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Arch Capital (ACGL)

Document and Entity Information

Document and Entity Information - shares6 Months Ended
Jun. 30, 2021Jul. 30, 2021
Document and Entity Information [Abstract]
Document Type10-Q
Document Quarterly Reporttrue
Document Period End DateJun. 30,
2021
Document Transition Reportfalse
Entity File Number001-16209
Entity Registrant NameARCH CAPITAL GROUP LTD.
Entity Incorporation, State or Country CodeD0
Entity Tax Identification Number98-0374481
Entity Address, Address Line OneWaterloo House, Ground Floor
Entity Address, Address Line Two100 Pitts Bay Road,
Entity Address, City or TownPembroke
Entity Address, Postal Zip CodeHM 08,
Entity Address, CountryBM
City Area Code(441)
Local Phone Number278-9250
Entity Listings [Line Items]
Entity Current Reporting StatusYes
Entity Interactive Data CurrentYes
Entity Filer CategoryLarge Accelerated Filer
Entity Small Businessfalse
Entity Emerging Growth Companyfalse
Entity Shell Companyfalse
Entity Common Stock, Shares Outstanding396,039,032
Document Fiscal Period FocusQ2
Document Fiscal Year Focus2021
Current Fiscal Year End Date--12-31
Entity Central Index Key0000947484
Amendment Flagfalse
Common shares
Entity Listings [Line Items]
Title of 12(b) SecurityCommon shares, $0.0011 par value per share
Trading SymbolACGL
Security Exchange NameNASDAQ
Depositary Series E Preferred Stock
Entity Listings [Line Items]
Title of 12(b) SecurityDepositary shares, each representing a 1/1000th interest in a 5.25% Series E preferred share
Trading SymbolACGLP
Security Exchange NameNASDAQ
Depositary Series F Preferred Stock
Entity Listings [Line Items]
Title of 12(b) SecurityDepositary shares, each representing a 1/1000th interest in a 5.45% Series F preferred share
Trading SymbolACGLO
Security Exchange NameNASDAQ
Depositary Series G Preferred Stock
Entity Listings [Line Items]
Title of 12(b) SecurityDepositary shares, each representing a 1/1000th interest in a 4.55% Series G preferred share
Trading SymbolACGLN
Security Exchange NameNASDAQ

Unaudited Consolidated Balance

Unaudited Consolidated Balance Sheets - USD ($) $ in ThousandsJun. 30, 2021Dec. 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 value1,693,552 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 method2,539,124 2,047,889
Total investments29,298,681 28,761,358
Cash1,234,059 906,448
Accrued investment income96,546 103,299
Securities pledged under securities lending, at fair value (amortized cost: $167,871 and $294,493)168,548 294,912
Investment in operating affiliates731,810 129,291
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 premiums1,541,093 1,234,075
Deferred acquisition costs1,013,657 790,708
Receivable for securities sold309,234 92,743
Goodwill and intangible assets667,153 692,863
Other assets2,357,064 1,724,288
Total assets46,481,886 43,282,297
Liabilities
Reserve for losses and loss adjustment expenses17,196,648 16,513,929
Unearned premiums6,011,369 4,838,965
Reinsurance balances payable1,079,106 683,263
Contractholder payables1,887,418 1,995,562
Collateral held for insured obligations235,618 215,581
Senior notes2,861,728 2,861,113
Revolving credit agreement borrowings155,687 155,687
Securities lending payable172,109 301,089
Payable for securities purchased586,881 218,779
Other liabilities1,332,843 1,510,888
Total liabilities31,519,407 29,294,856
Commitments and Contingencies
Redeemable noncontrolling interests57,533 58,548
Shareholders' Equity
Non-cumulative preferred shares1,280,000 780,000
Common shares ($0.0011 par, shares issued: 582,654,893 and 579,000,841)647 643
Additional paid-in capital2,028,919 1,977,794
Retained earnings13,454,036 12,362,463
Accumulated other comprehensive income (loss), net of deferred income tax230,048 488,895
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 Arch13,986,072 13,105,886
Non-redeemable noncontrolling interests918,874 823,007
Total shareholders' equity14,904,946 13,928,893
Total liabilities, noncontrolling interests and shareholders' equity $ 46,481,886 $ 43,282,297

Unaudited Consolidated Balanc_2

Unaudited Consolidated Balance Sheets (Parentheticals) - USD ($) $ in ThousandsJun. 30, 2021Dec. 31, 2020
Fixed maturities available for sale, at amortized cost $ 17,764,783 $ 18,143,305
Allowance for credit losses on investments2,124 2,397
Short-term investments available for sale, at amortized cost2,248,615 1,924,292
Collateral received under securities lending, at amortized cost172,109 301,089
Other investments measured at fair value4,071,497 3,824,796
Securities pledged under securities lending, at amortized cost167,871 294,493
Allowance for credit losses on premiums receivable35,979 37,781
Allowance for credit losses on reinsurance recoverable11,029 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.

Unaudited Consolidated Statemen

Unaudited Consolidated Statements of Income - USD ($) $ in Thousands3 Months Ended6 Months Ended
Jun. 30, 2021Jun. 30, 2020Jun. 30, 2021Jun. 30, 2020
Revenues
Net premiums earned $ 2,120,909 $ 1,665,354 $ 4,069,331 $ 3,409,798
Net investment income111,613 131,485 210,469 276,638
Net realized gains (losses)202,907 556,588 345,368 189,628
Other underwriting income5,529 6,667 11,639 13,519
Equity in net income (loss) of investment funds accounted for using the equity method122,186 (65,119)193,872 (69,328)
Other income (loss)6,852 33 5,111 65
Total revenues2,569,996 2,295,008 4,835,790 3,820,320
Expenses
Losses and loss adjustment expenses1,159,831 1,230,522 2,362,931 2,345,941
Acquisition expenses335,143 254,789 639,624 502,072
Other operating expenses244,943 209,249 505,976 443,793
Corporate expenses15,951 17,920 41,335 38,716
Amortization of intangible assets15,286 16,489 29,688 33,120
Interest expense35,700 31,139 74,046 63,694
Net foreign exchange (gains) losses17,775 39,211 (2,288)(33,460)
Total expenses1,824,629 1,799,319 3,651,312 3,393,876
Income (loss) before income taxes and income (loss) from operating affiliates745,367 495,689 1,184,478 426,444
Income tax expense(51,179)(26,127)(90,039)(54,072)
Income (loss) from operating affiliates24,476 (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 Arch675,486 298,821 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

Unaudited Consolidated Statem_2

Unaudited Consolidated Statements of Comprehensive Income - USD ($) $ in Thousands3 Months Ended6 Months Ended
Jun. 30, 2021Jun. 30, 2020Jun. 30, 2021Jun. 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 period78,571 492,796 (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 adjustments6,205 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

