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, 2021

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 5.25% Series E preferred share	ACGLP	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 30, 2021, there were 396,039,032 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	43
Item 3.	Quantitative and Qualitative Disclosures About Market Risk	69
Item 4.	Controls and Procedures	70
	PART II
	Other Information	70
Item 1.	Legal Proceedings	70
Item 1A.	Risk Factors	70
Item 2.	Unregistered Sales of Equity Securities and Use of Proceeds	71
Item 3.	Defaults Upon Senior Securities	71
Item 4.	Mine Safety Disclosures	71
Item 5.	Other Information	71
Item 6.	Exhibits	72
	Signatures	73

ARCH CAPITAL  1 2021 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 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 2021 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 potential replacement of LIBOR;

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

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

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

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

•statutory or regulatory developments, including as to tax matters and insurance and other regulatory matters such as the adoption of proposed legislation that would affect Bermuda-headquartered companies and/or Bermuda-based insurers or reinsurers and/or changes in regulations or tax laws applicable to us, our subsidiaries, brokers or customers, including the Tax Cuts and Jobs Act of 2017; 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, 2020, 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 2021 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, 2021 (unaudited) and December 31, 2020	6
Consolidated Statements of Income
For the three and six month periods ended June 30, 2021 and 2020 (unaudited)	7
Consolidated Statements of Comprehensive Income
For the three and six month periods ended June 30, 2021 and 2020 (unaudited)	8
Consolidated Statements of Changes in Shareholders’ Equity
For the three and six month periods ended June 30, 2021 and 2020 (unaudited)	9
Consolidated Statements of Cash Flows
For the six month periods ended June 30, 2021 and 2020 (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	30
Note 9 - Derivative Instruments	36
Note 10 - Commitments and Contingencies	37
Note 11 - Variable Interest Entities and Noncontrolling Interests	37
Note 12 - Other Comprehensive Income (Loss)	41
Note 13 - Income Taxes	42
Note 14 - Legal Proceedings	42
Note 15 - Transactions with Related Parties	42
Note 16 - Subsequent Event	42

ARCH CAPITAL  4 2021 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, 2021, 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, 2021 and 2020, and the consolidated statements of cash flows for the six-month periods ended June 30, 2021 and 2020, 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, 2020, 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 26, 2021, 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, 2020, 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, NY

August 5, 2021

ARCH CAPITAL  5 2021 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, 2021		December 31, 2020
Assets
Investments:
Fixed maturities available for sale, at fair value (amortized cost: $17,764,783 and $18,143,305; net of allowance for credit losses: $2,124 and $2,397 )	$	18,073,779	$	18,717,825
Short-term investments available for sale, at fair value (amortized cost: $2,248,615 and $1,924,292; net of allowance for credit losses: $0 and $0)	2,248,613		1,924,922
Collateral received under securities lending, at fair value (amortized cost: $172,109 and $301,089)	172,116		301,096
Equity securities, at fair value	1,693,552		1,444,830
Other investments (portion measured at fair value: $4,071,497 and $3,824,796)	4,571,497		4,324,796
Investments accounted for using the equity method	2,539,124		2,047,889
Total investments	29,298,681		28,761,358
Cash	1,234,059		906,448
Accrued investment income	96,546		103,299
Securities pledged under securities lending, at fair value (amortized cost: $167,871 and $294,493)	168,548		294,912
Investment in operating affiliates	731,810		129,291
Premiums receivable (net of allowance for credit losses: $35,979 and $37,781)	2,866,578		2,064,586
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $11,029 and $11,636)	4,314,515		4,500,802
Contractholder receivables (net of allowance for credit losses: $4,471 and $8,638)	1,882,948		1,986,924
Ceded unearned premiums	1,541,093		1,234,075
Deferred acquisition costs	1,013,657		790,708
Receivable for securities sold	309,234		92,743
Goodwill and intangible assets	667,153		692,863
Other assets	2,357,064		1,724,288
Total assets	$	46,481,886	$	43,282,297
Liabilities
Reserve for losses and loss adjustment expenses	$	17,196,648	$	16,513,929
Unearned premiums	6,011,369		4,838,965
Reinsurance balances payable	1,079,106		683,263
Contractholder payables	1,887,418		1,995,562
Collateral held for insured obligations	235,618		215,581
Senior notes	2,861,728		2,861,113
Revolving credit agreement borrowings	155,687		155,687
Securities lending payable	172,109		301,089
Payable for securities purchased	586,881		218,779
Other liabilities	1,332,843		1,510,888
Total liabilities	31,519,407		29,294,856
Commitments and Contingencies
Redeemable noncontrolling interests	57,533		58,548
Shareholders' Equity
Non-cumulative preferred shares	1,280,000		780,000
Common shares ($0.0011 par, shares issued: 582,654,893 and 579,000,841)	647		643
Additional paid-in capital	2,028,919		1,977,794
Retained earnings	13,454,036		12,362,463
Accumulated other comprehensive income (loss), net of deferred income tax	230,048		488,895
Common shares held in treasury, at cost (shares: 185,883,642 and 172,280,199)	(3,007,578)		(2,503,909)
Total shareholders' equity available to Arch	13,986,072		13,105,886
Non-redeemable noncontrolling interests	918,874		823,007
Total shareholders' equity	14,904,946		13,928,893
Total liabilities, noncontrolling interests and shareholders' equity	$	46,481,886	$	43,282,297

See Notes to Consolidated Financial Statements

ARCH CAPITAL 6 2021 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,
	2021		2020		2021		2020
Revenues
Net premiums earned	$	2,120,909	$	1,665,354	4,069,331		3,409,798
Net investment income	111,613		131,485		210,469		276,638
Net realized gains (losses)	202,907		556,588		345,368		189,628
Other underwriting income	5,529		6,667		11,639		13,519
Equity in net income (loss) of investment funds accounted for using the equity method	122,186		(65,119)		193,872		(69,328)
Other income (loss)	6,852		33		5,111		65
Total revenues	2,569,996		2,295,008		4,835,790		3,820,320
Expenses
Losses and loss adjustment expenses	1,159,831		1,230,522		2,362,931		2,345,941
Acquisition expenses	335,143		254,789		639,624		502,072
Other operating expenses	244,943		209,249		505,976		443,793
Corporate expenses	15,951		17,920		41,335		38,716
Amortization of intangible assets	15,286		16,489		29,688		33,120
Interest expense	35,700		31,139		74,046		63,694
Net foreign exchange (gains) losses	17,775		39,211		(2,288)		(33,460)
Total expenses	1,824,629		1,799,319		3,651,312		3,393,876
Income (loss) before income taxes and income (loss) from operating affiliates	745,367		495,689		1,184,478		426,444
Income tax expense	(51,179)		(26,127)		(90,039)		(54,072)
Income (loss) from operating affiliates	24,476		(3,173)		99,933		5,343
Net income (loss)	$	718,664	$	466,389	$	1,194,372	$	377,715
Net (income) loss attributable to noncontrolling interests	(43,178)		(167,568)		(80,730)		65,223
Net income (loss) available to Arch	675,486		298,821		1,113,642		442,938
Preferred dividends	(11,666)		(10,403)		(22,069)		(20,806)
Net income (loss) available to Arch common shareholders	$	663,820	$	288,418	$	1,091,573	$	422,132
Net income per common share and common share equivalent
Basic	$	1.67	$	0.72	$	2.73	$	1.05
Diluted	$	1.63	$	0.71	$	2.68	$	1.03
Weighted average common shares and common share equivalents outstanding
Basic	397,743,402		402,503,687		399,267,183		403,197,924
Diluted	406,485,994		408,119,681		407,687,680		411,005,591

See Notes to Consolidated Financial Statements

ARCH CAPITAL 7 2021 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,
	2021		2020		2021		2020
Comprehensive Income
Net income (loss)	$	718,664	$	466,389	$	1,194,372	$	377,715
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	78,571		492,796		(183,179)		435,509
Reclassification of net realized (gains) losses, included in net income (loss)	(60,547)		(167,391)		(57,850)		(288,620)
Foreign currency translation adjustments	6,205		22,251		(22,379)		(22,438)
Comprehensive income (loss)	742,893		814,045		930,964		502,166
Net (income) loss attributable to noncontrolling interests	(43,178)		(167,568)		(80,730)		65,223
Other comprehensive (income) loss attributable to noncontrolling interests	(10)		(20,111)		4,560		12,947
Comprehensive income (loss) available to Arch	$	699,705	$	626,366	$	854,794	$	580,336

See Notes to Consolidated Financial Statements

ARCH CAPITAL 8 2021 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,
	2021		2020		2021		2020
Non-cumulative preferred shares
Balance at beginning of period	$	780,000	$	780,000	$	780,000	$	780,000
Preferred shares issued	500,000		—		500,000		—
Balance at beginning and end of period	$	1,280,000	$	780,000	$	1,280,000	$	780,000
Common shares
Balance at beginning of period	645		642		643		638
Common shares issued, net	2		—		4		4
Balance at end of period	647		642		647		642
Additional paid-in capital
Balance at beginning of period	2,014,741		1,921,487		1,977,794		1,889,683
Amortization of share-based compensation	16,490		13,160		57,063		41,210
Issue costs on preferred shares	(14,179)		—		(14,179)		—
Other changes	11,867		867		8,241		4,621
Balance at end of period	2,028,919		1,935,514		2,028,919		1,935,514
Retained earnings
Balance at beginning of period	12,790,216		11,132,268		12,362,463		11,021,006
Cumulative effect of an accounting change (1)	—		—		—		(22,452)
Balance at beginning of period, as adjusted	12,790,216		11,132,268		12,362,463		10,998,554
Net income (loss)	718,664		466,389		1,194,372		377,715
Net (income) loss attributable to noncontrolling interests	(43,178)		(167,568)		(80,730)		65,223
Preferred share dividends	(11,666)		(10,403)		(22,069)		(20,806)
Balance at end of period	13,454,036		11,420,686		13,454,036		11,420,686
Accumulated other comprehensive income (loss), net of deferred income tax
Balance at beginning of period	205,827		21,944		488,895		212,091
Unrealized appreciation (decline) in value of available-for-sale investments, net of deferred income tax:
Balance at beginning of period	246,711		113,149		501,295		258,486
Unrealized holding gains (losses) during period, net of reclassification adjustment	18,024		325,405		(241,029)		146,889
Unrealized holding gains (losses) during period attributable to noncontrolling interests	(33)		(20,067)		4,436		13,112
Balance at end of period	264,702		418,487		264,702		418,487
Foreign currency translation adjustments, net of deferred income tax:
Balance at beginning of period	(40,884)		(91,205)		(12,400)		(46,395)
Foreign currency translation adjustments	6,205		22,251		(22,379)		(22,438)
Foreign currency translation adjustments attributable to noncontrolling interests	25		(45)		125		(166)
Balance at end of period	(34,654)		(68,999)		(34,654)		(68,999)
Balance at end of period	230,048		349,488		230,048		349,488
Common shares held in treasury, at cost
Balance at beginning of period	(2,694,957)		(2,489,097)		(2,503,909)		(2,406,047)
Shares repurchased for treasury	(312,621)		(5,408)		(503,669)		(88,458)
Balance at end of period	(3,007,578)		(2,494,505)		(3,007,578)		(2,494,505)
Total shareholders’ equity available to Arch	13,986,072		11,991,825		13,986,072		11,991,825
Non-redeemable noncontrolling interests	918,874		679,089		918,874		679,089
Total shareholders’ equity	$	14,904,946	$	12,670,914	$	14,904,946	$	12,670,914

(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

See Notes to Consolidated Financial Statements

ARCH CAPITAL 9 2021 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,
	2021		2020
Operating Activities
Net income (loss)	$	1,194,372	$	377,715
Adjustments to reconcile net income (loss) to net cash provided by operating activities:
Net realized (gains) losses	(379,049)		(194,776)
Equity in net (income) or loss of investment funds accounted for using the equity method and other income or loss	(181,028)		125,384
Amortization of intangible assets	29,688		33,120
Share-based compensation	57,564		41,912
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable	948,505		1,158,446
Unearned premiums, net of ceded unearned premiums	838,650		395,759
Premiums receivable	(781,391)		(463,638)
Deferred acquisition costs	(214,893)		(92,437)
Reinsurance balances payable	331,461		132,161
Other items, net	(231,307)		(192,066)
Net cash provided by (used for) operating activities	1,612,572		1,321,580
Investing Activities
Purchases of fixed maturity investments	(23,554,384)		(25,410,849)
Purchases of equity securities	(620,774)		(1,025,149)
Purchases of other investments	(1,033,134)		(501,692)
Proceeds from sales of fixed maturity investments	23,130,388		24,833,030
Proceeds from sales of equity securities	542,290		580,346
Proceeds from sales, redemptions and maturities of other investments	772,549		472,188
Proceeds from redemptions and maturities of fixed maturity investments	805,836		369,240
Net settlements of derivative instruments	17,286		150,471
Net (purchases) sales of short-term investments	(378,086)		(1,323,363)
Change in cash collateral related to securities lending	(826)		54,596
Purchase of operating affiliate	(546,349)		—
Purchases of fixed assets	(23,585)		(17,687)
Other	(204,889)		8,679
Net cash provided by (used for) investing activities	(1,093,678)		(1,810,190)
Financing Activities
Proceeds from issuance of preferred shares, net	485,821		—
Purchases of common shares under share repurchase program	(485,315)		(75,486)
Proceeds from common shares issued, net	185		(9,661)
Proceeds from borrowings	—		1,004,918
Repayments of borrowings	—		(165,000)
Change in cash collateral related to securities lending	826		(54,596)
Third party investment in non-redeemable noncontrolling interests	15,971		(2,867)
Dividends paid to redeemable noncontrolling interests	(1,907)		(2,540)
Other	27,639		(2,625)
Preferred dividends paid	(20,805)		(20,806)
Net cash provided by (used for) financing activities	22,415		671,337
Effects of exchange rate changes on foreign currency cash and restricted cash	(13,390)		(21,742)
Increase (decrease) in cash and restricted cash	527,919		160,985
Cash and restricted cash, beginning of year	1,290,544		903,698
Cash and restricted cash, end of period	$	1,818,463	$	1,064,683

See Notes to Consolidated Financial Statements

ARCH CAPITAL 10 2021 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. As of June 30, 2021, the Company’s consolidated financial statements included the results of Watford Holdings Ltd. and its wholly owned subsidiaries (“Watford”). Watford is a multi-line Bermuda reinsurance company. Watford’s own management and board of directors are responsible for its results and profitability. 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, 2020 (“2020 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, including the correct presentation of ‘income (loss) from operating affiliates’ on its consolidated statements of income for all periods presented to reclass such item from ‘other income (loss)’. The Company also changed its presentation of ‘investment in operating affiliates’ on its consolidated

balance sheet for all periods presented to reclass such item from ‘other assets’. Such reclassifications had no effect on the Company’s net income, comprehensive income, shareholders’ equity or cash flows. Management views the impact of the prior period misclassification as not material to the financial statements on a quantitative and qualitative basis. See note 7. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.

Recent Accounting Pronouncements

Recently Issued Accounting Standards Adopted

The Company adopted ASU 2019-12, “Simplifying the Accounting for Income Taxes.” This ASU eliminates certain exceptions for recognizing deferred taxes for investments, performing intraperiod tax allocations and calculating income taxes in interim periods. The ASU also clarifies the accounting for transactions that result in a step-up in the tax basis of goodwill. The adoption of this guidance did not have a material effect on the Company’s consolidated financial statements.

For information regarding additional accounting standards that the Company has not yet adopted, see note 3(r), “Significant Accounting Policies—Recent Accounting Pronouncements,” of the notes to consolidated financial statements in the Company’s 2020 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 402.3 million common shares for an aggregate purchase price of $4.54 billion. For the six months ended June 30, 2021, Arch Capital repurchased 13.1 million shares under the share repurchase program with an aggregate purchase price of $485.3 million. Arch Capital repurchased 2.6 million shares under the share repurchase program with an aggregate purchase price of $75.5 million during the six months ended June 30, 2020. At June 30, 2021, $431.2 million of share repurchases were available under the program, which may be effected from time to time in open market or privately negotiated transactions through December 31, 2021. 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.

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

ARCH CAPITAL  11 2021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

1/1,000th interest in a share of its 4.550% 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 non-cumulative basis, quarterly in arrears on the last day of March, June, September and December of each year, at an annual rate of 4.550%. Dividends on the Series G Preferred Shares are not cumulative. The Company will be restricted from paying dividends on or repurchasing its common shares unless certain dividend payments are made on the Series G Preferred Shares. The Company may not declare or pay a dividend on the Series G Preferred Shares under certain circumstances, including if the Company is or, after giving effect to such payment, would be in breach of applicable individual or group solvency and liquidity requirements or applicable individual or group enhanced capital requirements ("ECR.") The Series G Preferred Shares may not be

redeemed at any time if the ECR would be breached immediately before or after giving effect to such redemption, unless the Company replaces the capital represented by preference shares to be redeemed with capital having equal or better capital treatment.

Except in specified circumstances relating to certain tax or corporate events, the Series G Preferred Shares are not redeemable prior to June 11, 2026. On and after that date, the Series G Preferred Shares will be redeemable at the Company’s option, in whole or in part, at a redemption price of $25,000 per share of the Series G Preferred Shares (equivalent to $25 per depositary share), plus any declared and unpaid dividends, without accumulation of any undeclared dividends to, but excluding, the redemption date. The Depositary Shares will be redeemed if and to the extent the related Series G Preferred Shares are redeemed by the Company. Neither the Depositary Shares nor the Series G Preferred Shares have a stated maturity, nor will they be subject to any sinking fund or mandatory redemption. The Series G Preferred Shares are not convertible into any other securities. The Series G Preferred Shares do not have voting rights, except under limited circumstances.

The Company intends to use the net proceeds from the offering of approximately $485.8 million to redeem all or a portion of its issued and outstanding Series E Non-Cumulative Preferred Shares in September 2021, and to use any remaining amounts for general corporate purposes.

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,
	2021		2020		2021		2020
Numerator:
Net income (loss)	$	718,664	$	466,389	$	1,194,372	$	377,715
Amounts attributable to noncontrolling interests	(43,178)		(167,568)		(80,730)		65,223
Net income (loss) available to Arch	675,486		298,821		1,113,642		442,938
Preferred dividends	(11,666)		(10,403)		(22,069)		(20,806)
Net income (loss) available to Arch common shareholders	$	663,820	$	288,418	$	1,091,573	$	422,132
Denominator:
Weighted average common shares and common share equivalents outstanding — basic	397,743,402		402,503,687		399,267,183		403,197,924
Effect of dilutive common share equivalents:
Nonvested restricted shares	1,990,729		1,597,701		1,932,929		1,829,239
Stock options (1)	6,751,863		4,018,293		6,487,568		5,978,428
Weighted average common shares and common share equivalents outstanding — diluted	406,485,994		408,119,681		407,687,680		411,005,591
Earnings per common share:
Basic	$	1.67	$	0.72	$	2.73	$	1.05
Diluted	$	1.63	$	0.71	$	2.68	$	1.03

(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 2021 second quarter and 2020 second quarter, the number of stock options excluded were 1,974,849 and 6,982,107, respectively. For the six months ended June 30, 2021 and 2020 period, the number of stock options excluded were 2,395,749 and 2,038,758, respectively.

ARCH CAPITAL  12 2021 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 — ‘other’ and corporate (non-underwriting). 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. and international mortgage insurance and reinsurance operations as well as government sponsored enterprise (“GSE”) credit-risk sharing transactions. 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 (non-underwriting) segment results include net investment income, other income (loss), corporate expenses, transaction costs and other, interest expense, items related to the Company’s non-cumulative preferred shares, 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, income or loss from operating affiliates and income taxes. Such amounts exclude the results of the ‘other’ segment.

The ‘other’ segment includes the results of Watford (see note 11). For the ‘other’ segment, performance is measured based on net income or loss.

ARCH CAPITAL  13 2021 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, 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  14 2021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

	Three Months Ended
	June 30, 2020
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	1,030,362		$	807,065		$	369,144		$	2,206,410		$	157,927		$	2,317,692
Premiums ceded	(358,101)			(241,971)			(44,044)			(643,955)			(52,071)			(649,381)
Net premiums written	672,261			565,094			325,100			1,562,455			105,856			1,668,311
Change in unearned premiums	15,648			(84,897)			40,613			(28,636)			25,679			(2,957)
Net premiums earned	687,909			480,197			365,713			1,533,819			131,535			1,665,354
Other underwriting income (loss)	—			(651)			6,450			5,799			868			6,667
Losses and loss adjustment expenses	(518,203)			(383,433)			(224,100)			(1,125,736)			(104,786)			(1,230,522)
Acquisition expenses	(107,671)			(90,522)			(34,052)			(232,245)			(22,544)			(254,789)
Other operating expenses	(118,757)			(38,716)			(37,574)			(195,047)			(14,202)			(209,249)
Underwriting income (loss)	$	(56,722)		$	(33,125)		$	76,437		(13,410)			(9,129)			(22,539)
Net investment income										101,031			30,454			131,485
Net realized gains (losses)										385,089			171,499			556,588
Equity in net income (loss) of investment funds accounted for using the equity method										(65,119)			—			(65,119)
Other income (loss)										33			—			33
Corporate expenses (2)										(16,943)			—			(16,943)
Transaction costs and other (2)										(977)			—			(977)
Amortization of intangible assets										(16,489)			—			(16,489)
Interest expense										(25,130)			(6,009)			(31,139)
Net foreign exchange gains (losses)										(42,438)			3,227			(39,211)
Income (loss) before income taxes and income (loss) from operating affiliates										305,647			190,042			495,689
Income tax (expense) benefit										(26,529)			402			(26,127)
Income (loss) from operating affiliates										(3,173)			—			(3,173)
Net income (loss)										275,945			190,444			466,389
Amounts attributable to redeemable noncontrolling interests										(934)			(1,036)			(1,970)
Amounts attributable to nonredeemable noncontrolling interests										—			(165,598)			(165,598)
Net income (loss) available to Arch										275,011			23,810			298,821
Preferred dividends										(10,403)			—			(10,403)
Net income (loss) available to Arch common shareholders										$	264,608		$	23,810		$	288,418
Underwriting Ratios
Loss ratio	75.3		%	79.8		%	61.3		%	73.4		%	79.7		%	73.9		%
Acquisition expense ratio	15.7		%	18.9		%	9.3		%	15.1		%	17.1		%	15.3		%
Other operating expense ratio	17.3		%	8.1		%	10.3		%	12.7		%	10.8		%	12.6		%
Combined ratio	108.3		%	106.8		%	80.9		%	101.2		%	107.6		%	101.8		%
Goodwill and intangible assets	$	263,086		$	2,516		$	415,238		$	680,840		$	7,650		$	688,490

(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 2021 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  16 2021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

	Six Months Ended
	June 30, 2020
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	2,238,007		$	1,929,584		$	738,089		$	4,904,947		$	392,829		$	5,150,522
Premiums ceded	(736,998)			(567,310)			(88,371)			(1,391,946)			(100,273)			(1,344,965)
Net premiums written	1,501,009			1,362,274			649,718			3,513,001			292,556			3,805,557
Change in unearned premiums	(97,181)			(338,617)			61,021			(374,777)			(20,982)			(395,759)
Net premiums earned	1,403,828			1,023,657			710,739			3,138,224			271,574			3,409,798
Other underwriting income (loss)	—			1,469			11,049			12,518			1,001			13,519
Losses and loss adjustment expenses	(1,025,311)			(813,502)			(291,666)			(2,130,479)			(215,462)			(2,345,941)
Acquisition expenses	(215,008)			(170,128)			(72,588)			(457,724)			(44,348)			(502,072)
Other operating expenses	(248,406)			(84,013)			(83,470)			(415,889)			(27,904)			(443,793)
Underwriting income (loss)	$	(84,897)		$	(42,517)		$	274,064		$	146,650		$	(15,139)		$	131,511
Net investment income										214,059			62,579			276,638
Net realized gains (losses)										312,980			(123,352)			189,628
Equity in net income (loss) of investment funds accounted for using the equity method										(69,328)			—			(69,328)
Other income (loss)										65			—			65
Corporate expenses (2)										(35,144)			—			(35,144)
Transaction costs and other (2)										(3,572)			—			(3,572)
Amortization of intangible assets										(33,120)			—			(33,120)
Interest expense										(50,375)			(13,319)			(63,694)
Net foreign exchange gains (losses)										20,869			12,591			33,460
Income (loss) before income taxes and income (loss) from operating affiliates										503,084			(76,640)			426,444
Income tax (expense) benefit										(54,474)			402			(54,072)
Income (loss) from operating affiliates										5,343			—			5,343
Net income (loss)										453,953			(76,238)			377,715
Amounts attributable to redeemable noncontrolling interests										(991)			(2,132)			(3,123)
Amounts attributable to nonredeemable noncontrolling interests										—			68,346			68,346
Net income (loss) available to Arch										452,962			(10,024)			442,938
Preferred dividends										(20,806)			—			(20,806)
Net income (loss) available to Arch common shareholders										$	432,156		$	(10,024)		$	422,132
Underwriting Ratios
Loss ratio	73.0		%	79.5		%	41.0		%	67.9		%	79.3		%	68.8		%
Acquisition expense ratio	15.3		%	16.6		%	10.2		%	14.6		%	16.3		%	14.7		%
Other operating expense ratio	17.7		%	8.2		%	11.7		%	13.3		%	10.3		%	13.0		%
Combined ratio	106.0		%	104.3		%	62.9		%	95.8		%	105.9		%	96.5		%

(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.’

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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,
	2021		2020		2021		2020
Reserve for losses and loss adjustment expenses at beginning of period	$	16,443,952	$	14,309,580	$	16,513,929	$	13,891,842
Unpaid losses and loss adjustment expenses recoverable	3,916,650		4,070,114		4,314,855		4,082,650
Net reserve for losses and loss adjustment expenses at beginning of period	12,527,302		10,239,466		12,199,074		9,809,192
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year	1,219,081		1,274,589		2,463,853		2,409,031
Prior years	(59,250)		(44,067)		(100,922)		(63,090)
Total net incurred losses and loss adjustment expenses	1,159,831		1,230,522		2,362,931		2,345,941
Retroactive reinsurance transactions (1)	—		—		(183,893)		60,635
Net foreign exchange (gains) losses	135,847		51,157		88,970		(91,416)
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year	(164,441)		(128,174)		(223,425)		(169,434)
Prior years	(607,911)		(504,254)		(1,193,029)		(1,066,201)
Total net paid losses and loss adjustment expenses	(772,352)		(632,428)		(1,416,454)		(1,235,635)
Net reserve for losses and loss adjustment expenses at end of period	13,050,628		10,888,717		13,050,628		10,888,717
Unpaid losses and loss adjustment expenses recoverable	4,146,020		4,156,157		4,146,020		4,156,157
Reserve for losses and loss adjustment expenses at end of period	$	17,196,648	$	15,044,874	$	17,196,648	$	15,044,874

(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”). During the 2020 first quarter, the Company entered into a reinsurance to close agreement of the 2017 and prior years of account previously covered by a third party arrangement.

Development on Prior Year Loss Reserves

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 of adverse development 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 (i.e., the year in which a loss occurred), $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 (i.e., all premiums and losses attributable to contracts having an inception or renewal date within the given twelve-month period), which was partially offset by $17.1 million of net

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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.

2020 Second Quarter

During the 2020 second quarter, the Company recorded net favorable development on prior year loss reserves of $44.1 million, which consisted of $2.5 million from the insurance segment, $40.2 million from the reinsurance segment, $0.2 million from the mortgage segment and $1.1 million from the ‘other’ segment.

The insurance segment’s net favorable development of $2.5 million, or 0.4 loss ratio points, for the 2020 second quarter consisted of $19.7 million of net favorable development in short-tailed and long-tailed lines and $17.1 million of net adverse development in medium-tailed lines. Net favorable development of $11.5 million in short-tailed lines reflected $7.5 million of favorable development from property (excluding marine), primarily from the 2016 to 2019 accident years and $3.5 million of favorable development on travel and accident, primarily from the 2019 accident year. Net favorable development of $8.1 million in long-tailed lines reflected $2.4 million of favorable development in executive assurance, primarily from the 2013 accident year, and $4.9 million of favorable development related to other business, including alternative markets and excess workers’ compensation, across most accident years. Net adverse development in medium-tailed lines included $6.3 million of adverse development in professional liability, primarily from the 2009, 2016 and 2019 accident years, $6.1 million of adverse development in contract binding, across all accident years, and $4.0 million of adverse development on program business, primarily from the 2014 and 2017 accident years.

The reinsurance segment’s net favorable development of $40.2 million, or 8.4 loss ratio points, for the 2020 second quarter consisted of $46.2 million of net favorable development from short-tailed lines and net adverse development of $6.0 million from and medium-tailed and long-tailed lines. Net favorable development in short-tailed lines reflected $27.5 million of favorable development from

other specialty, across most underwriting years, and $18.3 million of favorable development related to property catastrophe and property other than property catastrophe business, primarily from the 2016 to 2019 underwriting years. Adverse development of $5.8 million in long-tailed lines reflected an increase in reserves from casualty, primarily from the 2012 to 2015 underwriting years.

The mortgage segment’s net favorable development was $0.2 million, or 0.1 loss ratio points, for the 2020 second quarter.

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 favorable from the insurance segment, $47.3 million from the reinsurance segment and $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

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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.

Six Months Ended June 30, 2020

During the six months ended June 30, 2020, the Company recorded net favorable development on prior year loss reserves of $63.1 million, which consisted of $3.6 million from the insurance segment, $51.8 million from the reinsurance segment, $6.3 million from the mortgage segment and $1.3 million from the ‘other’ segment.

The insurance segment’s net favorable development of $3.6 million, or 0.3 loss ratio points, for the 2020 period consisted of $28.7 million of net favorable development in short-tailed and long-tailed lines, partially offset by $25.1 million of net adverse development in medium-tailed lines. Net favorable development of $15.4 million in short-tailed lines reflected $9.6 million of favorable development from property (excluding marine), primarily from the 2015 to 2018 accident years and $3.1 million of favorable development in lenders products, primarily from the 2017 to 2019 accident years. Net favorable development of $13.3 million in long-tailed lines included $7.6 million of favorable development related to other business, including alternative markets and excess workers’ compensation, primarily in the 2016 and 2017 accident years. Net adverse development in medium-tailed lines reflected $19.3 million of adverse development in contract binding business, primarily in the 2016 to 2019 accident years, and $6.3 million of adverse development in program business, primarily from the 2017 and 2018 accident years.

The reinsurance segment’s net favorable development of $51.8 million, or 5.1 loss ratio points, for the 2020 period consisted of $67.4 million of net favorable development from short-tailed and medium-tailed lines, offset by $15.6 million of net adverse development from long-tailed lines. Net favorable development of $65.7 million in short-tailed lines reflected $39.3 million from other specialty lines and $21.3 million from property catastrophe, primarily from the 2015 to 2019 underwriting years. Adverse development in long-tailed lines reflected an increase in reserves from casualty, primarily from the 2012 to 2015 underwriting years.

The mortgage segment’s net favorable development was $6.3 million, or 0.9 loss ratio points, for the 2020 period. The 2020 development was primarily driven by subrogation recoveries on second lien business and student loan business.

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, 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
Three Months Ended June 30, 2020
Balance at beginning of period	$	2,155,204	$	27,990
Change for provision of expected credit losses (1)			8,064
Balance at end of period	$	2,203,753	$	36,054
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
Six Months Ended June 30, 2020
Balance at beginning of period	$	1,778,717	$	21,003
Cumulative effect of accounting change (2)			6,539
Change for provision of expected credit losses (1)			8,512
Balance at end of period	$	2,203,753	$	36,054

(1)Amounts deemed uncollectible are written-off in operating expenses. For the 2021 second quarter and 2020 second quarter, amounts written off were $1.1 million and $1.8 million, respectively. For the six months ended June 30, 2021 and 2020 period, amounts written off were were $1.2 million and $2.3 million, respectively.

(2)Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

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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, 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
Three Months Ended June 30, 2020
Balance at beginning of period	$	4,303,135	$	13,700
Change for provision of expected credit losses			(105)
Balance at end of period	$	4,363,507	$	13,595
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
Six Months Ended June 30, 2020
Balance at beginning of period	$	4,346,816	$	1,364
Cumulative effect of accounting change (1)			12,010
Change for provision of expected credit losses			221
Balance at end of period	$	4,363,507	$	13,595

(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

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

	June 30,			December 31
	2021			2020
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	$	4,314,515		$	4,500,802
% due from carriers with A.M. Best rating of “A-” or better	66.0		%	63.9		%
% due from all other carriers with no A.M. Best rating (1)	34.0		%	36.1		%
Largest balance due from any one carrier as % of total shareholders’ equity	2.4		%	1.8		%

(1)    At June 30, 2021 and December 31, 2020 over 91% and 94% 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, 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
Three Months Ended June 30, 2020
Balance at beginning of period	$	2,140,724	$	9,038
Change for provision of expected credit losses			(2,748)
Balance at end of period	2,179,124		$	6,290
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
Six Months Ended June 30, 2020
Balance at beginning of period	$	2,119,460	$	—
Cumulative effect of accounting change (1)			6,663
Change for provision of expected credit losses			(373)
Balance at end of period	$	2,179,124	$	6,290

(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

ARCH CAPITAL  21 2021 SECOND QUARTER FORM 10-Q

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

7.    Investment Information

At June 30, 2021, total investable assets of $30.2 billion included $27.3 billion held by the Company and $2.9 billion attributable to Watford.

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 (2)		Cost or Amortized Cost
June 30, 2021
Fixed maturities (1):
Corporate bonds	$	7,129,768	$	217,061	$	(34,751)	$	(1,232)	$	6,948,690
Mortgage backed securities	389,041		4,480		(3,479)		(269)		388,309
Municipal bonds	415,483		23,153		(1,660)		(6)		393,996
Commercial mortgage backed securities	266,733		4,017		(611)		(3)		263,330
U.S. government and government agencies	5,091,183		14,814		(14,013)		—		5,090,382
Non-U.S. government securities	2,449,782		108,823		(18,441)		(128)		2,359,528
Asset backed securities	2,487,845		16,460		(4,056)		(486)		2,475,927
Total	18,229,835		388,808		(77,011)		(2,124)		17,920,162
Short-term investments	2,248,613		1,404		(1,406)		—		2,248,615
Total	$	20,478,448	$	390,212	$	(78,417)	$	(2,124)	$	20,168,777
December 31, 2020
Fixed maturities (1):
Corporate bonds	$	7,856,571	$	414,247	$	(34,388)	$	(896)	$	7,477,608
Mortgage backed securities	630,001		8,939		(5,028)		(278)		626,368
Municipal bonds	494,522		27,291		(3,835)		(11)		471,077
Commercial mortgage backed securities	389,900		8,722		(2,954)		(122)		384,254
U.S. government and government agencies	5,557,077		22,612		(12,611)		—		5,547,076
Non-U.S. government securities	2,433,733		153,891		(8,060)		—		2,287,902
Asset backed securities	1,634,804		19,225		(10,715)		(1,090)		1,627,384
Total	18,996,608		654,927		(77,591)		(2,397)		18,421,669
Short-term investments	1,924,922		2,693		(2,063)		—		1,924,292
Total	$	20,921,530	$	657,620	$	(79,654)	$	(2,397)	$	20,345,961

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

(2)    Effective January 1, 2020, the Company adopted ASU 2016-13 and as a result any credit impairment losses on the Company’s available-for-sale investments are recorded as an allowance, subject to reversal.

ARCH CAPITAL  22 2021 SECOND QUARTER FORM 10-Q

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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, 2021
Fixed maturities (1):
Corporate bonds	$	2,264,801	$	(32,733)	$	22,895	$	(2,018)	$	2,287,696	$	(34,751)
Mortgage backed securities	196,765		(2,893)		13,632		(586)		210,397		(3,479)
Municipal bonds	24,711		(1,612)		2,859		(48)		27,570		(1,660)
Commercial mortgage backed securities	20,039		(180)		7,961		(431)		28,000		(611)
U.S. government and government agencies	2,920,944		(14,013)		—		—		2,920,944		(14,013)
Non-U.S. government securities	1,282,422		(17,562)		16,885		(879)		1,299,307		(18,441)
Asset backed securities	781,596		(2,364)		93,923		(1,692)		875,519		(4,056)
Total	7,491,278		(71,357)		158,155		(5,654)		7,649,433		(77,011)
Short-term investments	531,130		(1,406)		—		—		531,130		(1,406)
Total	$	8,022,408	$	(72,763)	$	158,155	$	(5,654)	$	8,180,563	$	(78,417)
December 31, 2020
Fixed maturities (1):
Corporate bonds	$	747,442	$	(33,086)	$	3,934	$	(1,302)	$	751,376	$	(34,388)
Mortgage backed securities	284,619		(4,788)		3,637		(240)		288,256		(5,028)
Municipal bonds	67,937		(3,835)		—		—		67,937		(3,835)
Commercial mortgage backed securities	126,624		(2,916)		2,655		(38)		129,279		(2,954)
U.S. government and government agencies	1,285,907		(12,611)		—		—		1,285,907		(12,611)
Non-U.S. government securities	543,844		(7,658)		2,441		(402)		546,285		(8,060)
Asset backed securities	634,470		(9,110)		57,737		(1,605)		692,207		(10,715)
Total	3,690,843		(74,004)		70,404		(3,587)		3,761,247		(77,591)
Short-term investments	97,920		(2,063)		—		—		97,920		(2,063)
Total	$	3,788,763	$	(76,067)	$	70,404	$	(3,587)	$	3,859,167	$	(79,654)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

At June 30, 2021, on a lot level basis, approximately 3,240 security lots out of a total of approximately 10,890 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 $2.4 million. At December 31, 2020, on a lot level basis, approximately 2,320 security lots out of a total of approximately 11,180 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 $0.9 million.

ARCH CAPITAL  23 2021 SECOND QUARTER FORM 10-Q

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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, 2021				December 31, 2020
Maturity	Estimated Fair Value		Amortized Cost		Estimated Fair Value		Amortized Cost
Due in one year or less	$	452,065	$	439,855	$	348,200	$	339,951
Due after one year through five years	10,114,276		9,942,182		10,629,959		10,340,819
Due after five years through 10 years	4,148,538		4,055,318		4,881,564		4,654,754
Due after 10 years	371,337		355,241		482,180		448,139
	15,086,216		14,792,596		16,341,903		15,783,663
Mortgage backed securities	389,041		388,309		630,001		626,368
Commercial mortgage backed securities	266,733		263,330		389,900		384,254
Asset backed securities	2,487,845		2,475,927		1,634,804		1,627,384
Total (1)	$	18,229,835	$	17,920,162	$	18,996,608	$	18,421,669

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

Securities Lending Agreements

The Company enters into securities lending agreements with financial institutions to enhance investment income whereby it loans certain of its securities to third parties, primarily major brokerage firms, for short periods of time through a lending agent. The Company maintains legal control over the securities it lends (shown as ‘Securities pledged under securities lending, at fair value’ on the Company’s balance sheet), retains the earnings and cash flows associated with the loaned securities and receives a fee from the borrower for the temporary use of the securities. An indemnification agreement with the lending agent protects the Company in the event a borrower becomes insolvent or fails to return any of the securities on loan from the Company.

The Company receives collateral (shown as ‘Collateral received under securities lending, at fair value’ on the Company’s balance sheet) in the form of cash or U.S. government and government agency securities. At June 30, 2021, the fair value of the cash collateral received on securities lending was $0.8 million and the fair value of security collateral received was $171.3 million. At December 31, 2020, the fair value of the cash collateral received on securities lending was nil, and the fair value of security collateral received was $301.1 million.

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The carrying value of collateral held under the Company’s securities lending transactions by significant investment category and remaining contractual maturity of the underlying agreements is as follows:

	Remaining Contractual Maturity of the Agreements
	Overnight and Continuous		Less than 30 Days		30-90 Days		90 Days or More		Total
June 30, 2021
U.S. government and government agencies	$	15,745	$	137,713	$	—	$	—	$	153,458
Corporate bonds	5,800		—		—		—		5,800
Equity securities	12,851		—		—		—		12,851
Total	$	34,396	$	137,713	$	—	$	—	$	172,109
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9									$	—
Amounts related to securities lending not included in offsetting disclosure in note 9									$	172,109
December 31, 2020
U.S. government and government agencies	$	142,317	$	—	$	139,290	$	—	$	281,607
Corporate bonds	3,021		—		—		—		3,021
Equity securities	16,461		—		—		—		16,461
Total	$	161,799	$	—	$	139,290	$	—	$	301,089
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9									$	—
Amounts related to securities lending not included in offsetting disclosure in note 9									$	301,089

Equity Securities, at Fair Value

At June 30, 2021, the Company held $1.7 billion of equity securities, at fair value, compared to $1.4 billion at December 31, 2020. 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

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

	June 30, 2021		December 31, 2020
Fixed maturities	$	995,980	$	843,354
Other investments	2,370,472		2,331,885
Short-term investments	610,114		557,008
Equity securities	94,931		92,549
Investments accounted for using the fair value option	$	4,071,497	$	3,824,796
Other investable assets (1)	500,000		500,000
Total other investments	$	4,571,497	$	4,324,796

(1) Participation interests in a receivable of a reverse repurchase agreement.

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

	June 30, 2021		December 31, 2020
Term loan investments	$	1,333,014	$	1,231,731
Lending	638,786		572,636
Credit related funds	73,171		90,780
Energy	84,891		65,813
Investment grade fixed income	110,375		138,646
Infrastructure	32,109		165,516
Private equity	70,878		48,750
Real estate	27,248		18,013
Total	$	2,370,472	$	2,331,885

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, 2021		December 31, 2020
Credit related funds	$	883,279	$	740,060
Equities	403,003		343,058
Real estate	323,566		258,518
Lending	295,228		179,629
Private equity	305,662		235,289
Infrastructure	210,174		175,882
Energy	118,212		115,453
Total	$	2,539,124	$	2,047,889

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

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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, 2021		December 31, 2020
Investments accounted for using the equity method (1)	2,539,124		2,047,889
Investments accounted for using the fair value option (2)	182,260		184,720
Total	$	2,721,384	$	2,232,609

(1)    Aggregate unfunded commitments were $2.0 billion at June 30, 2021, compared to $1.8 billion at December 31, 2020.

(2)    Aggregate unfunded commitments were $26.3 million at June 30, 2021, compared to $35.6 million at December 31, 2020.

Net Investment Income

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

	June 30,
	2021		2020
Three Months Ended
Fixed maturities	$	88,625	$	105,391
Term loans	16,879		20,512
Equity securities	8,584		6,219
Short-term investments	1,138		3,383
Other (1)	19,950		16,460
Gross investment income	135,176		151,965
Investment expenses	(23,563)		(20,480)
Net investment income	$	111,613	$	131,485
Six Months Ended
Fixed maturities	$	179,251	$	220,238
Term loans	31,607		43,682
Equity securities	14,234		12,226
Short-term investments	1,745		8,279
Other (1)	34,305		35,866
Gross investment income	261,142		320,291
Investment expenses	(50,673)		(43,653)
Net investment income	$	210,469	$	276,638

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

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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,
	2021		2020
Three Months Ended
Available for sale securities:
Gross gains on investment sales	$	115,541	$	232,153
Gross losses on investment sales	(50,627)		(49,824)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	10,912		68,181
Other investments	60,884		178,570
Equity securities	5,492		6,664
Short-term investments	(104)		3,368
Equity securities, at fair value:
Net realized gains (losses) on sales during the period	33,570		(18,250)
Net unrealized gains (losses) on equity securities still held at reporting date	65,847		145,686
Allowance for credit losses:
Investments related	896		3,225
Underwriting related	1,381		(5,834)
Derivative instruments (1)	(51,109)		(836)
Other	10,224		(6,515)
Net realized gains (losses)	$	202,907	$	556,588
Six Months Ended
Available for sale securities:
Gross gains on investment sales	$	180,543	$	410,353
Gross losses on investment sales	(113,625)		(81,792)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	27,465		(59,485)
Other investments	107,739		(129,230)
Equity securities	7,557		1,755
Short-term investments	632		(5,313)
Equity securities, at fair value:
Net realized gains (losses) on sales during the period	71,419		(18,789)
Net unrealized gains (losses) on equity securities still held at reporting date	85,555		(29,880)
Allowance for credit losses:
Investments related	(752)		(6,095)
Underwriting related	6,649		(9,104)
Net impairments losses	—		(533)
Derivative instruments (1)	(14,993)		126,353
Other	(12,821)		(8,612)
Net realized gains (losses)	$	345,368	$	189,628

(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 $122.2 million of equity in net income related to investment funds accounted for using the equity method in the 2021 second quarter, compared to loss of $65.1 million for the 2020 second quarter, and an income of $193.9 million for the six months ended June 30, 2021, compared to a loss of $69.3 million for six months ended June 30, 2020. In applying the equity method, investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the market value of the underlying securities in the funds). 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 and Premia Holdings Ltd. (“Premia”) and are generally recorded on a three month lag.

