(4,434)
Maximum Exposure to Loss - Off-Balance Sheet		34,088	42,202
Maximum Exposure to Loss, Total		28,963	37,768
Remaining Coverage, Amount		316,457
Variable Interest Entity, Not Primary Beneficiary | 2017-1 Ltd. (Oct-17)
Variable Interest Entity [Line Items]
Total VIE Assets		61,328	108,368
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(68)	(159)
Maximum Exposure to Loss - Off-Balance Sheet		274	424
Maximum Exposure to Loss, Total		206	265
Variable Interest Entity, Not Primary Beneficiary | 2018-1 Ltd. (Apr-18)
Variable Interest Entity [Line Items]
Total VIE Assets		122,190	181,136
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(342)	(528)
Maximum Exposure to Loss - Off-Balance Sheet		965	1,268
Maximum Exposure to Loss, Total		623	740
Variable Interest Entity, Not Primary Beneficiary | 2018-3 Ltd. (Oct-18)
Variable Interest Entity [Line Items]
Total VIE Assets		244,257	302,563
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(566)	(1,018)
Maximum Exposure to Loss - Off-Balance Sheet		1,522	2,496
Maximum Exposure to Loss, Total		956	1,478
Variable Interest Entity, Not Primary Beneficiary | 2019-1 Ltd. (Mar-19)
Variable Interest Entity [Line Items]
Total VIE Assets		134,972	181,324
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(127)	(380)
Maximum Exposure to Loss - Off-Balance Sheet		988	5,807
Maximum Exposure to Loss, Total		861	5,427
Variable Interest Entity, Not Primary Beneficiary | 2019-2 Ltd. (Apr-19)
Variable Interest Entity [Line Items]
Total VIE Assets		383,737	398,316
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(426)	(515)
Maximum Exposure to Loss - Off-Balance Sheet		5,323	3,998
Maximum Exposure to Loss, Total		4,897	3,483
Variable Interest Entity, Not Primary Beneficiary | 2019-3 Ltd. (Jul-19)
Variable Interest Entity [Line Items]
Total VIE Assets		296,466	409,859
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(282)	(584)
Maximum Exposure to Loss - Off-Balance Sheet		2,154	3,190
Maximum Exposure to Loss, Total		1,872	2,606
Variable Interest Entity, Not Primary Beneficiary | 2019-4 Ltd. (Oct-19)
Variable Interest Entity [Line Items]
Total VIE Assets		312,668	411,954
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(306)	(462)
Maximum Exposure to Loss - Off-Balance Sheet		4,702	4,759
Maximum Exposure to Loss, Total		4,396	4,297
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-2 Ltd (Sep-20)
Variable Interest Entity [Line Items]
Total VIE Assets		151,543	217,766
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(58)	(177)
Maximum Exposure to Loss - Off-Balance Sheet		1,331	1,984
Maximum Exposure to Loss, Total		1,273	1,807
Remaining Coverage, Amount	[1]	442
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-3 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		303,011	348,818
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(26)	(128)
Maximum Exposure to Loss - Off-Balance Sheet		4,388	5,793
Maximum Exposure to Loss, Total		4,362	5,665
Remaining Coverage, Amount	[1]	10,779
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-4 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		124,672	176,826
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		23	(50)
Maximum Exposure to Loss - Off-Balance Sheet		1,267	1,630
Maximum Exposure to Loss, Total		1,290	1,580
Remaining Coverage, Amount	[1]	5,900
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-1 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		519,641	568,986
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(1,006)	(303)
Maximum Exposure to Loss - Off-Balance Sheet		2,771	3,283
Maximum Exposure to Loss, Total		1,765	2,980
Remaining Coverage, Amount	[1]	48,841
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-2 Ltd. (Jun-21)
Variable Interest Entity [Line Items]
Total VIE Assets		492,837	522,807
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(577)	281
Maximum Exposure to Loss - Off-Balance Sheet		3,505	4,124
Maximum Exposure to Loss, Total		2,928	4,405
Remaining Coverage, Amount	[1]	85,717
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-3 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		507,873	507,873
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(1,082)	(411)
Maximum Exposure to Loss - Off-Balance Sheet		2,878	3,446
Maximum Exposure to Loss, Total		1,796	$ 3,035
Remaining Coverage, Amount	[1]	131,518
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2022-1 Ltd.
Variable Interest Entity [Line Items]
Total VIE Assets		283,500
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(282)
Maximum Exposure to Loss - Off-Balance Sheet		2,020
Maximum Exposure to Loss, Total		1,738
Remaining Coverage, Amount	[1]	$ 33,260

[1] Coverage from a separate panel of reinsurers remaining at June 30, 2022.