Unaudited Consolidated Statem_3

Unaudited Consolidated Statements of Changes in Shareholders' Equity - USD ($) $ in ThousandsTotalNon-cumulative preferred sharesCommon sharesAdditional paid-in capitalRetained earningsRetained earningsCumulative effect of an accounting changeRetained earningsBalance at beginning of period, as adjustedAccumulated other comprehensive income (loss), net of deferred income taxUnrealized appreciation (decline) in value of available-for-sale securities, net of deferred income taxForeign currency translation adjustments, net of deferred income taxCommon 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 issued0
Common shares issued, net4
Amortization of share-based compensation41,210
Issue costs on preferred shares0
Other changes4,621
Net income (loss) $ 377,715 377,715
Net (income) loss attributable to noncontrolling interests65,223 65,223
Preferred share dividends(20,806)(20,806)
Unrealized holding gains (losses) during period, net of reclassification adjustment146,889
Unrealized holding gains (losses) during period attributable to noncontrolling interests13,112
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, 202011,991,825 780,000 642 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, 2020679,089
Total shareholders’ equity at Jun. 30, 202012,670,914
Balance at beginning of period at Mar. 31, 2020780,000 642 1,921,487 11,132,268 0 11,132,268 21,944 113,149 (91,205)(2,489,097)
Preferred shares issued0
Common shares issued, net0
Amortization of share-based compensation13,160
Issue costs on preferred shares0
Other changes867
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 adjustment325,405
Unrealized holding gains (losses) during period attributable to noncontrolling interests(20,067)
Foreign currency translation adjustments22,251 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, 202011,991,825 780,000 642 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, 2020679,089
Total shareholders’ equity at Jun. 30, 202012,670,914
Balance at beginning of period at Dec. 31, 202013,105,886 780,000 643 1,977,794 12,362,463 0 12,362,463 488,895 501,295 (12,400)(2,503,909)
Preferred shares issued500,000
Common shares issued, net4
Amortization of share-based compensation57,063
Issue costs on preferred shares(14,179)
Other changes8,241
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 interests4,436
Foreign currency translation adjustments(22,379)(22,379)
Foreign currency translation adjustments attributable to noncontrolling interests125
Shares repurchased for treasury(503,669)
Balance at end of period at Jun. 30, 202113,986,072 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, 2021918,874
Total shareholders’ equity at Jun. 30, 2021 $ 14,904,946
Accounting Standards Updateus-gaap:AccountingStandardsUpdate201613Member
Balance at beginning of period at Mar. 31, 2021780,000 645 2,014,741 12,790,216 $ 0 $ 12,790,216 205,827 246,711 (40,884)(2,694,957)
Preferred shares issued500,000
Common shares issued, net2
Amortization of share-based compensation16,490
Issue costs on preferred shares(14,179)
Other changes11,867
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 adjustment18,024
Unrealized holding gains (losses) during period attributable to noncontrolling interests(33)
Foreign currency translation adjustments6,205 6,205
Foreign currency translation adjustments attributable to noncontrolling interests25
Shares repurchased for treasury(312,621)
Balance at end of period at Jun. 30, 202113,986,072 $ 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, 2021918,874
Total shareholders’ equity at Jun. 30, 2021 $ 14,904,946

Unaudited Consolidated Statem_4

Unaudited Consolidated Statements of Cash Flows - USD ($) $ in Thousands6 Months Ended
Jun. 30, 2021Jun. 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 assets29,688 33,120
Share-based compensation57,564 41,912
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable948,505 1,158,446
Unearned premiums, net of ceded unearned premiums838,650 395,759
Premiums receivable(781,391)(463,638)
Deferred acquisition costs(214,893)(92,437)
Reinsurance balances payable331,461 132,161
Other items, net(231,307)(192,066)
Net cash provided by (used for) operating activities1,612,572 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 investments23,130,388 24,833,030
Proceeds from sales of equity securities542,290 580,346
Proceeds from sales, redemptions and maturities of other investments772,549 472,188
Proceeds from redemptions and maturities of fixed maturity investments805,836 369,240
Net settlements of derivative instruments17,286 150,471
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, net485,821 0
Purchases of common shares under share repurchase program(485,315)(75,486)
Proceeds from common shares issued, net185 (9,661)
Proceeds from borrowings0 1,004,918
Repayments of borrowings0 (165,000)
Change in cash collateral related to securities lending826 (54,596)
Third party investment in non-redeemable noncontrolling interests15,971 (2,867)
Dividends paid to redeemable noncontrolling interests(1,907)(2,540)
Other27,639 (2,625)
Preferred dividends paid(20,805)(20,806)
Net cash provided by (used for) financing activities22,415 671,337
Effects of exchange rate changes on foreign currency cash and restricted cash(13,390)(21,742)
Increase (decrease) in cash and restricted cash527,919 160,985
Cash and restricted cash, beginning of year1,290,544 903,698
Cash and restricted cash, end of period $ 1,818,463 $ 1,064,683

Basis of Presentation and Recen

Basis of Presentation and Recent Accounting Pronouncements6 Months Ended
Jun. 30, 2021
Organization, Consolidation and Presentation of Financial Statements [Abstract]
Basis of Presentation and Recent Accounting PronouncementsBasis 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.

Share Transactions

Share Transactions6 Months Ended
Jun. 30, 2021
Stockholders' Equity Note [Abstract]
Share TransactionsShare 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.

Earnings Per Common Share

Earnings Per Common Share6 Months Ended
Jun. 30, 2021
Earnings Per Share [Abstract]
Earnings Per Common ShareEarnings 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.

Segment Information

Segment Information6 Months Ended
Jun. 30, 2021
Segment Reporting [Abstract]
Segment InformationSegment 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.

Reserve for Losses and Loss Adj

Reserve for Losses and Loss Adjustment Expenses6 Months Ended
Jun. 30, 2021
Liability for Future Policy Benefits and Unpaid Claims and Claims Adjustment Expense [Abstract]
Reserve for losses and loss adjustment expensesReserve 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.

Allowance for Expected Credit L

Allowance for Expected Credit Losses6 Months Ended
Jun. 30, 2021
Credit Loss [Abstract]
Allowance for expected credit lossesAllowance 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 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 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

Investment Information

Investment Information6 Months Ended
Jun. 30, 2021
Disclosure Investment Information [Abstract]
Investment InformationInvestment 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 Gross Gross Allowance for Expected Credit Losses (2) Cost or 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 Gross Estimated Gross Estimated Gross 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 Amortized Estimated Amortized 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, December 31, 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, December 31, 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, December 31, 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, December 31, 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 three 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 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 Corporate 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 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, December 31, 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, December 31, 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

Fair Value

Fair Value6 Months Ended
Jun. 30, 2021
Fair Value Disclosures [Abstract]
Fair ValueFair 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 Quoted Prices in Significant Significant 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 Quoted Prices in Significant Significant 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 Corporate Other Equity Equity 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.

Derivative Instruments

Derivative Instruments6 Months Ended
Jun. 30, 2021
Derivative Instruments and Hedging Activities Disclosure [Abstract]
Derivative InstrumentsDerivative 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 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.