In 2021, the Company completed the share purchase agreement with Natixis to purchase 29.5% of the common equity of Coface, a France-based leader in the global trade credit insurance market. The consideration paid was €9.95 per share, or an aggregate €453 million (approximately $546 million) including related fees. Income (loss) from operating affiliates reflected a one-time gain of $74.5 million realized from the acquisition. As a result of equity method accounting rules, approximately $36 million of additional gain was deferred and will generally be recognized over the next five years. At June 30, 2021 the Company’s carrying value in Coface was $601.9 million.

Income from operating affiliates for the 2021 second quarter was $24.5 million, compared to a loss of $3.2 million, for the 2020 second quarter, and income of $99.9 million for the six months ended June 30, 2021, compared to $5.3 million for the six months ended June 30, 2020. The income from operating affiliates for the 2021 period, primarily related to the Company’s recent acquisition of a 29.5% stake in Coface.

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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		Short Term Investments		Total
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
Three Months Ended June 30, 2020
Balance at beginning of period	$	2,654	$	23	$	7,232	$	29	$	9,938
Additions for current-period provision for expected credit losses	695		44		290		(29)		1,000
Additions (reductions) for previously recognized expected credit losses	(1,304)		(25)		(2,903)		—		(4,232)
Reductions due to disposals	(319)		(14)		(504)		—		(837)
Balance at end of period	$	1,726	$	28	$	4,115	$	—	$	5,869
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
Six Months Ended June 30, 2020
Balance at beginning of period	$	—	$	—	$	—	$	—	$	—
Cumulative effect of accounting change (2)	517		—		117		—		634
Additions for current-period provision for expected credit losses	2,841		67		7,441		—		10,349
Additions (reductions) for previously recognized expected credit losses	(1,306)		(25)		(2,924)		—		(4,255)
Reductions due to disposals	(326)		(14)		(519)		—		(859)
Balance at end of period	$	1,726	$	28	$	4,115	$	—	$	5,869

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

(2)    Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

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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 2020 Form 10-K.

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

	June 30, 2021		December 31, 2020
Assets used for collateral or guarantees:
Affiliated transactions	$	5,041,190	$	4,643,334
Third party agreements	3,441,929		3,083,324
Deposits with U.S. regulatory authorities	814,084		827,552
Deposits with non-U.S. regulatory authorities	428,132		179,099
Total restricted assets	$	9,725,335	$	8,733,309

In addition, Watford maintains secured credit facilities to provide borrowing capacity for investment purposes and a total return swap agreement and maintains assets pledged as collateral for such purposes. The Company does not guarantee or provide credit support for Watford, and the Company’s financial exposure to Watford is limited to its investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from reinsurance transactions. As of June 30, 2021 and December 31, 2020, Watford held $1.1 billion and $954.6 million, respectively, in pledged assets to collateralize the credit facility mentioned above.

Reconciliation of Cash and Restricted Cash

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

	June 30, 2021		December 31, 2020
Cash	$	1,234,059	$	906,448
Restricted cash (included in ‘other assets’)	$	584,404	$	384,096
Cash and restricted cash	$	1,818,463	$	1,290,544

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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 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, 2021.

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 $26.5 billion of financial assets and liabilities measured at fair value at June 30, 2021, approximately $187.6 million, or 0.7%, were priced using non-binding broker-dealer quotes or modeled valuations. Of the $26.5 billion of financial assets and liabilities measured at fair value at December 31, 2020, approximately $150.1 million, or 0.6%, 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

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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

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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.

Contingent consideration liabilities

Contingent consideration liabilities (included in ‘other liabilities’ in the consolidated balance sheets) include amounts related to various Company’s acquisitions. Such amounts 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 future payments using an income approach based on modeled inputs which include a weighted average cost of capital. The Company determined that contingent consideration liabilities would be included within Level 3.

ARCH CAPITAL  32 2021 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, 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 (1):
Available for sale securities:
Fixed maturities:
Corporate bonds	$	7,129,768	$	—	$	7,129,755	$	13
Mortgage backed securities	389,041		—		389,041		—
Municipal bonds	415,483		—		415,483		—
Commercial mortgage backed securities	266,733		—		266,733		—
U.S. government and government agencies	5,091,183		5,062,571		28,612		—
Non-U.S. government securities	2,449,782		—		2,449,782		—
Asset backed securities	2,487,845		—		2,484,421		3,424
Total	18,229,835		5,062,571		13,163,827		3,437
Short-term investments	2,248,613		1,996,304		252,309		—
Equity securities, at fair value	1,706,044		1,631,937		24,971		49,136
Derivative instruments (4)	98,488		—		98,488		—
Residential mortgage loans	44,925		—		44,925		—
Fair value option:
Corporate bonds	790,186		—		789,188		998
Non-U.S. government bonds	22,552		—		22,552		—
Mortgage backed securities	2,707		—		2,707		—
Commercial mortgage backed securities	841		—		841		—
Asset backed securities	179,423		—		179,423		—
U.S. government and government agencies	271		163		108		—
Short-term investments	610,114		482,815		127,299		—
Equity securities	94,930		21,252		—		73,678
Other investments	1,219,294		23,610		1,121,784		73,900
Other investments measured at net asset value (2)	1,151,178
Total	4,071,496		527,840		2,243,902		148,576
Total assets measured at fair value	$	26,399,401	$	9,218,652	$	15,828,422	$	201,149
Liabilities measured at fair value:
Contingent consideration liabilities	$	(466)	$	—	$	—	$	(466)
Securities sold but not yet purchased (3)	(28,068)		—		(28,068)		—
Derivative instruments (4)	(67,304)		—		(67,304)		—
Total liabilities measured at fair value	$	(95,838)	$	—	$	(95,372)	$	(466)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See note 7, “—Securities Lending Agreements.”

(2)    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.

(3)    Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets.

(4)    See note 9.

ARCH CAPITAL  33 2021 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, 2020:

			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 (1):
Available for sale securities:
Fixed maturities:
Corporate bonds	$	7,856,571	$	—	$	7,856,558	$	13
Mortgage backed securities	630,001		—		630,001		—
Municipal bonds	494,522		—		494,522		—
Commercial mortgage backed securities	389,900		—		389,900		—
U.S. government and government agencies	5,557,077		5,463,356		93,721		—
Non-U.S. government securities	2,433,733		—		2,433,733		—
Asset backed securities	1,634,804		—		1,631,378		3,426
Total	18,996,608		5,463,356		13,529,813		3,439
Short-term investments	1,924,922		1,920,565		4,357		—
Equity securities, at fair value	1,460,959		1,401,653		17,291		42,015
Derivative instruments (4)	177,383		—		177,383		—
Fair value option:
Corporate bonds	651,294		—		650,309		985
Non-U.S. government bonds	35,263		—		35,263		—
Mortgage backed securities	3,282		—		3,282		—
Commercial mortgage backed securities	1,090		—		1,090		—
Asset backed securities	152,151		—		152,151		—
U.S. government and government agencies	274		164		110		—
Short-term investments	557,008		420,131		136,877		—
Equity securities	92,549		23,373		188		68,988
Other investments	1,134,229		51,149		1,015,977		67,103
Other investments measured at net asset value (2)	1,197,656
Total	3,824,796		494,817		1,995,247		137,076
Total assets measured at fair value	$	26,384,668	$	9,280,391	$	15,724,091	$	182,530
Liabilities measured at fair value:
Contingent consideration liabilities	$	(461)	$	—	$	—	$	(461)
Securities sold but not yet purchased (3)	(21,679)		—		(21,679)		—
Derivative instruments (4)	(108,705)		—		(108,705)		—
Total liabilities measured at fair value	$	(130,845)	$	—	$	(130,384)	$	(461)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See note 7, “—Securities Lending Agreements.”

(2)    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.

(3)    Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets.

(4)    See note 9.

ARCH CAPITAL  34 2021 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		Contingent Consideration Liabilities
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		—
Included in other comprehensive income	(57)		—		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		—		5,638		—		5,102		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(301)		—		—		—
Settlements	(3)		—		—		—		—		—		(1)
Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of period	$	3,424	$	13	$	998	$	73,900	$	73,678	$	49,136	$	(466)
Three Months Ended June 30, 2020
Balance at beginning of period	$	3,846	$	1,980	$	965	$	54,620	$	60,015	$	55,632	$	(7,967)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	(64)		—		—		(987)		1,432		11,799		(18)
Included in other comprehensive income	(287)		(1,123)		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		33		3		—		—		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(7,183)		—		(15,450)		—
Settlements	(45)		—		—		—		—		—		6,735
Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of period	$	3,450	$	857	$	998	$	46,453	$	61,447	$	51,981	$	(1,250)
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		—
Included in other comprehensive income	57		—		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		—		13,003		—		5,295		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(7,087)		—		—		—
Settlements	(3)		—		—		—		—		—		(5)
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, 2020
Balance at beginning of year	$	5,216	$	8,851	$	932	$	68,817	$	58,094	$	55,889	$	(7,998)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	(55)		7		—		(1,014)		3,353		8,078		(72)
Included in other comprehensive income	(309)		(6,539)		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		66		24		—		3,464		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(24,358)		—		(15,450)		—
Settlements	(1,402)		(1,462)		—		—		—		—		6,820
Transfers in and/or out of Level 3	—		—		—		2,984		—		—		—
Balance at end of period	$	3,450	$	857	$	998	$	46,453	$	61,447	$	51,981	$	(1,250)

(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  35 2021 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, 2021, 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, 2021, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.9 billion and had a fair value of $3.5 billion. At December 31, 2020, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.9 billion and had a fair value of $3.7 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		Liability Derivatives		Notional Value (1)
June 30, 2021
Futures contracts (2)	$	36,277	$	(21,515)	$	2,907,342
Foreign currency forward contracts (2)	8,242		(20,729)		1,573,973
Other (2)	53,969		(25,060)		4,838,552
Total	$	98,488	$	(67,304)
December 31, 2020
Futures contracts (2)	$	11,046	$	(4,496)	$	3,099,796
Foreign currency forward contracts (2)	52,716		(6,202)		1,656,729
Other (2)	113,621		(98,007)		5,763,919
Total	$	177,383	$	(108,705)

(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.’

The Company did not hold any derivatives which were designated as hedging instruments at June 30, 2021 or December 31, 2020.

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, 2021, asset derivatives and liability derivatives of $89.9 million and $66.7 million, respectively, were subject to a master netting agreement, compared to $138.8 million and $93.0 million, respectively, at December 31, 2020. 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:

ARCH CAPITAL  36 2021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

Derivatives not designated as	June 30,
hedging instruments:	2021		2020
Three Months Ended
Net realized gains (losses):
Futures contracts	$	(54,759)	$	(1,607)
Foreign currency forward contracts	1,295		3,523
TBAs	—		264
Other (1)	2,355		(3,016)
Total	$	(51,109)	$	(836)
Six Months Ended
Net realized gains (losses):
Futures contracts	$	(7,321)	$	94,337
Foreign currency forward contracts	(20,776)		(7,347)
TBAs	—		1,009
Other (1)	13,104		38,354
Total	$	(14,993)	$	126,353

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

10.    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 $2.4 billion at June 30, 2021, compared to $2.1 billion at December 31, 2020.

Interest Paid

Interest paid on the Company’s senior notes and other borrowings were $74.7 million for the six months ended June 30, 2021, compared to $57.4 million for the 2020 period.

11.    Variable Interest Entities and Noncontrolling Interests

Watford

In March 2014, the Company invested $100.0 million and acquired 2,500,000 common shares, approximately 11% of Watford’s outstanding common equity. As of June 30, 2021, the Company owned approximately 10.2% of Watford’s outstanding common equity. The Company also owns $35.0 million in aggregate principal amount of Watford Holdings Ltd’s 6.5% senior notes, due July 2, 2029 and approximately 6.6% of Watford’s preference shares.

Watford is considered a VIE and the Company concluded that it is the primary beneficiary of Watford, through June 30, 2021. As such, the results of Watford are included in the

Company’s consolidated financial statements as of and for the periods ended June 30, 2021.

The Company does not guarantee or provide credit support for Watford, and the Company’s financial exposure to Watford is limited to its investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from reinsurance transactions.

In the 2020 fourth quarter, Arch Capital, Watford Holdings Ltd. and Greysbridge Ltd., a wholly-owned subsidiary of Arch Capital, entered into an Agreement and Plan of Merger (as amended, the “Merger Agreement”) pursuant to which, among other things, Arch Capital agreed to acquire all of the common shares of Watford Holdings Ltd. not owned by Arch for a cash purchase price of $35.00 per common share. Arch Capital assigned its rights under the Merger Agreement to Greysbridge Holdings Ltd., a wholly-owned subsidiary of Arch Capital (“Greysbridge”). The merger and the related Greysbridge equity financing closed on July 1, 2021. Effective July 1, 2021, Watford is wholly owned by Greysbridge and Greysbridge is owned 40% by Arch Re Bermuda, 30% by certain investment funds managed by Kelso & Company and 30% by certain investment funds managed by Warburg Pincus LLC. See note 16.

ARCH CAPITAL  37 2021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The following table provides the carrying amount and balance sheet caption in which the assets and liabilities of Watford are reported:

	June 30,		December 31,
	2021		2020
Assets
Investments accounted for using the fair value option (1)	$	1,984,919	$	1,790,385
Fixed maturities available for sale, at fair value	663,902		655,249
Equity securities, at fair value	97,623		52,410
Cash	349,202		211,451
Accrued investment income	14,549		14,679
Premiums receivable	305,026		224,377
Reinsurance recoverable on unpaid and paid losses and LAE	520,531		286,590
Ceded unearned premiums	123,272		122,339
Deferred acquisition costs	65,532		53,705
Receivable for securities sold	102,287		37,423
Goodwill and intangible assets	10,318		7,650
Other assets	112,794		75,801
Total assets of consolidated VIE	$	4,349,955	$	3,532,059
Liabilities
Reserve for losses and loss adjustment expenses	$	1,916,742	$	1,519,583
Unearned premiums	468,948		407,714
Reinsurance balances payable	132,929		63,269
Revolving credit agreement borrowings	155,687		155,687
Senior notes	172,825		172,689
Payable for securities purchased	199,342		25,881
Other liabilities	227,396		193,494
Total liabilities of consolidated VIE	$	3,273,869	$	2,538,317
Redeemable noncontrolling interests	$	52,444	$	52,398

(1)    Included in “other investments” on the Company’s balance sheet.

For the six months ended June 30, 2021, Watford 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, compared to $87.3 million of cash provided by operating activities, $78.0 million of cash provided by investing activities and $153.8 million of cash used for financing activities for the six months ended June 30, 2020.

Non-redeemable noncontrolling interests

The Company accounts for the portion of Watford’s common equity attributable to third party investors in the shareholders’ equity section of its consolidated balance sheets. The noncontrolling ownership in Watford’s common shares was approximately 90% at June 30, 2021. The portion of Watford’s income or loss attributable to third party investors is 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		2020
Three Months Ended
Balance, beginning of period	$	876,864	$	492,785
Additional paid in capital attributable to noncontrolling interests	383		595
Amounts attributable to noncontrolling interests	41,617		165,598
Other comprehensive income (loss) attributable to noncontrolling interests	10		20,111
Balance, end of period	$	918,874	$	679,089
Six Months Ended
Balance, beginning of year	$	823,007	$	762,777
Additional paid in capital attributable to noncontrolling interests	22,113		472
Repurchases attributable to non-redeemable noncontrolling interests (1)	—		(2,867)
Amounts attributable to noncontrolling interests	78,314		(68,346)
Other comprehensive income (loss) attributable to noncontrolling interests	(4,560)		(12,947)
Balance, end of period	$	918,874	$	679,089

(1) During 2020, Watford’s board of directors authorized the investment in Watford’s common shares through a share repurchase program.

Redeemable noncontrolling interests

The Company accounts for redeemable noncontrolling interests in the mezzanine section of its consolidated balance sheets in accordance with applicable accounting guidance. Such redeemable noncontrolling interests primarily relate to the Watford 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 Watford Preference Shares were issued at a discounted amount of $24.50 per share. Preferred dividends, including the accretion of the discount and issuance costs, are included in ‘net (income) loss attributable to noncontrolling interests’ in the Company’s consolidated statements of income.

ARCH CAPITAL  38 2021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

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

	June 30,
	2021		2020
Three Months Ended
Balance, beginning of period	$	57,670	$	55,376
Accretion of preference share issuance costs	23		23
Other	(160)		587
Balance, end of period	$	57,533	$	55,986
Six Months Ended
Balance, beginning of year	$	58,548	$	55,404
Accretion of preference share issuance costs	46		46
Other	(1,061)		536
Balance, end of period	$	57,533	$	55,986

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,
	2021		2020
Three Months Ended
Amounts attributable to non-redeemable noncontrolling interests	$	(41,617)	$	(165,598)
Amounts attributable to redeemable noncontrolling interests	(1,561)		(1,970)
Net (income) loss attributable to noncontrolling interests	$	(43,178)	$	(167,568)
Six Months Ended
Amounts attributable to non-redeemable noncontrolling interests	$	(78,314)	$	68,346
Amounts attributable to redeemable noncontrolling interests	(2,416)		(3,123)
Net (income) loss attributable to noncontrolling interests	$	(80,730)	$	65,223

ARCH CAPITAL  39 2021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

Bellemeade Re

The Company has entered into various aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda (the “Bellemeade Agreements”). 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 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, 2021								December 31, 2020
			Maximum Exposure to Loss								Maximum Exposure to Loss
Bellemeade Entities (Issue Date)	Total VIE Assets		On-Balance Sheet (Asset) Liability		Off-Balance Sheet		Total		Total VIE Assets		On-Balance Sheet (Asset) Liability		Off-Balance Sheet		Total
Bellemeade 2017-1 Ltd. (Oct-17)	$	145,573	$	(283)	$	779	$	496	$	145,573	$	(245)	$	844	$	599
Bellemeade 2018-1 Ltd. (Apr-18)	250,095		(909)		1,984		1,075		250,095		(903)		2,245		1,342
Bellemeade 2018-2 Ltd. (Aug-18)	—		—		—		—		108,395		(138)		280		142
Bellemeade 2018-3 Ltd. (Oct-18)	302,563		(1,622)		3,706		2,084		302,563		(1,320)		3,262		1,942
Bellemeade 2019-1 Ltd. (Mar-19)	219,256		(1,237)		8,204		6,967		219,256		(1,361)		8,461		7,100
Bellemeade 2019-2 Ltd. (Apr-19)	398,316		(1,042)		6,723		5,681		398,316		(730)		5,201		4,471
Bellemeade 2019-3 Ltd. (Jul-19)	528,084		(969)		4,527		3,558		528,084		(861)		5,079		4,218
Bellemeade 2019-4 Ltd. (Oct-19)	468,737		(1,051)		7,128		6,077		468,737		(890)		6,676		5,786
Bellemeade 2020-1 Ltd. (Jun-20) (1)	18,843		—		—		—		275,068		(178)		1,012		834
Bellemeade 2020-2 Ltd. (Sep-20) (2)	325,712		(442)		4,299		3,857		423,420		(556)		6,839		6,283
Bellemeade 2020-3 Ltd. (Nov-20) (3)	418,158		(618)		8,250		7,632		418,158		(631)		9,605		8,974
Bellemeade 2020-4 Ltd. (Dec-20) (4)	268,405		(150)		3,891		3,741		321,393		(156)		6,816		6,660
Bellemeade 2021-1 Ltd. (Mar-21) (5)	579,717		(83)		4,387		4,304		—		—		—		—
Bellemeade 2021-2 Ltd. (Jun-21) (6)	522,807		630		5,207		5,837		—		—		—		—
Total	$	4,446,266	$	(7,776)	$	59,085	$	51,309	$	3,859,058	$	(7,969)	$	56,320	$	48,351

(1)  An additional $79 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(2)  An additional $26 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(3)  An additional $34 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(4)  An additional $16 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(5)  An additional $64 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(6)  An additional $93 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

ARCH CAPITAL  40 2021 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	2021		2020		2021		2020
Unrealized appreciation on available-for-sale investments
	Net realized gains (losses)	$	64,914	$	182,329	$	66,918	$	328,561
	Provision for credit losses	896		3,225		(751)		(6,095)
	Other-than-temporary impairment losses	—		—		—		(533)
	Total before tax	65,810		185,554		66,167		321,933
	Income tax (expense) benefit	(5,263)		(18,163)		(8,317)		(33,313)
	Net of tax	$	60,547	$	167,391	$	57,850	$	288,620

	Before Tax Amount		Tax Expense (Benefit)		Net of Tax Amount
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
Three Months Ended June 30, 2020
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	555,576	$	62,780	$	492,796
Less reclassification of net realized gains (losses) included in net income	185,554		18,163		167,391
Foreign currency translation adjustments	22,595		344		22,251
Other comprehensive income (loss)	$	392,617	$	44,961	$	347,656
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)
Six Months Ended June 30, 2020
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	492,125	$	56,616	$	435,509
Less reclassification of net realized gains (losses) included in net income	321,933		33,313		288,620
Foreign currency translation adjustments	(22,829)		(391)		(22,438)
Other comprehensive income (loss)	$	147,363	$	22,912	$	124,451

ARCH CAPITAL  41 2021 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 7.0% for the six months ended June 30, 2021, compared to 12.5% for the six months ended June 30, 2020.

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 $93.0 million at June 30, 2021, compared to a net deferred tax asset of $15.7 million at December 31, 2020. The change is primarily a result of mortgage contingency reserves activity and market value fluctuations in the investment portfolio. In addition, the Company paid $141.1 million and $10.4 million of income taxes for the six months ended June 30, 2021 and 2020, 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, 2021, 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. Barbican recorded reinsurance recoverable on unpaid and paid losses and funds held liability of nil and $9.9 million, respectively, at June 30, 2021, compared to $199.8 million and $149.6 million, respectively, at December 31, 2020.

Certain directors and executive officers of the Company own common and preference shares of Watford. See note 11, “Variable Interest Entity and Noncontrolling Interests,” for information about Watford.

16.    Subsequent Event

In July 2021, the Company announced the completion of the previously disclosed acquisition of Watford by Greysbridge. Based on the governing documents of Greysbridge the Company has concluded that, while it will retain significant influence over Watford, Watford will no longer constitute a variable interest entity of which the Company is the primary beneficiary. Accordingly, effective July 1, 2021, Arch will no longer consolidate the results of Watford in its consolidated financial statements and footnotes. As a result of the closing of the transaction, we expect to report a net gain of approximately $65 million in the third quarter.

ARCH CAPITAL  42 2021 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, 2020 (“2020 Form 10-K”). In addition, readers should review “Risk Factors” set forth in Item 1A of Part I of our 2020 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” or “us”) is a publicly listed Bermuda exempted company with approximately $16.7 billion in capital at June 30, 2021 and, through operations in Bermuda, the United States, Europe, Canada, Australia and Hong Kong, writes insurance, reinsurance and mortgage insurance on a worldwide basis.

CURRENT OUTLOOK

Our three primary areas of focus for 2021 are to continue our growth in the sectors where rates allow for returns that are substantially more than our cost of capital, to optimize our mortgage insurance book as it transitions from forbearance to recovery on its way back to normalcy in the next few quarters, and to actively manage our investments and capital to enhance our returns over the long run.

From an operating perspective, the 2021 second quarter reflected the benefits of attractive pricing in almost all of our insurance markets. As a result, we currently expect the next several quarters to continue to show improved underwriting margins, partially due to the compounding of rate-on-rate increases and the rebalancing of our mix of business. Importantly, the market is showing discipline in maintaining its momentum. We believe that this time-tested strategy of protecting capital through soft markets and writing business aggressively 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.

Consequently, these rate improvements have enabled us to continue to expand writings in our property casualty segments. We are now in the sixth consecutive quarter of rate increases with a weighted increase of approximately 10% this quarter, comfortably in excess of loss cost trends. Premiums increased across most lines of business and geographic areas

as pricing improvements spread and, while rate increases have tapered off from previous highs in some lines, our insurance segment is seeing increases in lines that had been resistant to meaningful change.

In reinsurance, strong growth was observed across most of our lines of business, but especially in our casualty and other specialty lines where strong rates increases and growth in new accounts helped increase the top line. Consistent with our insurance segment, we expect the ongoing rate improvements to be reflected in our underwriting results over the next several quarters.

For our U.S. primary mortgage operations, reported delinquencies were 3.11% at June 30, 2021, roughly 40% lower than it was at the end of the 2020 second quarter. Delinquencies continue to be better than our expectations at the beginning of the COVID-19 pandemic but delinquency rates remain at elevated levels, reflecting the impact of the recession and forbearance programs under the CARES Act to borrowers experiencing a hardship. Forbearance allows for mortgage payments to be suspended for up to 360 days or longer along with a suspension of foreclosures and evictions. See “Results of Operations—Mortgage Segment” for further details on our mortgage operations.

In the second quarter, our U.S. primary mortgage operations insurance in force remained steady at approximately $278 billion and $422 billion for the total mortgage segment. The refinancing boom that began last year has slowed and we expect improving persistency through remainder of the year.

Outside of the U.S., we increased our writings in Australia as the housing market remains strong there. We like the long-term opportunity in Australia as demonstrated by our announcement in March to acquire Westpac's LMI business. The agreement allows us to free up capital even as we build our Australian presence and diversify our earning streams at attractive risk-adjusted returns.

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 enter into aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda and issue mortgage insurance linked notes, increasing our protection for mortgage tail risk. The Bellemeade structures provide approximately $4.7 billion of aggregate reinsurance coverage at June 30, 2021.

ARCH CAPITAL  43 2021 SECOND QUARTER FORM 10-Q

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 $32.02 at June 30, 2021, compared to $30.54 at March 31, 2021 and $27.62 at June 30, 2020. The 4.8% increase in book value per share for the 2021 second quarter and 15.9% increase in book value per share over the trailing twelve months reflected strong underwriting results and investment 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 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 Operating ROAE was 13.0% for the 2021 second quarter, compared to 0.6% for the 2020 second quarter, and 10.3% for the six months ended June 30, 2021, compared to 3.8% for the 2020 period. The higher 2021 period results, reflected strong underwriting returns and a one-time gain of $74.5 million realized during the 2021 first quarter from our acquisition of 29.5% stake in Coface, while the 2020 period

reflected the impact of COVID-19 on the underwriting results.

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, 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. 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):
2021 Second Quarter	1.58	%	1.80	%
2020 Second Quarter	3.72	%	6.06	%
Six Months Ended June 30, 2021	1.39	%	1.28	%
Six Months Ended June 30, 2020	2.82	%	1.23	%

Total return for the 2021 second quarter reflected movements in interest rates and credit spreads on our fixed income portfolio. We continue to maintain a short duration on our portfolio of 2.31 years at June 30, 2021.

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, 2021, the benchmark return index had an average credit quality of “Aa2” by Moody’s Investors Service (“Moody’s”), and an estimated duration of 3.13 years.

ARCH CAPITAL  44 2021 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 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 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 and transaction costs and other in any particular period are not indicative of the performance of, or trends in, our business. Although net realized gains or losses, equity in net income or loss of 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 the Company’s investments represent other-than-temporary declines in expected recovery values on securities without actual realization. The use of the equity method on certain of our investments in certain funds that invest in fixed maturity securities is driven by the ownership structure of such funds (either limited partnerships or limited liability companies). In applying the equity method, these investments are initially recorded at cost and are subsequently adjusted based on our proportionate share of the net income or loss of the funds (which include changes in the market value of the underlying securities in the funds). This method of accounting is different from the way we account for our other fixed maturity securities 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. 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 and transaction costs and other from the calculation of after-tax operating income available to Arch common shareholders.

We believe that showing net income available to Arch common shareholders exclusive of the items referred to above reflects the underlying fundamentals of our business

ARCH CAPITAL  45 2021 SECOND QUARTER FORM 10-Q

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. 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 (non-underwriting) 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, 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. For the ‘other’ segment, performance is measured based on net income or loss.

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 Watford Holdings Ltd. Watford Holdings Ltd. is the parent of Watford Re Ltd., a multi-line Bermuda reinsurance company (together with Watford Holdings Ltd., “Watford”). Pursuant to GAAP, Watford was considered a variable interest entity and we

concluded that we are the primary beneficiary of Watford. As such, we consolidated the results of Watford in our consolidated financial statements through June 30, 2021, although we only owned approximately 10% of Watford’s common equity. Watford’s own management and board of directors are responsible for its results and profitability. In addition, we do not guarantee or provide credit support for Watford. Since Watford is an independent company, the assets of Watford can be used only to settle obligations of Watford and Watford is solely responsible for its own liabilities and commitments. Our financial exposure to Watford is limited to our investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from the reinsurance transactions. We believe that presenting certain information excluding the ‘other’ segment enables investors and other users of our financial information to analyze our performance in a manner similar to how our management analyzes performance. See note 11, “Variable Interest Entities and Noncontrolling Interests,” note 4, “Segment Information,” and Note 16, “Subsequent Event,” to our consolidated financial statements for additional information on Watford.

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  46 2021 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. Each line item reflects the impact of our percentage ownership of Watford’s common equity during such period.

	Three Months Ended				Six Months Ended
	June 30,				June 30,
	2021		2020		2021		2020
Net income available to Arch common shareholders	$	663,820	$	288,418	$	1,091,573	$	422,132
Net realized (gains) losses	(167,438)		(406,645)		(272,989)		(297,281)
Equity in net (income) loss of investment funds accounted for using the equity method	(122,186)		65,119		(193,872)		69,328
Net foreign exchange (gains) losses	17,888		42,032		(3,444)		(22,459)
Transaction costs and other	(1,421)		977		(147)		3,572
Income tax expense (1)	16,553		26,713		25,864		31,078
After-tax operating income available to Arch common shareholders	$	407,216	$	16,614	$	646,985	$	206,370
Beginning common shareholders’ equity	$	12,316,472	$	10,587,244	$	12,325,886	$	10,717,371
Ending common shareholders’ equity	$	12,706,072	$	11,211,825	$	12,706,072	$	11,211,825
Average common shareholders’ equity	$	12,511,272	$	10,899,535	$	12,515,979	$	10,964,598
Annualized return on average common equity %	21.2		10.6		17.4		7.7
Annualized operating return on average common equity %	13.0		0.6		10.3		3.8

(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 (non-underwriting) 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,
	2021			2020			%  Change
Gross premiums written	$	1,368,867		$	1,030,362		32.9
Premiums ceded	(405,312)			(358,101)
Net premiums written	963,555			672,261			43.3
Change in unearned premiums	(98,128)			15,648
Net premiums earned	865,427			687,909			25.8
Losses and loss adjustment expenses	(545,880)			(518,203)
Acquisition expenses	(136,852)			(107,671)
Other operating expenses	(133,342)			(118,757)
Underwriting income (loss)	$	49,353		$	(56,722)		187.0
Underwriting Ratios							% Point Change
Loss ratio	63.1		%	75.3		%	(12.2)
Acquisition expense ratio	15.8		%	15.7		%	0.1
Other operating expense ratio	15.4		%	17.3		%	(1.9)
Combined ratio	94.3		%	108.3		%	(14.0)

ARCH CAPITAL  47 2021 SECOND QUARTER FORM 10-Q

	Six Months Ended June 30,
	2021			2020			% Change
Gross premiums written	$	2,784,753		$	2,238,007		24.4
Premiums ceded	(826,359)			(736,998)
Net premiums written	1,958,394			1,501,009			30.5
Change in unearned premiums	(273,493)			(97,181)
Net premiums earned	1,684,901			1,403,828			20.0
Losses and loss adjustment expenses	(1,081,627)			(1,025,311)
Acquisition expenses	(265,074)			(215,008)
Other operating expenses	(270,455)			(248,406)
Underwriting income (loss)	$	67,745		$	(84,897)		179.8
Underwriting Ratios							% Point Change
Loss ratio	64.2		%	73.0		%	(8.8)
Acquisition expense ratio	15.7		%	15.3		%	0.4
Other operating expense ratio	16.1		%	17.7		%	(1.6)
Combined ratio	96.0		%	106.0		%	(10.0)

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 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,
	2021			2020
	Amount		%	Amount		%
Property, energy, marine and aviation	$	207,762	21.6	$	159,801	23.8
Professional lines	254,961		26.5	157,899		23.5
Programs	149,373		15.5	104,930		15.6
Construction and national accounts	77,579		8.1	57,144		8.5
Excess and surplus casualty	74,346		7.7	64,703		9.6
Travel, accident and health	71,071		7.4	27,997		4.2
Lenders products	40,386		4.2	23,690		3.5
Other	88,077		9.1	76,097		11.3
Total	$	963,555	100.0	$	672,261	100.0

2021 Second Quarter versus 2020 Period. Gross premiums written by the insurance segment in the 2021 second quarter were 32.9% higher than in the 2020 second quarter, while net premiums written were 43.3% higher. The higher level of net premiums written reflected increases across most lines of business, due in part to rate increases, new business opportunities and growth in existing accounts.

ARCH CAPITAL  48 2021 SECOND QUARTER FORM 10-Q

	Six Months Ended June 30,
	2021			2020
	Amount		%	Amount		%
Property, energy, marine and aviation	$	378,260	19.3	$	287,386	19.1
Professional Lines	493,207		25.2	327,017		21.8
Programs	307,774		15.7	217,462		14.5
Construction and national accounts	212,371		10.8	173,143		11.5
Excess and surplus casualty	159,939		8.2	130,122		8.7
Travel, accident and health	163,377		8.3	154,043		10.3
Lenders products	75,246		3.8	56,982		3.8
Other	168,220		8.6	154,854		10.3
Total	$	1,958,394	100.0	$	1,501,009	100.0

Six Months Ended June 30, 2021 versus 2020 period. Gross premiums written by the insurance segment for the six months ended June 30, 2021 were 24.4% higher than in the 2020 period, while net premiums written were 30.5% higher than in the 2020 period. The increase in net premiums written reflected growth across most lines of business, due in part to rate increases, new business opportunities 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,
	2021			2020
	Amount		%	Amount		%
Property, energy, marine and aviation	$	167,716	19.4	$	120,781	17.6
Professional lines	214,098		24.7	154,812		22.5
Programs	118,974		13.7	108,464		15.8
Construction and national accounts	95,849		11.1	91,605		13.3
Excess and surplus casualty	72,899		8.4	60,966		8.9
Travel, accident and health	62,610		7.2	52,117		7.6
Lenders products	46,396		5.4	23,111		3.4
Other	86,885		10.0	76,053		11.1
Total	$	865,427	100.0	$	687,909	100.0

	Six Months Ended June 30,
	2021			2020
	Amount		%	Amount		%
Property, energy, marine and aviation	$	324,975	19.3	$	231,964	16.5
Professional Lines	413,769		24.6	306,512		21.8
Programs	231,814		13.8	217,342		15.5
Construction and national accounts	198,520		11.8	191,305		13.6
Excess and surplus casualty	148,266		8.8	126,063		9.0
Travel, accident and health	112,276		6.7	129,492		9.2
Lenders products	86,477		5.1	48,454		3.5
Other	168,804		10.0	152,696		10.9
Total	$	1,684,901	100.0	$	1,403,828	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 2021 second quarter were 25.8% higher than in the 2020 second quarter. Net premiums earned for the six months ended June 30, 2021 were 20.0% higher than in the 2020 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,
	2021		2020		2021		2020
Current year	63.6	%	75.7	%	64.7	%	73.3	%
Prior period reserve development	(0.5)	%	(0.4)	%	(0.5)	%	(0.3)	%
Loss ratio	63.1	%	75.3	%	64.2	%	73.0	%

Current Year Loss Ratio.

2021 Second Quarter versus 2020 Period. The insurance segment’s current year loss ratio in the 2021 second quarter was 12.1 points lower than in the 2020 second quarter. The 2021 second quarter loss ratio reflected 3.2 points of current year catastrophic activity, primarily from winter storms Uri and Viola, compared to 12.5 points of catastrophic activity for the 2020 second quarter, which included exposure to the COVID-19 global pandemic. The insurance segment’s current year loss ratio for the six months ended June 30, 2021 was 8.6 points lower than in the 2020 period and reflected 4.1 points of current year catastrophic activity, compared to 9.6 points in the 2020 period. The balance of the change in the 2021 loss ratios resulted, in part, from changes in mix of business and the level of large attritional losses.

ARCH CAPITAL  49 2021 SECOND QUARTER FORM 10-Q

Prior Period Reserve Development.

The insurance segment’s net favorable development was $4.0 million, or 0.5 points, for the 2021 second quarter, compared to $2.5 million, or 0.4 points, for the 2020 second quarter, and $8.1 million, or 0.5 points for the six months ended June 30, 2021, compared to $3.6 million, or 0.3 points, for the 2020 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.

2021 Second Quarter versus 2020 Period. The insurance segment’s underwriting expense ratio was 31.2% in the 2021 second quarter, compared to 33.0% in the 2020 second quarter, with the decrease primarily due to growth in net premiums earned.

Six Months Ended June 30, 2021 versus 2020 Period. The insurance segment’s underwriting expense ratio was 31.8% six months ended June 30, 2021, compared to 33.0% for the 2020 period, with the decrease primarily due to growth in net premiums earned.

Reinsurance Segment 

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

	Three Months Ended June 30,
	2021			2020			%  Change
Gross premiums written	$	1,358,020		$	807,065		68.3
Premiums ceded	(433,288)			(241,971)
Net premiums written	924,732			565,094			63.6
Change in unearned premiums	(187,708)			(84,897)
Net premiums earned	737,024			480,197			53.5
Other underwriting income (loss)	1,053			(651)
Losses and loss adjustment expenses	(463,823)			(383,433)
Acquisition expenses	(133,585)			(90,522)
Other operating expenses	(44,695)			(38,716)
Underwriting income (loss)	$	95,974		$	(33,125)		389.7
Underwriting Ratios							% Point Change
Loss ratio	62.9		%	79.8		%	(16.9)
Acquisition expense ratio	18.1		%	18.9		%	(0.8)
Other operating expense ratio	6.1		%	8.1		%	(2.0)
Combined ratio	87.1		%	106.8		%	(19.7)

	Six Months Ended June 30,
	2021			2020			% Change
Gross premiums written	$	2,829,080		$	1,929,584		46.6
Premiums ceded	(905,236)			(567,310)
Net premiums written	1,923,844			1,362,274			41.2
Change in unearned premiums	(541,920)			(338,617)
Net premiums earned	1,381,924			1,023,657			35.0
Other underwriting income	(145)			1,469
Losses and loss adjustment expenses	(948,693)			(813,502)
Acquisition expenses	(251,610)			(170,128)
Other operating expenses	(105,209)			(84,013)
Underwriting income (loss)	$	76,267		$	(42,517)		279.4
Underwriting Ratios							% Point Change
Loss ratio	68.7		%	79.5		%	(10.8)
Acquisition expense ratio	18.2		%	16.6		%	1.6
Other operating expense ratio	7.6		%	8.2		%	(0.6)
Combined ratio	94.5		%	104.3		%	(9.8)

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

•Casualty: provides coverage to ceding company clients on third party liability and workers’ compensation exposures from ceding company clients, primarily on a treaty basis. Exposures include, among others, executive assurance, professional liability, workers’ compensation, excess and umbrella liability, excess motor and healthcare business.

•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 to ceding company clients for proportional motor and other lines, including surety, accident and health, workers’ compensation catastrophe, agriculture, trade credit and political risk.

•Property catastrophe: provides protection for most catastrophic losses that are covered in the underlying policies written by reinsureds, including hurricane, earthquake, flood, tornado, hail and fire, and coverage for other perils on a case-by-case basis. Property catastrophe reinsurance provides coverage on an excess of loss basis 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 both personal lines and commercial property exposures and principally covers buildings, structures, equipment and contents. The primary perils in this business

ARCH CAPITAL  50 2021 SECOND QUARTER FORM 10-Q

include fire, explosion, collapse, riot, vandalism, wind, tornado, flood and earthquake. Business is assumed on both a proportional and excess of loss treaty basis and on a facultative basis. In addition, facultative business is written which focuses on commercial property risks on an excess of loss basis.

•Other: includes life reinsurance business on both a proportional and non-proportional basis, 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,
	2021			2020
	Amount		%	Amount		%
Property excluding property catastrophe	$	249,101	26.9	$	163,639	29.0
Property catastrophe	87,642		9.5	117,676		20.8
Other specialty	296,325		32.0	117,375		20.8
Casualty	225,890		24.4	105,049		18.6
Marine and aviation	50,248		5.4	32,372		5.7
Other	15,526		1.7	28,983		5.1
Total	$	924,732	100.0	$	565,094	100.0

2021 Second Quarter versus 2020 Period. Gross premiums written by the reinsurance segment in the 2021 second quarter were 68.3% higher than in the 2020 second quarter, while net premiums written were 63.6% higher. The growth in net premiums written was observed in most lines of business, primarily related to new business opportunities in other specialty, casualty and property excluding property catastrophe lines and the benefit of rate increases.

	Six Months Ended June 30,
	2021			2020
	Amount		%	Amount		%
Property excluding property catastrophe	$	541,934	28.2	$	322,563	23.7
Property catastrophe	204,849		10.6	206,768		15.2
Other Specialty	580,656		30.2	402,327		29.5
Casualty	444,146		23.1	295,929		21.7
Marine and aviation	111,886		5.8	82,157		6.0
Other	40,373		2.1	52,530		3.9
Total	$	1,923,844	100.0	$	1,362,274	100.0

Six Months Ended June 30, 2021 versus 2020 period. Gross premiums written by the reinsurance segment for the six months ended June 30, 2021 were 46.6% higher than in the 2020 period, while net premiums written were 41.2% higher than in the 2020 period. The increase in net premiums written reflected growth in property excluding property catastrophe,

other specialty and casualty 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,
	2021			2020
	Amount		%	Amount		%
Property excluding property catastrophe	$	202,780	27.5	$	124,019	25.8
Property catastrophe	76,167		10.3	55,226		11.5
Other specialty	211,817		28.7	123,006		25.6
Casualty	183,846		24.9	132,756		27.6
Marine and aviation	42,773		5.8	24,960		5.2
Other	19,641		2.7	20,230		4.2
Total	$	737,024	100.0	$	480,197	100.0

	Six Months Ended June 30,
	2021			2020
	Amount		%	Amount		%
Property excluding property catastrophe	$	390,562	28.3	$	236,671	23.1
Property catastrophe	164,178		11.9	108,226		10.6
Other Specialty	375,715		27.2	326,391		31.9
Casualty	332,877		24.1	267,827		26.2
Marine and aviation	82,881		6.0	49,818		4.9
Other	35,711		2.6	34,724		3.4
Total	$	1,381,924	100.0	$	1,023,657	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 2021 second quarter were 53.5% higher than in the 2020 second quarter, and reflect changes in net premiums written over the previous five quarters.

Other Underwriting Income (Loss).

Other underwriting income for the 2021 second quarter was $1.1 million, compared to a loss of $0.7 million for the 2020 second quarter, and a loss of $0.1 million for the six months ended June 30, 2021, compared to an income of $1.5 million for the 2020 period.

ARCH CAPITAL  51 2021 SECOND QUARTER FORM 10-Q

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,
	2021		2020		2021		2020
Current year	65.7	%	88.2	%	72.1	%	84.6	%
Prior period reserve development	(2.8)	%	(8.4)	%	(3.4)	%	(5.1)	%
Loss ratio	62.9	%	79.8	%	68.7	%	79.5	%

Current Year Loss Ratio.

2021 Second Quarter versus 2020 Period. The reinsurance segment’s current year loss ratio in the 2021 second quarter was 22.5 points lower than in the 2020 second quarter. The 2021 second quarter loss ratio reflected 2.6 points of current year catastrophic activity, including winter storms Uri and Viola as well as other minor global events. The 2020 second quarter included 26.3 points of catastrophic activity, which included exposure to the COVID-19 pandemic.

Six Months Ended June 30, 2021 versus 2020 period.The reinsurance segment’s current year loss ratio for the six months ended June 30, 2021 was 12.5 points lower than in the 2020 period and reflected 12.9 points of current year catastrophic activity, compared to 19.1 points in the 2020 period. The 2020 period loss ratio included exposure to the COVID-19 pandemic.

Prior Period Reserve Development.

The reinsurance segment’s net favorable development was $20.5 million, or 2.8 points, for the 2021 second quarter, compared to $40.2 million, or 8.4 points, for the 2020 second quarter, and $47.3 million, or 3.4 points, for the six months ended June 30, 2021, compared to $51.8 million, or 5.1 points, for the 2020 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.

2021 Second Quarter versus 2020 Period. The underwriting expense ratio for the reinsurance segment was 24.2% in the 2021 second quarter, compared to 27.0% in the 2020 second quarter. Approximately 2.1 points of the difference is due to a lower level of acquisition expenses related to favorable prior year loss reserve development this quarter than in the 2020 second quarter. The remainder of the decrease in the underwriting expense ratio was primarily related to growth in net premiums earned.