XML

Other Comprehensive Income (Loss) - Amounts reclassified from accumulated other comprehensive income (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
Provision for credit losses	$ (25,026)	$ 896	$ (56,748)	$ (752)
Income tax expense	(22,323)	(51,179)	(33,942)	(90,039)
Net of tax	403,945	718,664	601,377	1,194,372
Reclassification out of accumulated other comprehensive income | Unrealized appreciation on available-for-sale investments
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
Net realized gains (losses)	(41,990)	64,914	(130,630)	66,918
Provision for credit losses	(25,026)	896	(56,748)	(751)
Income (loss) before income taxes and income (loss) from operating affiliates	(67,016)	65,810	(187,378)	66,167
Income tax expense	9,306	(5,263)	27,390	(8,317)
Net of tax	$ (57,710)	$ 60,547	$ (159,988)	$ 57,850

XML

Other Comprehensive Income (Loss) - Components of other comprehensive income (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Before tax amount:
Unrealized holding gains (losses) arising during period, before tax	$ (676,048)	$ 91,057	$ (1,460,938)	$ (203,303)
Less reclassification of net realized gains included in net income, before tax	(67,016)	65,810	(187,378)	66,167
Foreign currency translation adjustments, before tax	(68,562)	6,392	(71,127)	(22,023)
Other comprehensive income (loss), before tax	(677,594)	31,639	(1,344,687)	(291,493)
Tax expense (benefit):
Unrealized holding gains (losses) arising during period, tax	(78,043)	12,486	(178,578)	(20,124)
Less reclassification of net realized gains included in net income, tax	(9,306)	5,263	(27,390)	8,317
Foreign currency translation adjustments, tax	(37)	187	166	356
Other comprehensive income (loss), tax	(68,774)	7,410	(151,022)	(28,085)
Net of tax amount:
Unrealized holding gains (losses) arising during period, net of tax	(598,005)	78,571	(1,282,360)	(183,179)
Less reclassification of net realized gains included in net income, net of tax	(57,710)	60,547	(159,988)	57,850
Foreign currency translation adjustments, net of tax	(68,525)	6,205	(71,293)	(22,379)
Net current period other comprehensive income (loss)	$ (608,820)	$ 24,229	$ (1,193,665)	$ (263,408)

XML

Income Taxes (Details) - USD ($) $ in Millions	6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Dec. 31, 2021
Income Tax Disclosure [Abstract]
Effective tax rate on income before income taxes (percentage)	5.30%	7.00%
Net deferred tax asset	$ 411.1		$ 194.0
Income taxes paid	$ 128.6	$ 141.1

XML

Transactions With Related Parties (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021	Mar. 31, 2022	Dec. 31, 2021	Jul. 01, 2021	Mar. 31, 2021	Jan. 01, 2021	Dec. 31, 2020
Related Party Transaction [Line Items]
Premiums ceded	$ 1,185,088	$ 886,767	$ 2,351,723	$ 1,775,516
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	5,938,511	$ 4,314,515	5,938,511	$ 4,314,515	$ 5,941,000	$ 5,880,735		$ 4,041,076		$ 4,500,802
Reinsurance balances payable	1,634,700		1,634,700			$ 1,583,253
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%
Warburg Pincus LLC | Greysbridge Holdings Ltd
Related Party Transaction [Line Items]
Percentage ownership							30.00%
Operating affiliates | Premia Holdings Ltd
Related Party Transaction [Line Items]
Legacy business, amount of liabilities transferred									$ 380,000
Operating affiliates | Somers Holdings Ltd
Related Party Transaction [Line Items]
Premiums ceded			424,600
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	964,700		964,700
Reinsurance balances payable	358,400		358,400
Senior notes, face amount	$ 35,000		$ 35,000
Senior notes, stated percentage	6.50%		6.50%
Operating affiliates | Somers Holdings Ltd | Non-cumulative preferred shares
Related Party Transaction [Line Items]
Percentage ownership	6.60%		6.60%