Commitments and Contingencies

Commitments and Contingencies6 Months Ended
Jun. 30, 2021
Commitments and Contingencies Disclosure [Abstract]
Commitments and ContingenciesCommitments 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

Variable Interest Entities and

Variable Interest Entities and Noncontrolling Interests6 Months Ended
Jun. 30, 2021
Noncontrolling Interest [Abstract]
Variable Interest Entity and Noncontrolling InterestsVariable 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.

Other Comprehensive Income (Los

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

Income Taxes

Income Taxes6 Months Ended
Jun. 30, 2021
Income Tax Disclosure [Abstract]
Income TaxesIncome 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.

Legal Proceedings

Legal Proceedings6 Months Ended
Jun. 30, 2021
Disclosure Legal Proceedings [Abstract]
Legal ProceedingsLegal 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.

Transactions With Related Parti

Transactions With Related Parties6 Months Ended
Jun. 30, 2021
Related Party Transactions [Abstract]
Transactions with related partiesTransactions 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,”

Subsequent Events

Subsequent Events6 Months Ended
Jun. 30, 2021
Subsequent Events [Abstract]
Subsequent EventSubsequent 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.

Basis of Presentation and Rec_2

Basis of Presentation and Recent Accounting Pronouncements (Policies)6 Months Ended
Jun. 30, 2021
Organization, Consolidation and Presentation of Financial Statements [Abstract]
Basis of accountingThe 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 estimatesThe 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 periodsThe 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 pronouncementsRecently 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.

Earnings Per Common Share (Tabl

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 shareThe 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.

Segment Information (Tables)

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 shareholdersThe 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.

Reserve for Losses and Loss A_2

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 balancesThe 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.

Allowance for Expected Credit_2

Allowance for Expected Credit Losses (Tables)6 Months Ended
Jun. 30, 2021
Credit Loss [Abstract]
Premiums receivableThe 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
Reinsurance recoverablesThe 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
Ceded credit riskThe 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 receivablesThe 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

Investment Information (Tables)

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 securitiesThe following table summarizes the fair value and cost or amortized cost of the Company’s securities classified as available for sale: Estimated Gross Gross Allowance for Expected Credit Losses (2) Cost or 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.”
Summary of available for sale securities in a continual unrealized loss positionThe 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 Gross Estimated Gross Estimated Gross 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 arrangementsThe 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 Amortized Estimated Amortized 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 categoryThe 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 optionThe following table summarizes the Company’s other investments and other investable assets: June 30, December 31, 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 investmentsThe following table summarizes the Company’s other investments, as detailed in the previous table, by strategy: June 30, December 31, 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 methodThe following table summarizes the Company’s investments accounted for using the equity method, by strategy: June 30, December 31, 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 interestThe following table summarizes investments in limited partnership interests where the Company has a variable interest by balance sheet line item: June 30, December 31, 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 incomeThe 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
Summary of net realized gains (losses), excluding other-than-temporary impairment provisionsNet 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 saleThe 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 Corporate 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
Summary of restricted assetsThe following table details the value of the Company’s restricted assets: June 30, December 31, 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 cashThe following table details reconciliation of cash and restricted cash within the Consolidated Balance Sheets: June 30, December 31, 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

Fair Value (Tables)

Fair Value (Tables)6 Months Ended
Jun. 30, 2021
Fair Value Disclosures [Abstract]
Fair value hierarchyThe 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 Quoted Prices in Significant Significant 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 Quoted Prices in Significant Significant 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 investmentsThe 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 Corporate Other Equity Equity 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.

Derivative Instruments (Tables)

Derivative Instruments (Tables)6 Months Ended
Jun. 30, 2021
Derivative Instruments and Hedging Activities Disclosure [Abstract]
Fair value and notional amount of derivativesThe 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 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 incomeRealized 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.

Variable Interest Entities an_2

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 entityThe 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
Activity in non-redeemable noncontrolling interestsThe 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 interestsThe 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 investorsThe 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 VIEsThe 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.

Other Comprehensive Income (L_2

Other Comprehensive Income (Loss) (Tables)6 Months Ended
Jun. 30, 2021
Comprehensive Income Note Disclosure [Abstract]
Details about amounts reclassified from AOCIThe 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

Share Transactions - Share repu

Share Transactions - Share repurchases (Details) - Common shares - USD ($) shares in Millions, $ in Millions6 Months Ended
Jun. 30, 2021Jun. 30, 2020
Class of Stock [Line Items]
Cumulative number of shares acquired since inception of share repurchase program402.3
Aggregate purchase price of shares acquired since inception of share repurchase program $ 4,540
Treasury stock, shares acquired (shares)13.1 2.6
Shares repurchased for treasury $ 485.3 $ 75.5
Remaining authorized repurchase amount $ 431.2

Share Transactions - Issuance o

Share Transactions - Issuance of preferred shares (Details) - USD ($) $ / shares in Units, $ in Thousands, shares in Millions1 Months Ended6 Months Ended
Jun. 30, 2021Jun. 30, 2021Jun. 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 share25,000 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 issued20
Proportionate interest of preference shares, per depositary share0.10%0.10%
Liquidation preference per share $ 25 $ 25
Preferred shares, redemption price per share $ 25 $ 25

Earnings Per Common Share (Deta

Earnings Per Common Share (Details) - USD ($) $ / shares in Units, $ in Thousands3 Months Ended6 Months Ended
Jun. 30, 2021Jun. 30, 2020Jun. 30, 2021Jun. 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 Arch675,486 298,821 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 — basic397,743,402 402,503,687 399,267,183 403,197,924
Effect of dilutive common share equivalents:
Nonvested restricted shares1,990,729 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 — diluted406,485,994 408,119,681 407,687,680 411,005,591
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.