Six Months Ended June 30, 2021 versus 2020 period. The underwriting expense ratio for the reinsurance segment was 25.8% for the six months ended June 30, 2021, compared to 24.8% for the 2020 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 2021 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. Our mortgage group includes direct mortgage insurance in the U.S. primarily through Arch Mortgage Insurance Company, United Guaranty Residential Insurance Company and Arch Mortgage Guaranty Company (together, “Arch MI U.S.”); mortgage reinsurance by Arch Reinsurance Ltd. (“Arch Re Bermuda”) to mortgage insurers on both a proportional and non-proportional basis globally; direct mortgage insurance in Europe through Arch Insurance (EU) Designated Activity Company (“Arch Insurance EU”); in Hong Kong through Arch MI Asia Limited (“Arch MI Asia”); in Australia through Arch LMI Pty Ltd (“Arch LMI”) and participation in various GSE credit risk-sharing products primarily through Arch Re Bermuda.

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

	Three Months Ended June 30,
	2021			2020			% Change
Gross premiums written	$	391,511		$	369,144		6.1
Premiums ceded	(55,665)			(44,044)
Net premiums written	335,846			325,100			3.3
Change in unearned premiums	(1,625)			40,613
Net premiums earned	334,221			365,713			(8.6)
Other underwriting income	4,148			6,450
Losses and loss adjustment expenses	(9,880)			(224,100)
Acquisition expenses	(30,117)			(34,052)
Other operating expenses	(48,312)			(37,574)
Underwriting income	$	250,060		$	76,437		227.1
Underwriting Ratios							% Point Change
Loss ratio	3.0		%	61.3		%	(58.3)
Acquisition expense ratio	9.0		%	9.3		%	(0.3)
Other operating expense ratio	14.5		%	10.3		%	4.2
Combined ratio	26.5		%	80.9		%	(54.4)

ARCH CAPITAL  52 2021 SECOND QUARTER FORM 10-Q

	Six Months Ended June 30,
	2021			2020			% Change
Gross premiums written	$	782,757		$	738,089		6.1
Premiums ceded	(111,716)			(88,371)
Net premiums written	671,041			649,718			3.3
Change in unearned premiums	(503)			61,021
Net premiums earned	670,538			710,739			(5.7)
Other underwriting income	11,045			11,049
Losses and loss adjustment expenses	(73,569)			(291,666)
Acquisition expenses	(60,199)			(72,588)
Other operating expenses	(97,443)			(83,470)
Underwriting income	$	450,372		$	274,064		64.3
Underwriting Ratios							% Point Change
Loss ratio	11.0		%	41.0		%	(30.0)
Acquisition expense ratio	9.0		%	10.2		%	(1.2)
Other operating expense ratio	14.5		%	11.7		%	2.8
Combined ratio	34.5		%	62.9		%	(28.4)

Premiums Written.

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

	Three Months Ended June 30,
	2021			2020
	Amount		%	Amount		%
Underwriting location:
United States	$	234,645	69.9	$	261,124	80.3
Other	101,201		30.1	63,976		19.7
Total	$	335,846	100.0	$	325,100	100.0

2021 Second Quarter versus 2020 Period. Gross premiums written by the mortgage segment in the 2021 second quarter were 6.1% higher than in the 2020 second quarter, while net premiums written were 3.3% higher, primarily reflecting growth in Australian single premium mortgage insurance and the benefit of premiums received related to the exercise of early redemption options by GSEs for certain seasoned callable credit risk transfer contracts. This growth was partially offset by a lower level of U.S. primary mortgage insurance in force on monthly premium policies, which resulted from the continued high level of refinancing activity.

	Six Months Ended June 30,
	2021			2020
	Amount		%	Amount		%
Underwriting location:
United States	$	482,174	71.9	$	525,232	80.8
Other	188,867		28.1	124,486		19.2
Total	$	671,041	100.0	$	649,718	100.0

Six Months Ended June 30, 2021 versus 2020 period. Gross premiums written by the mortgage segment for the six months ended June 30, 2021 were 6.1% higher than in the 2020 period, while net premiums written for the six months

ended June 30, 2021 were 3.3% higher than in the 2020 period, primarily reflecting growth in Australian single premium mortgage insurance and the benefit of premiums received related to the exercise of early redemption options by GSEs for certain seasoned callable credit risk transfer contracts. This growth was partially offset by a lower level of U.S. primary mortgage insurance in force on monthly premium policies, which resulted from the continued high level of refinancing activity.

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 54.8% for the Arch MI U.S. portfolio of mortgage insurance policies at June 30, 2021, reflecting the higher level of mortgage refinancing activity, compared to 58.7% at December 31, 2020.

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,
	2021			2020
	Amount		%	Amount		%
Total new insurance written (NIW) (1)	$	28,372		$	24,551
Credit quality (FICO):
>=740	$	19,240	67.8	$	15,851	64.6
680-739	8,113		28.6	7,781		31.7
620-679	1,019		3.6	919		3.7
Total	$	28,372	100.0	$	24,551	100.0
Loan-to-value (LTV):
95.01% and above	$	1,484	5.2	$	1,948	7.9
90.01% to 95.00%	13,936		49.1	9,403		38.3
85.01% to 90.00%	8,675		30.6	8,140		33.2
85.00% and below	4,277		15.1	5,060		20.6
Total	$	28,372	100.0	$	24,551	100.0
Monthly vs. single:
Monthly	$	26,725	94.2	$	23,391	95.3
Single	1,647		5.8	1,160		4.7
Total	$	28,372	100.0	$	24,551	100.0
Purchase vs. refinance:
Purchase	$	25,010	88.2	$	14,956	60.9
Refinance	3,362		11.8	9,595		39.1
Total	$	28,372	100.0	$	24,551	100.0

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

ARCH CAPITAL  53 2021 SECOND QUARTER FORM 10-Q

(U.S. Dollars in millions)	Six Months Ended June 30,
	2021			2020
	Amount		%	Amount		%
Total new insurance written (NIW) (1)	$	55,391		$	41,329
Credit quality (FICO):
>=740	$	37,058	66.9	$	25,920	62.7
680-739	16,531		29.8	13,568		32.8
620-679	1,802		3.3	1,841		4.5
Total	$	55,391	100.0	$	41,329	100.0
Loan-to-value (LTV):
95.01% and above	$	3,092	5.6	$	3,616	8.7
90.01% to 95.00%	26,224		47.3	16,602		40.2
85.01% to 90.00%	16,987		30.7	13,469		32.6
85.01% and below	9,088		16.4	7,642		18.5
Total	$	55,391	100.0	$	41,329	100.0
Monthly vs. single:
Monthly	$	51,714	93.4	$	39,083	94.6
Single	3,677		6.6	2,246		5.4
Total	$	55,391	100.0	$	41,329	100.0
Purchase vs. refinance:
Purchase	$	45,515	82.2	$	27,255	65.9
Refinance	9,876		17.8	14,074		34.1
Total	$	55,391	100.0	$	41,329	100.0

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

Net Premiums Earned.

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

	Three Months Ended June 30,
	2021			2020
	Amount		%	Amount		%
Underwriting location:
United States	$	248,388	74.3	$	304,652	83.3
Other	85,833		25.7	61,061		16.7
Total	$	334,221	100.0	$	365,713	100.0

2021 Second Quarter versus 2020 Period. Net premiums earned for the 2021 second quarter were 8.6% lower than in the 2020 second quarter, and reflected a lower level of single premium policy terminations and a decrease in U.S. primary mortgage insurance in force on monthly premium policies.

	Six Months Ended June 30,
	2021			2020
	Amount		%	Amount		%
Underwriting location:
United States	$	510,938	76.2	$	593,814	83.5
Other	159,600		23.8	116,925		16.5
Total	$	670,538	100.0	$	710,739	100.0

Six Months Ended June 30, 2021 versus 2020 Period. Net premiums earned for the six months ended June 30, 2021 were 5.7% lower than in the 2020 period, primarily reflecting a lower level of single premiums earned, partially offset by an increase in earnings from Australian single premium policy terminations.

Other Underwriting Income.

Other underwriting income, which is primarily related to GSE credit risk-sharing transactions was $4.1 million for the 2021 second quarter, compared to $6.5 million for the 2020 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,
	2021		2020		2021		2020
Current year	15.9	%	61.4	%	19.1	%	41.9	%
Prior period reserve development	(12.9)	%	(0.1)	%	(8.1)	%	(0.9)	%
Loss ratio	3.0	%	61.3	%	11.0	%	41.0	%

Current Year Loss Ratio.

2021 Second Quarter versus 2020 Period. The mortgage segment’s current year loss ratio was 45.5 points lower in the 2021 second quarter than in the 2020 second quarter. The mortgage segment’s current year loss ratio was 22.8 points lower for the six months ended June 30, 2021 than for the 2020 period. The lower current year loss ratios for the 2021 period reflect decrease in loss assumptions related to COVID-19 pandemic.

For the 2020 periods, the increase in incurred losses was primarily due to, the financial stress related to the COVID-19 pandemic. Segregating estimated losses due to COVID-19 from the overall mortgage segment estimated losses would require the number of delinquencies specifically attributable to COVID-19. As this analysis cannot be performed accurately, the Company is not reporting COVID-19 provisions separately from its overall loss provisions.

ARCH CAPITAL  54 2021 SECOND QUARTER FORM 10-Q

Prior Period Reserve Development.

The mortgage segment’s net favorable development was $43.1 million, or 12.9 points, for the 2021 second quarter, compared to $0.2 million, or 0.1 points, for the 2020 second quarter, and $54.0 million, or 8.1 points, for the six months ended June 30, 2021, compared to $6.3 million, or 0.9 points, for the 2020 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.

2021 Second Quarter versus 2020 Period. The underwriting expense ratio for the mortgage segment was 23.5% in the 2021 second quarter, compared to 19.6% in the 2020 second quarter, with the increase primarily reflecting higher operating expenses and, to a lesser extent, a decline in net premiums earned on U.S. primary mortgage insurance business.

Six Months Ended June 30, 2021 versus 2020 period. The underwriting expense ratio for the mortgage segment was 23.5% for the six months ended June 30, 2021, compared to 21.9% for the 2020 period, with the increase primarily reflecting higher operating expenses and, to a lesser extent, a decline in net premiums earned on U.S. primary mortgage insurance business.

Corporate (Non-Underwriting) Segment

The corporate (non-underwriting) segment results include net investment income, other income (loss), corporate expenses, transaction costs and other, amortization of intangible assets, interest expense, items related to our non-cumulative preferred shares, 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, income or loss from operating affiliates and income taxes. Such amounts exclude the results of the ‘other’ segment. See note 1, “Basis of Presentation and Recent Accounting Pronouncements,” to our consolidated financial statements for information about the change in presentation of income or loss from operating affiliates.

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,
	2021		2020		2021		2020
Fixed maturities	$	77,709	$	91,491	$	156,726	$	193,254
Equity securities	8,282		6,023		13,932		11,653
Short-term investments	972		897		1,616		4,282
Other (1)	21,026		17,825		36,585		38,304
Gross investment income	107,989		116,236		208,859		247,493
Investment expenses (2)	(18,559)		(15,205)		(40,700)		(33,434)
Net investment income	$	89,430	$	101,031	$	168,159	214,059

(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 0.30% of average invested assets for the 2021 second quarter, compared to 0.28% for the 2020 second quarter, and 0.32% for the six months ended June 30, 2021, compared to 0.32% for the 2020 period.

The lower level of net investment income for the 2021 second quarter primarily related to lower yields available in the financial market. The pre-tax investment income yield, calculated based on amortized cost and on an annualized basis, was 1.47% for the 2021 second quarter, compared to 1.92% for the 2020 second quarter, and 1.40% for the six months ended June 30, 2021, compared to 2.08% for the 2020 period.

Corporate Expenses.

Corporate expenses were $17.2 million for the 2021 second quarter, compared to $16.9 million for the 2020 second quarter, and $40.6 million for the six months ended June 30, 2021, compared to $35.1 million for the 2020 period. The increase in corporate expenses was primarily due to higher incentive compensation costs.

Transaction Costs and Other.

Transaction costs and other were a benefit of $1.4 million for the 2021 second quarter, compared to an expense of $1.0 million for the 2020 second quarter, and a benefit of $0.2 million for the six months ended June 30, 2021, compared to an expense of $3.6 million for the 2020 period. Amounts in the 2021 and 2020 periods are primarily related to acquisitions activity for the respective period.

Amortization of Intangible Assets.

Amortization of intangible assets for the 2021 second quarter was $14.4 million, compared to $16.5 million for the 2020

ARCH CAPITAL  55 2021 SECOND QUARTER FORM 10-Q

second quarter, and $28.8 million for the six months ended June 30, 2021, compared to $33.1 million for the 2020 period. Amounts in 2021 and 2020 primarily related to amortization of finite-lived intangible assets. See the consolidated financial statements contained in our 2020 Form 10-K for disclosures on our amortization pattern.

Interest Expense.

Interest expense was $31.4 million for the 2021 second quarter, compared to the $25.1 million for the 2020 second quarter, and $65.6 million for the six months ended June 30, 2021, compared to $50.4 million for the 2020 period.The higher level of interest expense mainly resulted from the issuance of $1.0 billion of 3.635% senior notes on June 30, 2020.

Net Realized Gains or Losses.

We recorded net realized gains of $163.4 million for the 2021 second quarter, compared to net realized gains of $385.1 million for the 2020 second quarter, and net realized gains of $264.7 million for the six months ended June 30, 2021, compared to net realized gains of $313.0 million for the 2020 period. Currently, our portfolio is actively managed to maximize total return within certain guidelines. The effect of financial market movements on the investment portfolio will directly impact net realized gains 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),” to our consolidated financial statements for additional information. See note 7, “Investment Information—Allowance for Credit Losses,” to our consolidated financial statements for additional information.

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

We recorded $122.2 million of equity in net income related to investment funds accounted for using the equity method in the 2021 second quarter, compared to a loss of $65.1 million for the 2020 second quarter, and $193.9 million of income for the six months ended June 30, 2021, compared to a loss of $69.3 million for the 2020 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 $2.5 billion at June 30, 2021, compared to $2.0 billion at December 31, 2020. 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 losses for the 2021 second quarter were $17.9 million, compared to net foreign exchange losses for the 2020 second quarter of $42.4 million. Net foreign exchange gains for the six months ended June 30, 2021 were $3.6 million, compared to net foreign exchange gains for the 2020 period of $20.9 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 7.1% for the 2021 second quarter, compared to 8.8% for the 2020 second quarter, and 7.5% for the six months ended June 30, 2021, compared to 10.7% for the 2020 period. Such amounts exclude the results of the ‘other’ segment. 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 (loss) from operating affiliates.

We recorded $24.5 million of net income from our operating affiliates in the 2021 second quarter, compared to a loss of $3.2 million for the 2020 second quarter, and $99.9 million of income for the six months ended June 30, 2021, compared to $5.3 million for the 2020 period. Results for the 2021 period, primarily reflected our acquisition of 29.5% of the common equity in Coface, which included a one-time gain of $74.5 million. As a result of equity method accounting rules, approximately $36 million of additional gain was deferred and will generally be recognized over the next five years.

Other Segment 

Through June 30, 2021, the ‘other’ segment included the results of Watford. Pursuant to GAAP, Watford was considered a variable interest entity and we concluded that we are the primary beneficiary of Watford. As such, we consolidated the results of Watford in our consolidated financial statements through June 30, 2021, although we only owned approximately 10% of Watford’s common equity. See note 11, “Variable Interest Entities and Noncontrolling Interests,” note 4, “Segment Information,” and Note 16,

ARCH CAPITAL  56 2021 SECOND QUARTER FORM 10-Q

“Subsequent Event,” to our consolidated financial statements for additional information on Watford.

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 2020 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 

At June 30, 2021, total investable assets held by Arch were $27.3 billion, excluding the $2.9 billion included in the ‘other’ segment (i.e., attributable to Watford).

Investable Assets Held by Arch 

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

Investable assets (1):	Estimated Fair Value			% of Total
June 30, 2021
Fixed maturities (2)	$	18,022,113		66.0
Short-term investments (2)	2,380,016			8.7
Cash	884,857			3.2
Equity securities (2)	1,633,579			6.0
Other investments (2)	1,512,317			5.5
Other investable assets (3)	500,000			1.8
Investments accounted for using the equity method	2,539,124			9.3
Securities transactions entered into but not settled at the balance sheet date	(180,592)			(0.7)
Total investable assets held by Arch	$	27,291,414		100.0
Average effective duration (in years)	2.31
Average S&P/Moody’s credit ratings (4)	AA/Aa2
Embedded book yield (5)	1.45		%
December 31, 2020
Fixed maturities (2)	$	18,771,296		69.9
Short-term investments (2)	2,063,240			7.7
Cash	694,997			2.6
Equity securities (2)	1,436,104			5.3
Other investments (2)	1,480,347			5.5
Other investable assets (3)	500,000			1.9
Investments accounted for using the equity method	2,047,889			7.6
Securities transactions entered into but not settled at the balance sheet date	(137,578)			(0.5)
Total investable assets held by Arch	$	26,856,295		100.0
Average effective duration (in years)	3.01
Average S&P/Moody’s credit ratings (4)	AA/Aa2
Embedded book yield (5)	1.56		%

(1)In securities lending transactions, we receive collateral in excess of the fair value of the securities pledged. For purposes of this table, we have excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value.

(2)Includes investments carried as available for sale, at fair value and at fair value under the fair value option.

(3)Represents participation interests in a receivable of a reverse repurchase agreement.

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

(5)Before investment expenses.

At June 30, 2021, approximately $18.5 billion, or 67.9%, of total investable assets held by Arch were internally managed, compared to $19.2 billion, or 71.4%, at December 31, 2020.

ARCH CAPITAL  57 2021 SECOND QUARTER FORM 10-Q

The following table summarizes our fixed maturities and fixed maturities pledged under securities lending agreements (“Fixed Maturities”) by type:

	Estimated Fair Value		% of Total
June 30, 2021
Corporate bonds	$	7,375,350	40.9
Residential mortgage backed securities	374,565		2.1
Municipal bonds	413,709		2.3
Commercial mortgage backed securities	267,574		1.5
U.S. government and government agencies	4,855,595		26.9
Non-U.S. government securities	2,308,403		12.8
Asset backed securities	2,426,917		13.5
Total	$	18,022,113	100.0
December 31, 2020
Corporate bonds	$	8,039,745	42.8
Residential mortgage backed securities	616,619		3.3
Municipal bonds	492,734		2.6
Commercial mortgage backed securities	390,990		2.1
U.S. government and government agencies	5,354,863		28.5
Non-U.S. government securities	2,310,157		12.3
Asset backed securities	1,566,188		8.3
Total	$	18,771,296	100.0

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, 2021
U.S. government and gov’t agencies (1)	$	5,221,296	29.0
AAA	3,432,285		19.0
AA	2,004,442		11.1
A	3,268,661		18.1
BBB	2,896,453		16.1
BB	544,730		3.0
B	330,639		1.8
Lower than B	48,230		0.3
Not rated	275,377		1.5
Total	$	18,022,113	100.0
December 31, 2020
U.S. government and gov’t agencies (1)	$	5,963,758	31.8
AAA	3,117,046		16.6
AA	2,063,738		11.0
A	3,760,280		20.0
BBB	2,699,201		14.4
BB	574,189		3.1
B	268,095		1.4
Lower than B	54,795		0.3
Not rated	270,194		1.4
Total	$	18,771,296	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, 2021
0-10%	$	7,387,667	$	(68,781)	92.0
10-20%	28,039		(4,166)		5.6
20-30%	1,999		(553)		0.7
Greater than 30%	1,326		(1,239)		1.7
Total	$	7,419,031	$	(74,739)	100.0
December 31, 2020
0-10%	$	3,583,981	$	(55,542)	79.4
10-20%	95,495		(12,183)		17.4
20-30%	1,061		(406)		0.6
Greater than 30%	1,249		(1,785)		2.6
Total	$	3,681,786	$	(69,916)	100.0

The following table summarizes our top ten exposures to fixed income corporate issuers by fair value at June 30, 2021, excluding guaranteed amounts and covered bonds:

	Estimated Fair Value		Credit Rating (1)
Bank of America Corporation	$	373,742	A-/A2
JPMorgan Chase & Co.	372,381		A-/A2
Citigroup Inc.	288,574		BBB+/A3
Morgan Stanley	253,549		BBB+/A1
Wells Fargo & Company	247,222		BBB+/A2
The Goldman Sachs Group, Inc.	185,647		BBB+/A2
Nestlé S.A.	129,191		AA-/Aa3
Amazon.com, Inc.	118,047		AA/A1
Nippon Telegraph and Telephone Corporation	95,958		A/A1
AT&T Inc.	92,795		BBB/Baa2
Total	$	2,157,106

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

ARCH CAPITAL  58 2021 SECOND QUARTER FORM 10-Q

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
Jun 30, 2021
RMBS	$	336,784	$	14,716	$	23,065	$	374,565
CMBS	28,917		213,655		25,002		267,574
ABS	—		2,206,453		220,464		2,426,917
Total	$	365,701	$	2,434,824	$	268,531	$	3,069,056
Dec 31, 2020
RMBS	$	584,499	$	4,102	$	28,018	$	616,619
CMBS	24,396		342,491		24,103		390,990
ABS	—		1,403,137		163,051		1,566,188
Total	$	608,895	$	1,749,730	$	215,172	$	2,573,797

The following table summarizes our equity securities, which include investments in exchange traded funds:

	June 30, 2021		December 31, 2020
Equities (1)	$	864,688	$	676,437
Exchange traded funds
Fixed income (2)	304,723		341,139
Equity and other (3)	464,168		418,528
Total	$	1,633,579	$	1,436,104

(1)Primarily in consumer non-cyclical, consumer cyclical, technology, communications and financial stocks at June 30, 2021.

(2)Primarily in corporate, MBS and municipal strategies at June 30, 2021.

(3)Primarily in utilities, large cap stocks and foreign equities at June 30, 2021.

The following table summarizes our other investments and other investable assets:

	June 30, 2021		December 31, 2020
Lending	$	638,786	$	572,636
Term loan investments	474,859		380,193
Energy	84,891		65,813
Credit related funds	73,171		90,780
Investment grade fixed income	110,375		138,646
Infrastructure	32,109		165,516
Private equity	70,878		48,750
Real estate	27,248		18,013
Total fair value option	$	1,512,317	$	1,480,347
Other investable assets	$	500,000	$	500,000
Total other investments	$	2,012,317	$	1,980,347

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.

Investable Assets in the ‘Other’ Segment

Investable assets in the ‘other’ segment are managed by Watford. The board of directors of Watford establishes its investment policies and guidelines. A significant amount of Watford’s investments are accounted for using the fair value option with changes in the carrying value of such investments recorded in net realized gains or losses.

The following table summarizes investable assets in the ‘other’ segment:

	June 30, 2021		December 31, 2020
Investments accounted for using the fair value option:
Other investments	$	858,155	$	851,538
Fixed maturities	578,280		455,163
Short-term investments	478,711		418,690
Equity securities	69,773		64,994
Total	1,984,919		1,790,385
Fixed maturities available for sale, at fair value	625,422		613,503
Equity securities, at fair value	97,623		52,410
Cash	349,202		211,451
Securities sold but not yet purchased	(28,068)		(21,679)
Securities transactions entered into but not settled at the balance sheet date	(97,055)		11,542
Total investable assets included in ‘other’ segment	$	2,932,043	$	2,657,612

ARCH CAPITAL  59 2021 SECOND QUARTER FORM 10-Q

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,
	2021		2020		2021		2020
Premiums written:
Direct	$	1,909,893	$	1,485,627	$	3,802,138	$	3,174,425
Assumed	1,376,398		832,065		2,881,359		1,976,097
Ceded	(886,767)		(649,381)		(1,775,516)		(1,344,965)
Net	$	2,399,524	$	1,668,311	$	4,907,981	$	3,805,557
Premiums earned:
Direct	$	1,795,899	$	1,559,222	$	3,508,824	$	3,105,047
Assumed	1,091,968		746,188		2,039,582		1,507,262
Ceded	(766,958)		(640,056)		(1,479,075)		(1,202,511)
Net	$	2,120,909	$	1,665,354	$	4,069,331	$	3,409,798
Losses and LAE:
Direct	$	1,046,579	$	1,162,958	$	2,032,512	$	2,148,041
Assumed	554,256		508,108		1,221,567		1,053,977
Ceded	(441,004)		(440,544)		(891,148)		(856,077)
Net	$	1,159,831	$	1,230,522	$	2,362,931	$	2,345,941

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 various aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda (the “Bellemeade Agreements”). For the respective coverage periods, 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, 2021:

			June 30, 2021
	Initial Coverage at Issuance		Current Coverage		Remaining Retention, Net
Bellemeade 2017-1 Ltd. (1)	$	368,114	$	145,573	$	125,297
Bellemeade 2018-1 Ltd. (2)	374,460		250,095		123,173
Bellemeade 2018-3 Ltd. (3)	506,110		302,563		126,127
Bellemeade 2019-1 Ltd. (4)	341,790		219,256		102,017
Bellemeade 2019-2 Ltd. (5)	621,022		398,316		156,718
Bellemeade 2019-3 Ltd. (6)	700,920		528,084		176,565
Bellemeade 2019-4 Ltd. (7)	577,267		468,737		113,415
Bellemeade 2020-1 Ltd. (8)	528,540		18,843		747,799
Bellemeade 2020-2 Ltd. (9)	449,167		328,375		232,481
Bellemeade 2020-3 Ltd. (10)	451,816		451,816		163,905
Bellemeade 2020-4 Ltd. (11)	337,013		281,750		138,183
Bellemeade 2021-1 Ltd. (12)	643,577		643,577		166,199
Bellemeade 2021-2 Ltd. (13)	616,017		616,017		152,734
Total	$	6,515,813	$	4,653,002	$	2,524,613

(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 June 2020, covering in-force policies issued between July 1, 2019 and December 31, 2019. $450 million was directly funded by Bellemeade 2020-1 Ltd. with an additional $79 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(9)    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.

(10)    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.

(11) 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.

(12) 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.

(13) 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.

ARCH CAPITAL  60 2021 SECOND QUARTER FORM 10-Q

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, 2021 and December 31, 2020, our Loss Reserves, net of unpaid losses and loss adjustment expenses recoverable, by type and by operating segment were as follows:

	June 30, 2021		December 31, 2020
Insurance segment:
Case reserves	$	2,100,109	$	2,051,640
IBNR reserves	4,117,169		3,889,823
Total net reserves	6,217,278		5,941,463
Reinsurance segment:
Case reserves	1,523,486		1,560,523
Additional case reserves	432,516		280,472
IBNR reserves	2,435,575		2,253,953
Total net reserves	4,391,577		4,094,948
Mortgage segment:
Case reserves	704,314		631,921
IBNR reserves	266,690		271,702
Total net reserves	971,004		903,623
Other segment:
Case reserves	682,341		566,587
Additional case reserves	47,774		32,321
IBNR reserves	740,654		660,132
Total net reserves	1,470,769		1,259,040
Total:
Case reserves	5,010,250		4,810,671
Additional case reserves	480,290		312,793
IBNR reserves	7,560,088		7,075,610
Total net reserves	$	13,050,628	$	12,199,074

At June 30, 2021 and December 31, 2020, 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, 2021		December 31, 2020
Insurance segment:
Professional lines (1)	$	1,516,878	$	1,482,820
Construction and national accounts	1,470,201		1,395,067
Excess and surplus casualty (2)	859,662		816,495
Programs	748,015		699,354
Property, energy, marine and aviation	500,880		517,692
Travel, accident and health	96,345		98,910
Lenders products	64,560		48,946
Other (3)	960,737		882,179
Total net reserves	$	6,217,278	$	5,941,463

(1)Includes professional liability, executive assurance and healthcare business.

(2)Includes casualty and contract binding business.

(3)Includes alternative markets, excess workers’ compensation and surety business.

At June 30, 2021 and December 31, 2020, 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, 2021		December 31, 2020
Reinsurance segment:
Casualty (1)	$	2,024,591	$	1,995,849
Other specialty (2)	955,770		917,178
Property excluding property catastrophe	668,339		594,033
Marine and aviation	215,345		204,205
Property catastrophe	410,034		268,858
Other (3)	117,498		114,825
Total net reserves	$	4,391,577	$	4,094,948

(1)Includes executive assurance, professional liability, workers’ compensation, excess motor, healthcare and other.

(2)Includes non-excess motor, surety, accident and health, workers’ compensation catastrophe, agriculture, trade credit and other.

(3)Includes life, casualty clash and other.

At June 30, 2021 and December 31, 2020, 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, 2021		December 31, 2020
U.S. primary mortgage insurance (1)	$	713,135	$	649,748
Other	257,869		253,875
Total net reserves	$	971,004	$	903,623

(1)    At June 30, 2021, 28.0% represents policy years 2011 and prior and the remainder from later policy years. At December 31, 2020, 28.3% of total net reserves represent policy years 2011 and prior and the remainder from later policy years.

ARCH CAPITAL  61 2021 SECOND QUARTER FORM 10-Q

Mortgage Operations Supplemental Information

The mortgage segment’s insurance in force (“IIF”) and risk in force (“RIF”) were as follows at June 30, 2021 and December 31, 2020:

(U.S. Dollars in millions)	June 30, 2021			December 31, 2020
	Amount		%	Amount		%
Insurance In Force (IIF) (1):
U.S. primary mortgage insurance	$	277,887	65.8	$	280,579	66.2
Mortgage reinsurance	32,666		7.7	31,220		7.4
Other (2)	111,884		26.5	111,740		26.4
Total	$	422,437	100.0	$	423,539	100.0
Risk In Force (RIF) (3):
U.S. primary mortgage insurance	$	69,587	90.3	$	70,522	90.5
Mortgage reinsurance	2,245		2.9	2,226		2.9
Other (2)	5,188		6.7	5,146		6.6
Total	$	77,020	100.0	$	77,894	100.0

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

(2)Includes GSE credit risk-sharing transactions and international insurance business.

(3)Represents 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 credit risk-sharing or reinsurance transactions.

The IIF and RIF for our U.S. primary mortgage insurance business by policy year were as follows at June 30, 2021:

(U.S. Dollars in millions)	IIF			RIF			Delinquency
	Amount		%	Amount		%	Rate (1)
Policy year:
2011 and prior	$	12,591	4.5	$	2,839	4.1	9.75	%
2012	2,261		0.8	587		0.8	3.00	%
2013	5,635		2.0	1,563		2.2	2.95	%
2014	6,288		2.3	1,729		2.5	3.52	%
2015	11,208		4.0	3,017		4.3	3.19	%
2016	18,500		6.7	4,958		7.1	4.11	%
2017	17,577		6.3	4,574		6.6	4.87	%
2018	19,044		6.9	4,827		6.9	6.25	%
2019	34,944		12.6	8,727		12.5	4.02	%
2020	95,419		34.3	23,316		33.5	0.88	%
2021	54,420		19.6	13,450		19.3	0.10	%
Total	$	277,887	100.0	$	69,587	100.0	3.11	%

(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, 2020:

(U.S. Dollars in millions)	IIF			RIF			Delinquency
	Amount		%	Amount		%	Rate (1)
Policy year:
2011 and prior	$	14,588	5.2	$	3,327	4.7	11.36	%
2012	3,651		1.3	992		1.4	2.98	%
2013	7,546		2.7	2,107		3.0	3.30	%
2014	8,261		2.9	2,273		3.2	4.06	%
2015	15,032		5.4	4,048		5.7	3.72	%
2016	24,958		8.9	6,648		9.4	4.77	%
2017	24,748		8.8	6,413		9.1	5.52	%
2018	27,304		9.7	6,918		9.8	6.76	%
2019	48,304		17.2	12,001		17.0	4.61	%
2020	106,187		37.8	25,795		36.6	0.76	%
Total	$	280,579	100.0	$	70,522	100.0	4.19	%

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

The following tables provide supplemental disclosures on risk in force for our U.S. primary mortgage insurance business at June 30, 2021 and December 31, 2020:

(U.S. Dollars in millions)	June 30, 2021				December 31, 2020
	Amount			%	Amount			%
Credit quality (FICO):
>=740	$	41,156		59.1	$	40,774		57.8
680-739	23,663			34.0	24,498			34.7
620-679	4,401			6.3	4,837			6.9
<620	367			0.5	413			0.6
Total	$	69,587		100.0	$	70,522		100.0
Weighted average FICO score	745				743
Loan-to-value (LTV):
95.01% and above	$	7,975		11.5	$	8,643		12.3
90.01% to 95.00%	37,619			54.1	37,877			53.7
85.01% to 90.00%	19,784			28.4	20,013			28.4
85.00% and below	4,209			6.0	3,989			5.7
Total	$	69,587		100.0	$	70,522		100.0
Weighted average LTV	92.8		%		92.8		%
Total RIF, net of external reinsurance	$	55,557			$	56,658

ARCH CAPITAL  62 2021 SECOND QUARTER FORM 10-Q

(U.S. Dollars in millions)	June 30, 2021			December 31, 2020
	Amount		%	Amount		%
Total RIF by State:
Texas	$	5,560	8.0	$	5,636	8.0
California	5,324		7.7	5,261		7.5
Florida	3,367		4.8	3,632		5.2
Minnesota	2,973		4.3	2,520		3.6
North Carolina	2,924		4.2	2,622		3.7
Georgia	2,886		4.1	2,959		4.2
Illinois	2,832		4.1	2,762		3.9
Massachusetts	2,459		3.5	2,464		3.5
Virginia	2,372		3.4	2,526		3.6
Ohio	2,229		3.2	2,264		3.2
Other	36,661		52.7	37,876		53.7
Total	$	69,587	100.0	$	70,522	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,
	2021			2020
Roll-forward of insured loans in default:
Beginning delinquent number of loans	52,234			20,163
New notices	18,415			67,793
Cures	(32,924)			(22,205)
Paid claims	(406)			(1,084)
Ending delinquent number of loans (1)	37,319			64,667
Ending number of policies in force (1)	1,199,918			1,259,328
Delinquency rate (1)	3.11		%	5.14		%
Losses:
Number of claims paid	406			1,084
Total paid claims	$	15,297		$	46,139
Average per claim	$	37.7		$	42.6
Severity (2)	81.0		%	94.3		%
Average case reserve per default (in thousands)	$	19.5		$	6.9

(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 8.5 to 1 at June 30, 2021, compared to 9.3 to 1 at December 31, 2020.

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, 2021		December 31, 2020
Total shareholders’ equity available to Arch	$	13,986,072	$	13,105,886
Less preferred shareholders’ equity	1,280,000		780,000
Common shareholders’ equity available to Arch	$	12,706,072	$	12,325,886
Common shares and common share equivalents outstanding, net of treasury shares (1)	396,771,251		406,720,642
Book value per share	$	32.02	$	30.31

(1)Excludes the effects of 17,717,327 and 17,839,333 stock options and 759,926 and 1,153,784 restricted stock units outstanding at June 30, 2021 and December 31, 2020, respectively.

LIQUIDITY

This section does not include information specific to Watford. We do not guarantee or provide credit support for Watford, and our financial exposure to Watford is limited to our investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from reinsurance transactions with Watford.

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, 2021, Arch Capital received dividends of $563.7 million from Arch Re Bermuda, our Bermuda-based reinsurer and insurer, which can pay approximately $3.2 billion to Arch Capital during the remainder of 2021 without providing an affidavit to the Bermuda Monetary Authority (“BMA”).

In June 2021, Arch Capital completed a $500.0 million underwritten public offering of 20.0 million depositary shares, each of which represents a 1/1,000th interest in a share of its 4.550% Non-Cumulative Preferred Shares. See note 2, “Share Transactions.”

ARCH CAPITAL  63 2021 SECOND QUARTER FORM 10-Q

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.

Cash Flows

The following table summarizes our cash flows from operating, investing and financing activities, excluding amounts related to the ‘other’ segment (i.e., Watford). See note 11, “Variable Interest Entities and Noncontrolling Interests,” for cash flows related to Watford.

	Six Months Ended
	June 30,
	2021		2020
Total cash provided by (used for):
Operating activities	$	1,565,718	$	1,234,383
Investing activities	(1,174,033)		(1,888,221)
Financing activities	8,352		824,990
Effects of exchange rate changes on foreign currency cash	(9,868)		(15,384)
Increase (decrease) in cash and restricted cash	$	390,169	$	155,768

•Cash provided by operating activities for the six months ended June 30, 2021 reflected a higher level of premiums collected than in the 2020 period.

•Cash used for investing activities for the six months ended June 30, 2021 was lower than in the 2020 period. Activity for the six months ended June 30, 2021 reflected our $546.3 million purchase of a 29.5% interest in Coface, while the 2020 period reflected a higher level of securities purchased, and the investing of proceeds from our issuance of the senior notes.

•Cash used for financing activities for the six months ended June 30, 2021 was lower than cash used in the 2020 period, reflecting $485.8 million inflow from issuance of preferred shares and $485.3 million of repurchases under our share repurchase program. Activity for the 2020 period primarily reflected the issuance of $1.0 billion of our senior notes and $75.5 million of repurchases under our share repurchase program.

CAPITAL RESOURCES

This section does not include information specific to Watford. We do not guarantee or provide credit support for Watford, and our financial exposure to Watford is limited to our investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from reinsurance transactions with Watford.

The following table provides an analysis of our capital structure:

(U.S. dollars in thousands, except  share data)	Jun 30, 2021		Dec 31, 2020
Senior notes	$	2,723,903	$	2,723,423
Shareholders’ equity available to Arch:
Series E non-cumulative preferred shares	$	450,000	$	450,000
Series F non-cumulative preferred shares	330,000		330,000
Series G non-cumulative preferred shares	500,000		—
Common shareholders’ equity	12,706,072		12,325,886
Total	$	13,986,072	$	13,105,886
Total capital available to Arch	$	16,709,975	$	15,829,309
Debt to total capital (%)	16.3		17.2
Preferred to total capital (%)	7.7		4.9
Debt and preferred to total capital (%)	24.0		22.1

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, 2021 with an estimated PMIER sufficiency ratio of 196%, compared to 173% at December 31, 2020.

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. The reinsurance agreements between our U.S.-based property casualty insurance and reinsurance subsidiaries and Arch Re Bermuda were canceled on a cutoff basis as of January 1,

ARCH CAPITAL  64 2021 SECOND QUARTER FORM 10-Q

2018. In 2019, certain reinsurance agreements between our insurance subsidiaries and Arch Re Bermuda were reinstated.

GUARANTOR INFORMATION

The below table provides a description of our senior notes payable at June 30, 2021, excluding amounts attributable to the ‘other’ segment (i.e., Watford):

	Interest		Principal		Carrying
Issuer/Due	(Fixed)		Amount		Amount
Arch Capital:
May 1, 2034	7.350	%	$	300,000	$	297,426
June 30, 2050	3.635	%	1,000,000		988,609
Arch-U.S.:
Nov. 1, 2043 (1)	5.144	%	500,000		495,003
Arch Finance:
Dec. 15, 2026 (1)	4.011	%	500,000		497,420
Dec. 15, 2046 (1)	5.031	%	450,000		445,445
Total			$	2,750,000	$	2,723,903

(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, 2021				December 31, 2020
	Arch Capital		Arch-U.S.		Arch Capital		Arch-U.S.
Assets
Total investments	$	508	$	373,784	$	172	$	396,547
Cash	15,239		27,434		18,932		11,368
Investment in operating affiliates	7,294		—		7,731		—
Due from subsidiaries and affiliates	—		225,006		—		201,515
Other assets	15,244		27,568		10,659		34,405
Total assets	$	38,285	$	653,792	$	37,494	$	643,835
Liabilities
Senior notes	1,286,035		495,003		1,285,867		494,944
Due to subsidiaries and affiliates	—		551,760		—		586,805
Other liabilities	20,172		42,582		23,270		41,876
Total liabilities	$	1,306,207	$	1,089,345	$	1,309,137	$	1,123,625
Non-cumulative preferred shares	$	1,280,000	—		$	780,000	—

ARCH CAPITAL  65 2021 SECOND QUARTER FORM 10-Q

	Six Months Ended				Year Ended
	June 30, 2021				December 31, 2020
	Arch Capital		Arch-U.S.		Arch Capital		Arch-U.S.
Revenues
Net investment income	$	796	$	5,007	$	53	$	18,084
Net realized gains (losses)	—		70,522		(2,110)		26,096
Equity in net income (loss) of investments accounted for using the equity method	—		10,678		—		2,507
Total revenues	796		86,207		(2,057)		46,687
Expenses
Corporate expenses	37,021		3,007		65,566		7,227
Interest expense	29,369		23,567		40,445		47,566
Net foreign exchange (gains) losses	6		—		3		—
Total expenses	66,396		26,574		106,014		54,793
Income (loss) before income taxes and income (loss) from operating affiliates	(65,600)		59,633		(108,071)		(8,106)
Income tax (expense) benefit	—		(14,731)		—		2,689
Income (loss) from operating affiliates	(317)		—		(437)		—
Net income available to Arch	(65,917)		44,902		(108,508)		(5,417)
Preferred dividends	(22,069)		—		(41,612)		—
Net income available to Arch common shareholders	$	(87,986)	$	44,902	$	(150,120)	$	(5,417)

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, 2021, Arch Capital repurchased 13.1 million shares under the share repurchase program with an aggregate purchase price of $485.3 million. Since the inception of the share repurchase program through June 30, 2021, Arch Capital has repurchased 402.3 million common shares for an aggregate purchase price of $4.54 billion. At June 30, 2021, approximately $431.2 million of share repurchases were available under the program, which may be effected from time to time in open market or privately negotiated transactions through December 31, 2021. 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.

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, 2021, our modeled peak zone catastrophe exposure was a windstorm affecting the Northeastern U.S., with a net probable maximum pre-tax loss of $676 million, followed by windstorms affecting the Florida Tri-County and the Gulf of Mexico regions with net probable maximum pre-tax losses of $669 and $662 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

ARCH CAPITAL  66 2021 SECOND QUARTER FORM 10-Q

hurricanes. As of July 1, 2021, our modeled peak zone earthquake exposure (San Francisco earthquake) represented approximately 75% 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.

Effective July 1, 2021, our insurance operations had in effect a reinsurance program which provided coverage for certain property-catastrophe related losses equal to $279 million in excess of various retentions per occurrence.

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 exposure estimated as of July 1, 2021, our modeled RDS loss was approximately 6% 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 2020 Form 10-K.

OFF-BALANCE SHEET ARRANGEMENTS

Off-balance sheet arrangements are discussed in Management’s Discussion and Analysis of Financial Condition and Results of Operations contained in our 2020 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, 2021. 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. We have not included Watford in the following analyses as we do not guarantee or provide credit support for Watford, and our financial exposure to Watford is limited to our investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from reinsurance transactions.

An analysis of material changes in market risk exposures at June 30, 2021 that affect the quantitative and qualitative disclosures presented in our 2020 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, fixed maturities pledged under securities lending agreements, 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

ARCH CAPITAL  67 2021 SECOND QUARTER FORM 10-Q

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
Jun 30, 2021
Total fair value	$	25.83		$	25.45		$	25.08	$	24.70		$	24.33
Change from base	3.0		%	1.5		%			(1.5)		%	(3.0)		%
Change in unrealized value	$	0.75		$	0.38				$	(0.38)		$	(0.75)
Dec 31, 2020
Total fair value	$	25.82		$	25.44		$	25.07	$	24.69		$	24.31
Change from base	3.0		%	1.5		%			(1.5)		%	(3.0)		%
Change in unrealized value	$	0.75		$	0.38				$	(0.38)		$	(0.75)

In addition, we consider the effect of credit spread movements on the market value of our Fixed Income Securities and the corresponding change in unrealized value. As credit spreads widen, the fair value of our Fixed Income Securities falls, and the converse is also true. In periods where the spreads on our Fixed Income Securities are much higher than their historical average due to short-term market dislocations, a parallel shift in credit spread levels would result in a much more pronounced change in unrealized value.

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

(U.S. dollars in  billions)	Credit Spread Shift in Percentage Points
	-100			-50			—		+50			+100
Jun 30, 2021
Total fair value	$	25.55		$	25.33		$	25.08	$	24.83		$	24.60
Change from base	1.9		%	1.0		%			(1.0)		%	(1.9)		%
Change in unrealized value	$	0.48		$	0.25				$	(0.25)		$	(0.48)
Dec 31, 2020
Total fair value	$	25.54		$	25.32		$	25.07	$	24.82		$	24.59
Change from base	1.9		%	1.0		%			(1.0)		%	(1.9)		%
Change in unrealized value	$	0.48		$	0.25				$	(0.25)		$	(0.48)

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, 2021, our portfolio’s VaR was estimated to be 6.1% compared to an estimated 4.3% at December 31, 2020. 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, 2021 and December 31, 2020, the fair value of our investments in equity securities (excluding securities included in Fixed Income Securities above) totaled $1.3 billion and $1.1 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 $132.9 million and $109.5 million at June 30, 2021 and December 31, 2020, respectively, and would have decreased book value per share by approximately $0.33 and $0.27, respectively. An immediate hypothetical 10% increase in the value of each position would increase the fair value of such investments by approximately $132.9 million and $109.5 million at June 30, 2021 and December 31, 2020, respectively, and would have increased book value per share by approximately $0.33 and $0.27, respectively.