Segment Information - Summary o

Segment Information - Summary of underwriting income or loss by segment (Details) $ in Thousands3 Months Ended6 Months Ended
Jun. 30, 2021USD ($)Jun. 30, 2020USD ($)Jun. 30, 2021USD ($)segmentJun. 30, 2020USD ($)Dec. 31, 2020USD ($)
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 written2,399,524 1,668,311 4,907,981 3,805,557
Change in unearned premiums(278,615)(2,957)(838,650)(395,759)
Net premiums earned2,120,909 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 income111,613 131,485 210,469 276,638
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 method122,186 (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 other1,224 (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 affiliates745,367 495,689 1,184,478 426,444
Income tax expense (benefit)(51,179)(26,127)(90,039)(54,072)
Income (loss) from operating affiliates24,476 (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 Arch675,486 298,821 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 ratio54.70%73.90%58.10%68.80%
Acquisition expense ratio15.80%15.30%15.70%14.70%
Other operating expense ratio11.50%12.60%12.40%13.00%
Combined ratio82.00%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 | segment2
Operating segments
Segment Reporting Information [Line Items]
Number of segments | segment3
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 written2,224,133 1,562,455 4,553,279 3,513,001
Change in unearned premiums(287,461)(28,636)(815,916)(374,777)
Net premiums earned1,936,672 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 ratio52.60%73.40%56.30%67.90%
Acquisition expense ratio15.50%15.10%15.40%14.60%
Other operating expense ratio11.70%12.70%12.70%13.30%
Combined ratio79.80%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 written963,555 672,261 1,958,394 1,501,009
Change in unearned premiums(98,128)15,648 (273,493)(97,181)
Net premiums earned865,427 687,909 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 ratio63.10%75.30%64.20%73.00%
Acquisition expense ratio15.80%15.70%15.70%15.30%
Other operating expense ratio15.40%17.30%16.10%17.70%
Combined ratio94.30%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 written924,732 565,094 1,923,844 1,362,274
Change in unearned premiums(187,708)(84,897)(541,920)(338,617)
Net premiums earned737,024 480,197 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 ratio62.90%79.80%68.70%79.50%
Acquisition expense ratio18.10%18.90%18.20%16.60%
Other operating expense ratio6.10%8.10%7.60%8.20%
Combined ratio87.10%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 written335,846 325,100 671,041 649,718
Change in unearned premiums(1,625)40,613 (503)61,021
Net premiums earned334,221 365,713 670,538 710,739
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 ratio3.00%61.30%11.00%41.00%
Acquisition expense ratio9.00%9.30%9.00%10.20%
Other operating expense ratio14.50%10.30%14.50%11.70%
Combined ratio26.50%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 income89,430 101,031 168,159 214,059
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 method122,186 (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 affiliates697,799 305,647 1,095,043 503,084
Income tax expense (benefit)(50,953)(26,529)(89,805)(54,474)
Income (loss) from operating affiliates24,476 (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 interests0 0 0 0
Net income (loss) available to Arch670,742 275,011 1,104,708 452,962
Preferred dividends(11,666)(10,403)(22,069)(20,806)
Net income (loss) available to Arch common shareholders659,076 264,608 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 written175,391 105,856 354,702 292,556
Change in unearned premiums8,846 25,679 (22,734)(20,982)
Net premiums earned184,237 131,535 331,968 271,574
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 income22,183 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 method0 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 affiliates47,568 190,042 89,435 (76,640)
Income tax expense (benefit)(226)402 (234)402
Income (loss) from operating affiliates0 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 Arch4,744 23,810 8,934 (10,024)
Preferred dividends0 0 0 0
Net income (loss) available to Arch common shareholders $ 4,744 $ 23,810 $ 8,934 $ (10,024)
Underwriting Ratios
Loss ratio76.10%79.70%78.00%79.30%
Acquisition expense ratio18.80%17.10%18.90%16.30%
Other operating expense ratio10.10%10.80%9.90%10.30%
Combined ratio105.00%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.’

Reserve for Losses and Loss A_3

Reserve for Losses and Loss Adjustment Expenses - Reconciliation of beginning and ending balances of losses and loss adjustment reserves (Details) - USD ($) $ in Thousands3 Months Ended6 Months Ended
Jun. 30, 2021Jun. 30, 2020Jun. 30, 2021Jun. 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 recoverable3,916,650 4,070,114 4,314,855 4,082,650
Net reserve for losses and loss adjustment expenses at beginning of period12,527,302 10,239,466 12,199,074 9,809,192
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year1,219,081 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 expenses1,159,831 1,230,522 2,362,931 2,345,941
Retroactive reinsurance transaction[1]0 0 (183,893)60,635
Net foreign exchange (gains) losses135,847 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 period13,050,628 10,888,717 13,050,628 10,888,717
Unpaid losses and loss adjustment expenses recoverable4,146,020 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.

Reserve for Losses and Loss A_4

Reserve for Losses and Loss Adjustment Expenses - Prior year development (Details) - USD ($) $ in Thousands3 Months Ended6 Months Ended
Jun. 30, 2021Jun. 30, 2020Jun. 30, 2021Jun. 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 development0.50%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 development2.80%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 development12.90%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

Allowance for Expected Credit_3

Allowance for Expected Credit Losses - Premiums receivable (Details) - USD ($) $ in Thousands3 Months Ended6 Months Ended
Jun. 30, 2021Jun. 30, 2020Jun. 30, 2021Jun. 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 period2,866,578 2,203,753 2,866,578 2,203,753
Allowance for Expected Credit Losses
Balance at beginning of period36,111 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 period35,979 36,054 35,979 36,054
Write-offs charged against the allowance $ 1,100 $ 1,800 $ 1,200 $ 2,300
Accounting Standards Updateus-gaap:AccountingStandardsUpdate201613Member
[1]Adoption of ASU 2016-13
[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.

Allowance for Expected Credit_4

Allowance for Expected Credit Losses - Reinsurance recoverables (Details) - USD ($) $ in Thousands3 Months Ended6 Months Ended
Jun. 30, 2021Jun. 30, 2020Jun. 30, 2021Jun. 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 period4,314,515 4,363,507 4,314,515 4,363,507
Allowance for Expected Credit Losses
Balance at beginning of period10,872 13,700 11,636 1,364
Cumulative effect of accounting change[1]12,010
Change for provision of expected credit losses157 (105)(607)221
Balance at end of period $ 11,029 $ 13,595 $ 11,029 $ 13,595
[1]Adoption of ASU 2016-13

Allowance for Expected Credit_5

Allowance for Expected Credit Losses - Ceded credit risk (Details) - USD ($) $ in Thousands6 Months Ended12 Months Ended
Jun. 30, 2021Dec. 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 percentage66.00%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 percentage91.00%94.00%
Stockholders' equity | Reinsurer concentration risk | Single Reinsurer
Ceded Credit Risk [Line Items]
Concentration risk percentage2.40%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

Allowance for Expected Credit_6

Allowance for Expected Credit Losses - Contractholder receivables (Details) - USD ($) $ in Thousands3 Months Ended6 Months Ended
Jun. 30, 2021Jun. 30, 2020Jun. 30, 2021Jun. 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 period1,882,948 2,179,124 1,882,948 2,179,124
Allowance for Expected Credit Losses
Balance at beginning of period5,853 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

Investment Information - Summar

Investment Information - Summary of available for sale securities (Details) - USD ($) $ in Thousands6 Months Ended
Jun. 30, 2021Mar. 31, 2021Dec. 31, 2020Jun. 30, 2020Mar. 31, 2020Dec. 31, 2019
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value $ 18,073,779 $ 18,717,825
Estimated Fair Value2,248,613 1,924,922
Estimated Fair Value20,478,448 20,921,530
Gross Unrealized Gains390,212 657,620
Gross Unrealized Losses(78,417)(79,654)
Allowance for expected credit losses(2,124) $ (3,830)(2,397) $ (5,869) $ (9,938) $ 0
Amortized cost17,764,783 18,143,305
Cost2,248,615 1,924,292
Cost or Amortized Cost $ 20,168,777 20,345,961
Accounting Standards Updateus-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 Value7,129,768 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 Value389,041 630,001
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 Value415,483 494,522
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 Value266,733 389,900
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 Value5,091,183 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 Value2,449,782 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 Value2,487,845 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 Value2,248,613 1,924,922
Gross Unrealized Gains1,404 2,693
Gross Unrealized Losses(1,406)(2,063)
Allowance for expected credit losses0 [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.

Investment Information - Aging

Investment Information - Aging of available for sale securities in an unrealized loss position (Details) - USD ($) $ in ThousandsJun. 30, 2021Dec. 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 More158,155 70,404
Estimated Fair Value8,180,563 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 Months531,130 97,920
Estimated Fair Value - 12 Months or More0 0
Estimated Fair Value531,130 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 More0 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.”

Investment Information - Maturi

Investment Information - Maturity profile of available for sale securities) (Details) - USD ($) $ in ThousandsJun. 30, 2021Dec. 31, 2020
Estimated Fair Value
Estimated Fair Value $ 18,073,779 $ 18,717,825
Amortized Cost
Amortized cost17,764,783 18,143,305
Fixed maturities
Estimated Fair Value
Due in one year or less452,065 348,200
Due after one year through five years10,114,276 10,629,959
Due after five years through 10 years4,148,538 4,881,564
Due after 10 years371,337 482,180
Single maturity date15,086,216 16,341,903
Estimated Fair Value[1]18,229,835 18,996,608
Amortized Cost
Due in one year or less439,855 339,951
Due after one year through five years9,942,182 10,340,819
Due after five years through 10 years4,055,318 4,654,754
Due after 10 years355,241 448,139
Single maturity date14,792,596 15,783,663
Amortized cost[1]17,920,162 18,421,669
Fixed maturities | Mortgage backed securities
Estimated Fair Value
Securities without single maturity date389,041 630,001
Estimated Fair Value389,041 630,001
Amortized Cost
Securities without single maturity date388,309 626,368
Amortized cost[1]388,309 626,368
Fixed maturities | Commercial mortgage backed securities
Estimated Fair Value
Securities without single maturity date266,733 389,900
Estimated Fair Value266,733 389,900
Amortized Cost
Securities without single maturity date263,330 384,254
Amortized cost[1]263,330 384,254
Fixed maturities | Asset backed securities
Estimated Fair Value
Securities without single maturity date2,487,845 1,634,804
Estimated Fair Value2,487,845 1,634,804
Amortized Cost
Securities without single maturity date2,475,927 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.”

Investment Information - Securi

Investment Information - Securities lending agreements (Details) - USD ($) $ in ThousandsJun. 30, 2021Dec. 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 lending171,300 301,100
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable172,109 301,089
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 90 0
Amounts related to securities lending not included in offsetting disclosure in note 9172,109 301,089
US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable153,458 281,607
Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable5,800 3,021
Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable12,851 16,461
Overnight and continuous
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable34,396 161,799
Overnight and continuous | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable15,745 142,317
Overnight and continuous | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable5,800 3,021
Overnight and continuous | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable12,851 16,461
Less than 30 days
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable137,713 0
Less than 30 days | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable137,713 0
Less than 30 days | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable0 0
Less than 30 days | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable0 0
30 - 90 days
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable0 139,290
30 - 90 days | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable0 139,290
30 - 90 days | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable0 0
30 - 90 days | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable0 0
90 days or more
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable0 0
90 days or more | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable0 0
90 days or more | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable0 0
90 days or more | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable $ 0 $ 0

Investment Information - Other

Investment Information - Other investments (Details) - USD ($) $ in ThousandsJun. 30, 2021Dec. 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 value995,980 843,354
Fair value option | Other investments
Schedule Of Other Investments [Line Items]
Other investments measured at fair value2,370,472 2,331,885
Fair value option | Other investments | Term loan investments
Schedule Of Other Investments [Line Items]
Other investments measured at fair value1,333,014 1,231,731
Fair value option | Other investments | Lending
Schedule Of Other Investments [Line Items]
Other investments measured at fair value638,786 572,636
Fair value option | Other investments | Credit related funds
Schedule Of Other Investments [Line Items]
Other investments measured at fair value73,171 90,780
Fair value option | Other investments | Energy
Schedule Of Other Investments [Line Items]
Other investments measured at fair value84,891 65,813
Fair value option | Other investments | Investment grade fixed income
Schedule Of Other Investments [Line Items]
Other investments measured at fair value110,375 138,646
Fair value option | Other investments | Infrastructure
Schedule Of Other Investments [Line Items]
Other investments measured at fair value32,109 165,516
Fair value option | Other investments | Private equity
Schedule Of Other Investments [Line Items]
Other investments measured at fair value70,878 48,750
Fair value option | Other investments | Real estate
Schedule Of Other Investments [Line Items]
Other investments measured at fair value27,248 18,013
Fair value option | Short-term investments
Schedule Of Other Investments [Line Items]
Other investments measured at fair value610,114 557,008
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

Investment Information - Equity

Investment Information - Equity method investments (Details) - USD ($) $ in ThousandsJun. 30, 2021Dec. 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 method883,279 740,060
Equity securities
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method403,003 343,058
Real estate
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method323,566 258,518
Lending
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method295,228 179,629
Private equity
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method305,662 235,289
Infrastructure
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method210,174 175,882
Energy
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method $ 118,212 $ 115,453

Investment Information - Limite

Investment Information - Limited partnership interests (Details) - USD ($) $ in ThousandsJun. 30, 2021Dec. 31, 2020
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss $ 2,721,384 $ 2,232,609
Aggregate unfunded commitments2,400,000 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 commitments2,000,000 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.

Investment Information - Net in

Investment Information - Net investment income (Details) - USD ($) $ in Thousands3 Months Ended6 Months Ended
Jun. 30, 2021Jun. 30, 2020Jun. 30, 2021Jun. 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 income111,613 131,485 210,469 276,638
Fixed maturities
Net investment income:
Gross investment income88,625 105,391 179,251 220,238
Term loans
Net investment income:
Gross investment income16,879 20,512 31,607 43,682
Equity securities
Net investment income:
Gross investment income8,584 6,219 14,234 12,226
Short-term investments
Net investment income:
Gross investment income1,138 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.

Investment Information - Net re

Investment Information - Net realized gains and losses (Details) - USD ($) $ in Thousands3 Months Ended6 Months Ended
Jun. 30, 2021Jun. 30, 2020Jun. 30, 2021Jun. 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 period33,570 (18,250)71,419 (18,789)
Net unrealized gains (losses) on equity securities still held at reporting date65,847 145,686 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 related1,381 (5,834)6,649 (9,104)
Net impairment losses0 (533)
Derivative instruments[1](51,109)(836)(14,993)126,353
Other10,224 (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 option10,912 68,181 27,465 (59,485)
Allowance for credit losses:
Allowance for credit losses - investment related896 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 option60,884 178,570 107,739 (129,230)
Equity securities
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option5,492 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.