Investment-Related Derivatives. At June 30, 2021, the notional value of all derivative instruments (excluding to-be-announced mortgage backed securities which are included in the fixed income securities analysis above and foreign currency forward contracts which are included in the foreign currency exchange risk analysis below) was $7.5 billion, compared to $8.6 billion at December 31, 2020. If the underlying exposure of each investment-related derivative held at June 30, 2021 depreciated by 100 basis points, it would have resulted in a reduction in net income of approximately $75.0 million, and a decrease in book value per share of approximately $0.19 per share, compared to $85.7 million and $0.21 per share, respectively, on investment-related derivatives held at December 31, 2020. If the underlying exposure of each investment-related derivative held at June 30, 2021 appreciated by 100 basis points, it would have resulted in an increase in net income of approximately $75.0 million, and an increase in book value per share of approximately $0.19 per share, compared to $85.7 million and $0.21 per share, respectively, on

ARCH CAPITAL  68 2021 SECOND QUARTER FORM 10-Q

investment-related derivatives held at December 31, 2020. 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.”

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, 2021		December 31, 2020
Net assets (liabilities), denominated in foreign currencies, excluding shareholders’ equity and derivatives	$	(11,717)	$	(309,968)
Shareholders’ equity denominated in foreign currencies (1)	808,505		695,355
Net foreign currency forward contracts outstanding (2)	456,727		1,108,161
Net exposures denominated in foreign currencies	$	1,253,515	$	1,493,548
Pre-tax impact of a hypothetical 10% appreciation of the U.S. Dollar against foreign currencies:
Shareholders’ equity	$	(125,352)	$	(149,355)
Book value per share	$	(0.32)	$	(0.37)
Pre-tax impact of a hypothetical 10% decline of the U.S. Dollar against foreign currencies:
Shareholders’ equity	$	125,352	$	149,355
Book value per share	$	0.32	$	0.37

(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

We do not believe that inflation has had a material effect on our consolidated results of operations, except insofar as inflation may affect our reserve for losses and loss adjustment expenses and interest rates. The potential exists, after a catastrophe loss or pandemic events like COVID-19, for the development of inflationary pressures in a local economy. The anticipated effects of inflation on us are considered in our catastrophe loss models. The actual effects of inflation on our results cannot be accurately known until claims are ultimately settled.

OTHER FINANCIAL INFORMATION

The consolidated financial statements as of June 30, 2021 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  69 2021 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 of the effectiveness of disclosure controls and procedures pursuant to applicable Exchange Act Rules as of the end of the period covered by this report. 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, 2021 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 despite the fact that most of our employees are working remotely due to the COVID-19. We are continually monitoring and assessing COVID-19 situation on our internal controls to minimize the impact on their design and operating effectiveness.

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, 2021, 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, 2020.

ARCH CAPITAL  70 2021 SECOND QUARTER FORM 10-Q

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

The following table summarizes our purchases of common shares for the 2021 second quarter:

	Issuer Purchases of Equity Securities
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 (2)
4/1/2021-4/30/2021	25,531	$	39.91	—	$	737,262
5/1/2021-5/31/2021	2,739,667	39.99		2,604,338	$	633,077
6/1/2021-6/30/2021	5,205,413	38.81		5,201,117	$	431,213
Total	7,970,611	$	39.22	7,805,455

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

(2)Remaining amount available at June 30, 2021 under Arch Capital’s share repurchase authorization, under which repurchases may be effected from time to time in open market or privately negotiated transactions through December 31, 2021.

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 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 2021 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  71 2021 SECOND QUARTER FORM 10-Q

ITEM 6. EXHIBITS

		Incorporated by Reference
Exhibit Number	Exhibit Description	Form	Original Number	Date Filed	Filed Herewith
1.01	Purchase Agreement dated as of June 2, 2021 among the Company and BofA Securities, Inc., J.P. Morgan Securities LLC, Morgan Stanley & Co. LLC, RBC Capital Markets, LLC and Wells Fargo Securities, LLC, as representatives of the several underwriters named therein.	8-K	1.01	6/3/2021
4.1	Certificate of Designations of 4.550% Non-Cumulative Preferred Shares, Series G	8-K	4.1	6/11/2021
4.2	Form of Share Certificate evidencing 4.550% Non-Cumulative Preferred Share, Series G	8-K	4.2	6/11/2021
4.3	Deposit Agreement, dated June 11, 2021, between Arch Capital Group Ltd., American Stock Transfer & Trust Company, LLC and the holders from time to time of the depositary receipts.	8-K	4.3	6/11/2021
4.4	Form of Depositary Receipt	8-K	4.4	6/11/2021
10.1	Employment Agreement, dated as of May 7, 2021, between ACGL and Christine Todd				X
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

ARCH CAPITAL  72 2021 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 5, 2021	Marc Grandisson
	Chief Executive Officer (Principal Executive Officer)
	/s/ François Morin
Date: August 5, 2021	François Morin
	Executive Vice President, Chief Financial Officer (Principal Financial and Accounting Officer) and Treasurer

ARCH CAPITAL  73 2021 SECOND QUARTER FORM 10-Q

EX-10.1

Exhibit 10.1

EMPLOYMENT AGREEMENT

EMPLOYMENT AGREEMENT (“Agreement”), dated May 7, 2021, between Arch Capital Group Ltd., a Bermuda corporation (the “Company”), and Christine Todd (the “Executive”).

The parties hereto agree as follows:

ARTICLE 1

DEFINITIONS

SECTION 1.01. Definitions. For purposes of this Agreement, the following terms have the meanings set forth below:

“Accounting Firm” has the meaning set forth in Section 12.10.

“Affiliate” means any Person, directly or indirectly, through one or more intermediaries,

Controlling, Controlled by, or under common Control with the Company. For purposes hereof, (a) “Control” means the ownership, directly or indirectly, of (i) in the case of a corporation, Voting Securities (as defined below) representing 50% or more of the total voting power or value of all the then outstanding Voting Securities of such corporation or (ii) in the case of a partnership, limited liability company, association or other business entity (“Business Entity”), 50% or more of the partnership or other similar ownership interest of such Business Entity; and (b) “Voting Security” means any security of a corporation which carries the right to vote generally in the election of directors. For purposes of the definition of “Control,” (x) a Person will be deemed to have a 50% or more ownership interest in a Business Entity if such Person is allocated 50% or more of Business Entity gains or losses or controls the managing director or member or general partner of such Business Entity; and (y) “Controlling” and “Controlled” have meanings correlative thereto.

“Base Salary” has the meaning set forth in Section 4.01.

“Bonus Amount” means the greater of (i) the Executive’s target annual bonus for the year during which Notice of Termination is given, or (ii) the average of the Executive’s actual annual bonus for the three years immediately preceding the year during which Notice of Termination is given (or such lesser number of years in which the Executive was employed by the Company or its Affiliate).

“Cause” means (a) theft or embezzlement by the Executive with respect to the Company or its Affiliates; (b) malfeasance or gross negligence in the performance of the Executive’s duties; (c) the Executive’s conviction of any felony or any crime involving moral turpitude; (d)

willful or prolonged absence from work by the Executive (other than by reason of disability due to physical or mental illness) or failure, neglect or refusal by the Executive to perform her duties and responsibilities without the same being corrected within ten (10) days after being given written notice thereof; (e) continued and habitual use of alcohol by the Executive to an extent which materially impairs the Executive’s performance of her duties; (f) the Executive’s use of illegal drugs; or (g) the material breach by the Executive of any provision of this Agreement.

“Code” means the U.S. Internal Revenue Code of 1986, as amended.

“Confidential Information” means information that is not generally known to the public and that was or is used, developed or obtained by the Company or its Affiliates in connection with their business. It shall not include information (a) required to be disclosed by court or administrative order or called for in a subpoena or discovery request regular on its face, (b) lawfully obtainable from other sources or which is in the public domain through no fault of the Executive; or (c) the disclosure of which is consented to in writing by the Company.

“Date of Termination” has the meaning set forth in Section 5.01.

“Employment Period” has the meaning set forth in Section 2.01.

    “Good Reason” means, without the Executive’s written consent and subject to the timely notice requirement and the Company’s opportunity to cure set forth in Section 5.05 below, (a) the material diminution of any material duties or responsibilities of the Executive; (b) a material reduction in the Executive’s Base Salary; or (c) any material breach by the Company of the provisions contained in this Agreement.

“Intellectual Property” has the meaning set forth in Section 7.01.

“Notice of Termination” has the meaning set forth in Section 5.05.

“Noncompetition Period”has the meaning set forth in Section 9.01.

“Nonsolicitation Period” has the meaning set forth in Section 9.02.

“Person” means an individual, a partnership, a corporation, a limited liability company, an association, a joint stock company, an estate, a trust, a joint venture, an unincorporated organization or a governmental entity or any department, agency or political subdivision thereof.

“Permanent Disability” means those circumstances where the Executive is a disabled person as defined in the Bermuda Human Rights Act 1981 (“HRA 1981”) and is unable to continue to perform the usual customary duties to the required standard (subject to Schedule 1 of the HRA 1981). Any questions as to the existence of a Permanent Disability shall be determined by a qualified, independent physician selected by the Company and approved by

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the Executive (which approval shall not be unreasonably withheld). The determination of any such physician shall be final and conclusive for all purposes of this Agreement.

“Reimbursable Expenses” has the meaning set forth in Section 4.04.

“Start Date” has the meaning set forth in Section 2.01.

ARTICLE 2

EMPLOYMENT

SECTION 2.01. Employment. The Company shall employ the Executive, and the Executive shall accept employment with the Company, for the period beginning on June 7, 2021 (the “Start Date”) and ending on the Date of Termination as provided in Section 5.01 (the “Employment Period”). This Agreement is conditional on the Executive being given approval by the Bermuda Department of Immigration to work and reside in Bermuda. If the Executive fails to satisfy the conditions set forth in this section, she shall forfeit all rights hereunder.

ARTICLE 3

POSITION AND DUTIES

SECTION 3.01. Position and Duties. During the Employment Period, the Executive shall serve as Chief Investment Officer of the Company and shall have such responsibilities, powers and duties as may from time to time be prescribed by the Chief Executive Officer of the Company; provided that such responsibilities, powers and duties are substantially consistent with those customarily assigned to individuals serving in such positions at comparable companies or as may be reasonably required by the conduct of the business of the Company. During the Employment Period the Executive shall devote substantially all of her working time and efforts to the business and affairs of the Company. The Executive shall not directly or indirectly render any services of a business, commercial or professional nature to any other person or for-profit organization not related to the business of the Company or its Affiliates, whether for compensation or otherwise, without prior written consent of the Company.

    SECTION 3.02. Work Permits. The Executive shall cooperate in all reasonable respects with the Company to obtain, maintain and renew a suitable (for the purposes of the Executive’s contemplated employment by the Company) work permit by the Bermuda government authorities and any other permits required by any Bermuda government authority. The Company shall be responsible for permit fees, and all other expenses, including legal expenses, in connection with obtaining and maintaining such work permit.

    SECTION 3.03. Work Location. While employed by the Company hereunder, the Executive shall perform her duties (when not traveling or engaged elsewhere in the performance of her duties) at the offices of the Company in Bermuda. The Executive shall travel

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to such places on the business of the Company in such manner and on such occasions as the Company may from time to time reasonably require.

SECTION 3.04. Relocation. Upon the termination of the Executive’s employment for any reason, other than for Cause, the Company shall reimburse the Executive for all reasonable expenses incurred by her for the cost of relocating all of her household items to Massachusetts and airfare for the Executive and her family to return to Massachusetts, in each case, subject to the Company’s requirements with respect to reporting and documentation of such expenses; provided, however, that any such expenses must be incurred by the Executive not later than the last day of the calendar year following the calendar year in which the Executive’s “separation from service” (within the meaning of Treas. Reg. Section 1.409A-1(h)) with the Company occurs, and any such reimbursement shall be made promptly upon presentation by the Executive to the Company of the required documentation and, in all events, no later than the last day of the second calendar year following the calendar year in which the Executive’s “separation from service” with the Company occurs.

ARTICLE 4

BASE SALARY AND BENEFITS

SECTION 4.01. Base Salary. During the Employment Period, the Executive’s base salary will be $575,000 per annum (the “Base Salary”). The Base Salary will be payable monthly on the 15th day of each month, two weeks in arrears and two weeks in advance. Annually during the Employment Period the Company shall review with the Executive her job performance and compensation, and if deemed appropriate by the Board of Directors of the Company, in its discretion, the Executive’s Base Salary may be increased. Normal hours of employment are 8:30 a.m. to 5:00 p.m., Monday to Friday. The Executive’s salary has been computed to reflect that her regular duties are likely, from time to time, to require more than the normal hours per week and the Executive shall not be entitled to receive any additional remuneration for work outside normal hours, and, for the avoidance of doubt, Section 9(1) of the Bermuda Employment Act 2000 shall not apply to the Executive’s employment.

SECTION 4.02. Bonuses. In addition to the Base Salary, the Executive shall be eligible to participate in an annual bonus plan on terms set forth from time to time by the Board of Directors of the Company. The Executive’s target annual bonus will be 125% of her Base Salary.

SECTION 4.03. Benefits. In addition to the Base Salary, and any bonuses payable to the Executive pursuant to this Agreement, the Executive shall be entitled to the following benefits during the Employment Period:

(a)    such medical, life insurance and disability insurance coverage as is, or may during the Employment Period, be provided generally for other senior executive officers of the Company as set forth from time to time in the applicable plan documents;

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(b)    in addition to the usual public holidays and eight (8) paid days off for sick leave, a maximum of five (5) weeks of paid vacation annually during the term of the Employment Period (Section 11 of the Bermuda Employment Act 2000 shall otherwise not apply to the Executive’s employment hereunder);

(c)    benefits under any plan or arrangement available generally for the senior executive officers of the Company, subject to and consistent with the terms and conditions and overall administration of such plans as set forth from time to time in the applicable plan documents;

(d)payment by the Company of the reasonable cost of preparation of annual tax returns and associated tax planning on a basis no less favorable than such arrangements provided on the date hereof to similarly situated senior executives residing in Bermuda, and the cost paid by the Company under this Section 4.03(d) for one calendar year shall be paid by the Company promptly upon presentation by the Executive to the Company of the required documentation and, in all events, not later than the end of the following calendar year; and

(e)fringe benefits customarily provided from time to time during the Employment Period to similarly situated senior executives residing in Bermuda.

SECTION 4.04. Expenses. The Company shall reimburse the Executive for all reasonable expenses incurred by her in the course of performing her duties under this Agreement which are consistent with the Company’s policies in effect from time to time with respect to travel, entertainment and other business expenses (“Reimbursable Expenses”),subject to the Company’s requirements with respect to reporting and documentation of expenses.

SECTION 4.05. Share-Based Awards. The Executive shall be eligible to participate in the Company’s Long Term Incentive and Share Award Plans (and any similar plan adopted by the Company) under which share-based awards may be granted, as determined by the Board of Directors of the Company in its discretion.

SECTION 4.06. Sign-On Awards. Subject to approval by the Board of Directors of the Company, on the Start Date (the “Grant Date”) you will receive a sign-on bonus consisting of the share-based awards determined in accordance with the following clauses (a) and (b) on the Grant Date: (a) a number of restricted common shares (“Common Shares”) of the Company (“Restricted Shares”) which, together with (b) non-qualified stock options (“Stock Options”) with respect to the same number of Common Shares subject to the Restricted Shares, have an aggregate value (determined as set forth below) equal to $1,000,000. The Restricted Shares and Stock Options will vest in three equal annual installments on the first, second and third anniversaries of the Grant Date, provided that on each such date the Executive is still an employee of the Company as set forth in the award agreements.

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For these purposes, the value of Restricted Shares will be equal to the closing market price of the number of Common Shares subject to the Restricted Shares on the Grant Date, and the value of the Stock Options will be determined by the Company based on a Black-Scholes valuation consistent with the manner in which the Company reflects Stock Options in its consolidated financial statements. The Stock Options will have an exercise price per share equal to the closing market price of the Common Shares on the Grant Date. The other terms and conditions of the Restricted Shares and the Stock Options would be as set forth in the award agreements.

ARTICLE 5

TERM AND TERMINATION

SECTION 5.01. Term. The expected term of this Agreement is for at least three years from the Start Date. Notwithstanding the foregoing, the Employment Period shall in all events end on the Date of Termination, whenever occurring. For purposes of this Agreement, the “Date of Termination” shall mean the first to occur of the following: (a) the six (6) month anniversary of the Company providing Notice of Termination (as defined below) without Cause to the Executive; (b) immediately upon the Company providing Notice of Termination for Cause to the Executive; (c) the six (6) month anniversary of the Executive providing Notice of Termination specifying her resignation for Good Reason to the Company; (d) the six (6) month anniversary of the Executive providing Notice of Termination by the Executive without Good Reason to the Company; (e) the fifth (5th) day following the Company providing Notice of Termination to the Executive as a result of the Executive’s Permanent Disability; and (f) the date of Executive’s death. In the event that there are circumstances which would give rise to a termination by the Company for Cause, the Company may, in its sole and exclusive discretion, treat such termination as a termination without Cause. Upon termination of the Executive’s employment with the Company for any reason, the Executive shall resign from all positions and in all capacities with the Company and its Affiliates or from any other company or other Person with which the Executive is serving at the Company’s request.

SECTION 5.02. Resignation by the Executive Without Good Reason. If the Employment Period shall be terminated as a result of the Executive’s resignation or leaving of her employment, other than for Good Reason, the Executive shall continue to: (a) receive Base Salary and benefits set forth in Section 4.03 through the Date of Termination, except that any amount payable after the Executive’s “separation from service” (within the meaning of Treas. Reg. Section 1.409A-1(h)) with the Company will be subject to Section 12.09 below; (b) the Company will make a cash lump sum payment to the Executive equal to one half of the sum of (I) the Bonus Amount, and (II) a pro-rated portion of the Bonus Amount based on the number of days elapsed in the calendar year through the date Notice of Termination is given, which payment shall be made on the date that is sixty (60) days following the Date of Termination, and (c) receive reimbursement of all Reimbursable Expenses incurred by the Executive prior to the Date of Termination. The Executive’s entitlements under all other benefit plans and programs of the Company shall be as determined thereunder.

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SECTION 5.03. Termination for Good Reason or Without Cause. If the Employment Period shall be terminated by the Executive for Good Reason or by the Company without Cause, the Executive shall continue to: (a) receive Base Salary through the six (6) month anniversary of the Date of Termination, such amount to be paid in accordance with the regular payroll practices of the Company (except that any amount otherwise payable after the Date of Termination and prior to the sixtieth (60th) day following the Date of Termination shall instead be paid on such sixtieth (60th) day), and except that any amount payable after the Executive’s “separation from service” (within the meaning of Treas. Reg. Section 1.409A-1(h)) with the Company will be subject to Section 12.09 below; (b) receive an amount equal to the sum of (i) the Executive’s target annual bonus plus (ii) a pro-rated portion of the Executive’s target annual bonus based on the number of days elapsed in the calendar year through the date Notice of Termination is given, one half of which amount shall be paid in cash in a single lump sum on the date that is sixty (60) days following the Date of Termination and the remaining half of which shall be paid in accordance with the regular payroll practices of the Company (except that any amount otherwise payable after the Date of Termination and prior to the sixtieth (60th) day following the Date of Termination shall instead be paid on such sixtieth (60th) day); (c) receive benefits set forth in Section 4.03 above through the Date of Termination, except that any amount payable after the Executive’s “separation from service” (within the meaning of Treas. Reg. Section 1.409A-1(h)) with the Company will be subject to Section 12.09 below; (d) receive her medical insurance coverage benefits from the Company’s plan in effect from time to time (provided the Executive continues to pay the portion of the premiums for such coverage that are charged to similarly situated active employees) for a period equal to the lesser of (i) six (6) months after the Date of Termination, and (ii) until the Executive is provided by another employer with benefits substantially comparable to the benefits provided by such plan; and (e) receive reimbursement for all Reimbursable Expenses incurred by the Executive prior to the Date of Termination. The Executive’s entitlements under all other benefit plans and programs of the Company shall be as determined thereunder. Notwithstanding the foregoing, the Executive shall be entitled to the amounts described above (other than Base Salary and benefits as set forth in Section 4.03 through the Date of Termination) only if (i) the Executive has entered into an irrevocable (except to the extent required by law, and to the extent required by law to be revocable, has not revoked) general release of claims, which, subject to Section 5.07 below, is reasonably satisfactory to the Company (“Release”), on or before the date that is fifty (50) days following the Date of Termination (but not prior to the Date of Termination), and (ii) the Executive has complied with, and continues to comply with, the provisions of Sections 6.01, 7.01, 8.01, 9.01, 9.02 or 11.01 of this Agreement.

SECTION 5.04. Termination for Other Reasons. If the Employment Period shall be terminated by the Company with Cause, as a result of the Executive’s Permanent Disability or upon the Executive’s death, the Executive (or her beneficiaries or estate, in the case of death) shall continue to (a) receive Base Salary and benefits set forth in Section 4.03 above through the Date of Termination, except that any amount payable after the Executive’s “separation from service” (within the meaning of Treas. Reg. Section 1.409A-1(h)) with the Company will be subject to Section 12.09 below; and (b) in the case of termination due to the Executive’s

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Permanent Disability or death, receive her medical insurance coverage benefits from the Company’s plan in effect at the time of such termination for a period equal to the lesser of (i) twelve (12) months after the Date of Termination, and (ii) until the Executive is provided by another employer with benefits substantially comparable to the benefits provided by such plan; and (c) receive reimbursement for all Reimbursable Expenses incurred by the Executive prior to the Date of Termination. The Executive’s entitlements under all other benefit plans and programs of the Company shall be as determined thereunder.

    SECTION 5.05. Notice of Termination and Opportunity to Cure. Any termination by the Company for Permanent Disability or Cause or without Cause or by the Executive for Good Reason or without Good Reason shall be communicated by written Notice of Termination to the other party hereto. For purposes of this Agreement, a “Notice of Termination” shall mean a notice which shall indicate the date the termination is to take effect (consistent with the terms of this Agreement), the specific termination provision in this Agreement relied upon and, for a termination for Permanent Disability or for Cause or for a resignation for Good Reason, shall set forth in reasonable detail the facts and circumstances claimed to provide a basis for termination of employment under the provision indicated. It shall be a condition precedent to the Executive’s right to terminate employment for Good Reason that (i) the Executive shall first have given the Company written notice that an event or condition constituting Good Reason has occurred within ninety (90) days after such occurrence, and any failure to give such written notice within such period will result in a waiver by the Executive of her right to terminate for Good Reason as a result of such event or condition, and (ii) a period of thirty (30) days from and after the giving of such written notice shall have elapsed without the Company having effectively cured or remedied such occurrence during such 30-day period, unless such occurrence cannot be cured or remedied within thirty (30) days, in which case the period for remedy or cure shall be extended for a reasonable time (not to exceed an additional fifteen (15) days) provided that the Company has made and continues to make a diligent effort to effect such remedy or cure.

    SECTION 5.06. Garden Leave. Following any Notice of Termination, whether by the Company or the Executive and until the end of the Employment Period, the Company may direct, in its sole and exclusive discretion, that the Executive perform no duties and exercise no powers or authorities in connection with her employment, resign from any office with the Company and its Affiliates and not attend any premises of any of the Company and its Affiliates; provided, however, that, following any such direction, the Executive will continue to be required to comply with her other obligations under this Agreement and will continue to owe a duty of good faith and fidelity to the Company as an employee (“Garden Leave”). Notwithstanding the above, the Company may at its discretion require the Executive to perform duties at any time during the Garden Leave, which duties may be withdrawn at any time at the Company’s discretion, and, during the Garden Leave, the Executive shall: (a) remain an employee of the Company and be bound by the express and implied terms of this Agreement; (b) not, without the prior written consent of the Company, attend her place of work or any other premises of any of the Company and its Affiliates or access the information technology systems of the Company and its Affiliates; (c) not, without the prior written consent of the

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Company, contact or deal with (or attempt to contact or deal with) any officer, employee, consultant, client, customer, investor, supplier, agent, distributor, shareholder, adviser or other business contact of any of the Company and its Affiliates; (d) promptly disclose in writing to the Company any attempt at contact with the Executive made by any such person or entity with whom the Executive has been required to have no contact pursuant to this Section 5.06; (e) be ready and available to perform such duties as the Company may require, ensuring that the Company knows where and how she can be contacted and complying with any written requests to contact a specified employee of the Company at specified intervals; and (f) be deemed to take any accrued holiday during the Garden Leave period.

SECTION 5.07. Release. In consideration of the mutual promises herein and the payments detailed in this Article 5, the Executive, on behalf of herself and her heirs and assigns, in a form reasonably satisfactory to the Company, shall, with respect to any termination of employment under Section 5.03, execute a Release which irrevocably and unconditionally releases and forever discharges, individually and collectively, the Company and its Affiliates, and each of their respective officers, directors, employees, shareholders, representatives, parent companies, subsidiaries, predecessors, successors, assigns, attorneys and all persons acting by, through or in concert with them, of and from any and all charges, claims, complaints, demands, liabilities or causes of action, known or unknown, that the Executive may have at the effective date of the Release or has ever had against any such Person. Notwithstanding any other provision hereof, the Executive shall not be required by any general release to release claims that the Executive may have against the Company that arise after the effective date of the Release, any rights the Executive may have to enforce Section 5.03 of this Agreement, or any rights of the Executive to be indemnified under the organizational documents of the Company and its Affiliates or under applicable law or pursuant to the Company’s directors’ and officers’ liability insurance policies.

ARTICLE 6

CONFIDENTIAL INFORMATION

SECTION 6.01. Nondisclosure and Nonuse of Confidential Information. The Executive will not disclose or use at any time during or after the Employment Period any Confidential Information of which the Executive is or becomes aware, whether or not such Confidential Information is developed by her, except to the extent that such disclosure or use is directly related to and required by the Executive’s performance of duties assigned to the Executive pursuant to this Agreement. Under all circumstances and at all times, the Executive will take all appropriate steps to safeguard Confidential Information in her possession and to protect it against disclosure, misuse, espionage, loss and theft.

SECTION 6.02. Defend Trade Secrets Act. Pursuant to 18 U.S.C. § 1833(b), the Executive understands that the Executive will not be held criminally or civilly liable under any Federal or State trade secret law for the disclosure of a trade secret of the Company that (i) is made (x) in confidence to a Federal, State, or local government official, either directly or indirectly, or to

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the Executive’s attorney and (y) solely for the purpose of reporting or investigating a suspected violation of law; or (ii) is made in a complaint or other document that is filed under seal in a lawsuit or other proceeding. The Executive understands that if the Executive files a lawsuit for retaliation by the Company for reporting a suspected violation of law, the Executive may disclose the trade secret to the Executive’s attorney and use the trade secret information in the court proceeding if the Executive (I) files any document containing the trade secret under seal, and (II) does not disclose the trade secret, except pursuant to court order. Nothing in this Agreement is intended to conflict with 18 U.S.C. § 1833(b) or create liability for disclosures of trade secrets that are expressly allowed by such section. Further, nothing in this Agreement or any other agreement or arrangement with the Company or any of its Affiliates shall prohibit or restrict the Executive from making any disclosure of information or documents to any governmental agency or legislative body, any self-regulatory organization, the Legal Department of the Company, and/or pursuant to the whistleblower provisions of the Dodd-Frank Act or Sarbanes-Oxley Act.

ARTICLE 7

INTELLECTUAL PROPERTY

SECTION 7.01. Ownership of Intellectual Property. In the event that the Executive as part of her activities on behalf of the Company generates, authors or contributes to any invention, design, new development, device, product, method of process (whether or not patentable or reduced to practice or comprising Confidential Information), any copyrightable work (whether or not comprising Confidential Information) or any other form of Confidential Information relating directly or indirectly to the business of the Company as now or hereinafter conducted (collectively, “Intellectual Property”), the Executive acknowledges that such Intellectual Property is the sole and exclusive property of the Company and hereby assigns all right title and interest in and to such Intellectual Property to the Company as allowable under applicable law. Any copyrightable work prepared in whole or in part by the Executive during the Employment Period will be deemed “a work made for hire” under Section 201(b) of the United States Copyright Act of 1976, as amended, and the Company will own all of the rights comprised in the copyright therein. The Executive will promptly and fully disclose all Intellectual Property and will cooperate with the Company to protect the Company’s interests in and rights to such Intellectual Property (including providing reasonable assistance in securing patent protection and copyright registrations and executing all documents as reasonably requested by the Company, whether such requests occur prior to or after termination of Executive’s employment hereunder).

ARTICLE 8

DELIVERY OF MATERIALS UPON TERMINATION OF EMPLOYMENT

SECTION 8.01. Delivery of Materials upon Termination of Employment. As requested by the Company, from time to time and upon the termination of the Executive’s employment with

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the Company for any reason, the Executive will promptly deliver to the Company all property of the Company in the Executive’s possession or within her control, including, without limitation, all copies and embodiments, in whatever form or medium, of all Confidential Information or Intellectual Property in the Executive’s possession or within her control (including written records, notes, photographs, manuals, notebooks, documentation, program listings, flow charts, magnetic media, disks, diskettes, tapes and all other materials containing any Confidential Information or Intellectual Property), irrespective of the location or form of such property and, if requested by the Company, will provide the Company with written confirmation that all such property have been delivered to the Company.

ARTICLE 9

NONCOMPETITION AND NONSOLICITATION

SECTION 9.01. Noncompetition.The Executive acknowledges that during her employment with the Company, she will become familiar with trade secrets and other Confidential Information concerning the Company and its Affiliates and their respective predecessors, and that her services will be of special, unique and extraordinary value to the Company. In addition, the Executive hereby agrees that at any time during the Employment Period, and for a period ending one (1) year after the termination of the Executive's employment (the “Noncompetition Period”), she will not directly or indirectly own, manage, control, participate in, consult with, render services for or in any manner engage in any Restricted Business;

provided, however, that if the Executive’s termination of employment occurs as a result of the Executive’s resignation or leaving of her employment other than for Good Reason, except as provided in clause (Y) below, the Noncompetition Period shall continue beyond the Date of Termination only if (i) the Company pays the Executive, for each day during which the Noncompetition Period so continues (taking into account Section 9.04 below), an amount equal to 1/365th of the sum of (A) the Executive’s annual Base Salary, plus (B) the Executive’s Bonus Amount, and (C) a pro-rated portion of the Executive’s Bonus Amount based on the number of days elapsed in the calendar year through the date Notice of Termination is given, such amount to be paid in accordance with the regular payroll practices of the Company (except that any amount otherwise payable after the Date of Termination and prior to the sixtieth (60th) day following the Date of Termination shall instead be paid on such sixtieth (60th) day); and (ii) the Executive shall continue to receive her medical insurance coverage benefits from the Company’s plan in effect from time to time (provided the Executive continues to pay the portion of the premiums for such coverage that are charged to similarly situated active employees) for a period equal to the lesser of (x) the end of the Noncompetition Period, and (y) until the Executive is provided by another employer with benefits substantially comparable (with no pre-existing condition limitations) to the benefits provided by such plan; and provided further, however, that:

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(X) the Company may elect, in its sole discretion, by written notice to the Executive given not more than ten (10) business days after the date Notice of Termination is given by the Executive without Good Reason, to not continue the Noncompetition Period beyond the Date of Termination or to reduce the Noncompetition Period under such circumstances so that it ends on the date set forth in such written notice (which shall not be later than twelve (12) months after the Date of Termination), in which case the Company’s obligation to make payments and provide benefits under this Section 9.01 shall end at the end of the Noncompetition Period, and

(Y) the Company’s requirement to make payments under this Section 9.01 as a condition to continuation of the Noncompetition Period shall apply only if the Executive has entered into a general release of claims reasonably satisfactory to the Company on or before the date that is fifty (50) days following the Date of Termination (but not prior to the Date of Termination) and does not revoke such release prior to the end of any applicable revocation period (it being understood that such general release will not require the Executive to release her rights under this Section 9.01 and will not contain any employment restrictions or non-solicitation obligations other than those set forth in this Agreement) and the Executive has complied with, and continues to comply with, the provisions of Sections 6.01, 7.01, 8.01, 9.01, 9.02 or 10.01 hereof.

“Restricted Business” means any business that is materially competitive with the businesses that (I) are at the time in question being conducted by the Company or its Affiliates with which the Executive was involved to a material extent in the twelve (12) months prior to termination of the Executive’s employment, or (II) were, during the Executive’s employment, either being conducted by, or being actively developed by, the Company or its Affiliates with which the Executive was involved to a material extent in the twelve (12) months prior to termination of Executive’s employment, in either case within any geographical area in which the Company or its Affiliates engage or plan to engage in such businesses. It shall not be considered a violation of this Section 9.01 for the Executive to be a passive owner of not more than 2% of the outstanding stock of any class of a corporation which is publicly traded, so long as the Executive has no active participation in the business of such corporation.

SECTION 9.02. Nonsolicitation. The Executive acknowledges that during her employment with the Company, she will become familiar with trade secrets and other Confidential Information concerning the Company, its Affiliates and their respective predecessors, and that her services will be of special, unique and extraordinary value to the Company. The Executive hereby agrees that (a) during the Employment Period and for a period of one (1) year after the date of termination of employment (the “Nonsolicitation Period”) the Executive will not, directly or indirectly, induce or attempt to induce any Relevant Employee of the Company or its Affiliates to leave the employ of the Company or its Affiliates, or in any way interfere with the relationship between the Company or its Affiliates and any Relevant Employee thereof or

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otherwise employ or receive the services of any individual who was a Relevant Employee of the Company or its Affiliates at the Date of Termination or within the twelve-month period prior thereto, and (b) during the Nonsolicitation Period, the Executive will not induce or attempt to induce any Restricted Customer to cease doing business with the Company or its Affiliates. For purposes of this Agreement, a “Relevant Employee” shall mean a director, officer, underwriter or manager of the Company or its Affiliates, in each case with whom the Executive had material dealings at any time during the period of twelve (12) months prior to the Date of Termination. A “Restricted Customer” shall mean any firm, company or Person who was a customer, investor, supplier, client, insured, reinsured, reinsurer, broker, agent, licensee or other business relation of the Company or its Affiliates and with whom Executive had material dealings during the twelve (12) months prior to termination of the Executive’s employment.

SECTION 9.03. Enforcement. If, at the enforcement of Sections 9.01 or 9.02, a court holds that the duration or scope stated herein are unreasonable under circumstances then existing, the parties agree that the maximum duration and scope reasonable under such circumstances will be substituted for the stated duration or scope and that the court will be permitted to revise the restrictions contained in this Article 9 to cover the maximum duration and scope permitted by law.

SECTION 9.04. Coordination with Garden Leave. The lengths of the Noncompetition Period and the Nonsolicitation Period shall be reduced by any period that the Executive is required to remain away from the office during her notice period or not undertake her normal duties pursuant to Section 5.06 above.

SECTION 9.05. Notice of Covenants. If the Executive receives an offer to directly or indirectly own, manage, control, participate in, consult with, render services for or in any manner engage in any Restricted Business during the Employment Period or before the expiry of the Noncompetition Period or the Nonsolicitation Period, she shall provide the Person making the offer a copy of this Article 9 prior to acceptance of such offer.

ARTICLE 10

EQUITABLE RELIEF

SECTION 10.01. Injunctive or Other Equitable Relief. The Executive acknowledges that (a) the covenants contained herein are reasonable, (b) the Executive’s services are unique, and (c) a breach or threatened breach by her of any of her covenants and agreements with the Company and its Affiliates contained in Sections 6.01, 7.01, 8.01, 9.01 or 9.02 could cause irreparable harm to the Company or its Affiliates for which they would have no adequate remedy at law. Accordingly, and in addition to any remedies which the Company and its Affiliates may have at law, in the event of an actual or threatened breach by the Executive of her covenants and agreements contained in Sections 6.01, 7.01, 8.01, 9.01 or 9.02, the Company and its Affiliates shall have the absolute right, without the need to post a bond or any other type of security, to commence a lawsuit or other proceeding in any court of competent

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jurisdiction (the “Selected Court”) seeking injunctive or other equitable relief (an “Injunction Proceeding”). In furtherance thereof, the Executive expressly and irrevocably agrees that the Selected Court may exercise personal jurisdiction over her in connection with any Injunction Proceeding and further agrees not to assert that any court other than the Selected Court is a more suitable forum for an Injunction Proceeding.

ARTICLE 11

EXECUTIVE REPRESENTATIONS

SECTION 11.01. Executive Representations. The Executive hereby represents and warrants to the Company that (a) the execution, delivery and performance of this Agreement by the Executive does not and will not conflict with, breach, violate or cause a default under any contract, agreement, instrument, order, judgment or decree to which the Executive is a party or by which she is bound, (b) the Executive is not a party to or bound by any employment agreement, noncompetition agreement or confidentiality agreement with any other Person that affects her right or ability to perform the duties contemplated by this Agreement, (c) the Executive did not, while working for any employer other than the Company: solicit her fellow employees to leave their employment and work with her at the Company; or solicit clients, or potential clients, of such employer, for the Company; or take any type of information that is proprietary information of such employer, and (d) upon the execution and delivery of this Agreement by the Company, this Agreement will be the valid and binding obligation of the Executive, enforceable in accordance with its terms.

SECTION 11.02. Company Representations. The Company hereby represents and

warrants to the Executive that (a) all acts required to be taken to authorize, deliver and perform this Agreement and the obligations of the Company provided for hereunder have been duly taken; and (b) upon the execution and delivery of this Agreement by the Company, this Agreement will be valid and binding obligation of the Company, enforceable in accordance with its terms.

ARTICLE 12

MISCELLANEOUS

SECTION 12.01. Remedies. The Company will have all rights and remedies set forth in this Agreement, all rights and remedies which the Company has been granted at any time under any other agreement or contract and all of the rights which the Company has under any law. The Company will be entitled to enforce such rights specifically, without posting a bond or other security, to recover damages by reason of any breach of any provision of this Agreement and to exercise all other rights granted by law. There are currently no disciplinary or grievance procedures in place, there is no collective agreement in place, and there is no probationary period.

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SECTION 12.02. Consent to Amendments. The provisions of this Agreement may be amended or waived only by a written agreement executed and delivered by the Company and the Executive. No other course of dealing between the parties to this Agreement or any delay in exercising any rights hereunder will operate as a waiver of any rights of any such parties.

SECTION 12.03. Successors and Assigns. All covenants and agreements contained in this Agreement by or on behalf of any of the parties hereto will bind and inure to the benefit of the respective successors and assigns of the parties hereto whether so expressed or not, provided that the Executive may not assign her rights or delegate her obligations under this Agreement without the written consent of the Company.

SECTION 12.04. Severability. Whenever possible, each provision of this Agreement will be interpreted in such manner as to be effective and valid under applicable law, but if any provision of this Agreement is held to be prohibited by or invalid under applicable law, such provision will be ineffective only to the extent of such prohibition or invalidity, without invalidating the remainder of this Agreement.

SECTION 12.05. Counterparts. This Agreement may be executed simultaneously in two counterparts, any one of which need not contain the signatures of more than one party, but all of which counterparts taken together will constitute one and the same agreement.

SECTION 12.06. Descriptive Headings. The descriptive headings of this Agreement are inserted for convenience only and do not constitute a part of this Agreement.

SECTION 12.07. Notices. All notices, demands or other communications to be given or delivered under or by reason of the provisions of this Agreement will be in writing and shall be delivered personally by hand, by electronic transmission (with a copy following by hand or by overnight courier), by registered or certified mail, postage prepaid, return receipt requested, or by overnight courier service (charges prepaid). Communications delivered personally by hand shall be deemed received on the date when delivered personally to the recipient; communications sent by electronic means shall be deemed received one (1) business day after the sending thereof; communications sent by registered or certified mail shall be deemed received four (4) business days after the sending thereof; and communications delivered by overnight courier shall be deemed received one (1) business day after the date when sent to the recipient. Such notices, demands and other communications will be sent to the Executive and to the Company at the addresses set forth below.

If to the Executive:    To the last address delivered to the Company by the Executive in the manner set forth herein.

    If to the Company:    Arch Capital Group Ltd.
        Waterloo House

    100 Pitts Bay Road

    Hamilton HM 12, Bermuda

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    Attention: Secretary

    Tel: (441) 278-9250

    Fax: (441) 278-9255

or to such other address or to the attention of such other person as the recipient party has specified by prior written notice to the sending party.

SECTION 12.08. Withholding. The Company may withhold from any amounts payable under this Agreement such federal, state, local or foreign taxes as shall be required to be withheld pursuant to any applicable law or regulation.

SECTION 12.09. 409A and 457A. This Section 12.09 shall apply to the Executive only if, and to the extent, she is subject to Section 409A or Section 457A of the Code. It is intended that this Agreement will comply with Sections 409A and 457A of the Code (and any regulations and guidelines issued thereunder), to the extent the Agreement is subject thereto, and the Agreement shall be interpreted on a basis consistent with such intent. If an amendment of the Agreement is necessary in order for it to comply with Section 409A or Section 457A, the parties hereto will negotiate in good faith to amend the Agreement in a manner that preserves the original intent of the parties to the extent reasonably possible. No action or failure to act, pursuant to this Section 12.09 shall subject the Company to any claim, liability, or expense, and the Company shall not have any obligation to indemnify or otherwise protect the Executive from the obligation to pay any taxes, interest or penalties pursuant to Section 409A or Section 457A of the Code.

Notwithstanding any provision to the contrary in this Agreement, if the Executive is deemed on the date of her “separation from service” (within the meaning of Treasury Regulation Section 1.409A-1(h)) to be a “specified employee” within the meaning of that term under Section 409A(a)(2)(B) of the Code, then with regard to any payment that is required to be delayed pursuant to Section 409A(a)(2)(B) of the Code (after taking into account the applicable provisions of Treasury Regulation Section 1.409A-1(b)(9)(iii)), the portion, if any, of such payment so required to be delayed shall not be made prior to the earlier of (i) the expiration of the six (6)-month period measured from the date of her “separation from service” or (ii) the date of her death (the “Delay Period”). Upon the expiration of the Delay Period, all payments and benefits delayed pursuant to this Section (whether they would have otherwise been payable in a single sum or in installments in the absence of such delay) shall be paid or reimbursed to the Executive in a lump sum, and any remaining payments due under this Agreement shall be paid in accordance with the normal payment dates specified for them herein. Whenever payments under this Agreement are to be made in installments, each such installment shall be deemed to be a separate payment for purposes of Section 409A of the Code. Notwithstanding any provision of this Agreement to the contrary, for purposes of any provision of this Agreement providing for the payment of any amounts or benefits upon or following a termination of employment that are considered deferred compensation under Section 409A, references to the Executive’s “termination of employment” (and corollary terms) with the Company shall be construed to refer to the Executive’s “separation from

16 | Page

service” (within the meaning of Treas. Reg. Section 1.409A-1(h)) with the Company. In no case will compliance with this Section by the Company constitute a breach of the Company’s obligations under this Agreement.

With respect to any reimbursement or in-kind benefit arrangements of the Company and its subsidiaries provided for herein that constitute deferred compensation for purposes of Section 409A, except as otherwise permitted by Section 409A, the following conditions shall be applicable: (i) the amount eligible for reimbursement, or in-kind benefits provided, under any such arrangement in one calendar year may not affect the amount eligible for reimbursement, or in-kind benefits to be provided, under such arrangement in any other calendar year (except that the health and dental plans may impose a limit on the amount that may be reimbursed or paid), (ii) any reimbursement must be made on or before the last day of the calendar year following the calendar year in which the expense was incurred, and (iii) the right to reimbursement or in-kind benefits is not subject to liquidation or exchange for another benefit.

    SECTION 12.10. Section 4999 of the Code. Anything in this Agreement or the Company’s Incentive Compensation Plan to the contrary notwithstanding, in the event it shall bedetermined that any payment, award, benefit or distribution (including, without limitation, the acceleration of any payment, award, distribution or benefit), by the Company or any of its affiliates to or for the benefit of the Executive (whether pursuant to the terms of this Agreement or otherwise) (a “Payment”) would be subject to the excise tax imposed by Section 4999 of the Code or any corresponding provisions of state or local tax law (the “Excise Tax”), then such Payments shall either (a) be delivered in full, or (b) subject to, and in a manner consistent with the requirements of Section 409A of the Code, be reduced to the minimum extent necessary to ensure that no portion thereof will be subject to the Excise Tax, whichever of the foregoing amounts, taking into account the applicable federal, state or local income and employment taxes and the Excise Tax, results in receipt by the Executive, on an after-tax basis, of the greatest amount of payments and benefits, notwithstanding that all or some portion of such payments and benefits may be subject to the Excise Tax. In the event that any Payments are to be reduced pursuant to this Section 12.10, then the reduction shall be applied as follows: (i) first, on a pro rata basis to the Executive’s cash severance payments under Section 5.03 above, and (ii) second, on a pro rata basis to Executive’s equity incentive awards. All determinations required to be made under this Article 12 shall be made by a nationally recognized accounting or consulting firm (other than the regular outside accounting firm retained by the Company) selected by the Company and agreed to by the Executive, which agreement shall not be unreasonably withheld (the “Accounting Firm”), which Accounting Firm shall provide detailed supporting calculations both to the Company and the Executive within 15 business days after the receipt of notice from the Company that the Executive has received a Payment, or such earlier time as is requested by the Company. Any determination by the Accounting Firm meeting the requirements of this Section 12.10 shall be binding upon the Company and the Executive. The fees and disbursements of the Accounting Firm shall be paid by the Company. If required, the Company shall enter into an engagement letter with the Accounting Firm containing reasonable and customary terms and provisions.