Investment Information - Invest

Investment Information - Investment in operating affiliates (Details) € / shares in Units, € in Thousands, $ in Thousands3 Months Ended6 Months Ended
Jun. 30, 2021USD ($)Jun. 30, 2020USD ($)Jun. 30, 2021USD ($)Jun. 30, 2021EUR (€)Jun. 30, 2020USD ($)Jun. 30, 2021€ / sharesDec. 31, 2020USD ($)
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 reporting3 months3 months
Coface
Schedule of Equity Method Investments [Line Items]
Percentage ownership29.50%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 affiliates74,500
Purchase Of Affiliate, Deferred Gain $ 36,000 $ 36,000
Purchase Of Operating Affiliate, Deferred Gain, Period Of Recognition5 years5 years

Investment Information - Allowa

Investment Information - Allowance for expected credit losses (Details) - USD ($) $ in Thousands3 Months Ended6 Months Ended
Jun. 30, 2021Jun. 30, 2020Jun. 30, 2021Jun. 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 losses59 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 period2,124 5,869 $ 2,124 5,869
Accounting Standards Updateus-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 period2,124 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 period759 1,726 759 1,726
Fixed maturities | Municipal bonds
Allowance for expected credit losses
Balance at beginning of period2 23 11 0
Cumulative effect of accounting change[1]0
Additions for current-period provision for expected credit losses0 44 0 67
Additions (reductions) for previously recognized expected credit losses4 (25)(5)(25)
Reductions due to disposals0 (14)0 (14)
Balance at end of period6 28 6 28
Fixed maturities | Corporate bonds
Allowance for expected credit losses
Balance at beginning of period2,621 7,232 896 0
Cumulative effect of accounting change[1]117
Additions for current-period provision for expected credit losses7 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 period1,359 4,115 1,359 4,115
Short-term investments
Allowance for expected credit losses
Balance at beginning of period0 29 0 [3]0
Cumulative effect of accounting change[1]0
Additions for current-period provision for expected credit losses0 (29)0 0
Additions (reductions) for previously recognized expected credit losses0 0 0 0
Reductions due to disposals0 0 0 0
Balance at end of period $ 0 [3] $ 0 $ 0 [3] $ 0
[1]Adoption of ASU 2016-13
[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.

Investment Information - Restri

Investment Information - Restricted assets (Details) - USD ($) $ in ThousandsJun. 30, 2021Dec. 31, 2020
Restricted Assets [Line Items]
Restricted assets $ 9,725,335 $ 8,733,309
Collateral or guarantees - affiliated transactions
Restricted Assets [Line Items]
Restricted assets5,041,190 4,643,334
Collateral or guarantees - third party agreements
Restricted Assets [Line Items]
Restricted assets3,441,929 3,083,324
Deposits with US regulatory authorities
Restricted Assets [Line Items]
Restricted assets814,084 827,552
Deposits with non-US regulatory authorities
Restricted Assets [Line Items]
Restricted assets428,132 179,099
Watford Holdings Ltd
Restricted Assets [Line Items]
Assets pledged as collateral $ 1,100,000 $ 954,600

Investment Information - Cash a

Investment Information - Cash and restricted cash (Details) - USD ($) $ in ThousandsJun. 30, 2021Dec. 31, 2020Jun. 30, 2020Dec. 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

Investment Information - Narrat

Investment Information - Narrative (Details) $ in Thousands3 Months Ended6 Months Ended
Jun. 30, 2021USD ($)lotsJun. 30, 2020USD ($)Jun. 30, 2021USD ($)lotsJun. 30, 2020USD ($)Dec. 31, 2020USD ($)lots
Narrative items:
Investable assets $ 30,200,000 $ 30,200,000
Equity in net (loss) income of investment funds accounted for using the equity method122,186 $ (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) | lots3,240 3,240 2,320
Total number of positions (lots) | lots10,890 10,890 11,180
Largest single loss $ 2,400 $ 2,400 $ 900
Consolidated Entity, Excluding Consolidated VIE
Narrative items:
Investable assets27,300,000 27,300,000
Variable Interest Entity, Primary Beneficiary
Narrative items:
Investable assets $ 2,900,000 $ 2,900,000
Minimum
Narrative items:
Time lag for reporting1 month
Maximum
Narrative items:
Time lag for reporting3 months

Fair Value - Fair Value Hierarc

Fair Value - Fair Value Hierarchy (Details) - Recurring - USD ($) $ in ThousandsJun. 30, 2021Dec. 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 value0 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 value0 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 value0 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 value0
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 value1,996,304 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 value1,631,937 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 value0 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 value527,840 494,817
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 value0 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 value0 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 value0 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 value163 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 value0 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 value0 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 value482,815 420,131
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 value21,252 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 value23,610 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 value15,828,422 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 value0 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 value44,925
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 value252,309 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 value24,971 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 value98,488 177,383
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 value2,243,902 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 value789,188 650,309
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 value2,707 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 value841 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 value108 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 value22,552 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 value179,423 152,151
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 value127,299 136,877
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 value0 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 value1,121,784 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 value201,149 182,530
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 value0 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 value0
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 value0 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 value49,136 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 value0 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 value148,576 137,076
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 value998 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 value0 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 value0 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 value0 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 value0 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 value0 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 value0 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 value73,678 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 value73,900 67,103
Estimated Fair Value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value26,399,401 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 value44,925
Estimated Fair Value | Fixed maturities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value18,229,835 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 value7,129,768 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 value389,041 630,001
Estimated Fair Value | Fixed maturities | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value415,483 494,522
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 value266,733 389,900
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 value5,091,183 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 value2,449,782 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 value2,487,845 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 value2,248,613 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 value1,706,044 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 value98,488 177,383
Estimated Fair Value | Fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value4,071,496 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 value790,186 651,294
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 value2,707 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 value841 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 value271 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 value22,552 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 value179,423 152,151
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 value610,114 557,008
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 value94,930 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 value1,219,294 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.

Fair Value - Rollforward of Lev

Fair Value - Rollforward of Level 3 assets and liabilities (Details) - Recurring - USD ($) $ in Thousands3 Months Ended6 Months Ended
Jun. 30, 2021Jun. 30, 2020Jun. 30, 2021Jun. 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 income0 0 0 0
Purchases, issuances, sales and settlements
Purchases0 0 0 0
Issuances0 0 0 0
Sales0 0 0 0
Settlements(1)6,735 (5)6,820
Transfers in and/or out of Level 30 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 period13 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 income0 (1,123)0 (6,539)
Purchases, issuances, sales and settlements
Purchases0 0 0 0
Issuances0 0 0 0
Sales0 0 0 0
Settlements0 0 0 (1,462)
Transfers in and/or out of Level 30 0 0 0
Balance at end of period13 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 period989 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 income0 0 0 0
Purchases, issuances, sales and settlements
Purchases0 33 0 66
Issuances0 0 0 0
Sales0 0 0 0
Settlements0 0 0 0
Transfers in and/or out of Level 30 0 0 0
Balance at end of period998 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 period67,930 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 income0 0 0 0
Purchases, issuances, sales and settlements
Purchases5,638 3 13,003 24
Issuances0 0 0 0
Sales(301)(7,183)(7,087)(24,358)
Settlements0 0 0 0
Transfers in and/or out of Level 30 0 0 2,984
Balance at end of period73,900 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 period71,176 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 income0 0 0 0
Purchases, issuances, sales and settlements
Purchases0 0 0 0
Issuances0 0 0 0
Sales0 0 0 0
Settlements0 0 0 0
Transfers in and/or out of Level 30 0 0 0
Balance at end of period73,678 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 period43,112 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 income0 0 0 0
Purchases, issuances, sales and settlements
Purchases5,102 0 5,295 3,464
Issuances0 0 0 0
Sales0 (15,450)0 (15,450)
Settlements0 0 0 0
Transfers in and/or out of Level 30 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.

Fair Value - Narrative (Details

Fair Value - Narrative (Details) - USD ($) $ in ThousandsJun. 30, 2021Dec. 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

Derivative Instruments - Fair v

Derivative Instruments - Fair value and notional amount of derivatives (Details) - USD ($) $ in ThousandsJun. 30, 2021Dec. 31, 2020
Derivative offsetting
Derivative assets subject to master netting agreements $ 89,900 $ 138,800
Derivative liabilities subject to master netting agreements66,700 93,000
Not designated as hedging instrument
Derivative [Line Items]
Asset derivatives - fair value98,488 177,383
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.’

Derivative Instruments - Summar

Derivative Instruments - Summary of net realized gains (losses) recorded in the consolidated statements of income (Details) - USD ($) $ in Thousands3 Months Ended6 Months Ended
Jun. 30, 2021Jun. 30, 2020Jun. 30, 2021Jun. 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 instruments1,295 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 instruments0 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

Commitments and Contingencies (

Commitments and Contingencies (Details) - USD ($) $ in Millions6 Months Ended
Jun. 30, 2021Jun. 30, 2020Dec. 31, 2020
Commitments and Contingencies Disclosure [Abstract]
Investment commitments $ 2,400 $ 2,100
Interest paid on senior notes and other borrowings $ 74.7 $ 57.4

Variable Interest Entities an_3

Variable Interest Entities and Noncontrolling Interests - Variable interest entity (Details) - USD ($) $ / shares in Units, $ in Thousands1 Months Ended6 Months Ended12 Months Ended
Mar. 31, 2014Jun. 30, 2021Jun. 30, 2020Dec. 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
Variable Interest Entity, Primary Beneficiary | Watford Holdings Ltd
Variable Interest Entity [Line Items]
Initial investment contribution amount $ 100,000
Number of shares acquired2,500,000
Ownership percentage11.00%10.20%
Senior notes, face amount $ 35,000
Senior notes, stated percentage6.50%
Net cash provided by (used for) operating activities $ 47,000 87,300
Net cash provided by (used for) investing activities96,300 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 transaction40.00%
Variable Interest Entity, Primary Beneficiary | Watford Holdings Ltd | Kelso And Company
Variable Interest Entity [Line Items]
Noncontrolling interest, ownership percentage by noncontrolling owners30.00%
Variable Interest Entity, Primary Beneficiary | Watford Holdings Ltd | Warburg Pincus LLC
Variable Interest Entity [Line Items]
Noncontrolling interest, ownership percentage by noncontrolling owners30.00%
Variable Interest Entity, Primary Beneficiary | Watford Holdings Ltd | Non-cumulative preferred shares
Variable Interest Entity [Line Items]
Ownership percentage6.60%

Variable Interest Entities an_4

Variable Interest Entities and Noncontrolling Interests - Carrying amount of assets and liabilities of variable interest entity (Details) - USD ($) $ in ThousandsJun. 30, 2021Mar. 31, 2021Dec. 31, 2020Jun. 30, 2020Mar. 31, 2020Dec. 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 value18,073,779 18,717,825
Equity securities, at fair value1,693,552 1,444,830
Cash1,234,059 906,448
Accrued investment income96,546 103,299
Premiums receivable2,866,578 $ 2,618,175 2,064,586 $ 2,203,753 $ 2,155,204 $ 1,778,717
Reinsurance recoverable on unpaid and paid losses and LAE4,314,515 4,041,076 4,500,802 4,363,507 4,303,135 4,346,816
Ceded unearned premiums1,541,093 1,234,075
Deferred acquisition costs1,013,657 790,708
Receivable for securities sold309,234 92,743
Goodwill and intangible assets667,153 692,863 688,490
Other assets2,357,064 1,724,288
Total VIE Assets46,481,886 43,282,297
Reserve for losses and loss adjustment expenses17,196,648 16,443,952 16,513,929 15,044,874 14,309,580 13,891,842
Unearned premiums6,011,369 4,838,965
Reinsurance balances payable1,079,106 683,263
Revolving credit agreement borrowings155,687 155,687
Senior notes2,861,728 2,861,113
Payable for securities purchased586,881 218,779
Other liabilities1,332,843 1,510,888
Total liabilities31,519,407 29,294,856
Redeemable noncontrolling interests57,533 58,548
Watford Holdings Ltd
Variable Interest Entity [Line Items]
Redeemable noncontrolling interests57,533 $ 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 value663,902 655,249
Equity securities, at fair value97,623 52,410
Cash349,202 211,451
Accrued investment income14,549 14,679
Premiums receivable305,026 224,377
Reinsurance recoverable on unpaid and paid losses and LAE520,531 286,590
Ceded unearned premiums123,272 122,339
Deferred acquisition costs65,532 53,705
Receivable for securities sold102,287 37,423
Goodwill and intangible assets10,318 7,650
Other assets112,794 75,801
Total VIE Assets4,349,955 3,532,059
Reserve for losses and loss adjustment expenses1,916,742 1,519,583
Unearned premiums468,948 407,714
Reinsurance balances payable132,929 63,269
Revolving credit agreement borrowings155,687 155,687
Senior notes172,825 172,689
Payable for securities purchased199,342 25,881
Other liabilities227,396 193,494
Total liabilities3,273,869 2,538,317
Redeemable noncontrolling interests $ 52,444 $ 52,398
[1]Included in “other investments” on the Company’s balance sheet.

Variable Interest Entities an_5

Variable Interest Entities and Noncontrolling Interests - Non-redeemable noncontrolling interests (Details) - USD ($) $ in Thousands3 Months Ended6 Months Ended
Jun. 30, 2021Jun. 30, 2020Jun. 30, 2021Jun. 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 interests10 20,111 (4,560)(12,947)
Non-redeemable noncontrolling interests, end of period918,874 679,089 918,874 679,089
Watford Holdings Ltd
Noncontrolling Interest [Line Items]
Non-redeemable noncontrolling interests, beginning of period876,864 492,785 823,007 762,777
Additional paid in capital attributable to noncontrolling interests383 595 22,113 472
Repurchases attributable to non-redeemable noncontrolling interests[1]0 (2,867)
Amounts attributable to noncontrolling interests41,617 165,598 78,314 (68,346)
Other comprehensive (income) loss attributable to noncontrolling interests10 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 owners90.00%90.00%
[1]During 2020, Watford’s board of directors authorized the investment in Watford’s common shares through a share repurchase program.