17 | Page

SECTION 12.11. No Third Party Beneficiary. This Agreement will not confer any rights or remedies upon any person other than the Company, the Executive and their respective heirs, executors, successors and assigns.

SECTION 12.12. Entire Agreement. This Agreement (including the documents referred to herein) constitutes the entire agreement among the parties and supersedes any prior understandings, agreements or representations by or among the parties, written or oral, that may have related in any way to the subject matter hereof. This Agreement shall serve as a written statement of employment for purposes of Section 6 of the Bermuda Employment Act 2000.

SECTION 12.13. Construction. The language used in this Agreement will be deemed to be the language chosen by the parties to express their mutual intent, and no rule of strict construction will be applied against any party. Any reference to any federal, state, local or foreign statute or law will be deemed also to refer to all rules and regulations promulgated thereunder, unless the context requires otherwise. The use of the word “including” in this Agreement means including without limitation and is intended by the parties to be by way of example rather than limitation.

SECTION 12.14. Survival. Sections 3.04, 5.03, 5.04, 6.01, 6.02, 7.01, 8.01 and Articles 9, 10, 11 and 12 will survive and continue in full force in accordance with their terms notwithstanding any termination of the Employment Period.

SECTION 12.15. GOVERNING LAW. ALL QUESTIONS CONCERNING THE CONSTRUCTION, VALIDITY AND INTERPRETATION OF THIS AGREEMENT WILL BE GOVERNED BY THE LAW OF BERMUDA, WITHOUT REGARD TO PRINCIPLES OF CONFLICT OF LAWS, SAVE THAT WHERE PROVISIONS OF FOREIGN LAW APPLY IN THIS AGREEMENT, THEY WILL BE INTERPRETED AND CONSTRUED IN ACCORDANCE WITH SUCH FOREIGN LAW.

    SECTION 12.16. Arbitration. Save for where the Company chooses to exercise its rights as described in Section 10.01, any dispute or difference arising out of or relating in any way whatsoever to this Agreement or the subject matter hereof shall be referred to and finally determined by arbitration (the “Arbitration”). The seat, or legal place, of the Arbitration shall be Bermuda. The Arbitration shall be conducted before a sole arbitrator appointed by agreement between the parties or, failing such agreement, by the Appointments’ Committee of the Chartered Institute of Arbitrators Bermuda Branch (the “Arbitrator”). Unless the parties agree otherwise, the Arbitration shall be conducted in accordance with the UNCITRAL rules in force at the time the Arbitration is commenced. The courts of Bermuda (as the supervisory courts of the Arbitration) shall have exclusive jurisdiction to hear and determine any application for relief in aid of the Arbitration (including any application for interim or conservatory measures prior to the appointment of the Arbitrator), except that either party may bring proceedings before any court or other judicial authority of competent jurisdiction for the purposes of enforcing any partial or final award rendered by the Arbitrator hereunder. Each party agrees that it shall maintain confidentiality in respect to the Arbitration (including any

18 | Page

award or other decision rendered in such Arbitration), except as necessary in connection with a proceeding to enforce the Arbitrator's award or as otherwise required by law. The parties shall bear their respective costs (including attorney’s fees) and shall split the fee of the Arbitrator (50% paid by the Company and 50% by the Executive).

19 | Page

IN WITNESS WHEREOF, the parties hereto have executed this Agreement on the date in the year first above written.

Arch Capital Group Ltd.

By: /s/ Marc Grandisson    

Name: Marc Grandisson    

Title: Chief Executive Officer    

/s/ Christine Todd    

                        Christine Todd

20 | Page

EX-15

Exhibit 15

August 5, 2021

Securities and Exchange Commission

100 F Street, N.E.

Washington, DC 20549

Commissioners:

We are aware that our report dated August 5, 2021, 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. 333-224783, 333-211193, 333-142835, 333-181308 and 333- 203993) of Arch Capital Group Ltd.

Very truly yours,

/s/ PricewaterhouseCoopers LLP

New York, NY

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 5, 2021
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 5, 2021
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, 2021 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 5, 2021
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, 2021 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 5, 2021
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, 2021	Jul. 30, 2021
Document and Entity Information [Abstract]
Document Type	10-Q
Document Quarterly Report	true
Document Period End Date	Jun. 30, 2021
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		396,039,032
Document Fiscal Period Focus	Q2
Document Fiscal Year Focus	2021
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
Depositary Series E Preferred Stock
Entity Listings [Line Items]
Title of 12(b) Security	Depositary shares, each representing a 1/1000th interest in a 5.25% Series E preferred share
Trading Symbol	ACGLP
Security Exchange Name	NASDAQ
Depositary Series F Preferred Stock
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
Depositary Series G Preferred Stock
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, 2021	Dec. 31, 2020
Investments:
Fixed maturities available for sale, at fair value (amortized cost: $17,764,783 and $18,143,305; net of allowance for credit losses: $2,124 and $2,397 )	$ 18,073,779	$ 18,717,825
Short-term investments available for sale, at fair value (amortized cost: $2,248,615 and $1,924,292; net of allowance for credit losses: $0 and $0)	2,248,613	1,924,922
Collateral received under securities lending, at fair value (amortized cost: $172,109 and $301,089)	172,116	301,096
Equity securities, at fair value	1,693,552	1,444,830
Other investments (portion measured at fair value: $4,071,497 and $3,824,796)	4,571,497	4,324,796
Investments accounted for using the equity method	2,539,124	2,047,889
Total investments	29,298,681	28,761,358
Cash	1,234,059	906,448
Accrued investment income	96,546	103,299
Securities pledged under securities lending, at fair value (amortized cost: $167,871 and $294,493)	168,548	294,912
Investment in operating affiliates	731,810	129,291
Premiums receivable (net of allowance for credit losses: $35,979 and $37,781)	2,866,578	2,064,586
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $11,029 and $11,636)	4,314,515	4,500,802
Contractholder receivables (net of allowance for credit losses: $4,471 and $8,638)	1,882,948	1,986,924
Ceded unearned premiums	1,541,093	1,234,075
Deferred acquisition costs	1,013,657	790,708
Receivable for securities sold	309,234	92,743
Goodwill and intangible assets	667,153	692,863
Other assets	2,357,064	1,724,288
Total assets	46,481,886	43,282,297
Liabilities
Reserve for losses and loss adjustment expenses	17,196,648	16,513,929
Unearned premiums	6,011,369	4,838,965
Reinsurance balances payable	1,079,106	683,263
Contractholder payables	1,887,418	1,995,562
Collateral held for insured obligations	235,618	215,581
Senior notes	2,861,728	2,861,113
Revolving credit agreement borrowings	155,687	155,687
Securities lending payable	172,109	301,089
Payable for securities purchased	586,881	218,779
Other liabilities	1,332,843	1,510,888
Total liabilities	31,519,407	29,294,856
Commitments and Contingencies
Redeemable noncontrolling interests	57,533	58,548
Shareholders' Equity
Non-cumulative preferred shares	1,280,000	780,000
Common shares ($0.0011 par, shares issued: 582,654,893 and 579,000,841)	647	643
Additional paid-in capital	2,028,919	1,977,794
Retained earnings	13,454,036	12,362,463
Accumulated other comprehensive income (loss), net of deferred income tax	230,048	488,895
Common shares held in treasury, at cost (shares: 185,883,642 and 172,280,199)	(3,007,578)	(2,503,909)
Total shareholders' equity available to Arch	13,986,072	13,105,886
Non-redeemable noncontrolling interests	918,874	823,007
Total shareholders' equity	14,904,946	13,928,893
Total liabilities, noncontrolling interests and shareholders' equity	$ 46,481,886	$ 43,282,297

XML

Unaudited Consolidated Balance Sheets (Parentheticals) - USD ($) $ in Thousands		Jun. 30, 2021	Dec. 31, 2020
Fixed maturities available for sale, at amortized cost		$ 17,764,783	$ 18,143,305
Allowance for credit losses on investments		2,124	2,397
Short-term investments available for sale, at amortized cost		2,248,615	1,924,292
Collateral received under securities lending, at amortized cost		172,109	301,089
Other investments measured at fair value		4,071,497	3,824,796
Securities pledged under securities lending, at amortized cost		167,871	294,493
Allowance for credit losses on premiums receivable		35,979	37,781
Allowance for credit losses on reinsurance recoverable		11,029	11,636
Allowance for credit losses on contractholder receivable		$ 4,471	$ 8,638
Common shares, par value per share		$ 0.0011	$ 0.0011
Common shares issued (shares)		582,654,893	579,000,841
Common shares held in treasury (shares)		185,883,642	172,280,199
Fixed maturities
Allowance for credit losses on investments		$ 2,124	$ 2,397
Short-term investments
Allowance for credit losses on investments	[1]	0	0
Short-term investments available for sale, at amortized cost		$ 2,248,615	$ 1,924,292

[1] Effective January 1, 2020, the Company adopted ASU 2016-13 and as a result any credit impairment losses on the Company’s available-for-sale investments are recorded as an allowance, subject to reversal.

XML

Unaudited Consolidated Statements of Income - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020
Revenues
Net premiums earned	$ 2,120,909	$ 1,665,354	$ 4,069,331	$ 3,409,798
Net investment income	111,613	131,485	210,469	276,638
Net realized gains (losses)	202,907	556,588	345,368	189,628
Other underwriting income	5,529	6,667	11,639	13,519
Equity in net income (loss) of investment funds accounted for using the equity method	122,186	(65,119)	193,872	(69,328)
Other income (loss)	6,852	33	5,111	65
Total revenues	2,569,996	2,295,008	4,835,790	3,820,320
Expenses
Losses and loss adjustment expenses	1,159,831	1,230,522	2,362,931	2,345,941
Acquisition expenses	335,143	254,789	639,624	502,072
Other operating expenses	244,943	209,249	505,976	443,793
Corporate expenses	15,951	17,920	41,335	38,716
Amortization of intangible assets	15,286	16,489	29,688	33,120
Interest expense	35,700	31,139	74,046	63,694
Net foreign exchange (gains) losses	17,775	39,211	(2,288)	(33,460)
Total expenses	1,824,629	1,799,319	3,651,312	3,393,876
Income (loss) before income taxes and income (loss) from operating affiliates	745,367	495,689	1,184,478	426,444
Income tax expense	(51,179)	(26,127)	(90,039)	(54,072)
Income (loss) from operating affiliates	24,476	(3,173)	99,933	5,343
Net income (loss)	718,664	466,389	1,194,372	377,715
Net (income) loss attributable to noncontrolling interests	(43,178)	(167,568)	(80,730)	65,223
Net income (loss) available to Arch	675,486	298,821	1,113,642	442,938
Preferred dividends	(11,666)	(10,403)	(22,069)	(20,806)
Net income (loss) available to Arch common shareholders	$ 663,820	$ 288,418	$ 1,091,573	$ 422,132
Net income per common share and common share equivalent
Basic (per share)	$ 1.67	$ 0.72	$ 2.73	$ 1.05
Diluted (per share)	$ 1.63	$ 0.71	$ 2.68	$ 1.03
Weighted average common shares and common share equivalents outstanding
Basic (shares)	397,743,402	402,503,687	399,267,183	403,197,924
Diluted (shares)	406,485,994	408,119,681	407,687,680	411,005,591

XML

Unaudited Consolidated Statements of Comprehensive Income - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020
Comprehensive Income
Net income (loss)	$ 718,664	$ 466,389	$ 1,194,372	$ 377,715
Unrealized appreciation (decline) in value of available-for-sale investments:
Unrealized holding gains (losses) arising during period	78,571	492,796	(183,179)	435,509
Reclassification of net realized (gains) losses, included in net income (loss)	(60,547)	(167,391)	(57,850)	(288,620)
Foreign currency translation adjustments	6,205	22,251	(22,379)	(22,438)
Comprehensive income (loss)	742,893	814,045	930,964	502,166
Net (income) loss attributable to noncontrolling interests	(43,178)	(167,568)	(80,730)	65,223
Other comprehensive (income) loss attributable to noncontrolling interests	(10)	(20,111)	4,560	12,947
Comprehensive income (loss) available to Arch	$ 699,705	$ 626,366	$ 854,794	$ 580,336

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	Retained earnings Cumulative effect of an accounting change	Retained earnings Balance at beginning of period, as adjusted	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, 2019		$ 780,000	$ 638	$ 1,889,683	$ 11,021,006	$ (22,452)	$ 10,998,554	$ 212,091	$ 258,486	$ (46,395)	$ (2,406,047)
Preferred shares issued		0
Common shares issued, net			4
Amortization of share-based compensation				41,210
Issue costs on preferred shares				0
Other changes				4,621
Net income (loss)	$ 377,715				377,715
Net (income) loss attributable to noncontrolling interests	65,223				65,223
Preferred share dividends	(20,806)				(20,806)
Unrealized holding gains (losses) during period, net of reclassification adjustment									146,889
Unrealized holding gains (losses) during period attributable to noncontrolling interests									13,112
Foreign currency translation adjustments	(22,438)									(22,438)
Foreign currency translation adjustments attributable to noncontrolling interests										(166)
Shares repurchased for treasury											(88,458)
Balance at end of period at Jun. 30, 2020	11,991,825	780,000	642	1,935,514	11,420,686			349,488	418,487	(68,999)	(2,494,505)
Non-redeemable noncontrolling interests, end of period at Jun. 30, 2020	679,089
Total shareholders’ equity at Jun. 30, 2020	12,670,914
Balance at beginning of period at Mar. 31, 2020		780,000	642	1,921,487	11,132,268	0	11,132,268	21,944	113,149	(91,205)	(2,489,097)
Preferred shares issued		0
Common shares issued, net			0
Amortization of share-based compensation				13,160
Issue costs on preferred shares				0
Other changes				867
Net income (loss)	466,389				466,389
Net (income) loss attributable to noncontrolling interests	(167,568)				(167,568)
Preferred share dividends	(10,403)				(10,403)
Unrealized holding gains (losses) during period, net of reclassification adjustment									325,405
Unrealized holding gains (losses) during period attributable to noncontrolling interests									(20,067)
Foreign currency translation adjustments	22,251									22,251
Foreign currency translation adjustments attributable to noncontrolling interests										(45)
Shares repurchased for treasury											(5,408)
Balance at end of period at Jun. 30, 2020	11,991,825	780,000	642	1,935,514	11,420,686			349,488	418,487	(68,999)	(2,494,505)
Non-redeemable noncontrolling interests, end of period at Jun. 30, 2020	679,089
Total shareholders’ equity at Jun. 30, 2020	12,670,914
Balance at beginning of period at Dec. 31, 2020	13,105,886	780,000	643	1,977,794	12,362,463	0	12,362,463	488,895	501,295	(12,400)	(2,503,909)
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
Accounting Standards Update	us-gaap:AccountingStandardsUpdate201613Member
Balance at beginning of period at Mar. 31, 2021		780,000	645	2,014,741	12,790,216	$ 0	$ 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

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Unaudited Consolidated Statements of Cash Flows - USD ($) $ in Thousands	6 Months Ended
	Jun. 30, 2021	Jun. 30, 2020
Operating Activities
Net income (loss)	$ 1,194,372	$ 377,715
Adjustments to reconcile net income (loss) to net cash provided by operating activities:
Net realized (gains) losses	(379,049)	(194,776)
Equity in net (income) or loss of investment funds accounted for using the equity method and other income or loss	(181,028)	125,384
Amortization of intangible assets	29,688	33,120
Share-based compensation	57,564	41,912
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable	948,505	1,158,446
Unearned premiums, net of ceded unearned premiums	838,650	395,759
Premiums receivable	(781,391)	(463,638)
Deferred acquisition costs	(214,893)	(92,437)
Reinsurance balances payable	331,461	132,161
Other items, net	(231,307)	(192,066)
Net cash provided by (used for) operating activities	1,612,572	1,321,580
Investing Activities
Purchases of fixed maturity investments	(23,554,384)	(25,410,849)
Purchases of equity securities	(620,774)	(1,025,149)
Purchases of other investments	(1,033,134)	(501,692)
Proceeds from sales of fixed maturity investments	23,130,388	24,833,030
Proceeds from sales of equity securities	542,290	580,346
Proceeds from sales, redemptions and maturities of other investments	772,549	472,188
Proceeds from redemptions and maturities of fixed maturity investments	805,836	369,240
Net settlements of derivative instruments	17,286	150,471
Net (purchases) sales of short-term investments	(378,086)	(1,323,363)
Change in cash collateral related to securities lending	(826)	54,596
Purchase of operating affiliate	(546,349)	0
Purchases of fixed assets	(23,585)	(17,687)
Other	(204,889)	8,679
Net cash provided by (used for) investing activities	(1,093,678)	(1,810,190)
Financing Activities
Proceeds from issuance of preferred shares, net	485,821	0
Purchases of common shares under share repurchase program	(485,315)	(75,486)
Proceeds from common shares issued, net	185	(9,661)
Proceeds from borrowings	0	1,004,918
Repayments of borrowings	0	(165,000)
Change in cash collateral related to securities lending	826	(54,596)
Third party investment in non-redeemable noncontrolling interests	15,971	(2,867)
Dividends paid to redeemable noncontrolling interests	(1,907)	(2,540)
Other	27,639	(2,625)
Preferred dividends paid	(20,805)	(20,806)
Net cash provided by (used for) financing activities	22,415	671,337
Effects of exchange rate changes on foreign currency cash and restricted cash	(13,390)	(21,742)
Increase (decrease) in cash and restricted cash	527,919	160,985
Cash and restricted cash, beginning of year	1,290,544	903,698
Cash and restricted cash, end of period	$ 1,818,463	$ 1,064,683

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Basis of Presentation and Recent Accounting Pronouncements

6 Months Ended

Jun. 30, 2021

Organization, Consolidation and Presentation of Financial Statements [Abstract]

Basis of Presentation and Recent Accounting Pronouncements

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. As of June 30, 2021, the Company’s consolidated financial statements included the results of Watford Holdings Ltd. and its wholly owned subsidiaries (“Watford”). Watford is a multi-line Bermuda reinsurance company. Watford’s own management and board of directors are responsible for its results and profitability. 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, 2020 (“2020 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, including the correct presentation of ‘income (loss) from operating affiliates’ on its consolidated statements of income for all periods presented to reclass such item from ‘other income (loss)’. The Company also changed its presentation of ‘investment in operating affiliates’ on its consolidated

balance sheet for all periods presented to reclass such item from ‘other assets’. Such reclassifications had no effect on the Company’s net income, comprehensive income, shareholders’ equity or cash flows. Management views the impact of the prior period misclassification as not material to the financial statements on a quantitative and qualitative basis. See note 7. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.

Recent Accounting Pronouncements

Recently Issued Accounting Standards Adopted

The Company adopted ASU 2019-12, “Simplifying the Accounting for Income Taxes.” This ASU eliminates certain exceptions for recognizing deferred taxes for investments, performing intraperiod tax allocations and calculating income taxes in interim periods. The ASU also clarifies the accounting for transactions that result in a step-up in the tax basis of goodwill. The adoption of this guidance did not have a material effect on the Company’s consolidated financial statements.

For information regarding additional accounting standards that the Company has not yet adopted, see note 3(r), “Significant Accounting Policies—Recent Accounting Pronouncements,” of the notes to consolidated financial statements in the Company’s 2020 Form 10-K.

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Share Transactions

6 Months Ended

Jun. 30, 2021

Stockholders' Equity Note [Abstract]

Share Transactions

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 402.3 million common shares for an aggregate purchase price of $4.54 billion. For the six months ended June 30, 2021, Arch Capital repurchased 13.1 million shares under the share repurchase program with an aggregate purchase price of $485.3 million. Arch Capital repurchased 2.6 million shares under the share repurchase program with an aggregate purchase price of $75.5 million during the six months ended June 30, 2020. At June 30, 2021, $431.2 million of share repurchases were available under the program, which may be effected from time to time in open market or privately negotiated transactions through December 31, 2021. 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.

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 4.550% 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 non-cumulative basis, quarterly in arrears on the last day of March, June, September and December of each year, at an annual rate of 4.550%. Dividends on the Series G Preferred Shares are not cumulative. The Company will be restricted from paying dividends on or repurchasing its common shares unless certain dividend payments are made on the Series G Preferred Shares. The Company may not declare or pay a dividend on the Series G Preferred Shares under certain circumstances, including if the Company is or, after giving effect to such payment, would be in breach of applicable individual or group solvency and liquidity requirements or applicable individual or group enhanced capital requirements ("ECR.") The Series G Preferred Shares may not be

redeemed at any time if the ECR would be breached immediately before or after giving effect to such redemption, unless the Company replaces the capital represented by preference shares to be redeemed with capital having equal or better capital treatment.

Except in specified circumstances relating to certain tax or corporate events, the Series G Preferred Shares are not redeemable prior to June 11, 2026. On and after that date, the Series G Preferred Shares will be redeemable at the Company’s option, in whole or in part, at a redemption price of $25,000 per share of the Series G Preferred Shares (equivalent to $25 per depositary share), plus any declared and unpaid dividends, without accumulation of any undeclared dividends to, but excluding, the redemption date. The Depositary Shares will be redeemed if and to the extent the related Series G Preferred Shares are redeemed by the Company. Neither the Depositary Shares nor the Series G Preferred Shares have a stated maturity, nor will they be subject to any sinking fund or mandatory redemption. The Series G Preferred Shares are not convertible into any other securities. The Series G Preferred Shares do not have voting rights, except under limited circumstances.

The Company intends to use the net proceeds from the offering of approximately $485.8 million to redeem all or a portion of its issued and outstanding Series E Non-Cumulative Preferred Shares in September 2021, and to use any remaining amounts for general corporate purposes.

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Earnings Per Common Share

6 Months Ended

Jun. 30, 2021

Earnings Per Share [Abstract]

Earnings Per Common Share

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,
	2021		2020		2021		2020
Numerator:
Net income (loss)	$	718,664	$	466,389	$	1,194,372	$	377,715
Amounts attributable to noncontrolling interests	(43,178)		(167,568)		(80,730)		65,223
Net income (loss) available to Arch	675,486		298,821		1,113,642		442,938
Preferred dividends	(11,666)		(10,403)		(22,069)		(20,806)
Net income (loss) available to Arch common shareholders	$	663,820	$	288,418	$	1,091,573	$	422,132
Denominator:
Weighted average common shares and common share equivalents outstanding — basic	397,743,402		402,503,687		399,267,183		403,197,924
Effect of dilutive common share equivalents:
Nonvested restricted shares	1,990,729		1,597,701		1,932,929		1,829,239
Stock options (1)	6,751,863		4,018,293		6,487,568		5,978,428
Weighted average common shares and common share equivalents outstanding — diluted	406,485,994		408,119,681		407,687,680		411,005,591
Earnings per common share:
Basic	$	1.67	$	0.72	$	2.73	$	1.05
Diluted	$	1.63	$	0.71	$	2.68	$	1.03

(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 2021 second quarter and 2020 second quarter, the number of stock options excluded were 1,974,849 and 6,982,107, respectively. For the six months ended June 30, 2021 and 2020 period, the number of stock options excluded were 2,395,749 and 2,038,758, respectively.

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Segment Information

6 Months Ended

Jun. 30, 2021

Segment Reporting [Abstract]

Segment Information

Segment Information

The Company classifies its businesses into three underwriting segments — insurance, reinsurance and mortgage — and two other operating segments — ‘other’ and corporate (non-underwriting). 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. and international mortgage insurance and reinsurance operations as well as government sponsored enterprise (“GSE”) credit-risk sharing transactions. 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 (non-underwriting) segment results include net investment income, other income (loss), corporate expenses, transaction costs and other, interest expense, items related to the Company’s non-cumulative preferred shares, 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, income or loss from operating affiliates and income taxes. Such amounts exclude the results of the ‘other’ segment.

The ‘other’ segment includes the results of Watford (see note 11). For the ‘other’ segment, performance is measured based on net income or loss.

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, 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.’

	Three Months Ended
	June 30, 2020
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	1,030,362		$	807,065		$	369,144		$	2,206,410		$	157,927		$	2,317,692
Premiums ceded	(358,101)			(241,971)			(44,044)			(643,955)			(52,071)			(649,381)
Net premiums written	672,261			565,094			325,100			1,562,455			105,856			1,668,311
Change in unearned premiums	15,648			(84,897)			40,613			(28,636)			25,679			(2,957)
Net premiums earned	687,909			480,197			365,713			1,533,819			131,535			1,665,354
Other underwriting income (loss)	—			(651)			6,450			5,799			868			6,667
Losses and loss adjustment expenses	(518,203)			(383,433)			(224,100)			(1,125,736)			(104,786)			(1,230,522)
Acquisition expenses	(107,671)			(90,522)			(34,052)			(232,245)			(22,544)			(254,789)
Other operating expenses	(118,757)			(38,716)			(37,574)			(195,047)			(14,202)			(209,249)
Underwriting income (loss)	$	(56,722)		$	(33,125)		$	76,437		(13,410)			(9,129)			(22,539)
Net investment income										101,031			30,454			131,485
Net realized gains (losses)										385,089			171,499			556,588
Equity in net income (loss) of investment funds accounted for using the equity method										(65,119)			—			(65,119)
Other income (loss)										33			—			33
Corporate expenses (2)										(16,943)			—			(16,943)
Transaction costs and other (2)										(977)			—			(977)
Amortization of intangible assets										(16,489)			—			(16,489)
Interest expense										(25,130)			(6,009)			(31,139)
Net foreign exchange gains (losses)										(42,438)			3,227			(39,211)
Income (loss) before income taxes and income (loss) from operating affiliates										305,647			190,042			495,689
Income tax (expense) benefit										(26,529)			402			(26,127)
Income (loss) from operating affiliates										(3,173)			—			(3,173)
Net income (loss)										275,945			190,444			466,389
Amounts attributable to redeemable noncontrolling interests										(934)			(1,036)			(1,970)
Amounts attributable to nonredeemable noncontrolling interests										—			(165,598)			(165,598)
Net income (loss) available to Arch										275,011			23,810			298,821
Preferred dividends										(10,403)			—			(10,403)
Net income (loss) available to Arch common shareholders										$	264,608		$	23,810		$	288,418
Underwriting Ratios
Loss ratio	75.3		%	79.8		%	61.3		%	73.4		%	79.7		%	73.9		%
Acquisition expense ratio	15.7		%	18.9		%	9.3		%	15.1		%	17.1		%	15.3		%
Other operating expense ratio	17.3		%	8.1		%	10.3		%	12.7		%	10.8		%	12.6		%
Combined ratio	108.3		%	106.8		%	80.9		%	101.2		%	107.6		%	101.8		%
Goodwill and intangible assets	$	263,086		$	2,516		$	415,238		$	680,840		$	7,650		$	688,490

(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.’

	Six Months Ended
	June 30, 2020
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	2,238,007		$	1,929,584		$	738,089		$	4,904,947		$	392,829		$	5,150,522
Premiums ceded	(736,998)			(567,310)			(88,371)			(1,391,946)			(100,273)			(1,344,965)
Net premiums written	1,501,009			1,362,274			649,718			3,513,001			292,556			3,805,557
Change in unearned premiums	(97,181)			(338,617)			61,021			(374,777)			(20,982)			(395,759)
Net premiums earned	1,403,828			1,023,657			710,739			3,138,224			271,574			3,409,798
Other underwriting income (loss)	—			1,469			11,049			12,518			1,001			13,519
Losses and loss adjustment expenses	(1,025,311)			(813,502)			(291,666)			(2,130,479)			(215,462)			(2,345,941)
Acquisition expenses	(215,008)			(170,128)			(72,588)			(457,724)			(44,348)			(502,072)
Other operating expenses	(248,406)			(84,013)			(83,470)			(415,889)			(27,904)			(443,793)
Underwriting income (loss)	$	(84,897)		$	(42,517)		$	274,064		$	146,650		$	(15,139)		$	131,511
Net investment income										214,059			62,579			276,638
Net realized gains (losses)										312,980			(123,352)			189,628
Equity in net income (loss) of investment funds accounted for using the equity method										(69,328)			—			(69,328)
Other income (loss)										65			—			65
Corporate expenses (2)										(35,144)			—			(35,144)
Transaction costs and other (2)										(3,572)			—			(3,572)
Amortization of intangible assets										(33,120)			—			(33,120)
Interest expense										(50,375)			(13,319)			(63,694)
Net foreign exchange gains (losses)										20,869			12,591			33,460
Income (loss) before income taxes and income (loss) from operating affiliates										503,084			(76,640)			426,444
Income tax (expense) benefit										(54,474)			402			(54,072)
Income (loss) from operating affiliates										5,343			—			5,343
Net income (loss)										453,953			(76,238)			377,715
Amounts attributable to redeemable noncontrolling interests										(991)			(2,132)			(3,123)
Amounts attributable to nonredeemable noncontrolling interests										—			68,346			68,346
Net income (loss) available to Arch										452,962			(10,024)			442,938
Preferred dividends										(20,806)			—			(20,806)
Net income (loss) available to Arch common shareholders										$	432,156		$	(10,024)		$	422,132
Underwriting Ratios
Loss ratio	73.0		%	79.5		%	41.0		%	67.9		%	79.3		%	68.8		%
Acquisition expense ratio	15.3		%	16.6		%	10.2		%	14.6		%	16.3		%	14.7		%
Other operating expense ratio	17.7		%	8.2		%	11.7		%	13.3		%	10.3		%	13.0		%
Combined ratio	106.0		%	104.3		%	62.9		%	95.8		%	105.9		%	96.5		%

(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.’

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Reserve for Losses and Loss Adjustment Expenses

6 Months Ended

Jun. 30, 2021

Liability for Future Policy Benefits and Unpaid Claims and Claims Adjustment Expense [Abstract]

Reserve for losses and loss adjustment expenses

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,
	2021		2020		2021		2020
Reserve for losses and loss adjustment expenses at beginning of period	$	16,443,952	$	14,309,580	$	16,513,929	$	13,891,842
Unpaid losses and loss adjustment expenses recoverable	3,916,650		4,070,114		4,314,855		4,082,650
Net reserve for losses and loss adjustment expenses at beginning of period	12,527,302		10,239,466		12,199,074		9,809,192
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year	1,219,081		1,274,589		2,463,853		2,409,031
Prior years	(59,250)		(44,067)		(100,922)		(63,090)
Total net incurred losses and loss adjustment expenses	1,159,831		1,230,522		2,362,931		2,345,941
Retroactive reinsurance transactions (1)	—		—		(183,893)		60,635
Net foreign exchange (gains) losses	135,847		51,157		88,970		(91,416)
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year	(164,441)		(128,174)		(223,425)		(169,434)
Prior years	(607,911)		(504,254)		(1,193,029)		(1,066,201)
Total net paid losses and loss adjustment expenses	(772,352)		(632,428)		(1,416,454)		(1,235,635)
Net reserve for losses and loss adjustment expenses at end of period	13,050,628		10,888,717		13,050,628		10,888,717
Unpaid losses and loss adjustment expenses recoverable	4,146,020		4,156,157		4,146,020		4,156,157
Reserve for losses and loss adjustment expenses at end of period	$	17,196,648	$	15,044,874	$	17,196,648	$	15,044,874

(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”). During the 2020 first quarter, the Company entered into a reinsurance to close agreement of the 2017 and prior years of account previously covered by a third party arrangement.

Development on Prior Year Loss Reserves

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 of adverse development 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 (i.e., the year in which a loss occurred), $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 (i.e., all premiums and losses attributable to contracts having an inception or renewal date within the given twelve-month period), 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.

2020 Second Quarter

During the 2020 second quarter, the Company recorded net favorable development on prior year loss reserves of $44.1 million, which consisted of $2.5 million from the insurance segment, $40.2 million from the reinsurance segment, $0.2 million from the mortgage segment and $1.1 million from the ‘other’ segment.

The insurance segment’s net favorable development of $2.5 million, or 0.4 loss ratio points, for the 2020 second quarter consisted of $19.7 million of net favorable development in short-tailed and long-tailed lines and $17.1 million of net adverse development in medium-tailed lines. Net favorable development of $11.5 million in short-tailed lines reflected $7.5 million of favorable development from property (excluding marine), primarily from the 2016 to 2019 accident years and $3.5 million of favorable development on travel and accident, primarily from the 2019 accident year. Net favorable development of $8.1 million in long-tailed lines reflected $2.4 million of favorable development in executive assurance, primarily from the 2013 accident year, and $4.9 million of favorable development related to other business, including alternative markets and excess workers’ compensation, across most accident years. Net adverse development in medium-tailed lines included $6.3 million of adverse development in professional liability, primarily from the 2009, 2016 and 2019 accident years, $6.1 million of adverse development in contract binding, across all accident years, and $4.0 million of adverse development on program business, primarily from the 2014 and 2017 accident years.

The reinsurance segment’s net favorable development of $40.2 million, or 8.4 loss ratio points, for the 2020 second quarter consisted of $46.2 million of net favorable development from short-tailed lines and net adverse development of $6.0 million from and medium-tailed and long-tailed lines. Net favorable development in short-tailed lines reflected $27.5 million of favorable development from

other specialty, across most underwriting years, and $18.3 million of favorable development related to property catastrophe and property other than property catastrophe business, primarily from the 2016 to 2019 underwriting years. Adverse development of $5.8 million in long-tailed lines reflected an increase in reserves from casualty, primarily from the 2012 to 2015 underwriting years.

The mortgage segment’s net favorable development was $0.2 million, or 0.1 loss ratio points, for the 2020 second quarter.

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 favorable from the insurance segment, $47.3 million from the reinsurance segment and $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.

Six Months Ended June 30, 2020

During the six months ended June 30, 2020, the Company recorded net favorable development on prior year loss reserves of $63.1 million, which consisted of $3.6 million from the insurance segment, $51.8 million from the reinsurance segment, $6.3 million from the mortgage segment and $1.3 million from the ‘other’ segment.

The insurance segment’s net favorable development of $3.6 million, or 0.3 loss ratio points, for the 2020 period consisted of $28.7 million of net favorable development in short-tailed and long-tailed lines, partially offset by $25.1 million of net adverse development in medium-tailed lines. Net favorable development of $15.4 million in short-tailed lines reflected $9.6 million of favorable development from property (excluding marine), primarily from the 2015 to 2018 accident years and $3.1 million of favorable development in lenders products, primarily from the 2017 to 2019 accident years. Net favorable development of $13.3 million in long-tailed lines included $7.6 million of favorable development related to other business, including alternative markets and excess workers’ compensation, primarily in the 2016 and 2017 accident years. Net adverse development in medium-tailed lines reflected $19.3 million of adverse development in contract binding business, primarily in the 2016 to 2019 accident years, and $6.3 million of adverse development in program business, primarily from the 2017 and 2018 accident years.

The reinsurance segment’s net favorable development of $51.8 million, or 5.1 loss ratio points, for the 2020 period consisted of $67.4 million of net favorable development from short-tailed and medium-tailed lines, offset by $15.6 million of net adverse development from long-tailed lines. Net favorable development of $65.7 million in short-tailed lines reflected $39.3 million from other specialty lines and $21.3 million from property catastrophe, primarily from the 2015 to 2019 underwriting years. Adverse development in long-tailed lines reflected an increase in reserves from casualty, primarily from the 2012 to 2015 underwriting years.

The mortgage segment’s net favorable development was $6.3 million, or 0.9 loss ratio points, for the 2020 period. The 2020 development was primarily driven by subrogation recoveries on second lien business and student loan business.

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Allowance for Expected Credit Losses

6 Months Ended

Jun. 30, 2021

Credit Loss [Abstract]

Allowance for expected credit losses

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, 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
Three Months Ended June 30, 2020
Balance at beginning of period	$	2,155,204	$	27,990
Change for provision of expected credit losses (1)			8,064
Balance at end of period	$	2,203,753	$	36,054
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
Six Months Ended June 30, 2020
Balance at beginning of period	$	1,778,717	$	21,003
Cumulative effect of accounting change (2)			6,539
Change for provision of expected credit losses (1)			8,512
Balance at end of period	$	2,203,753	$	36,054

(1)Amounts deemed uncollectible are written-off in operating expenses. For the 2021 second quarter and 2020 second quarter, amounts written off were $1.1 million and $1.8 million, respectively. For the six months ended June 30, 2021 and 2020 period, amounts written off were were $1.2 million and $2.3 million, respectively.

(2)Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

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, 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
Three Months Ended June 30, 2020
Balance at beginning of period	$	4,303,135	$	13,700
Change for provision of expected credit losses			(105)
Balance at end of period	$	4,363,507	$	13,595
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
Six Months Ended June 30, 2020
Balance at beginning of period	$	4,346,816	$	1,364
Cumulative effect of accounting change (1)			12,010
Change for provision of expected credit losses			221
Balance at end of period	$	4,363,507	$	13,595

(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

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

	June 30,			December 31
	2021			2020
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	$	4,314,515		$	4,500,802
% due from carriers with A.M. Best rating of “A-” or better	66.0		%	63.9		%
% due from all other carriers with no A.M. Best rating (1)	34.0		%	36.1		%
Largest balance due from any one carrier as % of total shareholders’ equity	2.4		%	1.8		%

(1)    At June 30, 2021 and December 31, 2020 over 91% and 94% 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, 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
Three Months Ended June 30, 2020
Balance at beginning of period	$	2,140,724	$	9,038
Change for provision of expected credit losses			(2,748)
Balance at end of period	2,179,124		$	6,290
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
Six Months Ended June 30, 2020
Balance at beginning of period	$	2,119,460	$	—
Cumulative effect of accounting change (1)			6,663
Change for provision of expected credit losses			(373)
Balance at end of period	$	2,179,124	$	6,290

(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

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Investment Information

6 Months Ended

Jun. 30, 2021

Disclosure Investment Information [Abstract]

Investment Information

Investment Information

At June 30, 2021, total investable assets of $30.2 billion included $27.3 billion held by the Company and $2.9 billion attributable to Watford.

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 (2)		Cost or Amortized Cost
June 30, 2021
Fixed maturities (1):
Corporate bonds	$	7,129,768	$	217,061	$	(34,751)	$	(1,232)	$	6,948,690
Mortgage backed securities	389,041		4,480		(3,479)		(269)		388,309
Municipal bonds	415,483		23,153		(1,660)		(6)		393,996
Commercial mortgage backed securities	266,733		4,017		(611)		(3)		263,330
U.S. government and government agencies	5,091,183		14,814		(14,013)		—		5,090,382
Non-U.S. government securities	2,449,782		108,823		(18,441)		(128)		2,359,528
Asset backed securities	2,487,845		16,460		(4,056)		(486)		2,475,927
Total	18,229,835		388,808		(77,011)		(2,124)		17,920,162
Short-term investments	2,248,613		1,404		(1,406)		—		2,248,615
Total	$	20,478,448	$	390,212	$	(78,417)	$	(2,124)	$	20,168,777
December 31, 2020
Fixed maturities (1):
Corporate bonds	$	7,856,571	$	414,247	$	(34,388)	$	(896)	$	7,477,608
Mortgage backed securities	630,001		8,939		(5,028)		(278)		626,368
Municipal bonds	494,522		27,291		(3,835)		(11)		471,077
Commercial mortgage backed securities	389,900		8,722		(2,954)		(122)		384,254
U.S. government and government agencies	5,557,077		22,612		(12,611)		—		5,547,076
Non-U.S. government securities	2,433,733		153,891		(8,060)		—		2,287,902
Asset backed securities	1,634,804		19,225		(10,715)		(1,090)		1,627,384
Total	18,996,608		654,927		(77,591)		(2,397)		18,421,669
Short-term investments	1,924,922		2,693		(2,063)		—		1,924,292
Total	$	20,921,530	$	657,620	$	(79,654)	$	(2,397)	$	20,345,961

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

(2)    Effective January 1, 2020, the Company adopted ASU 2016-13 and as a result any credit impairment losses on the Company’s available-for-sale investments are recorded as an allowance, subject to reversal.

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, 2021
Fixed maturities (1):
Corporate bonds	$	2,264,801	$	(32,733)	$	22,895	$	(2,018)	$	2,287,696	$	(34,751)
Mortgage backed securities	196,765		(2,893)		13,632		(586)		210,397		(3,479)
Municipal bonds	24,711		(1,612)		2,859		(48)		27,570		(1,660)
Commercial mortgage backed securities	20,039		(180)		7,961		(431)		28,000		(611)
U.S. government and government agencies	2,920,944		(14,013)		—		—		2,920,944		(14,013)
Non-U.S. government securities	1,282,422		(17,562)		16,885		(879)		1,299,307		(18,441)
Asset backed securities	781,596		(2,364)		93,923		(1,692)		875,519		(4,056)
Total	7,491,278		(71,357)		158,155		(5,654)		7,649,433		(77,011)
Short-term investments	531,130		(1,406)		—		—		531,130		(1,406)
Total	$	8,022,408	$	(72,763)	$	158,155	$	(5,654)	$	8,180,563	$	(78,417)
December 31, 2020
Fixed maturities (1):
Corporate bonds	$	747,442	$	(33,086)	$	3,934	$	(1,302)	$	751,376	$	(34,388)
Mortgage backed securities	284,619		(4,788)		3,637		(240)		288,256		(5,028)
Municipal bonds	67,937		(3,835)		—		—		67,937		(3,835)
Commercial mortgage backed securities	126,624		(2,916)		2,655		(38)		129,279		(2,954)
U.S. government and government agencies	1,285,907		(12,611)		—		—		1,285,907		(12,611)
Non-U.S. government securities	543,844		(7,658)		2,441		(402)		546,285		(8,060)
Asset backed securities	634,470		(9,110)		57,737		(1,605)		692,207		(10,715)
Total	3,690,843		(74,004)		70,404		(3,587)		3,761,247		(77,591)
Short-term investments	97,920		(2,063)		—		—		97,920		(2,063)
Total	$	3,788,763	$	(76,067)	$	70,404	$	(3,587)	$	3,859,167	$	(79,654)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

At June 30, 2021, on a lot level basis, approximately 3,240 security lots out of a total of approximately 10,890 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 $2.4 million. At December 31, 2020, on a lot level basis, approximately 2,320 security lots out of a total of approximately 11,180 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 $0.9 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, 2021				December 31, 2020
Maturity	Estimated Fair Value		Amortized Cost		Estimated Fair Value		Amortized Cost
Due in one year or less	$	452,065	$	439,855	$	348,200	$	339,951
Due after one year through five years	10,114,276		9,942,182		10,629,959		10,340,819
Due after five years through 10 years	4,148,538		4,055,318		4,881,564		4,654,754
Due after 10 years	371,337		355,241		482,180		448,139
	15,086,216		14,792,596		16,341,903		15,783,663
Mortgage backed securities	389,041		388,309		630,001		626,368
Commercial mortgage backed securities	266,733		263,330		389,900		384,254
Asset backed securities	2,487,845		2,475,927		1,634,804		1,627,384
Total (1)	$	18,229,835	$	17,920,162	$	18,996,608	$	18,421,669

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

Securities Lending Agreements

The Company enters into securities lending agreements with financial institutions to enhance investment income whereby it loans certain of its securities to third parties, primarily major brokerage firms, for short periods of time through a lending agent. The Company maintains legal control over the securities it lends (shown as ‘Securities pledged under securities lending, at fair value’ on the Company’s balance sheet), retains the earnings and cash flows associated with the loaned securities and receives a fee from the borrower for the temporary use of the securities. An indemnification agreement with the lending agent protects the Company in the event a borrower becomes insolvent or fails to return any of the securities on loan from the Company.

The Company receives collateral (shown as ‘Collateral received under securities lending, at fair value’ on the Company’s balance sheet) in the form of cash or U.S. government and government agency securities. At June 30, 2021, the fair value of the cash collateral received on securities lending was $0.8 million and the fair value of security collateral received was $171.3 million. At December 31, 2020, the fair value of the cash collateral received on securities lending was nil, and the fair value of security collateral received was $301.1 million.