Variable Interest Entities an_6

Variable Interest Entities and Noncontrolling Interests - Redeemable noncontrolling interests (Details) - USD ($) $ / shares in Units, $ in Thousands3 Months Ended6 Months Ended
Jun. 30, 2021Jun. 30, 2020Jun. 30, 2021Jun. 30, 2020Mar. 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 period57,670 $ 55,376 58,548 $ 55,404
Accretion of preference share issuance costs23 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 share25
Issue price per share $ 24.50

Variable Interest Entities an_7

Variable Interest Entities and Noncontrolling Interests - Income or loss attributable to third party investors (Details) - USD ($) $ in Thousands3 Months Ended6 Months Ended
Jun. 30, 2021Jun. 30, 2020Jun. 30, 2021Jun. 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

Variable Interest Entities an_8

Variable Interest Entities and Noncontrolling Interests - Other variable interest entity disclosures (Details) - USD ($) $ in ThousandsJun. 30, 2021Dec. 31, 2020
Variable Interest Entity [Line Items]
Total VIE Assets $ 46,481,886 $ 43,282,297
Maximum Exposure to Loss, Total2,721,384 2,232,609
Variable Interest Entity, Not Primary Beneficiary
Variable Interest Entity [Line Items]
Total VIE Assets4,446,266 3,859,058
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability(7,776)(7,969)
Maximum Exposure to Loss - Off-Balance Sheet59,085 56,320
Maximum Exposure to Loss, Total51,309 48,351
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2017-1 Ltd. (Oct-17)
Variable Interest Entity [Line Items]
Total VIE Assets145,573 145,573
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability(283)(245)
Maximum Exposure to Loss - Off-Balance Sheet779 844
Maximum Exposure to Loss, Total496 599
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-1 Ltd. (Apr-18)
Variable Interest Entity [Line Items]
Total VIE Assets250,095 250,095
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability(909)(903)
Maximum Exposure to Loss - Off-Balance Sheet1,984 2,245
Maximum Exposure to Loss, Total1,075 1,342
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-2 Ltd. (Aug-18)
Variable Interest Entity [Line Items]
Total VIE Assets0 108,395
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability0 (138)
Maximum Exposure to Loss - Off-Balance Sheet0 280
Maximum Exposure to Loss, Total0 142
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-3 Ltd. (Oct-18)
Variable Interest Entity [Line Items]
Total VIE Assets302,563 302,563
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability(1,622)(1,320)
Maximum Exposure to Loss - Off-Balance Sheet3,706 3,262
Maximum Exposure to Loss, Total2,084 1,942
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-1 Ltd. (Mar-19)
Variable Interest Entity [Line Items]
Total VIE Assets219,256 219,256
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability(1,237)(1,361)
Maximum Exposure to Loss - Off-Balance Sheet8,204 8,461
Maximum Exposure to Loss, Total6,967 7,100
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-2 Ltd. (Apr-19)
Variable Interest Entity [Line Items]
Total VIE Assets398,316 398,316
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability(1,042)(730)
Maximum Exposure to Loss - Off-Balance Sheet6,723 5,201
Maximum Exposure to Loss, Total5,681 4,471
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-3 Ltd. (Jul-19)
Variable Interest Entity [Line Items]
Total VIE Assets528,084 528,084
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability(969)(861)
Maximum Exposure to Loss - Off-Balance Sheet4,527 5,079
Maximum Exposure to Loss, Total3,558 4,218
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-4 Ltd. (Oct-19)
Variable Interest Entity [Line Items]
Total VIE Assets468,737 468,737
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability(1,051)(890)
Maximum Exposure to Loss - Off-Balance Sheet7,128 6,676
Maximum Exposure to Loss, Total6,077 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, Amount79,000
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, Amount26,000
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, Amount34,000
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, Amount16,000
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-1 Ltd. (Mar-21)
Variable Interest Entity [Line Items]
Total VIE Assets579,717 [5]0
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability(83)[5]0
Maximum Exposure to Loss - Off-Balance Sheet4,387 [5]0
Maximum Exposure to Loss, Total4,304 [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, Amount64,000
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-2 Ltd. (Jun-21)
Variable Interest Entity [Line Items]
Total VIE Assets522,807 [6]0
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability630 [6]0
Maximum Exposure to Loss - Off-Balance Sheet5,207 [6]0
Maximum Exposure to Loss, Total5,837 $ 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.

Other Comprehensive Income (L_3

Other Comprehensive Income (Loss) - Amounts reclassified from accumulated other comprehensive income (Details) - USD ($) $ in Thousands3 Months Ended6 Months Ended
Jun. 30, 2021Jun. 30, 2020Jun. 30, 2021Jun. 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 losses0 (533)
Income (loss) before income taxes and income (loss) from operating affiliates745,367 495,689 1,184,478 426,444
Income tax expense(51,179)(26,127)(90,039)(54,072)
Net of tax675,486 298,821 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 losses896 3,225 (751)(6,095)
Other-than-temporary impairment losses0 0 0 (533)
Income (loss) before income taxes and income (loss) from operating affiliates65,810 185,554 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

Other Comprehensive Income (L_4

Other Comprehensive Income (Loss) - Components of other comprehensive income (Details) - USD ($) $ in Thousands3 Months Ended6 Months Ended
Jun. 30, 2021Jun. 30, 2020Jun. 30, 2021Jun. 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 tax65,810 185,554 66,167 321,933
Foreign currency translation adjustments, before tax6,392 22,595 (22,023)(22,829)
Other comprehensive income (loss), before tax31,639 392,617 (291,493)147,363
Tax expense (benefit):
Unrealized holding gains (losses) arising during period, tax12,486 62,780 (20,124)56,616
Less reclassification of net realized gains included in net income, tax5,263 18,163 8,317 33,313
Foreign currency translation adjustments, tax187 344 356 (391)
Other comprehensive income (loss), tax7,410 44,961 (28,085)22,912
Net of tax amount:
Unrealized holding gains (losses) arising during period, net of tax78,571 492,796 (183,179)435,509
Less reclassification of net realized gains included in net income, net of tax60,547 167,391 57,850 288,620
Foreign currency translation adjustments, net of tax6,205 22,251 (22,379)(22,438)
Net current period other comprehensive income (loss) $ 24,229 $ 347,656 $ (263,408) $ 124,451

Income Taxes (Details)

Income Taxes (Details) - USD ($) $ in Millions6 Months Ended
Jun. 30, 2021Jun. 30, 2020Dec. 31, 2020
Income Tax Disclosure [Abstract]
Effective tax rate on income before income taxes (percentage)7.00%12.50%
Net deferred tax asset $ 93 $ 15.7
Income taxes paid $ 141.1 $ 10.4

Transactions With Related Par_2

Transactions With Related Parties (Details) - USD ($) $ in ThousandsJun. 30, 2021Mar. 31, 2021Jan. 01, 2021Dec. 31, 2020Jun. 30, 2020Mar. 31, 2020Dec. 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 LAE0 199,800
Funds held liability $ 9,900 $ 149,600

Subsequent Events (Details)

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