The carrying value of collateral held under the Company’s securities lending transactions by significant investment category and remaining contractual maturity of the underlying agreements is as follows:

	Remaining Contractual Maturity of the Agreements
	Overnight and Continuous		Less than 30 Days		30-90 Days		90 Days or More		Total
June 30, 2021
U.S. government and government agencies	$	15,745	$	137,713	$	—	$	—	$	153,458
Corporate bonds	5,800		—		—		—		5,800
Equity securities	12,851		—		—		—		12,851
Total	$	34,396	$	137,713	$	—	$	—	$	172,109
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9									$	—
Amounts related to securities lending not included in offsetting disclosure in note 9									$	172,109
December 31, 2020
U.S. government and government agencies	$	142,317	$	—	$	139,290	$	—	$	281,607
Corporate bonds	3,021		—		—		—		3,021
Equity securities	16,461		—		—		—		16,461
Total	$	161,799	$	—	$	139,290	$	—	$	301,089
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9									$	—
Amounts related to securities lending not included in offsetting disclosure in note 9									$	301,089

Equity Securities, at Fair Value

At June 30, 2021, the Company held $1.7 billion of equity securities, at fair value, compared to $1.4 billion at December 31, 2020. 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

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

	June 30, 2021		December 31, 2020
Fixed maturities	$	995,980	$	843,354
Other investments	2,370,472		2,331,885
Short-term investments	610,114		557,008
Equity securities	94,931		92,549
Investments accounted for using the fair value option	$	4,071,497	$	3,824,796
Other investable assets (1)	500,000		500,000
Total other investments	$	4,571,497	$	4,324,796

(1) Participation interests in a receivable of a reverse repurchase agreement.

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

	June 30, 2021		December 31, 2020
Term loan investments	$	1,333,014	$	1,231,731
Lending	638,786		572,636
Credit related funds	73,171		90,780
Energy	84,891		65,813
Investment grade fixed income	110,375		138,646
Infrastructure	32,109		165,516
Private equity	70,878		48,750
Real estate	27,248		18,013
Total	$	2,370,472	$	2,331,885

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, 2021		December 31, 2020
Credit related funds	$	883,279	$	740,060
Equities	403,003		343,058
Real estate	323,566		258,518
Lending	295,228		179,629
Private equity	305,662		235,289
Infrastructure	210,174		175,882
Energy	118,212		115,453
Total	$	2,539,124	$	2,047,889

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, 2021		December 31, 2020
Investments accounted for using the equity method (1)	2,539,124		2,047,889
Investments accounted for using the fair value option (2)	182,260		184,720
Total	$	2,721,384	$	2,232,609

(1)    Aggregate unfunded commitments were $2.0 billion at June 30, 2021, compared to $1.8 billion at December 31, 2020.

(2)    Aggregate unfunded commitments were $26.3 million at June 30, 2021, compared to $35.6 million at December 31, 2020.

Net Investment Income

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

	June 30,
	2021		2020
Three Months Ended
Fixed maturities	$	88,625	$	105,391
Term loans	16,879		20,512
Equity securities	8,584		6,219
Short-term investments	1,138		3,383
Other (1)	19,950		16,460
Gross investment income	135,176		151,965
Investment expenses	(23,563)		(20,480)
Net investment income	$	111,613	$	131,485
Six Months Ended
Fixed maturities	$	179,251	$	220,238
Term loans	31,607		43,682
Equity securities	14,234		12,226
Short-term investments	1,745		8,279
Other (1)	34,305		35,866
Gross investment income	261,142		320,291
Investment expenses	(50,673)		(43,653)
Net investment income	$	210,469	$	276,638

(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,
	2021		2020
Three Months Ended
Available for sale securities:
Gross gains on investment sales	$	115,541	$	232,153
Gross losses on investment sales	(50,627)		(49,824)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	10,912		68,181
Other investments	60,884		178,570
Equity securities	5,492		6,664
Short-term investments	(104)		3,368
Equity securities, at fair value:
Net realized gains (losses) on sales during the period	33,570		(18,250)
Net unrealized gains (losses) on equity securities still held at reporting date	65,847		145,686
Allowance for credit losses:
Investments related	896		3,225
Underwriting related	1,381		(5,834)
Derivative instruments (1)	(51,109)		(836)
Other	10,224		(6,515)
Net realized gains (losses)	$	202,907	$	556,588
Six Months Ended
Available for sale securities:
Gross gains on investment sales	$	180,543	$	410,353
Gross losses on investment sales	(113,625)		(81,792)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	27,465		(59,485)
Other investments	107,739		(129,230)
Equity securities	7,557		1,755
Short-term investments	632		(5,313)
Equity securities, at fair value:
Net realized gains (losses) on sales during the period	71,419		(18,789)
Net unrealized gains (losses) on equity securities still held at reporting date	85,555		(29,880)
Allowance for credit losses:
Investments related	(752)		(6,095)
Underwriting related	6,649		(9,104)
Net impairments losses	—		(533)
Derivative instruments (1)	(14,993)		126,353
Other	(12,821)		(8,612)
Net realized gains (losses)	$	345,368	$	189,628

(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 $122.2 million of equity in net income related to investment funds accounted for using the equity method in the 2021 second quarter, compared to loss of $65.1 million for the 2020 second quarter, and an income of $193.9 million for the six months ended June 30, 2021, compared to a loss of $69.3 million for six months ended June 30, 2020. In applying the equity method, investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the market value of the underlying securities in the funds). 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 and Premia Holdings Ltd. (“Premia”) and are generally recorded on a three month lag.

In 2021, the Company completed the share purchase agreement with Natixis to purchase 29.5% of the common equity of Coface, a France-based leader in the global trade credit insurance market. The consideration paid was €9.95 per share, or an aggregate €453 million (approximately $546 million) including related fees. Income (loss) from operating affiliates reflected a one-time gain of $74.5 million realized from the acquisition. As a result of equity method accounting rules, approximately $36 million of additional gain was deferred and will generally be recognized over the next five years. At June 30, 2021 the Company’s carrying value in Coface was $601.9 million.

Income from operating affiliates for the 2021 second quarter was $24.5 million, compared to a loss of $3.2 million, for the 2020 second quarter, and income of $99.9 million for the six months ended June 30, 2021, compared to $5.3 million for the six months ended June 30, 2020. The income from operating affiliates for the 2021 period, primarily related to the Company’s recent acquisition of a 29.5% stake in Coface.

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		Short Term Investments		Total
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
Three Months Ended June 30, 2020
Balance at beginning of period	$	2,654	$	23	$	7,232	$	29	$	9,938
Additions for current-period provision for expected credit losses	695		44		290		(29)		1,000
Additions (reductions) for previously recognized expected credit losses	(1,304)		(25)		(2,903)		—		(4,232)
Reductions due to disposals	(319)		(14)		(504)		—		(837)
Balance at end of period	$	1,726	$	28	$	4,115	$	—	$	5,869
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
Six Months Ended June 30, 2020
Balance at beginning of period	$	—	$	—	$	—	$	—	$	—
Cumulative effect of accounting change (2)	517		—		117		—		634
Additions for current-period provision for expected credit losses	2,841		67		7,441		—		10,349
Additions (reductions) for previously recognized expected credit losses	(1,306)		(25)		(2,924)		—		(4,255)
Reductions due to disposals	(326)		(14)		(519)		—		(859)
Balance at end of period	$	1,726	$	28	$	4,115	$	—	$	5,869

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

(2)    Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

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 2020 Form 10-K.

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

	June 30, 2021		December 31, 2020
Assets used for collateral or guarantees:
Affiliated transactions	$	5,041,190	$	4,643,334
Third party agreements	3,441,929		3,083,324
Deposits with U.S. regulatory authorities	814,084		827,552
Deposits with non-U.S. regulatory authorities	428,132		179,099
Total restricted assets	$	9,725,335	$	8,733,309

In addition, Watford maintains secured credit facilities to provide borrowing capacity for investment purposes and a total return swap agreement and maintains assets pledged as collateral for such purposes. The Company does not guarantee or provide credit support for Watford, and the Company’s financial exposure to Watford is limited to its investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from reinsurance transactions. As of June 30, 2021 and December 31, 2020, Watford held $1.1 billion and $954.6 million, respectively, in pledged assets to collateralize the credit facility mentioned above.

Reconciliation of Cash and Restricted Cash

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

	June 30, 2021		December 31, 2020
Cash	$	1,234,059	$	906,448
Restricted cash (included in ‘other assets’)	$	584,404	$	384,096
Cash and restricted cash	$	1,818,463	$	1,290,544

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Fair Value

6 Months Ended

Jun. 30, 2021

Fair Value Disclosures [Abstract]

Fair Value

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, 2021.

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 $26.5 billion of financial assets and liabilities measured at fair value at June 30, 2021, approximately $187.6 million, or 0.7%, were priced using non-binding broker-dealer quotes or modeled valuations. Of the $26.5 billion of financial assets and liabilities measured at fair value at December 31, 2020, approximately $150.1 million, or 0.6%, 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.

Contingent consideration liabilities

Contingent consideration liabilities (included in ‘other liabilities’ in the consolidated balance sheets) include amounts related to various Company’s acquisitions. Such amounts 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 future payments using an income approach based on modeled inputs which include a weighted average cost of capital. The Company determined that contingent 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, 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 (1):
Available for sale securities:
Fixed maturities:
Corporate bonds	$	7,129,768	$	—	$	7,129,755	$	13
Mortgage backed securities	389,041		—		389,041		—
Municipal bonds	415,483		—		415,483		—
Commercial mortgage backed securities	266,733		—		266,733		—
U.S. government and government agencies	5,091,183		5,062,571		28,612		—
Non-U.S. government securities	2,449,782		—		2,449,782		—
Asset backed securities	2,487,845		—		2,484,421		3,424
Total	18,229,835		5,062,571		13,163,827		3,437
Short-term investments	2,248,613		1,996,304		252,309		—
Equity securities, at fair value	1,706,044		1,631,937		24,971		49,136
Derivative instruments (4)	98,488		—		98,488		—
Residential mortgage loans	44,925		—		44,925		—
Fair value option:
Corporate bonds	790,186		—		789,188		998
Non-U.S. government bonds	22,552		—		22,552		—
Mortgage backed securities	2,707		—		2,707		—
Commercial mortgage backed securities	841		—		841		—
Asset backed securities	179,423		—		179,423		—
U.S. government and government agencies	271		163		108		—
Short-term investments	610,114		482,815		127,299		—
Equity securities	94,930		21,252		—		73,678
Other investments	1,219,294		23,610		1,121,784		73,900
Other investments measured at net asset value (2)	1,151,178
Total	4,071,496		527,840		2,243,902		148,576
Total assets measured at fair value	$	26,399,401	$	9,218,652	$	15,828,422	$	201,149
Liabilities measured at fair value:
Contingent consideration liabilities	$	(466)	$	—	$	—	$	(466)
Securities sold but not yet purchased (3)	(28,068)		—		(28,068)		—
Derivative instruments (4)	(67,304)		—		(67,304)		—
Total liabilities measured at fair value	$	(95,838)	$	—	$	(95,372)	$	(466)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See note 7, “—Securities Lending Agreements.”

(2)    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.

(3)    Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets.

(4)    See note 9.

The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2020:

			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 (1):
Available for sale securities:
Fixed maturities:
Corporate bonds	$	7,856,571	$	—	$	7,856,558	$	13
Mortgage backed securities	630,001		—		630,001		—
Municipal bonds	494,522		—		494,522		—
Commercial mortgage backed securities	389,900		—		389,900		—
U.S. government and government agencies	5,557,077		5,463,356		93,721		—
Non-U.S. government securities	2,433,733		—		2,433,733		—
Asset backed securities	1,634,804		—		1,631,378		3,426
Total	18,996,608		5,463,356		13,529,813		3,439
Short-term investments	1,924,922		1,920,565		4,357		—
Equity securities, at fair value	1,460,959		1,401,653		17,291		42,015
Derivative instruments (4)	177,383		—		177,383		—
Fair value option:
Corporate bonds	651,294		—		650,309		985
Non-U.S. government bonds	35,263		—		35,263		—
Mortgage backed securities	3,282		—		3,282		—
Commercial mortgage backed securities	1,090		—		1,090		—
Asset backed securities	152,151		—		152,151		—
U.S. government and government agencies	274		164		110		—
Short-term investments	557,008		420,131		136,877		—
Equity securities	92,549		23,373		188		68,988
Other investments	1,134,229		51,149		1,015,977		67,103
Other investments measured at net asset value (2)	1,197,656
Total	3,824,796		494,817		1,995,247		137,076
Total assets measured at fair value	$	26,384,668	$	9,280,391	$	15,724,091	$	182,530
Liabilities measured at fair value:
Contingent consideration liabilities	$	(461)	$	—	$	—	$	(461)
Securities sold but not yet purchased (3)	(21,679)		—		(21,679)		—
Derivative instruments (4)	(108,705)		—		(108,705)		—
Total liabilities measured at fair value	$	(130,845)	$	—	$	(130,384)	$	(461)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See note 7, “—Securities Lending Agreements.”

(2)    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.

(3)    Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets.

(4)    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		Contingent Consideration Liabilities
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		—
Included in other comprehensive income	(57)		—		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		—		5,638		—		5,102		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(301)		—		—		—
Settlements	(3)		—		—		—		—		—		(1)
Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of period	$	3,424	$	13	$	998	$	73,900	$	73,678	$	49,136	$	(466)
Three Months Ended June 30, 2020
Balance at beginning of period	$	3,846	$	1,980	$	965	$	54,620	$	60,015	$	55,632	$	(7,967)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	(64)		—		—		(987)		1,432		11,799		(18)
Included in other comprehensive income	(287)		(1,123)		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		33		3		—		—		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(7,183)		—		(15,450)		—
Settlements	(45)		—		—		—		—		—		6,735
Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of period	$	3,450	$	857	$	998	$	46,453	$	61,447	$	51,981	$	(1,250)
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		—
Included in other comprehensive income	57		—		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		—		13,003		—		5,295		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(7,087)		—		—		—
Settlements	(3)		—		—		—		—		—		(5)
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, 2020
Balance at beginning of year	$	5,216	$	8,851	$	932	$	68,817	$	58,094	$	55,889	$	(7,998)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	(55)		7		—		(1,014)		3,353		8,078		(72)
Included in other comprehensive income	(309)		(6,539)		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		66		24		—		3,464		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(24,358)		—		(15,450)		—
Settlements	(1,402)		(1,462)		—		—		—		—		6,820
Transfers in and/or out of Level 3	—		—		—		2,984		—		—		—
Balance at end of period	$	3,450	$	857	$	998	$	46,453	$	61,447	$	51,981	$	(1,250)

(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, 2021, 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, 2021, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.9 billion and had a fair value of $3.5 billion. At December 31, 2020, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.9 billion and had a fair value of $3.7 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.

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Derivative Instruments

6 Months Ended

Jun. 30, 2021

Derivative Instruments and Hedging Activities Disclosure [Abstract]

Derivative Instruments

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		Liability Derivatives		Notional Value (1)
June 30, 2021
Futures contracts (2)	$	36,277	$	(21,515)	$	2,907,342
Foreign currency forward contracts (2)	8,242		(20,729)		1,573,973
Other (2)	53,969		(25,060)		4,838,552
Total	$	98,488	$	(67,304)
December 31, 2020
Futures contracts (2)	$	11,046	$	(4,496)	$	3,099,796
Foreign currency forward contracts (2)	52,716		(6,202)		1,656,729
Other (2)	113,621		(98,007)		5,763,919
Total	$	177,383	$	(108,705)

(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.’

The Company did not hold any derivatives which were designated as hedging instruments at June 30, 2021 or December 31, 2020.

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, 2021, asset derivatives and liability derivatives of $89.9 million and $66.7 million, respectively, were subject to a master netting agreement, compared to $138.8 million and $93.0 million, respectively, at December 31, 2020. 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:	2021		2020
Three Months Ended
Net realized gains (losses):
Futures contracts	$	(54,759)	$	(1,607)
Foreign currency forward contracts	1,295		3,523
TBAs	—		264
Other (1)	2,355		(3,016)
Total	$	(51,109)	$	(836)
Six Months Ended
Net realized gains (losses):
Futures contracts	$	(7,321)	$	94,337
Foreign currency forward contracts	(20,776)		(7,347)
TBAs	—		1,009
Other (1)	13,104		38,354
Total	$	(14,993)	$	126,353

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

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Commitments and Contingencies

6 Months Ended

Jun. 30, 2021

Commitments and Contingencies Disclosure [Abstract]

Commitments and Contingencies

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 $2.4 billion at June 30, 2021, compared to $2.1 billion at December 31, 2020.

Interest Paid

Interest paid on the Company’s senior notes and other borrowings were $74.7 million for the six months ended June 30, 2021, compared to $57.4 million for the 2020 period.

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Variable Interest Entities and Noncontrolling Interests

6 Months Ended

Jun. 30, 2021

Noncontrolling Interest [Abstract]

Variable Interest Entity and Noncontrolling Interests

Variable Interest Entities and Noncontrolling Interests

Watford

In March 2014, the Company invested $100.0 million and acquired 2,500,000 common shares, approximately 11% of Watford’s outstanding common equity. As of June 30, 2021, the Company owned approximately 10.2% of Watford’s outstanding common equity. The Company also owns $35.0 million in aggregate principal amount of Watford Holdings Ltd’s 6.5% senior notes, due July 2, 2029 and approximately 6.6% of Watford’s preference shares.

Watford is considered a VIE and the Company concluded that it is the primary beneficiary of Watford, through June 30, 2021. As such, the results of Watford are included in the

Company’s consolidated financial statements as of and for the periods ended June 30, 2021.

The Company does not guarantee or provide credit support for Watford, and the Company’s financial exposure to Watford is limited to its investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from reinsurance transactions.

In the 2020 fourth quarter, Arch Capital, Watford Holdings Ltd. and Greysbridge Ltd., a wholly-owned subsidiary of Arch Capital, entered into an Agreement and Plan of Merger (as amended, the “Merger Agreement”) pursuant to which, among other things, Arch Capital agreed to acquire all of the common shares of Watford Holdings Ltd. not owned by Arch for a cash purchase price of $35.00 per common share. Arch Capital assigned its rights under the Merger Agreement to Greysbridge Holdings Ltd., a wholly-owned subsidiary of Arch Capital (“Greysbridge”). The merger and the related Greysbridge equity financing closed on July 1, 2021. Effective July 1, 2021, Watford is wholly owned by Greysbridge and Greysbridge is owned 40% by Arch Re Bermuda, 30% by certain investment funds managed by Kelso & Company and 30% by certain investment funds managed by Warburg Pincus LLC. See note 16.

The following table provides the carrying amount and balance sheet caption in which the assets and liabilities of Watford are reported:

	June 30,		December 31,
	2021		2020
Assets
Investments accounted for using the fair value option (1)	$	1,984,919	$	1,790,385
Fixed maturities available for sale, at fair value	663,902		655,249
Equity securities, at fair value	97,623		52,410
Cash	349,202		211,451
Accrued investment income	14,549		14,679
Premiums receivable	305,026		224,377
Reinsurance recoverable on unpaid and paid losses and LAE	520,531		286,590
Ceded unearned premiums	123,272		122,339
Deferred acquisition costs	65,532		53,705
Receivable for securities sold	102,287		37,423
Goodwill and intangible assets	10,318		7,650
Other assets	112,794		75,801
Total assets of consolidated VIE	$	4,349,955	$	3,532,059
Liabilities
Reserve for losses and loss adjustment expenses	$	1,916,742	$	1,519,583
Unearned premiums	468,948		407,714
Reinsurance balances payable	132,929		63,269
Revolving credit agreement borrowings	155,687		155,687
Senior notes	172,825		172,689
Payable for securities purchased	199,342		25,881
Other liabilities	227,396		193,494
Total liabilities of consolidated VIE	$	3,273,869	$	2,538,317
Redeemable noncontrolling interests	$	52,444	$	52,398

(1)    Included in “other investments” on the Company’s balance sheet.

For the six months ended June 30, 2021, Watford 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, compared to $87.3 million of cash provided by operating activities, $78.0 million of cash provided by investing activities and $153.8 million of cash used for financing activities for the six months ended June 30, 2020.

Non-redeemable noncontrolling interests

The Company accounts for the portion of Watford’s common equity attributable to third party investors in the shareholders’ equity section of its consolidated balance sheets. The noncontrolling ownership in Watford’s common shares was approximately 90% at June 30, 2021. The portion of Watford’s income or loss attributable to third party investors is 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		2020
Three Months Ended
Balance, beginning of period	$	876,864	$	492,785
Additional paid in capital attributable to noncontrolling interests	383		595
Amounts attributable to noncontrolling interests	41,617		165,598
Other comprehensive income (loss) attributable to noncontrolling interests	10		20,111
Balance, end of period	$	918,874	$	679,089
Six Months Ended
Balance, beginning of year	$	823,007	$	762,777
Additional paid in capital attributable to noncontrolling interests	22,113		472
Repurchases attributable to non-redeemable noncontrolling interests (1)	—		(2,867)
Amounts attributable to noncontrolling interests	78,314		(68,346)
Other comprehensive income (loss) attributable to noncontrolling interests	(4,560)		(12,947)
Balance, end of period	$	918,874	$	679,089

(1) During 2020, Watford’s board of directors authorized the investment in Watford’s common shares through a share repurchase program.

Redeemable noncontrolling interests

The Company accounts for redeemable noncontrolling interests in the mezzanine section of its consolidated balance sheets in accordance with applicable accounting guidance. Such redeemable noncontrolling interests primarily relate to the Watford 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 Watford Preference Shares were issued at a discounted amount of $24.50 per share. Preferred dividends, including the accretion of the discount and issuance costs, are 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,
	2021		2020
Three Months Ended
Balance, beginning of period	$	57,670	$	55,376
Accretion of preference share issuance costs	23		23
Other	(160)		587
Balance, end of period	$	57,533	$	55,986
Six Months Ended
Balance, beginning of year	$	58,548	$	55,404
Accretion of preference share issuance costs	46		46
Other	(1,061)		536
Balance, end of period	$	57,533	$	55,986

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,
	2021		2020
Three Months Ended
Amounts attributable to non-redeemable noncontrolling interests	$	(41,617)	$	(165,598)
Amounts attributable to redeemable noncontrolling interests	(1,561)		(1,970)
Net (income) loss attributable to noncontrolling interests	$	(43,178)	$	(167,568)
Six Months Ended
Amounts attributable to non-redeemable noncontrolling interests	$	(78,314)	$	68,346
Amounts attributable to redeemable noncontrolling interests	(2,416)		(3,123)
Net (income) loss attributable to noncontrolling interests	$	(80,730)	$	65,223

Bellemeade Re

The Company has entered into various aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda (the “Bellemeade Agreements”). 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 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, 2021								December 31, 2020
			Maximum Exposure to Loss								Maximum Exposure to Loss
Bellemeade Entities (Issue Date)	Total VIE Assets		On-Balance Sheet (Asset) Liability		Off-Balance Sheet		Total		Total VIE Assets		On-Balance Sheet (Asset) Liability		Off-Balance Sheet		Total
Bellemeade 2017-1 Ltd. (Oct-17)	$	145,573	$	(283)	$	779	$	496	$	145,573	$	(245)	$	844	$	599
Bellemeade 2018-1 Ltd. (Apr-18)	250,095		(909)		1,984		1,075		250,095		(903)		2,245		1,342
Bellemeade 2018-2 Ltd. (Aug-18)	—		—		—		—		108,395		(138)		280		142
Bellemeade 2018-3 Ltd. (Oct-18)	302,563		(1,622)		3,706		2,084		302,563		(1,320)		3,262		1,942
Bellemeade 2019-1 Ltd. (Mar-19)	219,256		(1,237)		8,204		6,967		219,256		(1,361)		8,461		7,100
Bellemeade 2019-2 Ltd. (Apr-19)	398,316		(1,042)		6,723		5,681		398,316		(730)		5,201		4,471
Bellemeade 2019-3 Ltd. (Jul-19)	528,084		(969)		4,527		3,558		528,084		(861)		5,079		4,218
Bellemeade 2019-4 Ltd. (Oct-19)	468,737		(1,051)		7,128		6,077		468,737		(890)		6,676		5,786
Bellemeade 2020-1 Ltd. (Jun-20) (1)	18,843		—		—		—		275,068		(178)		1,012		834
Bellemeade 2020-2 Ltd. (Sep-20) (2)	325,712		(442)		4,299		3,857		423,420		(556)		6,839		6,283
Bellemeade 2020-3 Ltd. (Nov-20) (3)	418,158		(618)		8,250		7,632		418,158		(631)		9,605		8,974
Bellemeade 2020-4 Ltd. (Dec-20) (4)	268,405		(150)		3,891		3,741		321,393		(156)		6,816		6,660
Bellemeade 2021-1 Ltd. (Mar-21) (5)	579,717		(83)		4,387		4,304		—		—		—		—
Bellemeade 2021-2 Ltd. (Jun-21) (6)	522,807		630		5,207		5,837		—		—		—		—
Total	$	4,446,266	$	(7,776)	$	59,085	$	51,309	$	3,859,058	$	(7,969)	$	56,320	$	48,351

(1)  An additional $79 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(2)  An additional $26 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(3)  An additional $34 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(4)  An additional $16 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(5)  An additional $64 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(6)  An additional $93 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

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Other Comprehensive Income (Loss)

6 Months Ended

Jun. 30, 2021

Comprehensive Income Note Disclosure [Abstract]

Other Comprehensive Income (Loss)

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	2021		2020		2021		2020
Unrealized appreciation on available-for-sale investments
	Net realized gains (losses)	$	64,914	$	182,329	$	66,918	$	328,561
	Provision for credit losses	896		3,225		(751)		(6,095)
	Other-than-temporary impairment losses	—		—		—		(533)
	Total before tax	65,810		185,554		66,167		321,933
	Income tax (expense) benefit	(5,263)		(18,163)		(8,317)		(33,313)
	Net of tax	$	60,547	$	167,391	$	57,850	$	288,620

	Before Tax Amount		Tax Expense (Benefit)		Net of Tax Amount
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
Three Months Ended June 30, 2020
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	555,576	$	62,780	$	492,796
Less reclassification of net realized gains (losses) included in net income	185,554		18,163		167,391
Foreign currency translation adjustments	22,595		344		22,251
Other comprehensive income (loss)	$	392,617	$	44,961	$	347,656
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)
Six Months Ended June 30, 2020
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	492,125	$	56,616	$	435,509
Less reclassification of net realized gains (losses) included in net income	321,933		33,313		288,620
Foreign currency translation adjustments	(22,829)		(391)		(22,438)
Other comprehensive income (loss)	$	147,363	$	22,912	$	124,451

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Income Taxes

6 Months Ended

Jun. 30, 2021

Income Tax Disclosure [Abstract]

Income Taxes

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 7.0% for the six months ended June 30, 2021, compared to 12.5% for the six months ended June 30, 2020.

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 $93.0 million at June 30, 2021, compared to a net deferred tax asset of $15.7 million at December 31, 2020. The change is primarily a result of mortgage contingency reserves activity and market value fluctuations in the investment portfolio. In addition, the Company paid $141.1 million and $10.4 million of income taxes for the six months ended June 30, 2021 and 2020, respectively.

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Legal Proceedings	6 Months Ended
	Jun. 30, 2021
Disclosure Legal Proceedings [Abstract]
Legal Proceedings	Legal ProceedingsThe 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, 2021, the Company was not a party to any litigation or arbitration which is expected by management to have a material adverse effect on the Company’s results of operations and financial condition and liquidity.

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Transactions With Related Parties	6 Months Ended
	Jun. 30, 2021
Related Party Transactions [Abstract]
Transactions with related parties	Transactions with Related PartiesIn 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. Barbican recorded reinsurance recoverable on unpaid and paid losses and funds held liability of nil and $9.9 million, respectively, at June 30, 2021, compared to $199.8 million and $149.6 million, respectively, at December 31, 2020. Certain directors and executive officers of the Company own common and preference shares of Watford. See note 11, “Variable Interest Entity and Noncontrolling Interests,” for information about Watford.

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Subsequent Events	6 Months Ended
	Jun. 30, 2021
Subsequent Events [Abstract]
Subsequent Event	Subsequent EventIn July 2021, the Company announced the completion of the previously disclosed acquisition of Watford by Greysbridge. Based on the governing documents of Greysbridge the Company has concluded that, while it will retain significant influence over Watford, Watford will no longer constitute a variable interest entity of which the Company is the primary beneficiary. Accordingly, effective July 1, 2021, Arch will no longer consolidate the results of Watford in its consolidated financial statements and footnotes. As a result of the closing of the transaction, we expect to report a net gain of approximately $65 million in the third quarter.

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Basis of Presentation and Recent Accounting Pronouncements (Policies)

6 Months Ended

Jun. 30, 2021

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, including the correct presentation of ‘income (loss) from operating affiliates’ on its consolidated statements of income for all periods presented to reclass such item from ‘other income (loss)’. The Company also changed its presentation of ‘investment in operating affiliates’ on its consolidated balance sheet for all periods presented to reclass such item from ‘other assets’. Such reclassifications had no effect on the Company’s net income, comprehensive income, shareholders’ equity or cash flows. Management views the impact of the prior period misclassification as not material to the financial statements on a quantitative and qualitative basis. See note 7.

Recent accounting pronouncements

Recently Issued Accounting Standards Adopted

The Company adopted ASU 2019-12, “Simplifying the Accounting for Income Taxes.” This ASU eliminates certain exceptions for recognizing deferred taxes for investments, performing intraperiod tax allocations and calculating income taxes in interim periods. The ASU also clarifies the accounting for transactions that result in a step-up in the tax basis of goodwill. The adoption of this guidance did not have a material effect on the Company’s consolidated financial statements.

For information regarding additional accounting standards that the Company has not yet adopted, see note 3(r), “Significant Accounting Policies—Recent Accounting Pronouncements,” of the notes to consolidated financial statements in the Company’s 2020 Form 10-K

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Earnings Per Common Share (Tables)

6 Months Ended

Jun. 30, 2021

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,
	2021		2020		2021		2020
Numerator:
Net income (loss)	$	718,664	$	466,389	$	1,194,372	$	377,715
Amounts attributable to noncontrolling interests	(43,178)		(167,568)		(80,730)		65,223
Net income (loss) available to Arch	675,486		298,821		1,113,642		442,938
Preferred dividends	(11,666)		(10,403)		(22,069)		(20,806)
Net income (loss) available to Arch common shareholders	$	663,820	$	288,418	$	1,091,573	$	422,132
Denominator:
Weighted average common shares and common share equivalents outstanding — basic	397,743,402		402,503,687		399,267,183		403,197,924
Effect of dilutive common share equivalents:
Nonvested restricted shares	1,990,729		1,597,701		1,932,929		1,829,239
Stock options (1)	6,751,863		4,018,293		6,487,568		5,978,428
Weighted average common shares and common share equivalents outstanding — diluted	406,485,994		408,119,681		407,687,680		411,005,591
Earnings per common share:
Basic	$	1.67	$	0.72	$	2.73	$	1.05
Diluted	$	1.63	$	0.71	$	2.68	$	1.03

(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 2021 second quarter and 2020 second quarter, the number of stock options excluded were 1,974,849 and 6,982,107, respectively. For the six months ended June 30, 2021 and 2020 period, the number of stock options excluded were 2,395,749 and 2,038,758, respectively.

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Segment Information (Tables)

6 Months Ended

Jun. 30, 2021

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, 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.’

	Three Months Ended
	June 30, 2020
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	1,030,362		$	807,065		$	369,144		$	2,206,410		$	157,927		$	2,317,692
Premiums ceded	(358,101)			(241,971)			(44,044)			(643,955)			(52,071)			(649,381)
Net premiums written	672,261			565,094			325,100			1,562,455			105,856			1,668,311
Change in unearned premiums	15,648			(84,897)			40,613			(28,636)			25,679			(2,957)
Net premiums earned	687,909			480,197			365,713			1,533,819			131,535			1,665,354
Other underwriting income (loss)	—			(651)			6,450			5,799			868			6,667
Losses and loss adjustment expenses	(518,203)			(383,433)			(224,100)			(1,125,736)			(104,786)			(1,230,522)
Acquisition expenses	(107,671)			(90,522)			(34,052)			(232,245)			(22,544)			(254,789)
Other operating expenses	(118,757)			(38,716)			(37,574)			(195,047)			(14,202)			(209,249)
Underwriting income (loss)	$	(56,722)		$	(33,125)		$	76,437		(13,410)			(9,129)			(22,539)
Net investment income										101,031			30,454			131,485
Net realized gains (losses)										385,089			171,499			556,588
Equity in net income (loss) of investment funds accounted for using the equity method										(65,119)			—			(65,119)
Other income (loss)										33			—			33
Corporate expenses (2)										(16,943)			—			(16,943)
Transaction costs and other (2)										(977)			—			(977)
Amortization of intangible assets										(16,489)			—			(16,489)
Interest expense										(25,130)			(6,009)			(31,139)
Net foreign exchange gains (losses)										(42,438)			3,227			(39,211)
Income (loss) before income taxes and income (loss) from operating affiliates										305,647			190,042			495,689
Income tax (expense) benefit										(26,529)			402			(26,127)
Income (loss) from operating affiliates										(3,173)			—			(3,173)
Net income (loss)										275,945			190,444			466,389
Amounts attributable to redeemable noncontrolling interests										(934)			(1,036)			(1,970)
Amounts attributable to nonredeemable noncontrolling interests										—			(165,598)			(165,598)
Net income (loss) available to Arch										275,011			23,810			298,821
Preferred dividends										(10,403)			—			(10,403)
Net income (loss) available to Arch common shareholders										$	264,608		$	23,810		$	288,418
Underwriting Ratios
Loss ratio	75.3		%	79.8		%	61.3		%	73.4		%	79.7		%	73.9		%
Acquisition expense ratio	15.7		%	18.9		%	9.3		%	15.1		%	17.1		%	15.3		%
Other operating expense ratio	17.3		%	8.1		%	10.3		%	12.7		%	10.8		%	12.6		%
Combined ratio	108.3		%	106.8		%	80.9		%	101.2		%	107.6		%	101.8		%
Goodwill and intangible assets	$	263,086		$	2,516		$	415,238		$	680,840		$	7,650		$	688,490

(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.’

	Six Months Ended
	June 30, 2020
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	2,238,007		$	1,929,584		$	738,089		$	4,904,947		$	392,829		$	5,150,522
Premiums ceded	(736,998)			(567,310)			(88,371)			(1,391,946)			(100,273)			(1,344,965)
Net premiums written	1,501,009			1,362,274			649,718			3,513,001			292,556			3,805,557
Change in unearned premiums	(97,181)			(338,617)			61,021			(374,777)			(20,982)			(395,759)
Net premiums earned	1,403,828			1,023,657			710,739			3,138,224			271,574			3,409,798
Other underwriting income (loss)	—			1,469			11,049			12,518			1,001			13,519
Losses and loss adjustment expenses	(1,025,311)			(813,502)			(291,666)			(2,130,479)			(215,462)			(2,345,941)
Acquisition expenses	(215,008)			(170,128)			(72,588)			(457,724)			(44,348)			(502,072)
Other operating expenses	(248,406)			(84,013)			(83,470)			(415,889)			(27,904)			(443,793)
Underwriting income (loss)	$	(84,897)		$	(42,517)		$	274,064		$	146,650		$	(15,139)		$	131,511
Net investment income										214,059			62,579			276,638
Net realized gains (losses)										312,980			(123,352)			189,628
Equity in net income (loss) of investment funds accounted for using the equity method										(69,328)			—			(69,328)
Other income (loss)										65			—			65
Corporate expenses (2)										(35,144)			—			(35,144)
Transaction costs and other (2)										(3,572)			—			(3,572)
Amortization of intangible assets										(33,120)			—			(33,120)
Interest expense										(50,375)			(13,319)			(63,694)
Net foreign exchange gains (losses)										20,869			12,591			33,460
Income (loss) before income taxes and income (loss) from operating affiliates										503,084			(76,640)			426,444
Income tax (expense) benefit										(54,474)			402			(54,072)
Income (loss) from operating affiliates										5,343			—			5,343
Net income (loss)										453,953			(76,238)			377,715
Amounts attributable to redeemable noncontrolling interests										(991)			(2,132)			(3,123)
Amounts attributable to nonredeemable noncontrolling interests										—			68,346			68,346
Net income (loss) available to Arch										452,962			(10,024)			442,938
Preferred dividends										(20,806)			—			(20,806)
Net income (loss) available to Arch common shareholders										$	432,156		$	(10,024)		$	422,132
Underwriting Ratios
Loss ratio	73.0		%	79.5		%	41.0		%	67.9		%	79.3		%	68.8		%
Acquisition expense ratio	15.3		%	16.6		%	10.2		%	14.6		%	16.3		%	14.7		%
Other operating expense ratio	17.7		%	8.2		%	11.7		%	13.3		%	10.3		%	13.0		%
Combined ratio	106.0		%	104.3		%	62.9		%	95.8		%	105.9		%	96.5		%

(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.’

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Reserve for Losses and Loss Adjustment Expenses (Tables)

6 Months Ended

Jun. 30, 2021

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,
	2021		2020		2021		2020
Reserve for losses and loss adjustment expenses at beginning of period	$	16,443,952	$	14,309,580	$	16,513,929	$	13,891,842
Unpaid losses and loss adjustment expenses recoverable	3,916,650		4,070,114		4,314,855		4,082,650
Net reserve for losses and loss adjustment expenses at beginning of period	12,527,302		10,239,466		12,199,074		9,809,192
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year	1,219,081		1,274,589		2,463,853		2,409,031
Prior years	(59,250)		(44,067)		(100,922)		(63,090)
Total net incurred losses and loss adjustment expenses	1,159,831		1,230,522		2,362,931		2,345,941
Retroactive reinsurance transactions (1)	—		—		(183,893)		60,635
Net foreign exchange (gains) losses	135,847		51,157		88,970		(91,416)
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year	(164,441)		(128,174)		(223,425)		(169,434)
Prior years	(607,911)		(504,254)		(1,193,029)		(1,066,201)
Total net paid losses and loss adjustment expenses	(772,352)		(632,428)		(1,416,454)		(1,235,635)
Net reserve for losses and loss adjustment expenses at end of period	13,050,628		10,888,717		13,050,628		10,888,717
Unpaid losses and loss adjustment expenses recoverable	4,146,020		4,156,157		4,146,020		4,156,157
Reserve for losses and loss adjustment expenses at end of period	$	17,196,648	$	15,044,874	$	17,196,648	$	15,044,874

(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”). During the 2020 first quarter, the Company entered into a reinsurance to close agreement of the 2017 and prior years of account previously covered by a third party arrangement.

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Allowance for Expected Credit Losses (Tables)

6 Months Ended

Jun. 30, 2021

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, 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
Three Months Ended June 30, 2020
Balance at beginning of period	$	2,155,204	$	27,990
Change for provision of expected credit losses (1)			8,064
Balance at end of period	$	2,203,753	$	36,054
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
Six Months Ended June 30, 2020
Balance at beginning of period	$	1,778,717	$	21,003
Cumulative effect of accounting change (2)			6,539
Change for provision of expected credit losses (1)			8,512
Balance at end of period	$	2,203,753	$	36,054

(1)Amounts deemed uncollectible are written-off in operating expenses. For the 2021 second quarter and 2020 second quarter, amounts written off were $1.1 million and $1.8 million, respectively. For the six months ended June 30, 2021 and 2020 period, amounts written off were were $1.2 million and $2.3 million, respectively.

(2)Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

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, 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
Three Months Ended June 30, 2020
Balance at beginning of period	$	4,303,135	$	13,700
Change for provision of expected credit losses			(105)
Balance at end of period	$	4,363,507	$	13,595
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
Six Months Ended June 30, 2020
Balance at beginning of period	$	4,346,816	$	1,364
Cumulative effect of accounting change (1)			12,010
Change for provision of expected credit losses			221
Balance at end of period	$	4,363,507	$	13,595

(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

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
	2021			2020
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	$	4,314,515		$	4,500,802
% due from carriers with A.M. Best rating of “A-” or better	66.0		%	63.9		%
% due from all other carriers with no A.M. Best rating (1)	34.0		%	36.1		%
Largest balance due from any one carrier as % of total shareholders’ equity	2.4		%	1.8		%

(1)    At June 30, 2021 and December 31, 2020 over 91% and 94% 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, 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
Three Months Ended June 30, 2020
Balance at beginning of period	$	2,140,724	$	9,038
Change for provision of expected credit losses			(2,748)
Balance at end of period	2,179,124		$	6,290
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
Six Months Ended June 30, 2020
Balance at beginning of period	$	2,119,460	$	—
Cumulative effect of accounting change (1)			6,663
Change for provision of expected credit losses			(373)
Balance at end of period	$	2,179,124	$	6,290

(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

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Investment Information (Tables)

6 Months Ended

Jun. 30, 2021

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 (2)		Cost or Amortized Cost
June 30, 2021
Fixed maturities (1):
Corporate bonds	$	7,129,768	$	217,061	$	(34,751)	$	(1,232)	$	6,948,690
Mortgage backed securities	389,041		4,480		(3,479)		(269)		388,309
Municipal bonds	415,483		23,153		(1,660)		(6)		393,996
Commercial mortgage backed securities	266,733		4,017		(611)		(3)		263,330
U.S. government and government agencies	5,091,183		14,814		(14,013)		—		5,090,382
Non-U.S. government securities	2,449,782		108,823		(18,441)		(128)		2,359,528
Asset backed securities	2,487,845		16,460		(4,056)		(486)		2,475,927
Total	18,229,835		388,808		(77,011)		(2,124)		17,920,162
Short-term investments	2,248,613		1,404		(1,406)		—		2,248,615
Total	$	20,478,448	$	390,212	$	(78,417)	$	(2,124)	$	20,168,777
December 31, 2020
Fixed maturities (1):
Corporate bonds	$	7,856,571	$	414,247	$	(34,388)	$	(896)	$	7,477,608
Mortgage backed securities	630,001		8,939		(5,028)		(278)		626,368
Municipal bonds	494,522		27,291		(3,835)		(11)		471,077
Commercial mortgage backed securities	389,900		8,722		(2,954)		(122)		384,254
U.S. government and government agencies	5,557,077		22,612		(12,611)		—		5,547,076
Non-U.S. government securities	2,433,733		153,891		(8,060)		—		2,287,902
Asset backed securities	1,634,804		19,225		(10,715)		(1,090)		1,627,384
Total	18,996,608		654,927		(77,591)		(2,397)		18,421,669
Short-term investments	1,924,922		2,693		(2,063)		—		1,924,292
Total	$	20,921,530	$	657,620	$	(79,654)	$	(2,397)	$	20,345,961

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

(2)    Effective January 1, 2020, the Company adopted ASU 2016-13 and as a result any credit impairment losses on the Company’s available-for-sale investments are recorded as an allowance, subject to reversal.

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, 2021
Fixed maturities (1):
Corporate bonds	$	2,264,801	$	(32,733)	$	22,895	$	(2,018)	$	2,287,696	$	(34,751)
Mortgage backed securities	196,765		(2,893)		13,632		(586)		210,397		(3,479)
Municipal bonds	24,711		(1,612)		2,859		(48)		27,570		(1,660)
Commercial mortgage backed securities	20,039		(180)		7,961		(431)		28,000		(611)
U.S. government and government agencies	2,920,944		(14,013)		—		—		2,920,944		(14,013)
Non-U.S. government securities	1,282,422		(17,562)		16,885		(879)		1,299,307		(18,441)
Asset backed securities	781,596		(2,364)		93,923		(1,692)		875,519		(4,056)
Total	7,491,278		(71,357)		158,155		(5,654)		7,649,433		(77,011)
Short-term investments	531,130		(1,406)		—		—		531,130		(1,406)
Total	$	8,022,408	$	(72,763)	$	158,155	$	(5,654)	$	8,180,563	$	(78,417)
December 31, 2020
Fixed maturities (1):
Corporate bonds	$	747,442	$	(33,086)	$	3,934	$	(1,302)	$	751,376	$	(34,388)
Mortgage backed securities	284,619		(4,788)		3,637		(240)		288,256		(5,028)
Municipal bonds	67,937		(3,835)		—		—		67,937		(3,835)
Commercial mortgage backed securities	126,624		(2,916)		2,655		(38)		129,279		(2,954)
U.S. government and government agencies	1,285,907		(12,611)		—		—		1,285,907		(12,611)
Non-U.S. government securities	543,844		(7,658)		2,441		(402)		546,285		(8,060)
Asset backed securities	634,470		(9,110)		57,737		(1,605)		692,207		(10,715)
Total	3,690,843		(74,004)		70,404		(3,587)		3,761,247		(77,591)
Short-term investments	97,920		(2,063)		—		—		97,920		(2,063)
Total	$	3,788,763	$	(76,067)	$	70,404	$	(3,587)	$	3,859,167	$	(79,654)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

Contractual maturities of the Company's fixed maturities and fixed maturities pledged under securities lending arrangements

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, 2021				December 31, 2020
Maturity	Estimated Fair Value		Amortized Cost		Estimated Fair Value		Amortized Cost
Due in one year or less	$	452,065	$	439,855	$	348,200	$	339,951
Due after one year through five years	10,114,276		9,942,182		10,629,959		10,340,819
Due after five years through 10 years	4,148,538		4,055,318		4,881,564		4,654,754
Due after 10 years	371,337		355,241		482,180		448,139
	15,086,216		14,792,596		16,341,903		15,783,663
Mortgage backed securities	389,041		388,309		630,001		626,368
Commercial mortgage backed securities	266,733		263,330		389,900		384,254
Asset backed securities	2,487,845		2,475,927		1,634,804		1,627,384
Total (1)	$	18,229,835	$	17,920,162	$	18,996,608	$	18,421,669

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

Securities lending transactions accounted for as secured borrowings, by significant investment category

The carrying value of collateral held under the Company’s securities lending transactions by significant investment category and remaining contractual maturity of the underlying agreements is as follows:

	Remaining Contractual Maturity of the Agreements
	Overnight and Continuous		Less than 30 Days		30-90 Days		90 Days or More		Total
June 30, 2021
U.S. government and government agencies	$	15,745	$	137,713	$	—	$	—	$	153,458
Corporate bonds	5,800		—		—		—		5,800
Equity securities	12,851		—		—		—		12,851
Total	$	34,396	$	137,713	$	—	$	—	$	172,109
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9									$	—
Amounts related to securities lending not included in offsetting disclosure in note 9									$	172,109
December 31, 2020
U.S. government and government agencies	$	142,317	$	—	$	139,290	$	—	$	281,607
Corporate bonds	3,021		—		—		—		3,021
Equity securities	16,461		—		—		—		16,461
Total	$	161,799	$	—	$	139,290	$	—	$	301,089
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9									$	—
Amounts related to securities lending not included in offsetting disclosure in note 9									$	301,089

Summary of assets and liabilities accounted for using the fair value option

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

	June 30, 2021		December 31, 2020
Fixed maturities	$	995,980	$	843,354
Other investments	2,370,472		2,331,885
Short-term investments	610,114		557,008
Equity securities	94,931		92,549
Investments accounted for using the fair value option	$	4,071,497	$	3,824,796
Other investable assets (1)	500,000		500,000
Total other investments	$	4,571,497	$	4,324,796

(1) Participation interests in a receivable of a reverse repurchase agreement.

Summary of other investments

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

	June 30, 2021		December 31, 2020
Term loan investments	$	1,333,014	$	1,231,731
Lending	638,786		572,636
Credit related funds	73,171		90,780
Energy	84,891		65,813
Investment grade fixed income	110,375		138,646
Infrastructure	32,109		165,516
Private equity	70,878		48,750
Real estate	27,248		18,013
Total	$	2,370,472	$	2,331,885

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, 2021		December 31, 2020
Credit related funds	$	883,279	$	740,060
Equities	403,003		343,058
Real estate	323,566		258,518
Lending	295,228		179,629
Private equity	305,662		235,289
Infrastructure	210,174		175,882
Energy	118,212		115,453
Total	$	2,539,124	$	2,047,889

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, 2021		December 31, 2020
Investments accounted for using the equity method (1)	2,539,124		2,047,889
Investments accounted for using the fair value option (2)	182,260		184,720
Total	$	2,721,384	$	2,232,609

(1)    Aggregate unfunded commitments were $2.0 billion at June 30, 2021, compared to $1.8 billion at December 31, 2020.

(2)    Aggregate unfunded commitments were $26.3 million at June 30, 2021, compared to $35.6 million at December 31, 2020.

Components of net investment income

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

	June 30,
	2021		2020
Three Months Ended
Fixed maturities	$	88,625	$	105,391
Term loans	16,879		20,512
Equity securities	8,584		6,219
Short-term investments	1,138		3,383
Other (1)	19,950		16,460
Gross investment income	135,176		151,965
Investment expenses	(23,563)		(20,480)
Net investment income	$	111,613	$	131,485
Six Months Ended
Fixed maturities	$	179,251	$	220,238
Term loans	31,607		43,682
Equity securities	14,234		12,226
Short-term investments	1,745		8,279
Other (1)	34,305		35,866
Gross investment income	261,142		320,291
Investment expenses	(50,673)		(43,653)
Net investment income	$	210,469	$	276,638

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

Summary of net realized gains (losses), excluding other-than-temporary impairment provisions

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,
	2021		2020
Three Months Ended
Available for sale securities:
Gross gains on investment sales	$	115,541	$	232,153
Gross losses on investment sales	(50,627)		(49,824)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	10,912		68,181
Other investments	60,884		178,570
Equity securities	5,492		6,664
Short-term investments	(104)		3,368
Equity securities, at fair value:
Net realized gains (losses) on sales during the period	33,570		(18,250)
Net unrealized gains (losses) on equity securities still held at reporting date	65,847		145,686
Allowance for credit losses:
Investments related	896		3,225
Underwriting related	1,381		(5,834)
Derivative instruments (1)	(51,109)		(836)
Other	10,224		(6,515)
Net realized gains (losses)	$	202,907	$	556,588
Six Months Ended
Available for sale securities:
Gross gains on investment sales	$	180,543	$	410,353
Gross losses on investment sales	(113,625)		(81,792)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	27,465		(59,485)
Other investments	107,739		(129,230)
Equity securities	7,557		1,755
Short-term investments	632		(5,313)
Equity securities, at fair value:
Net realized gains (losses) on sales during the period	71,419		(18,789)
Net unrealized gains (losses) on equity securities still held at reporting date	85,555		(29,880)
Allowance for credit losses:
Investments related	(752)		(6,095)
Underwriting related	6,649		(9,104)
Net impairments losses	—		(533)
Derivative instruments (1)	(14,993)		126,353
Other	(12,821)		(8,612)
Net realized gains (losses)	$	345,368	$	189,628

(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		Short Term Investments		Total
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
Three Months Ended June 30, 2020
Balance at beginning of period	$	2,654	$	23	$	7,232	$	29	$	9,938
Additions for current-period provision for expected credit losses	695		44		290		(29)		1,000
Additions (reductions) for previously recognized expected credit losses	(1,304)		(25)		(2,903)		—		(4,232)
Reductions due to disposals	(319)		(14)		(504)		—		(837)
Balance at end of period	$	1,726	$	28	$	4,115	$	—	$	5,869
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
Six Months Ended June 30, 2020
Balance at beginning of period	$	—	$	—	$	—	$	—	$	—
Cumulative effect of accounting change (2)	517		—		117		—		634
Additions for current-period provision for expected credit losses	2,841		67		7,441		—		10,349
Additions (reductions) for previously recognized expected credit losses	(1,306)		(25)		(2,924)		—		(4,255)
Reductions due to disposals	(326)		(14)		(519)		—		(859)
Balance at end of period	$	1,726	$	28	$	4,115	$	—	$	5,869

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

(2)    Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

Summary of restricted assets

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

	June 30, 2021		December 31, 2020
Assets used for collateral or guarantees:
Affiliated transactions	$	5,041,190	$	4,643,334
Third party agreements	3,441,929		3,083,324
Deposits with U.S. regulatory authorities	814,084		827,552
Deposits with non-U.S. regulatory authorities	428,132		179,099
Total restricted assets	$	9,725,335	$	8,733,309

Reconciliation of cash and restricted cash

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

	June 30, 2021		December 31, 2020
Cash	$	1,234,059	$	906,448
Restricted cash (included in ‘other assets’)	$	584,404	$	384,096
Cash and restricted cash	$	1,818,463	$	1,290,544

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Fair Value (Tables)

6 Months Ended

Jun. 30, 2021

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, 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 (1):
Available for sale securities:
Fixed maturities:
Corporate bonds	$	7,129,768	$	—	$	7,129,755	$	13
Mortgage backed securities	389,041		—		389,041		—
Municipal bonds	415,483		—		415,483		—
Commercial mortgage backed securities	266,733		—		266,733		—
U.S. government and government agencies	5,091,183		5,062,571		28,612		—
Non-U.S. government securities	2,449,782		—		2,449,782		—
Asset backed securities	2,487,845		—		2,484,421		3,424
Total	18,229,835		5,062,571		13,163,827		3,437
Short-term investments	2,248,613		1,996,304		252,309		—
Equity securities, at fair value	1,706,044		1,631,937		24,971		49,136
Derivative instruments (4)	98,488		—		98,488		—
Residential mortgage loans	44,925		—		44,925		—
Fair value option:
Corporate bonds	790,186		—		789,188		998
Non-U.S. government bonds	22,552		—		22,552		—
Mortgage backed securities	2,707		—		2,707		—
Commercial mortgage backed securities	841		—		841		—
Asset backed securities	179,423		—		179,423		—
U.S. government and government agencies	271		163		108		—
Short-term investments	610,114		482,815		127,299		—
Equity securities	94,930		21,252		—		73,678
Other investments	1,219,294		23,610		1,121,784		73,900
Other investments measured at net asset value (2)	1,151,178
Total	4,071,496		527,840		2,243,902		148,576
Total assets measured at fair value	$	26,399,401	$	9,218,652	$	15,828,422	$	201,149
Liabilities measured at fair value:
Contingent consideration liabilities	$	(466)	$	—	$	—	$	(466)
Securities sold but not yet purchased (3)	(28,068)		—		(28,068)		—
Derivative instruments (4)	(67,304)		—		(67,304)		—
Total liabilities measured at fair value	$	(95,838)	$	—	$	(95,372)	$	(466)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See note 7, “—Securities Lending Agreements.”

(2)    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.

(3)    Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets.

(4)    See note 9.

The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2020:

			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 (1):
Available for sale securities:
Fixed maturities:
Corporate bonds	$	7,856,571	$	—	$	7,856,558	$	13
Mortgage backed securities	630,001		—		630,001		—
Municipal bonds	494,522		—		494,522		—
Commercial mortgage backed securities	389,900		—		389,900		—
U.S. government and government agencies	5,557,077		5,463,356		93,721		—
Non-U.S. government securities	2,433,733		—		2,433,733		—
Asset backed securities	1,634,804		—		1,631,378		3,426
Total	18,996,608		5,463,356		13,529,813		3,439
Short-term investments	1,924,922		1,920,565		4,357		—
Equity securities, at fair value	1,460,959		1,401,653		17,291		42,015
Derivative instruments (4)	177,383		—		177,383		—
Fair value option:
Corporate bonds	651,294		—		650,309		985
Non-U.S. government bonds	35,263		—		35,263		—
Mortgage backed securities	3,282		—		3,282		—
Commercial mortgage backed securities	1,090		—		1,090		—
Asset backed securities	152,151		—		152,151		—
U.S. government and government agencies	274		164		110		—
Short-term investments	557,008		420,131		136,877		—
Equity securities	92,549		23,373		188		68,988
Other investments	1,134,229		51,149		1,015,977		67,103
Other investments measured at net asset value (2)	1,197,656
Total	3,824,796		494,817		1,995,247		137,076
Total assets measured at fair value	$	26,384,668	$	9,280,391	$	15,724,091	$	182,530
Liabilities measured at fair value:
Contingent consideration liabilities	$	(461)	$	—	$	—	$	(461)
Securities sold but not yet purchased (3)	(21,679)		—		(21,679)		—
Derivative instruments (4)	(108,705)		—		(108,705)		—
Total liabilities measured at fair value	$	(130,845)	$	—	$	(130,384)	$	(461)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See note 7, “—Securities Lending Agreements.”

(2)    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.

(3)    Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets.

(4)    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		Contingent Consideration Liabilities
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		—
Included in other comprehensive income	(57)		—		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		—		5,638		—		5,102		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(301)		—		—		—
Settlements	(3)		—		—		—		—		—		(1)
Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of period	$	3,424	$	13	$	998	$	73,900	$	73,678	$	49,136	$	(466)
Three Months Ended June 30, 2020
Balance at beginning of period	$	3,846	$	1,980	$	965	$	54,620	$	60,015	$	55,632	$	(7,967)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	(64)		—		—		(987)		1,432		11,799		(18)
Included in other comprehensive income	(287)		(1,123)		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		33		3		—		—		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(7,183)		—		(15,450)		—
Settlements	(45)		—		—		—		—		—		6,735
Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of period	$	3,450	$	857	$	998	$	46,453	$	61,447	$	51,981	$	(1,250)
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		—
Included in other comprehensive income	57		—		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		—		13,003		—		5,295		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(7,087)		—		—		—
Settlements	(3)		—		—		—		—		—		(5)
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, 2020
Balance at beginning of year	$	5,216	$	8,851	$	932	$	68,817	$	58,094	$	55,889	$	(7,998)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	(55)		7		—		(1,014)		3,353		8,078		(72)
Included in other comprehensive income	(309)		(6,539)		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		66		24		—		3,464		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(24,358)		—		(15,450)		—
Settlements	(1,402)		(1,462)		—		—		—		—		6,820
Transfers in and/or out of Level 3	—		—		—		2,984		—		—		—
Balance at end of period	$	3,450	$	857	$	998	$	46,453	$	61,447	$	51,981	$	(1,250)

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

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

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Derivative Instruments (Tables)

6 Months Ended

Jun. 30, 2021

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		Liability Derivatives		Notional Value (1)
June 30, 2021
Futures contracts (2)	$	36,277	$	(21,515)	$	2,907,342
Foreign currency forward contracts (2)	8,242		(20,729)		1,573,973
Other (2)	53,969		(25,060)		4,838,552
Total	$	98,488	$	(67,304)
December 31, 2020
Futures contracts (2)	$	11,046	$	(4,496)	$	3,099,796
Foreign currency forward contracts (2)	52,716		(6,202)		1,656,729
Other (2)	113,621		(98,007)		5,763,919
Total	$	177,383	$	(108,705)

(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.’

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:	2021		2020
Three Months Ended
Net realized gains (losses):
Futures contracts	$	(54,759)	$	(1,607)
Foreign currency forward contracts	1,295		3,523
TBAs	—		264
Other (1)	2,355		(3,016)
Total	$	(51,109)	$	(836)
Six Months Ended
Net realized gains (losses):
Futures contracts	$	(7,321)	$	94,337
Foreign currency forward contracts	(20,776)		(7,347)
TBAs	—		1,009
Other (1)	13,104		38,354
Total	$	(14,993)	$	126,353

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

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Variable Interest Entities and Noncontrolling Interests (Tables)

6 Months Ended

Jun. 30, 2021

Noncontrolling Interest [Abstract]

Carrying value of assets and liabilities of variable interest entity

The following table provides the carrying amount and balance sheet caption in which the assets and liabilities of Watford are reported:

	June 30,		December 31,
	2021		2020
Assets
Investments accounted for using the fair value option (1)	$	1,984,919	$	1,790,385
Fixed maturities available for sale, at fair value	663,902		655,249
Equity securities, at fair value	97,623		52,410
Cash	349,202		211,451
Accrued investment income	14,549		14,679
Premiums receivable	305,026		224,377
Reinsurance recoverable on unpaid and paid losses and LAE	520,531		286,590
Ceded unearned premiums	123,272		122,339
Deferred acquisition costs	65,532		53,705
Receivable for securities sold	102,287		37,423
Goodwill and intangible assets	10,318		7,650
Other assets	112,794		75,801
Total assets of consolidated VIE	$	4,349,955	$	3,532,059
Liabilities
Reserve for losses and loss adjustment expenses	$	1,916,742	$	1,519,583
Unearned premiums	468,948		407,714
Reinsurance balances payable	132,929		63,269
Revolving credit agreement borrowings	155,687		155,687
Senior notes	172,825		172,689
Payable for securities purchased	199,342		25,881
Other liabilities	227,396		193,494
Total liabilities of consolidated VIE	$	3,273,869	$	2,538,317
Redeemable noncontrolling interests	$	52,444	$	52,398

(1)    Included in “other investments” on the Company’s balance sheet.

Activity in non-redeemable noncontrolling interests

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

	June 30,
	2021		2020
Three Months Ended
Balance, beginning of period	$	876,864	$	492,785
Additional paid in capital attributable to noncontrolling interests	383		595
Amounts attributable to noncontrolling interests	41,617		165,598
Other comprehensive income (loss) attributable to noncontrolling interests	10		20,111
Balance, end of period	$	918,874	$	679,089
Six Months Ended
Balance, beginning of year	$	823,007	$	762,777
Additional paid in capital attributable to noncontrolling interests	22,113		472
Repurchases attributable to non-redeemable noncontrolling interests (1)	—		(2,867)
Amounts attributable to noncontrolling interests	78,314		(68,346)
Other comprehensive income (loss) attributable to noncontrolling interests	(4,560)		(12,947)
Balance, end of period	$	918,874	$	679,089

(1) During 2020, Watford’s board of directors authorized the investment in Watford’s common shares through a share repurchase program.

Activity in redeemable noncontrolling interests

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

	June 30,
	2021		2020
Three Months Ended
Balance, beginning of period	$	57,670	$	55,376
Accretion of preference share issuance costs	23		23
Other	(160)		587
Balance, end of period	$	57,533	$	55,986
Six Months Ended
Balance, beginning of year	$	58,548	$	55,404
Accretion of preference share issuance costs	46		46
Other	(1,061)		536
Balance, end of period	$	57,533	$	55,986

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,
	2021		2020
Three Months Ended
Amounts attributable to non-redeemable noncontrolling interests	$	(41,617)	$	(165,598)
Amounts attributable to redeemable noncontrolling interests	(1,561)		(1,970)
Net (income) loss attributable to noncontrolling interests	$	(43,178)	$	(167,568)
Six Months Ended
Amounts attributable to non-redeemable noncontrolling interests	$	(78,314)	$	68,346
Amounts attributable to redeemable noncontrolling interests	(2,416)		(3,123)
Net (income) loss attributable to noncontrolling interests	$	(80,730)	$	65,223

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 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, 2021								December 31, 2020
			Maximum Exposure to Loss								Maximum Exposure to Loss
Bellemeade Entities (Issue Date)	Total VIE Assets		On-Balance Sheet (Asset) Liability		Off-Balance Sheet		Total		Total VIE Assets		On-Balance Sheet (Asset) Liability		Off-Balance Sheet		Total
Bellemeade 2017-1 Ltd. (Oct-17)	$	145,573	$	(283)	$	779	$	496	$	145,573	$	(245)	$	844	$	599
Bellemeade 2018-1 Ltd. (Apr-18)	250,095		(909)		1,984		1,075		250,095		(903)		2,245		1,342
Bellemeade 2018-2 Ltd. (Aug-18)	—		—		—		—		108,395		(138)		280		142
Bellemeade 2018-3 Ltd. (Oct-18)	302,563		(1,622)		3,706		2,084		302,563		(1,320)		3,262		1,942
Bellemeade 2019-1 Ltd. (Mar-19)	219,256		(1,237)		8,204		6,967		219,256		(1,361)		8,461		7,100
Bellemeade 2019-2 Ltd. (Apr-19)	398,316		(1,042)		6,723		5,681		398,316		(730)		5,201		4,471
Bellemeade 2019-3 Ltd. (Jul-19)	528,084		(969)		4,527		3,558		528,084		(861)		5,079		4,218
Bellemeade 2019-4 Ltd. (Oct-19)	468,737		(1,051)		7,128		6,077		468,737		(890)		6,676		5,786
Bellemeade 2020-1 Ltd. (Jun-20) (1)	18,843		—		—		—		275,068		(178)		1,012		834
Bellemeade 2020-2 Ltd. (Sep-20) (2)	325,712		(442)		4,299		3,857		423,420		(556)		6,839		6,283
Bellemeade 2020-3 Ltd. (Nov-20) (3)	418,158		(618)		8,250		7,632		418,158		(631)		9,605		8,974
Bellemeade 2020-4 Ltd. (Dec-20) (4)	268,405		(150)		3,891		3,741		321,393		(156)		6,816		6,660
Bellemeade 2021-1 Ltd. (Mar-21) (5)	579,717		(83)		4,387		4,304		—		—		—		—
Bellemeade 2021-2 Ltd. (Jun-21) (6)	522,807		630		5,207		5,837		—		—		—		—
Total	$	4,446,266	$	(7,776)	$	59,085	$	51,309	$	3,859,058	$	(7,969)	$	56,320	$	48,351

(1)  An additional $79 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(2)  An additional $26 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(3)  An additional $34 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(4)  An additional $16 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(5)  An additional $64 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(6)  An additional $93 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

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Other Comprehensive Income (Loss) (Tables)

6 Months Ended

Jun. 30, 2021

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	2021		2020		2021		2020
Unrealized appreciation on available-for-sale investments
	Net realized gains (losses)	$	64,914	$	182,329	$	66,918	$	328,561
	Provision for credit losses	896		3,225		(751)		(6,095)
	Other-than-temporary impairment losses	—		—		—		(533)
	Total before tax	65,810		185,554		66,167		321,933
	Income tax (expense) benefit	(5,263)		(18,163)		(8,317)		(33,313)
	Net of tax	$	60,547	$	167,391	$	57,850	$	288,620

Schedule of comprehensive income (loss)

	Before Tax Amount		Tax Expense (Benefit)		Net of Tax Amount
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
Three Months Ended June 30, 2020
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	555,576	$	62,780	$	492,796
Less reclassification of net realized gains (losses) included in net income	185,554		18,163		167,391
Foreign currency translation adjustments	22,595		344		22,251
Other comprehensive income (loss)	$	392,617	$	44,961	$	347,656
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)
Six Months Ended June 30, 2020
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	492,125	$	56,616	$	435,509
Less reclassification of net realized gains (losses) included in net income	321,933		33,313		288,620
Foreign currency translation adjustments	(22,829)		(391)		(22,438)
Other comprehensive income (loss)	$	147,363	$	22,912	$	124,451

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Share Transactions - Share repurchases (Details) - Common shares - USD ($) shares in Millions, $ in Millions	6 Months Ended
	Jun. 30, 2021	Jun. 30, 2020
Class of Stock [Line Items]
Cumulative number of shares acquired since inception of share repurchase program	402.3
Aggregate purchase price of shares acquired since inception of share repurchase program	$ 4,540.0
Treasury stock, shares acquired (shares)	13.1	2.6
Shares repurchased for treasury	$ 485.3	$ 75.5
Remaining authorized repurchase amount	$ 431.2

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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, 2021	Jun. 30, 2020
Class of Stock [Line Items]
Proceeds from issuance of preferred shares, net		$ 485,821	$ 0
Series G Preferred Shares
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
Proceeds from issuance of preferred shares, net	$ 485,800
Series G Depositary Share Equivalent
Class of Stock [Line Items]
Preference shares, number of shares issued	20.0
Proportionate interest of preference shares, per depositary share	0.10%	0.10%
Liquidation preference per share	$ 25	$ 25
Preferred shares, redemption price per share	$ 25	$ 25

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Earnings Per Common Share (Details) - USD ($) $ / shares in Units, $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020
Numerator:
Net income (loss)		$ 718,664	$ 466,389	$ 1,194,372	$ 377,715
Amounts attributable to noncontrolling interests		(43,178)	(167,568)	(80,730)	65,223
Net income available to Arch		675,486	298,821	1,113,642	442,938
Preferred dividends		(11,666)	(10,403)	(22,069)	(20,806)
Net income (loss) available to Arch common shareholders		$ 663,820	$ 288,418	$ 1,091,573	$ 422,132
Denominator:
Weighted average common shares outstanding — basic		397,743,402	402,503,687	399,267,183	403,197,924
Effect of dilutive common share equivalents:
Nonvested restricted shares		1,990,729	1,597,701	1,932,929	1,829,239
Stock options	[1]	6,751,863	4,018,293	6,487,568	5,978,428
Weighted average common shares and common share equivalents outstanding — diluted		406,485,994	408,119,681	407,687,680	411,005,591
Earnings per common share:
Basic (per share)		$ 1.67	$ 0.72	$ 2.73	$ 1.05
Diluted (per share)		$ 1.63	$ 0.71	$ 2.68	$ 1.03
Stock options
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Antidilutive securities excluded from computation of earnings per common share (shares)		1,974,849	6,982,107	2,395,749	2,038,758

[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 2021 second quarter and 2020 second quarter, the number of stock options excluded were 1,974,849 and 6,982,107, respectively. For the six months ended June 30, 2021 and 2020 period, the number of stock options excluded were 2,395,749 and 2,038,758, respectively.

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Segment Information - Summary of underwriting income or loss by segment (Details) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2021 USD ($)	Jun. 30, 2020 USD ($)	Jun. 30, 2021 USD ($) segment	Jun. 30, 2020 USD ($)	Dec. 31, 2020 USD ($)
Segment Reporting Information [Line Items]
Gross premiums written		$ 3,286,291	$ 2,317,692	$ 6,683,497	$ 5,150,522
Premiums ceded		(886,767)	(649,381)	(1,775,516)	(1,344,965)
Net premiums written		2,399,524	1,668,311	4,907,981	3,805,557
Change in unearned premiums		(278,615)	(2,957)	(838,650)	(395,759)
Net premiums earned		2,120,909	1,665,354	4,069,331	3,409,798
Other underwriting income (loss)		5,529	6,667	11,639	13,519
Losses and loss adjustment expenses		(1,159,831)	(1,230,522)	(2,362,931)	(2,345,941)
Acquisition expenses		(335,143)	(254,789)	(639,624)	(502,072)
Other operating expenses		(244,943)	(209,249)	(505,976)	(443,793)
Underwriting income (loss)		386,521	(22,539)	572,439	131,511
Net investment income		111,613	131,485	210,469	276,638
Net realized gains (losses)		202,907	556,588	345,368	189,628
Equity in net income (loss) of investment funds accounted for using the equity method		122,186	(65,119)	193,872	(69,328)
Other income (loss)		6,852	33	5,111	65
Corporate expenses		(17,175)	(16,943)	(40,643)	(35,144)
Transaction costs and other		1,224	(977)	(692)	(3,572)
Amortization of intangible assets		(15,286)	(16,489)	(29,688)	(33,120)
Interest expense		(35,700)	(31,139)	(74,046)	(63,694)
Net foreign exchange gains (losses)		(17,775)	(39,211)	2,288	33,460
Income (loss) before income taxes and income (loss) from operating affiliates		745,367	495,689	1,184,478	426,444
Income tax expense (benefit)		(51,179)	(26,127)	(90,039)	(54,072)
Income (loss) from operating affiliates		24,476	(3,173)	99,933	5,343
Net income (loss)		718,664	466,389	1,194,372	377,715
Amounts attributable to redeemable noncontrolling interests		(1,561)	(1,970)	(2,416)	(3,123)
Amounts attributable to non-redeemable noncontrolling interests		(41,617)	(165,598)	(78,314)	68,346
Net income (loss) available to Arch		675,486	298,821	1,113,642	442,938
Preferred dividends		(11,666)	(10,403)	(22,069)	(20,806)
Net income (loss) available to Arch common shareholders		$ 663,820	$ 288,418	$ 1,091,573	$ 422,132
Underwriting Ratios
Loss ratio		54.70%	73.90%	58.10%	68.80%
Acquisition expense ratio		15.80%	15.30%	15.70%	14.70%
Other operating expense ratio		11.50%	12.60%	12.40%	13.00%
Combined ratio		82.00%	101.80%	86.20%	96.50%
Goodwill and intangible assets		$ 667,153	$ 688,490	$ 667,153	$ 688,490	$ 692,863
Corporate and Other Segments
Segment Reporting Information [Line Items]
Number of segments | segment				2
Operating segments
Segment Reporting Information [Line Items]
Number of segments | segment				3
Operating segments | Underwriting Segments
Segment Reporting Information [Line Items]
Gross premiums written	[1]	3,117,505	2,206,410	$ 6,394,798	4,904,947
Premiums ceded		(893,372)	(643,955)	(1,841,519)	(1,391,946)
Net premiums written		2,224,133	1,562,455	4,553,279	3,513,001
Change in unearned premiums		(287,461)	(28,636)	(815,916)	(374,777)
Net premiums earned		1,936,672	1,533,819	3,737,363	3,138,224
Other underwriting income (loss)		5,201	5,799	10,900	12,518
Losses and loss adjustment expenses		(1,019,583)	(1,125,736)	(2,103,889)	(2,130,479)
Acquisition expenses		(300,554)	(232,245)	(576,883)	(457,724)
Other operating expenses		(226,349)	(195,047)	(473,107)	(415,889)
Underwriting income (loss)		$ 395,387	$ (13,410)	$ 594,384	$ 146,650
Underwriting Ratios
Loss ratio		52.60%	73.40%	56.30%	67.90%
Acquisition expense ratio		15.50%	15.10%	15.40%	14.60%
Other operating expense ratio		11.70%	12.70%	12.70%	13.30%
Combined ratio		79.80%	101.20%	84.40%	95.80%
Goodwill and intangible assets		$ 656,835	$ 680,840	$ 656,835	$ 680,840
Operating segments | Insurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	1,368,867	1,030,362	2,784,753	2,238,007
Premiums ceded		(405,312)	(358,101)	(826,359)	(736,998)
Net premiums written		963,555	672,261	1,958,394	1,501,009
Change in unearned premiums		(98,128)	15,648	(273,493)	(97,181)
Net premiums earned		865,427	687,909	1,684,901	1,403,828
Other underwriting income (loss)		0	0	0	0
Losses and loss adjustment expenses		(545,880)	(518,203)	(1,081,627)	(1,025,311)
Acquisition expenses		(136,852)	(107,671)	(265,074)	(215,008)
Other operating expenses		(133,342)	(118,757)	(270,455)	(248,406)
Underwriting income (loss)		$ 49,353	$ (56,722)	$ 67,745	$ (84,897)
Underwriting Ratios
Loss ratio		63.10%	75.30%	64.20%	73.00%
Acquisition expense ratio		15.80%	15.70%	15.70%	15.30%
Other operating expense ratio		15.40%	17.30%	16.10%	17.70%
Combined ratio		94.30%	108.30%	96.00%	106.00%
Goodwill and intangible assets		$ 270,262	$ 263,086	$ 270,262	$ 263,086
Operating segments | Reinsurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	1,358,020	807,065	2,829,080	1,929,584
Premiums ceded		(433,288)	(241,971)	(905,236)	(567,310)
Net premiums written		924,732	565,094	1,923,844	1,362,274
Change in unearned premiums		(187,708)	(84,897)	(541,920)	(338,617)
Net premiums earned		737,024	480,197	1,381,924	1,023,657
Other underwriting income (loss)		1,053	(651)	(145)	1,469
Losses and loss adjustment expenses		(463,823)	(383,433)	(948,693)	(813,502)
Acquisition expenses		(133,585)	(90,522)	(251,610)	(170,128)
Other operating expenses		(44,695)	(38,716)	(105,209)	(84,013)
Underwriting income (loss)		$ 95,974	$ (33,125)	$ 76,267	$ (42,517)
Underwriting Ratios
Loss ratio		62.90%	79.80%	68.70%	79.50%
Acquisition expense ratio		18.10%	18.90%	18.20%	16.60%
Other operating expense ratio		6.10%	8.10%	7.60%	8.20%
Combined ratio		87.10%	106.80%	94.50%	104.30%
Goodwill and intangible assets		$ 16,168	$ 2,516	$ 16,168	$ 2,516
Operating segments | Mortgage
Segment Reporting Information [Line Items]
Gross premiums written	[1]	391,511	369,144	782,757	738,089
Premiums ceded		(55,665)	(44,044)	(111,716)	(88,371)
Net premiums written		335,846	325,100	671,041	649,718
Change in unearned premiums		(1,625)	40,613	(503)	61,021
Net premiums earned		334,221	365,713	670,538	710,739
Other underwriting income (loss)		4,148	6,450	11,045	11,049
Losses and loss adjustment expenses		(9,880)	(224,100)	(73,569)	(291,666)
Acquisition expenses		(30,117)	(34,052)	(60,199)	(72,588)
Other operating expenses		(48,312)	(37,574)	(97,443)	(83,470)
Underwriting income (loss)		$ 250,060	$ 76,437	$ 450,372	$ 274,064
Underwriting Ratios
Loss ratio		3.00%	61.30%	11.00%	41.00%
Acquisition expense ratio		9.00%	9.30%	9.00%	10.20%
Other operating expense ratio		14.50%	10.30%	14.50%	11.70%
Combined ratio		26.50%	80.90%	34.50%	62.90%
Goodwill and intangible assets		$ 370,405	$ 415,238	$ 370,405	$ 415,238
Operating segments | Corporate
Segment Reporting Information [Line Items]
Net investment income		89,430	101,031	168,159	214,059
Net realized gains (losses)		163,394	385,089	264,730	312,980
Equity in net income (loss) of investment funds accounted for using the equity method		122,186	(65,119)	193,872	(69,328)
Other income (loss)		6,852	33	5,111	65
Corporate expenses	[2]	(17,175)	(16,943)	(40,643)	(35,144)
Transaction costs and other	[2]	1,444	(977)	243	(3,572)
Amortization of intangible assets		(14,388)	(16,489)	(28,790)	(33,120)
Interest expense		(31,439)	(25,130)	(65,636)	(50,375)
Net foreign exchange gains (losses)		(17,892)	(42,438)	3,613	20,869
Income (loss) before income taxes and income (loss) from operating affiliates		697,799	305,647	1,095,043	503,084
Income tax expense (benefit)		(50,953)	(26,529)	(89,805)	(54,474)
Income (loss) from operating affiliates		24,476	(3,173)	99,933	5,343
Net income (loss)		671,322	275,945	1,105,171	453,953
Amounts attributable to redeemable noncontrolling interests		(580)	(934)	(463)	(991)
Amounts attributable to non-redeemable noncontrolling interests		0	0	0	0
Net income (loss) available to Arch		670,742	275,011	1,104,708	452,962
Preferred dividends		(11,666)	(10,403)	(22,069)	(20,806)
Net income (loss) available to Arch common shareholders		659,076	264,608	1,082,639	432,156
Operating segments | Other
Segment Reporting Information [Line Items]
Gross premiums written	[1]	240,942	157,927	457,465	392,829
Premiums ceded		(65,551)	(52,071)	(102,763)	(100,273)
Net premiums written		175,391	105,856	354,702	292,556
Change in unearned premiums		8,846	25,679	(22,734)	(20,982)
Net premiums earned		184,237	131,535	331,968	271,574
Other underwriting income (loss)		328	868	739	1,001
Losses and loss adjustment expenses		(140,248)	(104,786)	(259,042)	(215,462)
Acquisition expenses		(34,589)	(22,544)	(62,741)	(44,348)
Other operating expenses		(18,594)	(14,202)	(32,869)	(27,904)
Underwriting income (loss)		(8,866)	(9,129)	(21,945)	(15,139)
Net investment income		22,183	30,454	42,310	62,579
Net realized gains (losses)		39,513	171,499	80,638	(123,352)
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]	(220)	0	(935)	0
Amortization of intangible assets		(898)	0	(898)	0
Interest expense		(4,261)	(6,009)	(8,410)	(13,319)
Net foreign exchange gains (losses)		117	3,227	(1,325)	12,591
Income (loss) before income taxes and income (loss) from operating affiliates		47,568	190,042	89,435	(76,640)
Income tax expense (benefit)		(226)	402	(234)	402
Income (loss) from operating affiliates		0	0	0	0
Net income (loss)		47,342	190,444	89,201	(76,238)
Amounts attributable to redeemable noncontrolling interests		(981)	(1,036)	(1,953)	(2,132)
Amounts attributable to non-redeemable noncontrolling interests		(41,617)	(165,598)	(78,314)	68,346
Net income (loss) available to Arch		4,744	23,810	8,934	(10,024)
Preferred dividends		0	0	0	0
Net income (loss) available to Arch common shareholders		$ 4,744	$ 23,810	$ 8,934	$ (10,024)
Underwriting Ratios
Loss ratio		76.10%	79.70%	78.00%	79.30%
Acquisition expense ratio		18.80%	17.10%	18.90%	16.30%
Other operating expense ratio		10.10%	10.80%	9.90%	10.30%
Combined ratio		105.00%	107.60%	106.80%	105.90%
Goodwill and intangible assets		$ 10,318	$ 7,650	$ 10,318	$ 7,650

[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.’

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Reserve for Losses and Loss Adjustment Expenses - Reconciliation of beginning and ending balances of losses and loss adjustment reserves (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020
Liability for Future Policy Benefits and Unpaid Claims and Claims Adjustment Expense [Abstract]
Reserve for losses and loss adjustment expenses at beginning of period		$ 16,443,952	$ 14,309,580	$ 16,513,929	$ 13,891,842
Unpaid losses and loss adjustment expenses recoverable		3,916,650	4,070,114	4,314,855	4,082,650
Net reserve for losses and loss adjustment expenses at beginning of period		12,527,302	10,239,466	12,199,074	9,809,192
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year		1,219,081	1,274,589	2,463,853	2,409,031
Prior years		(59,250)	(44,067)	(100,922)	(63,090)
Total net incurred losses and loss adjustment expenses		1,159,831	1,230,522	2,362,931	2,345,941
Retroactive reinsurance transaction	[1]	0	0	(183,893)	60,635
Net foreign exchange (gains) losses		135,847	51,157	88,970	(91,416)
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year		(164,441)	(128,174)	(223,425)	(169,434)
Prior years		(607,911)	(504,254)	(1,193,029)	(1,066,201)
Total net paid losses and loss adjustment expenses		(772,352)	(632,428)	(1,416,454)	(1,235,635)
Net reserve for losses and loss adjustment expenses at end of period		13,050,628	10,888,717	13,050,628	10,888,717
Unpaid losses and loss adjustment expenses recoverable		4,146,020	4,156,157	4,146,020	4,156,157
Reserve for losses and loss adjustment expenses at end of period		$ 17,196,648	$ 15,044,874	$ 17,196,648	$ 15,044,874

[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”). During the 2020 first quarter, the Company entered into a reinsurance to close agreement of the 2017 and prior years of account previously covered by a third party arrangement.

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Reserve for Losses and Loss Adjustment Expenses - Prior year development (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 59,250	$ 44,067	$ 100,922	$ 63,090
Operating segments | Insurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 4,000	$ 2,500	$ 8,100	$ 3,600
Percentage of prior year development	0.50%	0.40%	0.50%	0.30%
Operating segments | Insurance | Short tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		$ 11,500	$ 49,400	$ 15,400
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	7,500	21,600	9,600
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	3,500	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)	10,700		18,600	3,100
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)	(17,100)	(45,400)	(25,100)
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)		(4,000)	(12,600)	(6,300)
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)	(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)	(19,300)
Operating segments | Insurance | Long tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		8,100		13,300
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
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)		2,400
Operating segments | Insurance | Long tailed lines | Other product lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		4,900		7,600
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	19,700	53,500	28,700
Operating segments | Reinsurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 20,500	$ 40,200	$ 47,300	$ 51,800
Percentage of prior year development	2.80%	8.40%	3.40%	5.10%
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)		$ 46,200	$ 67,200	$ 65,700
Operating segments | Reinsurance | Short tailed lines | Property catastrophe and property other than property catastrophe
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		18,300	28,800
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)	$ (17,100)		(39,600)	21,300
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)	61,600	27,500	78,200	39,300
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)	4,000
Operating segments | Reinsurance | Long tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(33,200)		(24,800)	(15,600)
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)	(5,800)
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)	53,700		72,100	67,400
Operating segments | Reinsurance | 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)		(6,000)
Operating segments | Mortgage
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 43,100	$ 200	$ 54,000	$ 6,300
Percentage of prior year development	12.90%	0.10%	8.10%	0.90%
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)	$ 1,100	$ (8,400)	$ 1,300

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Allowance for Expected Credit Losses - Premiums receivable (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020
Credit Loss [Abstract]
Balance at beginning of period		$ 2,618,175	$ 2,155,204	$ 2,064,586	$ 1,778,717
Balance at end of period		2,866,578	2,203,753	2,866,578	2,203,753
Allowance for Expected Credit Losses
Balance at beginning of period		36,111	27,990	37,781	21,003
Cumulative effect of accounting change (1)	[1]				6,539
Change for provision of expected credit losses (1)	[2]	(132)	8,064	(1,802)	8,512
Balance at end of period		35,979	36,054	35,979	36,054
Write-offs charged against the allowance		$ 1,100	$ 1,800	$ 1,200	$ 2,300
Accounting Standards Update				us-gaap:AccountingStandardsUpdate201613Member

[1] Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”

[2] Amounts deemed uncollectible are written-off in operating expenses. For the 2021 second quarter and 2020 second quarter, amounts written off were $1.1 million and $1.8 million, respectively. For the six months ended June 30, 2021 and 2020 period, amounts written off were were $1.2 million and $2.3 million, respectively.

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Allowance for Expected Credit Losses - Reinsurance recoverables (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020
Credit Loss [Abstract]
Balance at beginning of period		$ 4,041,076	$ 4,303,135	$ 4,500,802	$ 4,346,816
Balance at end of period		4,314,515	4,363,507	4,314,515	4,363,507
Allowance for Expected Credit Losses
Balance at beginning of period		10,872	13,700	11,636	1,364
Cumulative effect of accounting change	[1]				12,010
Change for provision of expected credit losses		157	(105)	(607)	221
Balance at end of period		$ 11,029	$ 13,595	$ 11,029	$ 13,595

[1] Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”

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Allowance for Expected Credit Losses - Ceded credit risk (Details) - USD ($) $ in Thousands		6 Months Ended	12 Months Ended
		Jun. 30, 2021	Dec. 31, 2020
Ceded Credit Risk [Line Items]
Reinsurance recoverable on unpaid and paid losses and LAE		$ 4,314,515	$ 4,500,802
Reinsurance recoverable | Reinsurer concentration risk | AM Best A minus Or Better Rating
Ceded Credit Risk [Line Items]
Concentration risk percentage		66.00%	63.90%
Reinsurance recoverable | Reinsurer concentration risk | Not Rated
Ceded Credit Risk [Line Items]
Concentration risk percentage	[1]	34.00%	36.10%
Reinsurance recoverable | Reinsurer concentration risk | Not Rated | Reinsurance trusts or letters of credit
Ceded Credit Risk [Line Items]
Concentration risk percentage		91.00%	94.00%
Stockholders' equity | Reinsurer concentration risk | Single Reinsurer
Ceded Credit Risk [Line Items]
Concentration risk percentage		2.40%	1.80%

[1] At June 30, 2021 and December 31, 2020 over 91% and 94% of such amount were collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other, respectively

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Allowance for Expected Credit Losses - Contractholder receivables (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020
Credit Loss [Abstract]
Balance at beginning of period		$ 1,919,655	$ 2,140,724	$ 1,986,924	$ 2,119,460
Balance at end of period		1,882,948	2,179,124	1,882,948	2,179,124
Allowance for Expected Credit Losses
Balance at beginning of period		5,853	9,038	8,638	0
Cumulative effect of accounting change	[1]				6,663
Change for provision of expected credit losses		(1,382)	(2,748)	(4,167)	(373)
Balance at end of period		$ 4,471	$ 6,290	$ 4,471	$ 6,290

[1] Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”

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Investment Information - Summary of available for sale securities (Details) - USD ($) $ in Thousands		6 Months Ended
		Jun. 30, 2021		Mar. 31, 2021	Dec. 31, 2020		Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		$ 18,073,779			$ 18,717,825
Estimated Fair Value		2,248,613			1,924,922
Estimated Fair Value		20,478,448			20,921,530
Gross Unrealized Gains		390,212			657,620
Gross Unrealized Losses		(78,417)			(79,654)
Allowance for expected credit losses		(2,124)		$ (3,830)	(2,397)		$ (5,869)	$ (9,938)	$ 0
Amortized cost		17,764,783			18,143,305
Cost		2,248,615			1,924,292
Cost or Amortized Cost		$ 20,168,777			20,345,961
Accounting Standards Update		us-gaap:AccountingStandardsUpdate201613Member
Fixed maturities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	[1]	$ 18,229,835			18,996,608
Gross Unrealized Gains	[1]	388,808			654,927
Gross Unrealized Losses	[1]	(77,011)			(77,591)
Allowance for expected credit losses	[2]	(2,124)	[1]		(2,397)
Amortized cost	[1]	17,920,162			18,421,669
Fixed maturities | Corporate bonds
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		7,129,768			7,856,571
Gross Unrealized Gains	[1]	217,061			414,247
Gross Unrealized Losses	[1]	(34,751)			(34,388)
Allowance for expected credit losses	[2]	(1,232)	[1]		(896)
Amortized cost	[1]	6,948,690			7,477,608
Fixed maturities | Mortgage backed securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		389,041			630,001
Gross Unrealized Gains	[1]	4,480			8,939
Gross Unrealized Losses	[1]	(3,479)			(5,028)
Allowance for expected credit losses	[2]	(269)	[1]		(278)
Amortized cost	[1]	388,309			626,368
Fixed maturities | Municipal bonds
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		415,483			494,522
Gross Unrealized Gains	[1]	23,153			27,291
Gross Unrealized Losses	[1]	(1,660)			(3,835)
Allowance for expected credit losses	[2]	(6)	[1]		(11)
Amortized cost	[1]	393,996			471,077
Fixed maturities | Commercial mortgage backed securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		266,733			389,900
Gross Unrealized Gains	[1]	4,017			8,722
Gross Unrealized Losses	[1]	(611)			(2,954)
Allowance for expected credit losses	[2]	(3)	[1]		(122)
Amortized cost	[1]	263,330			384,254
Fixed maturities | US government and government agencies
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		5,091,183			5,557,077
Gross Unrealized Gains	[1]	14,814			22,612
Gross Unrealized Losses	[1]	(14,013)			(12,611)
Allowance for expected credit losses	[2]	0	[1]		0
Amortized cost	[1]	5,090,382			5,547,076
Fixed maturities | Non-US government securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		2,449,782			2,433,733
Gross Unrealized Gains	[1]	108,823			153,891
Gross Unrealized Losses	[1]	(18,441)			(8,060)
Allowance for expected credit losses	[2]	(128)	[1]		0
Amortized cost	[1]	2,359,528			2,287,902
Fixed maturities | Asset backed securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		2,487,845			1,634,804
Gross Unrealized Gains	[1]	16,460			19,225
Gross Unrealized Losses	[1]	(4,056)			(10,715)
Allowance for expected credit losses	[2]	(486)	[1]		(1,090)
Amortized cost	[1]	2,475,927			1,627,384
Short-term investments
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		2,248,613			1,924,922
Gross Unrealized Gains		1,404			2,693
Gross Unrealized Losses		(1,406)			(2,063)
Allowance for expected credit losses		0	[2]	$ 0	0	[2]	$ 0	$ (29)	$ 0
Cost		$ 2,248,615			$ 1,924,292

[1] In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

[2] Effective January 1, 2020, the Company adopted ASU 2016-13 and as a result any credit impairment losses on the Company’s available-for-sale investments are recorded as an allowance, subject to reversal.

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Investment Information - Aging of available for sale securities in an unrealized loss position (Details) - USD ($) $ in Thousands		Jun. 30, 2021	Dec. 31, 2020
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months		$ 8,022,408	$ 3,788,763
Estimated Fair Value - 12 Months or More		158,155	70,404
Estimated Fair Value		8,180,563	3,859,167
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months		(72,763)	(76,067)
Gross Unrealized Losses - 12 Months or More		(5,654)	(3,587)
Gross Unrealized Losses		(78,417)	(79,654)
Fixed maturities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	[1]	7,491,278	3,690,843
Estimated Fair Value - 12 Months or More	[1]	158,155	70,404
Estimated Fair Value	[1]	7,649,433	3,761,247
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(71,357)	(74,004)
Gross Unrealized Losses - 12 Months or More	[1]	(5,654)	(3,587)
Gross Unrealized Losses	[1]	(77,011)	(77,591)
Fixed maturities | Corporate bonds
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	[1]	2,264,801	747,442
Estimated Fair Value - 12 Months or More	[1]	22,895	3,934
Estimated Fair Value	[1]	2,287,696	751,376
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(32,733)	(33,086)
Gross Unrealized Losses - 12 Months or More	[1]	(2,018)	(1,302)
Gross Unrealized Losses	[1]	(34,751)	(34,388)
Fixed maturities | Mortgage backed securities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	[1]	196,765	284,619
Estimated Fair Value - 12 Months or More	[1]	13,632	3,637
Estimated Fair Value	[1]	210,397	288,256
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(2,893)	(4,788)
Gross Unrealized Losses - 12 Months or More	[1]	(586)	(240)
Gross Unrealized Losses	[1]	(3,479)	(5,028)
Fixed maturities | Municipal bonds
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	[1]	24,711	67,937
Estimated Fair Value - 12 Months or More	[1]	2,859	0
Estimated Fair Value	[1]	27,570	67,937
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(1,612)	(3,835)
Gross Unrealized Losses - 12 Months or More	[1]	(48)	0
Gross Unrealized Losses	[1]	(1,660)	(3,835)
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	[1]	20,039	126,624
Estimated Fair Value - 12 Months or More	[1]	7,961	2,655
Estimated Fair Value	[1]	28,000	129,279
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(180)	(2,916)
Gross Unrealized Losses - 12 Months or More	[1]	(431)	(38)
Gross Unrealized Losses	[1]	(611)	(2,954)
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	[1]	2,920,944	1,285,907
Estimated Fair Value - 12 Months or More	[1]	0	0
Estimated Fair Value	[1]	2,920,944	1,285,907
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(14,013)	(12,611)
Gross Unrealized Losses - 12 Months or More	[1]	0	0
Gross Unrealized Losses	[1]	(14,013)	(12,611)
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]	1,282,422	543,844
Estimated Fair Value - 12 Months or More	[1]	16,885	2,441
Estimated Fair Value	[1]	1,299,307	546,285
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(17,562)	(7,658)
Gross Unrealized Losses - 12 Months or More	[1]	(879)	(402)
Gross Unrealized Losses	[1]	(18,441)	(8,060)
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]	781,596	634,470
Estimated Fair Value - 12 Months or More	[1]	93,923	57,737
Estimated Fair Value	[1]	875,519	692,207
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(2,364)	(9,110)
Gross Unrealized Losses - 12 Months or More	[1]	(1,692)	(1,605)
Gross Unrealized Losses	[1]	(4,056)	(10,715)
Short-term investments
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months		531,130	97,920
Estimated Fair Value - 12 Months or More		0	0
Estimated Fair Value		531,130	97,920
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months		(1,406)	(2,063)
Gross Unrealized Losses - 12 Months or More		0	0
Gross Unrealized Losses		$ (1,406)	$ (2,063)

[1] In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

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Investment Information - Maturity profile of available for sale securities) (Details) - USD ($) $ in Thousands		Jun. 30, 2021	Dec. 31, 2020
Estimated Fair Value
Estimated Fair Value		$ 18,073,779	$ 18,717,825
Amortized Cost
Amortized cost		17,764,783	18,143,305
Fixed maturities
Estimated Fair Value
Due in one year or less		452,065	348,200
Due after one year through five years		10,114,276	10,629,959
Due after five years through 10 years		4,148,538	4,881,564
Due after 10 years		371,337	482,180
Single maturity date		15,086,216	16,341,903
Estimated Fair Value	[1]	18,229,835	18,996,608
Amortized Cost
Due in one year or less		439,855	339,951
Due after one year through five years		9,942,182	10,340,819
Due after five years through 10 years		4,055,318	4,654,754
Due after 10 years		355,241	448,139
Single maturity date		14,792,596	15,783,663
Amortized cost	[1]	17,920,162	18,421,669
Fixed maturities | Mortgage backed securities
Estimated Fair Value
Securities without single maturity date		389,041	630,001
Estimated Fair Value		389,041	630,001
Amortized Cost
Securities without single maturity date		388,309	626,368
Amortized cost	[1]	388,309	626,368
Fixed maturities | Commercial mortgage backed securities
Estimated Fair Value
Securities without single maturity date		266,733	389,900
Estimated Fair Value		266,733	389,900
Amortized Cost
Securities without single maturity date		263,330	384,254
Amortized cost	[1]	263,330	384,254
Fixed maturities | Asset backed securities
Estimated Fair Value
Securities without single maturity date		2,487,845	1,634,804
Estimated Fair Value		2,487,845	1,634,804
Amortized Cost
Securities without single maturity date		2,475,927	1,627,384
Amortized cost	[1]	$ 2,475,927	$ 1,627,384

[1] In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

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Investment Information - Securities lending agreements (Details) - USD ($) $ in Thousands	Jun. 30, 2021	Dec. 31, 2020
Disclosure Investment Information [Abstract]
Fair value of cash collateral received on securities lending	$ 800	$ 0
Fair value of non-cash collateral received on securities lending	171,300	301,100
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	172,109	301,089
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9	0	0
Amounts related to securities lending not included in offsetting disclosure in note 9	172,109	301,089
US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	153,458	281,607
Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	5,800	3,021
Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	12,851	16,461
Overnight and continuous
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	34,396	161,799
Overnight and continuous | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	15,745	142,317
Overnight and continuous | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	5,800	3,021
Overnight and continuous | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	12,851	16,461
Less than 30 days
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	137,713	0
Less than 30 days | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	137,713	0
Less than 30 days | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
Less than 30 days | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
30 - 90 days
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	139,290
30 - 90 days | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	139,290
30 - 90 days | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
30 - 90 days | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
90 days or more
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
90 days or more | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
90 days or more | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
90 days or more | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	$ 0	$ 0

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Investment Information - Other investments (Details) - USD ($) $ in Thousands		Jun. 30, 2021	Dec. 31, 2020
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		$ 4,071,497	$ 3,824,796
Other investable assets	[1]	500,000	500,000
Other investments (portion measured at fair value: $4,071,497 and $3,824,796)		4,571,497	4,324,796
Fair value option | Fixed maturities
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		995,980	843,354
Fair value option | Other investments
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		2,370,472	2,331,885
Fair value option | Other investments | Term loan investments
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		1,333,014	1,231,731
Fair value option | Other investments | Lending
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		638,786	572,636
Fair value option | Other investments | Credit related funds
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		73,171	90,780
Fair value option | Other investments | Energy
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		84,891	65,813
Fair value option | Other investments | Investment grade fixed income
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		110,375	138,646
Fair value option | Other investments | Infrastructure
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		32,109	165,516
Fair value option | Other investments | Private equity
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		70,878	48,750
Fair value option | Other investments | Real estate
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		27,248	18,013
Fair value option | Short-term investments
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		610,114	557,008
Fair value option | Equity securities
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		$ 94,931	$ 92,549

[1] Participation interests in a receivable of a reverse repurchase agreement

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Investment Information - Equity method investments (Details) - USD ($) $ in Thousands	Jun. 30, 2021	Dec. 31, 2020
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	$ 2,539,124	$ 2,047,889
Credit related funds
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	883,279	740,060
Equity securities
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	403,003	343,058
Real estate
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	323,566	258,518
Lending
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	295,228	179,629
Private equity
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	305,662	235,289
Infrastructure
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	210,174	175,882
Energy
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	$ 118,212	$ 115,453

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Investment Information - Limited partnership interests (Details) - USD ($) $ in Thousands		Jun. 30, 2021	Dec. 31, 2020
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss		$ 2,721,384	$ 2,232,609
Aggregate unfunded commitments		2,400,000	2,100,000
Equity method investments
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss	[1]	2,539,124	2,047,889
Aggregate unfunded commitments		2,000,000	1,800,000
Fair value option
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss	[2]	182,260	184,720
Aggregate unfunded commitments		$ 26,300	$ 35,600

[1] Aggregate unfunded commitments were $2.0 billion at June 30, 2021, compared to $1.8 billion at December 31, 2020.

[2] Aggregate unfunded commitments were $26.3 million at June 30, 2021, compared to $35.6 million at December 31, 2020.

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Investment Information - Net investment income (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020
Net investment income:
Gross investment income		$ 135,176	$ 151,965	$ 261,142	$ 320,291
Investment expenses		(23,563)	(20,480)	(50,673)	(43,653)
Net investment income		111,613	131,485	210,469	276,638
Fixed maturities
Net investment income:
Gross investment income		88,625	105,391	179,251	220,238
Term loans
Net investment income:
Gross investment income		16,879	20,512	31,607	43,682
Equity securities
Net investment income:
Gross investment income		8,584	6,219	14,234	12,226
Short-term investments
Net investment income:
Gross investment income		1,138	3,383	1,745	8,279
Other
Net investment income:
Gross investment income	[1]	$ 19,950	$ 16,460	$ 34,305	$ 35,866

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

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Investment Information - Net realized gains and losses (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020
Available for sale securities:
Available for sale securities, gross gains on investment sales		$ 115,541	$ 232,153	$ 180,543	$ 410,353
Available for sale securities, gross losses on investment sales		(50,627)	(49,824)	(113,625)	(81,792)
Equity securities, at fair value:
Net realized gains (losses) on sales during the period		33,570	(18,250)	71,419	(18,789)
Net unrealized gains (losses) on equity securities still held at reporting date		65,847	145,686	85,555	(29,880)
Allowance for credit losses:
Allowance for credit losses - investment related		(59)	(1,000)	(2,662)	(10,349)
Allowance for credit losses - underwriting related		1,381	(5,834)	6,649	(9,104)
Net impairment losses				0	(533)
Derivative instruments	[1]	(51,109)	(836)	(14,993)	126,353
Other		10,224	(6,515)	(12,821)	(8,612)
Net realized gains (losses)		202,907	556,588	345,368	189,628
Fixed maturities
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		10,912	68,181	27,465	(59,485)
Allowance for credit losses:
Allowance for credit losses - investment related		896	3,225	(752)	(6,095)
Other investments
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		60,884	178,570	107,739	(129,230)
Equity securities
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		5,492	6,664	7,557	1,755
Short-term investments
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		$ (104)	$ 3,368	$ 632	$ (5,313)

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

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Investment Information - Investment in operating affiliates (Details) € / shares in Units, € in Thousands, $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2021 USD ($)	Jun. 30, 2020 USD ($)	Jun. 30, 2021 USD ($)	Jun. 30, 2021 EUR (€)	Jun. 30, 2020 USD ($)	Jun. 30, 2021 € / shares	Dec. 31, 2020 USD ($)
Schedule of Equity Method Investments [Line Items]
Payments to Acquire Interest in Subsidiaries and Affiliates			$ 546,349		$ 0
Investment in operating affiliates	$ 731,810		731,810				$ 129,291
Income (loss) from operating affiliates	$ 24,476	$ (3,173)	$ 99,933		$ 5,343
Operating Affiliates
Schedule of Equity Method Investments [Line Items]
Time lag for reporting			3 months	3 months
Coface
Schedule of Equity Method Investments [Line Items]
Percentage ownership	29.50%		29.50%
Consideration paid per share | € / shares						€ 9.95
Payments to Acquire Interest in Subsidiaries and Affiliates			$ 546,000	€ 453,000
Investment in operating affiliates	$ 601,900		601,900
Income (loss) from operating affiliates			74,500
Purchase Of Affiliate, Deferred Gain	$ 36,000		$ 36,000
Purchase Of Operating Affiliate, Deferred Gain, Period Of Recognition			5 years	5 years

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Investment Information - Allowance for expected credit losses (Details) - USD ($) $ in Thousands		3 Months Ended			6 Months Ended
		Jun. 30, 2021		Jun. 30, 2020	Jun. 30, 2021		Jun. 30, 2020
Allowance for expected credit losses
Balance at beginning of period		$ 3,830		$ 9,938	$ 2,397		$ 0
Cumulative effect of accounting change	[1]						634
Additions for current-period provision for expected credit losses		59		1,000	2,662		10,349
Additions (reductions) for previously recognized expected credit losses		(791)		(4,232)	(1,722)		(4,255)
Reductions due to disposals		(974)		(837)	(1,213)		(859)
Balance at end of period		2,124		5,869	$ 2,124		5,869
Accounting Standards Update					us-gaap:AccountingStandardsUpdate201613Member
Fixed maturities
Allowance for expected credit losses
Balance at beginning of period					$ 2,397
Additions for current-period provision for expected credit losses		(896)		(3,225)	752		6,095
Balance at end of period		2,124			2,124
Fixed maturities | Structured securities
Allowance for expected credit losses
Balance at beginning of period	[2]	1,207		2,654	1,490		0
Cumulative effect of accounting change	[1],[2]						517
Additions for current-period provision for expected credit losses	[2]	52		695	234		2,841
Additions (reductions) for previously recognized expected credit losses	[2]	(383)		(1,304)	(765)		(1,306)
Reductions due to disposals	[2]	(117)		(319)	(200)		(326)
Balance at end of period		759		1,726	759		1,726
Fixed maturities | Municipal bonds
Allowance for expected credit losses
Balance at beginning of period		2		23	11		0
Cumulative effect of accounting change	[1]						0
Additions for current-period provision for expected credit losses		0		44	0		67
Additions (reductions) for previously recognized expected credit losses		4		(25)	(5)		(25)
Reductions due to disposals		0		(14)	0		(14)
Balance at end of period		6		28	6		28
Fixed maturities | Corporate bonds
Allowance for expected credit losses
Balance at beginning of period		2,621		7,232	896		0
Cumulative effect of accounting change	[1]						117
Additions for current-period provision for expected credit losses		7		290	2,428		7,441
Additions (reductions) for previously recognized expected credit losses		(412)		(2,903)	(952)		(2,924)
Reductions due to disposals		(857)		(504)	(1,013)		(519)
Balance at end of period		1,359		4,115	1,359		4,115
Short-term investments
Allowance for expected credit losses
Balance at beginning of period		0		29	0	[3]	0
Cumulative effect of accounting change	[1]						0
Additions for current-period provision for expected credit losses		0		(29)	0		0
Additions (reductions) for previously recognized expected credit losses		0		0	0		0
Reductions due to disposals		0		0	0		0
Balance at end of period		$ 0	[3]	$ 0	$ 0	[3]	$ 0

[1] Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”

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

[3] Effective January 1, 2020, the Company adopted ASU 2016-13 and as a result any credit impairment losses on the Company’s available-for-sale investments are recorded as an allowance, subject to reversal.

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Investment Information - Restricted assets (Details) - USD ($) $ in Thousands	Jun. 30, 2021	Dec. 31, 2020
Restricted Assets [Line Items]
Restricted assets	$ 9,725,335	$ 8,733,309
Collateral or guarantees - affiliated transactions
Restricted Assets [Line Items]
Restricted assets	5,041,190	4,643,334
Collateral or guarantees - third party agreements
Restricted Assets [Line Items]
Restricted assets	3,441,929	3,083,324
Deposits with US regulatory authorities
Restricted Assets [Line Items]
Restricted assets	814,084	827,552
Deposits with non-US regulatory authorities
Restricted Assets [Line Items]
Restricted assets	428,132	179,099
Watford Holdings Ltd
Restricted Assets [Line Items]
Assets pledged as collateral	$ 1,100,000	$ 954,600

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Investment Information - Cash and restricted cash (Details) - USD ($) $ in Thousands	Jun. 30, 2021	Dec. 31, 2020	Jun. 30, 2020	Dec. 31, 2019
Disclosure Investment Information [Abstract]
Cash	$ 1,234,059	$ 906,448
Restricted cash (included in ‘other assets’)	584,404	384,096
Cash and restricted cash	$ 1,818,463	$ 1,290,544	$ 1,064,683	$ 903,698

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Investment Information - Narrative (Details) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2021 USD ($) lots	Jun. 30, 2020 USD ($)	Jun. 30, 2021 USD ($) lots	Jun. 30, 2020 USD ($)	Dec. 31, 2020 USD ($) lots
Narrative items:
Investable assets	$ 30,200,000		$ 30,200,000
Equity in net (loss) income of investment funds accounted for using the equity method	122,186	$ (65,119)	193,872	$ (69,328)
Equity securities, at fair value	$ 1,693,552		$ 1,693,552		$ 1,444,830
Continuous unrealized loss, qualitative disclosures:
Number of positions in an unrealized loss position (lots) | lots	3,240		3,240		2,320
Total number of positions (lots) | lots	10,890		10,890		11,180
Largest single loss	$ 2,400		$ 2,400		$ 900
Consolidated Entity, Excluding Consolidated VIE
Narrative items:
Investable assets	27,300,000		27,300,000
Variable Interest Entity, Primary Beneficiary
Narrative items:
Investable assets	$ 2,900,000		$ 2,900,000
Minimum
Narrative items:
Time lag for reporting			1 month
Maximum
Narrative items:
Time lag for reporting			3 months

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Fair Value - Fair Value Hierarchy (Details) - Recurring - USD ($) $ in Thousands		Jun. 30, 2021	Dec. 31, 2020
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		$ 9,218,652	$ 9,280,391
Liabilities measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Contingent consideration liability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Securities sold but not yet purchased
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value	[1]	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
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	[2]	5,062,571	5,463,356
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	[2]	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	[2]	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	[2]	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	[2]	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	[2]	5,062,571	5,463,356
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	[2]	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	[2]	0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,996,304	1,920,565
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		1,631,937	1,401,653
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		527,840	494,817
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 | 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) | Fair value option | 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) | Fair value option | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		163	164
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		482,815	420,131
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		21,252	23,373
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		23,610	51,149
Significant Other Observable Inputs (Level 2)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		15,828,422	15,724,091
Liabilities measured at fair value		(95,372)	(130,384)
Significant Other Observable Inputs (Level 2) | Contingent consideration liability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		0	0
Significant Other Observable Inputs (Level 2) | Securities sold but not yet purchased
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value	[1]	(28,068)	(21,679)
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		(67,304)	(108,705)
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		44,925
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	[2]	13,163,827	13,529,813
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	[2]	7,129,755	7,856,558
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	[2]	389,041	630,001
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	[2]	415,483	494,522
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	[2]	266,733	389,900
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	[2]	28,612	93,721
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]	2,449,782	2,433,733
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	[2]	2,484,421	1,631,378
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		252,309	4,357
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		24,971	17,291
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		98,488	177,383
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		2,243,902	1,995,247
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		789,188	650,309
Significant Other Observable Inputs (Level 2) | Fair value option | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,707	3,282
Significant Other Observable Inputs (Level 2) | Fair value option | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		841	1,090
Significant Other Observable Inputs (Level 2) | Fair value option | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		108	110
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		22,552	35,263
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		179,423	152,151
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		127,299	136,877
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	188
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		1,121,784	1,015,977
Significant Unobservable Inputs (Level 3)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		201,149	182,530
Liabilities measured at fair value		(466)	(461)
Significant Unobservable Inputs (Level 3) | Contingent consideration liability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(466)	(461)
Significant Unobservable Inputs (Level 3) | Securities sold but not yet purchased
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value	[1]	0	0
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
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	[2]	3,437	3,439
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	[2]	13	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	[2]	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	[2]	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	[2]	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	[2]	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	[2]	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]	3,424	3,426
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		49,136	42,015
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		148,576	137,076
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		998	985
Significant Unobservable Inputs (Level 3) | Fair value option | 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) | Fair value option | 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) | Fair value option | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		73,678	68,988
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		73,900	67,103
Estimated Fair Value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		26,399,401	26,384,668
Liabilities measured at fair value		(95,838)	(130,845)
Estimated Fair Value | Contingent consideration liability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(466)	(461)
Estimated Fair Value | Securities sold but not yet purchased
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value	[1]	(28,068)	(21,679)
Estimated Fair Value | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(67,304)	(108,705)
Estimated Fair Value | Residential mortgage loans
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		44,925
Estimated Fair Value | Fixed maturities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		18,229,835	18,996,608
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		7,129,768	7,856,571
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		389,041	630,001
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		415,483	494,522
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		266,733	389,900
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		5,091,183	5,557,077
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		2,449,782	2,433,733
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		2,487,845	1,634,804
Estimated Fair Value | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,248,613	1,924,922
Estimated Fair Value | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,706,044	1,460,959
Estimated Fair Value | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		98,488	177,383
Estimated Fair Value | Fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		4,071,496	3,824,796
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		790,186	651,294
Estimated Fair Value | Fair value option | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,707	3,282
Estimated Fair Value | Fair value option | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		841	1,090
Estimated Fair Value | Fair value option | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		271	274
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		22,552	35,263
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		179,423	152,151
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		610,114	557,008
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		94,930	92,549
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		1,219,294	1,134,229
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	[3]	$ 1,151,178	$ 1,197,656

[1] Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets.

[2] In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See note 7, “—Securities Lending Agreements.”

[3] In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.

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Fair Value - Rollforward of Level 3 assets and liabilities (Details) - Recurring - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020
Contingent consideration liability
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		$ (465)	$ (7,967)	$ (461)	$ (7,998)
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	0	(18)	0	(72)
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		(1)	6,735	(5)	6,820
Transfers in and/or out of Level 3		0	0	0	0
Balance at end of period		(466)	(1,250)	(466)	(1,250)
Available for sale | Structured securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period	[2]	3,472	3,846	3,426	5,216
Total gains or (losses) (realized/unrealized) - included in earnings	[1],[2]	12	(64)	(56)	(55)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income	[2]	(57)	(287)	57	(309)
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]	(3)	(45)	(3)	(1,402)
Transfers in and/or out of Level 3	[2]	0	0	0	0
Balance at end of period	[2]	3,424	3,450	3,424	3,450
Available for sale | Corporate bonds
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		13	1,980	13	8,851
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	0	0	0	7
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	(1,123)	0	(6,539)
Purchases, issuances, sales and settlements
Purchases		0	0	0	0
Issuances		0	0	0	0
Sales		0	0	0	0
Settlements		0	0	0	(1,462)
Transfers in and/or out of Level 3		0	0	0	0
Balance at end of period		13	857	13	857
Fair value option | Corporate bonds
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		989	965	985	932
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	9	0	13	0
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0	0	0
Purchases, issuances, sales and settlements
Purchases		0	33	0	66
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		998	998	998	998
Fair value option | Other investments
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		67,930	54,620	67,103	68,817
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	633	(987)	881	(1,014)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0	0	0
Purchases, issuances, sales and settlements
Purchases		5,638	3	13,003	24
Issuances		0	0	0	0
Sales		(301)	(7,183)	(7,087)	(24,358)
Settlements		0	0	0	0
Transfers in and/or out of Level 3		0	0	0	2,984
Balance at end of period		73,900	46,453	73,900	46,453
Fair value option | Equity securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		71,176	60,015	68,988	58,094
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	2,502	1,432	4,690	3,353
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		73,678	61,447	73,678	61,447
Equity securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		43,112	55,632	42,015	55,889
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	922	11,799	1,826	8,078
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0	0	0
Purchases, issuances, sales and settlements
Purchases		5,102	0	5,295	3,464
Issuances		0	0	0	0
Sales		0	(15,450)	0	(15,450)
Settlements		0	0	0	0
Transfers in and/or out of Level 3		0	0	0	0
Balance at end of period		$ 49,136	$ 51,981	$ 49,136	$ 51,981

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

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

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Fair Value - Narrative (Details) - USD ($) $ in Thousands	Jun. 30, 2021	Dec. 31, 2020
Fair Value Disclosures [Abstract]
Total assets and liabilities measured at fair value	$ 26,500,000	$ 26,500,000
Total assets and liabilities measured at fair value priced using non-binding broker quotes	$ 187,600	$ 150,100
Total assets and liabilities measured at fair value priced using non-binding broker quotes (percentage)	0.70%	0.60%
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Senior notes	$ 2,861,728	$ 2,861,113
Estimated fair value of senior notes	$ 3,500,000	$ 3,700,000

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Derivative Instruments - Fair value and notional amount of derivatives (Details) - USD ($) $ in Thousands		Jun. 30, 2021	Dec. 31, 2020
Derivative offsetting
Derivative assets subject to master netting agreements		$ 89,900	$ 138,800
Derivative liabilities subject to master netting agreements		66,700	93,000
Not designated as hedging instrument
Derivative [Line Items]
Asset derivatives - fair value		98,488	177,383
Liability derivatives - fair value		(67,304)	(108,705)
Not designated as hedging instrument | Futures contracts
Derivative [Line Items]
Net derivatives - notional value	[1],[2]	2,907,342	3,099,796
Not designated as hedging instrument | Futures contracts | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[2]	36,277	11,046
Not designated as hedging instrument | Futures contracts | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[2]	(21,515)	(4,496)
Not designated as hedging instrument | Foreign currency forward contracts
Derivative [Line Items]
Net derivatives - notional value	[1],[2]	1,573,973	1,656,729
Not designated as hedging instrument | Foreign currency forward contracts | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[2]	8,242	52,716
Not designated as hedging instrument | Foreign currency forward contracts | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[2]	(20,729)	(6,202)
Not designated as hedging instrument | Other
Derivative [Line Items]
Net derivatives - notional value	[1],[2]	4,838,552	5,763,919
Not designated as hedging instrument | Other | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[2]	53,969	113,621
Not designated as hedging instrument | Other | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[2]	$ (25,060)	$ (98,007)

[1] Represents the absolute notional value of all outstanding contracts, consisting of long and short positions.

[2] The fair value of asset derivatives are included in ‘other assets’ and the fair value of liability derivatives are included in ‘other liabilities.’

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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, 2021		Jun. 30, 2020		Jun. 30, 2021	Jun. 30, 2020
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments	[1]	$ (51,109)		$ (836)		$ (14,993)	$ 126,353
Not designated as hedging instrument
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(51,109)		(836)		(14,993)	126,353
Futures contracts | Not designated as hedging instrument
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(54,759)		(1,607)		(7,321)	94,337
Foreign currency forward contracts | Not designated as hedging instrument
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		1,295		3,523		(20,776)	(7,347)
TBAs | Not designated as hedging instrument
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		0		264		0	1,009
Other | Not designated as hedging instrument
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		$ 2,355	[2]	$ (3,016)	[2]	$ 13,104	$ 38,354

[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

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Commitments and Contingencies (Details) - USD ($) $ in Millions	6 Months Ended
	Jun. 30, 2021	Jun. 30, 2020	Dec. 31, 2020
Commitments and Contingencies Disclosure [Abstract]
Investment commitments	$ 2,400.0		$ 2,100.0
Interest paid on senior notes and other borrowings	$ 74.7	$ 57.4

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Variable Interest Entities and Noncontrolling Interests - Variable interest entity (Details) - USD ($) $ / shares in Units, $ in Thousands	1 Months Ended	6 Months Ended		12 Months Ended
	Mar. 31, 2014	Jun. 30, 2021	Jun. 30, 2020	Dec. 31, 2020
Variable Interest Entity [Line Items]
Net cash provided by (used for) operating activities		$ 1,612,572	$ 1,321,580
Net cash provided by (used for) investing activities		(1,093,678)	(1,810,190)
Net cash (used for) provided by financing activities		$ 22,415	671,337
Watford Holdings Ltd | Merger Agreement
Variable Interest Entity [Line Items]
Business acquisition, share price (per share)				$ 35.00
Variable Interest Entity, Primary Beneficiary | Watford Holdings Ltd
Variable Interest Entity [Line Items]
Initial investment contribution amount	$ 100,000
Number of shares acquired	2,500,000
Ownership percentage	11.00%	10.20%
Senior notes, face amount		$ 35,000
Senior notes, stated percentage		6.50%
Net cash provided by (used for) operating activities		$ 47,000	87,300
Net cash provided by (used for) investing activities		96,300	78,000
Net cash (used for) provided by financing activities		$ (2,000)	$ (153,800)
Variable Interest Entity, Primary Beneficiary | Watford Holdings Ltd | Watford Merger Transaction
Variable Interest Entity [Line Items]
Percentage ownership after merger transaction				40.00%
Variable Interest Entity, Primary Beneficiary | Watford Holdings Ltd | Kelso And Company
Variable Interest Entity [Line Items]
Noncontrolling interest, ownership percentage by noncontrolling owners				30.00%
Variable Interest Entity, Primary Beneficiary | Watford Holdings Ltd | Warburg Pincus LLC
Variable Interest Entity [Line Items]
Noncontrolling interest, ownership percentage by noncontrolling owners				30.00%
Variable Interest Entity, Primary Beneficiary | Watford Holdings Ltd | Non-cumulative preferred shares
Variable Interest Entity [Line Items]
Ownership percentage		6.60%

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Variable Interest Entities and Noncontrolling Interests - Carrying amount of assets and liabilities of variable interest entity (Details) - USD ($) $ in Thousands		Jun. 30, 2021	Mar. 31, 2021	Dec. 31, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019
Variable Interest Entity [Line Items]
Other investments measured at fair value		$ 4,071,497		$ 3,824,796
Fixed maturities available for sale, at fair value		18,073,779		18,717,825
Equity securities, at fair value		1,693,552		1,444,830
Cash		1,234,059		906,448
Accrued investment income		96,546		103,299
Premiums receivable		2,866,578	$ 2,618,175	2,064,586	$ 2,203,753	$ 2,155,204	$ 1,778,717
Reinsurance recoverable on unpaid and paid losses and LAE		4,314,515	4,041,076	4,500,802	4,363,507	4,303,135	4,346,816
Ceded unearned premiums		1,541,093		1,234,075
Deferred acquisition costs		1,013,657		790,708
Receivable for securities sold		309,234		92,743
Goodwill and intangible assets		667,153		692,863	688,490
Other assets		2,357,064		1,724,288
Total VIE Assets		46,481,886		43,282,297
Reserve for losses and loss adjustment expenses		17,196,648	16,443,952	16,513,929	15,044,874	14,309,580	13,891,842
Unearned premiums		6,011,369		4,838,965
Reinsurance balances payable		1,079,106		683,263
Revolving credit agreement borrowings		155,687		155,687
Senior notes		2,861,728		2,861,113
Payable for securities purchased		586,881		218,779
Other liabilities		1,332,843		1,510,888
Total liabilities		31,519,407		29,294,856
Redeemable noncontrolling interests		57,533		58,548
Watford Holdings Ltd
Variable Interest Entity [Line Items]
Redeemable noncontrolling interests		57,533	$ 57,670	58,548	$ 55,986	$ 55,376	$ 55,404
Variable Interest Entity, Primary Beneficiary | Watford Holdings Ltd
Variable Interest Entity [Line Items]
Other investments measured at fair value	[1]	1,984,919		1,790,385
Fixed maturities available for sale, at fair value		663,902		655,249
Equity securities, at fair value		97,623		52,410
Cash		349,202		211,451
Accrued investment income		14,549		14,679
Premiums receivable		305,026		224,377
Reinsurance recoverable on unpaid and paid losses and LAE		520,531		286,590
Ceded unearned premiums		123,272		122,339
Deferred acquisition costs		65,532		53,705
Receivable for securities sold		102,287		37,423
Goodwill and intangible assets		10,318		7,650
Other assets		112,794		75,801
Total VIE Assets		4,349,955		3,532,059
Reserve for losses and loss adjustment expenses		1,916,742		1,519,583
Unearned premiums		468,948		407,714
Reinsurance balances payable		132,929		63,269
Revolving credit agreement borrowings		155,687		155,687
Senior notes		172,825		172,689
Payable for securities purchased		199,342		25,881
Other liabilities		227,396		193,494
Total liabilities		3,273,869		2,538,317
Redeemable noncontrolling interests		$ 52,444		$ 52,398

[1] Included in “other investments” on the Company’s balance sheet.

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Variable Interest Entities and Noncontrolling Interests - Non-redeemable noncontrolling interests (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020
Noncontrolling Interest [Line Items]
Non-redeemable noncontrolling interests, beginning of period				$ 823,007
Amounts attributable to noncontrolling interests		$ 41,617	$ 165,598	78,314	$ (68,346)
Other comprehensive (income) loss attributable to noncontrolling interests		10	20,111	(4,560)	(12,947)
Non-redeemable noncontrolling interests, end of period		918,874	679,089	918,874	679,089
Watford Holdings Ltd
Noncontrolling Interest [Line Items]
Non-redeemable noncontrolling interests, beginning of period		876,864	492,785	823,007	762,777
Additional paid in capital attributable to noncontrolling interests		383	595	22,113	472
Repurchases attributable to non-redeemable noncontrolling interests	[1]			0	(2,867)
Amounts attributable to noncontrolling interests		41,617	165,598	78,314	(68,346)
Other comprehensive (income) loss attributable to noncontrolling interests		10	20,111	(4,560)	(12,947)
Non-redeemable noncontrolling interests, end of period		$ 918,874	$ 679,089	$ 918,874	$ 679,089
Noncontrolling shareholders | Watford Holdings Ltd
Noncontrolling Interest [Line Items]
Noncontrolling interest, ownership percentage by noncontrolling owners		90.00%		90.00%

[1] During 2020, Watford’s board of directors authorized the investment in Watford’s common shares through a share repurchase program.

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Variable Interest Entities and Noncontrolling Interests - Redeemable noncontrolling interests (Details) - USD ($) $ / shares in Units, $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020	Mar. 31, 2014
Redeemable Noncontrolling Interest [Line Items]
Redeemable noncontrolling interests, beginning of period			$ 58,548
Redeemable noncontrolling interests, end of period	$ 57,533		57,533
Watford Holdings Ltd
Redeemable Noncontrolling Interest [Line Items]
Redeemable noncontrolling interests, beginning of period	57,670	$ 55,376	58,548	$ 55,404
Accretion of preference share issuance costs	23	23	46	46
Other	(160)	587	(1,061)	536
Redeemable noncontrolling interests, end of period	$ 57,533	$ 55,986	$ 57,533	$ 55,986
Cumulative redeemable preference shares | Watford 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

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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, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020
Noncontrolling Interest [Abstract]
Amounts attributable to non-redeemable noncontrolling interests	$ (41,617)	$ (165,598)	$ (78,314)	$ 68,346
Amounts attributable to redeemable noncontrolling interests	(1,561)	(1,970)	(2,416)	(3,123)
Net (income) loss attributable to noncontrolling interests	$ (43,178)	$ (167,568)	$ (80,730)	$ 65,223

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Variable Interest Entities and Noncontrolling Interests - Other variable interest entity disclosures (Details) - USD ($) $ in Thousands		Jun. 30, 2021		Dec. 31, 2020
Variable Interest Entity [Line Items]
Total VIE Assets		$ 46,481,886		$ 43,282,297
Maximum Exposure to Loss, Total		2,721,384		2,232,609
Variable Interest Entity, Not Primary Beneficiary
Variable Interest Entity [Line Items]
Total VIE Assets		4,446,266		3,859,058
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(7,776)		(7,969)
Maximum Exposure to Loss - Off-Balance Sheet		59,085		56,320
Maximum Exposure to Loss, Total		51,309		48,351
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2017-1 Ltd. (Oct-17)
Variable Interest Entity [Line Items]
Total VIE Assets		145,573		145,573
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(283)		(245)
Maximum Exposure to Loss - Off-Balance Sheet		779		844
Maximum Exposure to Loss, Total		496		599
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-1 Ltd. (Apr-18)
Variable Interest Entity [Line Items]
Total VIE Assets		250,095		250,095
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(909)		(903)
Maximum Exposure to Loss - Off-Balance Sheet		1,984		2,245
Maximum Exposure to Loss, Total		1,075		1,342
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-2 Ltd. (Aug-18)
Variable Interest Entity [Line Items]
Total VIE Assets		0		108,395
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		0		(138)
Maximum Exposure to Loss - Off-Balance Sheet		0		280
Maximum Exposure to Loss, Total		0		142
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-3 Ltd. (Oct-18)
Variable Interest Entity [Line Items]
Total VIE Assets		302,563		302,563
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(1,622)		(1,320)
Maximum Exposure to Loss - Off-Balance Sheet		3,706		3,262
Maximum Exposure to Loss, Total		2,084		1,942
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-1 Ltd. (Mar-19)
Variable Interest Entity [Line Items]
Total VIE Assets		219,256		219,256
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(1,237)		(1,361)
Maximum Exposure to Loss - Off-Balance Sheet		8,204		8,461
Maximum Exposure to Loss, Total		6,967		7,100
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-2 Ltd. (Apr-19)
Variable Interest Entity [Line Items]
Total VIE Assets		398,316		398,316
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(1,042)		(730)
Maximum Exposure to Loss - Off-Balance Sheet		6,723		5,201
Maximum Exposure to Loss, Total		5,681		4,471
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-3 Ltd. (Jul-19)
Variable Interest Entity [Line Items]
Total VIE Assets		528,084		528,084
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(969)		(861)
Maximum Exposure to Loss - Off-Balance Sheet		4,527		5,079
Maximum Exposure to Loss, Total		3,558		4,218
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-4 Ltd. (Oct-19)
Variable Interest Entity [Line Items]
Total VIE Assets		468,737		468,737
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(1,051)		(890)
Maximum Exposure to Loss - Off-Balance Sheet		7,128		6,676
Maximum Exposure to Loss, Total		6,077		5,786
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-1 Ltd. (Jun-20)
Variable Interest Entity [Line Items]
Total VIE Assets	[1]	18,843		275,068
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability	[1]	0		(178)
Maximum Exposure to Loss - Off-Balance Sheet	[1]	0		1,012
Maximum Exposure to Loss, Total	[1]	0		834
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-1 Ltd. (Jun-20) | Funded by directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage, Amount		79,000
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-2 Ltd (Sep-20)
Variable Interest Entity [Line Items]
Total VIE Assets	[2]	325,712		423,420
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability	[2]	(442)		(556)
Maximum Exposure to Loss - Off-Balance Sheet	[2]	4,299		6,839
Maximum Exposure to Loss, Total	[2]	3,857		6,283
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-2 Ltd (Sep-20) | Funded by directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage, Amount		26,000
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-3 Ltd. (Nov-20)
Variable Interest Entity [Line Items]
Total VIE Assets	[3]	418,158		418,158
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability	[3]	(618)		(631)
Maximum Exposure to Loss - Off-Balance Sheet	[3]	8,250		9,605
Maximum Exposure to Loss, Total	[3]	7,632		8,974
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-3 Ltd. (Nov-20) | Funded by directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage, Amount		34,000
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-4 Ltd. (Dec-20)
Variable Interest Entity [Line Items]
Total VIE Assets	[4]	268,405		321,393
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability	[4]	(150)		(156)
Maximum Exposure to Loss - Off-Balance Sheet	[4]	3,891		6,816
Maximum Exposure to Loss, Total	[4]	3,741		6,660
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-4 Ltd. (Dec-20) | Funded by directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage, Amount		16,000
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-1 Ltd. (Mar-21)
Variable Interest Entity [Line Items]
Total VIE Assets		579,717	[5]	0
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(83)	[5]	0
Maximum Exposure to Loss - Off-Balance Sheet		4,387	[5]	0
Maximum Exposure to Loss, Total		4,304	[5]	0
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-1 Ltd. (Mar-21) | Funded by directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage, Amount		64,000
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-2 Ltd. (Jun-21)
Variable Interest Entity [Line Items]
Total VIE Assets		522,807	[6]	0
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		630	[6]	0
Maximum Exposure to Loss - Off-Balance Sheet		5,207	[6]	0
Maximum Exposure to Loss, Total		5,837		$ 0
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-2 Ltd. (Jun-21) | Funded by directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage, Amount		$ 93,000

[1]  An additional $79 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table

[2] An additional $26 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

[3] An additional $34 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

[4] An additional $16 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

[5] An additional $64 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table

[6]  An additional $93 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

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Other Comprehensive Income (Loss) - Amounts reclassified from accumulated other comprehensive income (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
Provision for credit losses	$ (59)	$ (1,000)	$ (2,662)	$ (10,349)
Other-than-temporary impairment losses			0	(533)
Income (loss) before income taxes and income (loss) from operating affiliates	745,367	495,689	1,184,478	426,444
Income tax expense	(51,179)	(26,127)	(90,039)	(54,072)
Net of tax	675,486	298,821	1,113,642	442,938
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)	64,914	182,329	66,918	328,561
Provision for credit losses	896	3,225	(751)	(6,095)
Other-than-temporary impairment losses	0	0	0	(533)
Income (loss) before income taxes and income (loss) from operating affiliates	65,810	185,554	66,167	321,933
Income tax expense	(5,263)	(18,163)	(8,317)	(33,313)
Net of tax	$ 60,547	$ 167,391	$ 57,850	$ 288,620

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Other Comprehensive Income (Loss) - Components of other comprehensive income (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020
Before tax amount:
Unrealized holding gains (losses) arising during period, before tax	$ 91,057	$ 555,576	$ (203,303)	$ 492,125
Less reclassification of net realized gains included in net income, before tax	65,810	185,554	66,167	321,933
Foreign currency translation adjustments, before tax	6,392	22,595	(22,023)	(22,829)
Other comprehensive income (loss), before tax	31,639	392,617	(291,493)	147,363
Tax expense (benefit):
Unrealized holding gains (losses) arising during period, tax	12,486	62,780	(20,124)	56,616
Less reclassification of net realized gains included in net income, tax	5,263	18,163	8,317	33,313
Foreign currency translation adjustments, tax	187	344	356	(391)
Other comprehensive income (loss), tax	7,410	44,961	(28,085)	22,912
Net of tax amount:
Unrealized holding gains (losses) arising during period, net of tax	78,571	492,796	(183,179)	435,509
Less reclassification of net realized gains included in net income, net of tax	60,547	167,391	57,850	288,620
Foreign currency translation adjustments, net of tax	6,205	22,251	(22,379)	(22,438)
Net current period other comprehensive income (loss)	$ 24,229	$ 347,656	$ (263,408)	$ 124,451

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Income Taxes (Details) - USD ($) $ in Millions	6 Months Ended
	Jun. 30, 2021	Jun. 30, 2020	Dec. 31, 2020
Income Tax Disclosure [Abstract]
Effective tax rate on income before income taxes (percentage)	7.00%	12.50%
Net deferred tax asset	$ 93.0		$ 15.7
Income taxes paid	$ 141.1	$ 10.4

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Transactions With Related Parties (Details) - USD ($) $ in Thousands	Jun. 30, 2021	Mar. 31, 2021	Jan. 01, 2021	Dec. 31, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019
Related Party Transaction [Line Items]
Reinsurance recoverable on unpaid and paid losses and LAE	$ 4,314,515	$ 4,041,076		$ 4,500,802	$ 4,363,507	$ 4,303,135	$ 4,346,816
Premia Holdings Ltd. | Barbican Group Holdings Limited
Related Party Transaction [Line Items]
Legacy business, amount of liabilities transferred			$ 380,000
Reinsurance recoverable on unpaid and paid losses and LAE	0			199,800
Funds held liability	$ 9,900			$ 149,600

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Subsequent Events (Details) $ in Millions	Jul. 01, 2021 USD ($)
Subsequent Event | Variable Interest Entity, Primary Beneficiary | Watford Holdings Ltd
Subsequent Event [Line Items]
Net gain on deconsolidation	$ 65