Arch Capital (ACGL) 10-Q 6 Aug 20 2020 Q2 Quarterly report Financial data

Document and Entity Information

Document and Entity Information - shares	6 Months Ended
	Jun. 30, 2020	Jul. 31, 2020
Document and Entity Information [Abstract]
Document Type	10-Q
Document Quarterly Report	true
Document Period End Date	Jun. 30, 2020
Document Transition Report	false
Entity File Number	001-16209
Entity Registrant Name	ARCH CAPITAL GROUP LTD.
Entity Incorporation, State or Country Code	D0
Entity Tax Identification Number	98-0374481
Entity Address, Address Line One	Waterloo House, Ground Floor
Entity Address, Address Line Two	100 Pitts Bay Road,
Entity Address, City or Town	Pembroke
Entity Address, Postal Zip Code	HM 08,
Entity Address, Country	BM
City Area Code	(441)
Local Phone Number	278-9250
Entity Listings [Line Items]
Entity Current Reporting Status	Yes
Entity Interactive Data Current	Yes
Entity Filer Category	Large Accelerated Filer
Entity Small Business	false
Entity Emerging Growth Company	false
Entity Shell Company	false
Entity Common Stock, Shares Outstanding		405,972,280
Document Fiscal Period Focus	Q2
Document Fiscal Year Focus	2020
Current Fiscal Year End Date	--12-31
Entity Central Index Key	0000947484
Amendment Flag	false
Common shares
Entity Listings [Line Items]
Title of 12(b) Security	Common shares, $0.0011 par value per share
Trading Symbol	ACGL
Security Exchange Name	NASDAQ
Depositary Series E Preferred Stock
Entity Listings [Line Items]
Title of 12(b) Security	Depositary shares, each representing a 1/1000th interest in a 5.25% Series E preferred share
Trading Symbol	ACGLP
Security Exchange Name	NASDAQ
Depositary Series F Preferred Stock
Entity Listings [Line Items]
Title of 12(b) Security	Depositary shares, each representing a 1/1000th interest in a 5.45% Series F preferred share
Trading Symbol	ACGLO
Security Exchange Name	NASDAQ

Unaudited Consolidated Balance

Unaudited Consolidated Balance Sheets - USD ($) $ in Thousands	Jun. 30, 2020	Dec. 31, 2019
Investments:
Fixed maturities available for sale, at fair value (amortized cost: $16,733,493 and $16,598,808; net of allowance for credit losses: $5,869 at June 30, 2020)	$ 17,207,731	$ 16,894,526
Short-term investments available for sale, at fair value (amortized cost: $2,276,413 and $957,283; net of allowance for credit losses: $0 at June 30, 2020)	2,277,866	956,546
Collateral received under securities lending, at fair value (amortized cost: $473,783 and $388,366)	473,790	388,376
Equity securities, at fair value	1,257,317	838,925
Investments accounted for using the fair value option	3,520,771	3,663,477
Investments accounted for using the equity method	1,727,302	1,660,396
Total investments	26,464,777	24,402,246
Cash	854,259	726,230
Accrued investment income	102,064	117,937
Securities pledged under securities lending, at fair value (amortized cost: $460,760 and $378,738)	464,503	379,868
Premiums receivable (net of allowance for credit losses: $36,054 and $21,003)	2,203,753	1,778,717
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $13,595 and $1,364)	4,363,507	4,346,816
Contractholder receivables (net of allowance for credit losses: $6,290 and $0)	2,179,124	2,119,460
Ceded unearned premiums	1,364,603	1,234,683
Deferred acquisition costs	714,531	633,400
Receivable for securities sold	167,281	24,133
Goodwill and intangible assets	688,490	738,083
Other assets	1,632,756	1,383,788
Total assets	41,199,648	37,885,361
Liabilities
Reserve for losses and loss adjustment expenses	15,044,874	13,891,842
Unearned premiums	4,827,445	4,339,549
Reinsurance balances payable	793,467	667,072
Contractholder payables	2,185,414	2,119,460
Collateral held for insured obligations	208,449	206,698
Senior notes	2,860,733	1,871,626
Revolving credit agreement borrowings	335,587	484,287
Securities lending payable	473,783	388,366
Payable for securities purchased	275,257	87,579
Other liabilities	1,467,739	1,513,330
Total liabilities	28,472,748	25,569,809
Commitments and Contingencies
Redeemable noncontrolling interests	55,986	55,404
Shareholders' Equity
Non-cumulative preferred shares	780,000	780,000
Common shares ($0.0011 par, shares issued: 577,956,232 and 574,617,195)	642	638
Additional paid-in capital	1,935,514	1,889,683
Retained earnings	11,420,686	11,021,006
Accumulated other comprehensive income (loss), net of deferred income tax	349,488	212,091
Common shares held in treasury, at cost (shares: 171,985,981 and 168,997,994)	(2,494,505)	(2,406,047)
Total shareholders' equity available to Arch	11,991,825	11,497,371
Non-redeemable noncontrolling interests	679,089	762,777
Total shareholders' equity	12,670,914	12,260,148
Total liabilities, noncontrolling interests and shareholders' equity	$ 41,199,648	$ 37,885,361

Unaudited Consolidated Balanc_2

Unaudited Consolidated Balance Sheets (Parentheticals) - USD ($) $ in Thousands	Jun. 30, 2020		Dec. 31, 2019
Fixed maturities available for sale, at amortized cost	$ 16,733,493		$ 16,598,808
Allowance for credit losses on investments	5,869		0
Short-term investments available for sale, at amortized cost	2,276,413		957,283
Collateral received under securities lending, at amortized cost	473,783		388,366
Securities pledged under securities lending, at amortized cost	460,760		378,738
Allowance for credit losses on premiums receivable	36,054		21,003
Allowance for credit losses on reinsurance recoverable	13,595		1,364
Allowance for credit losses on contractholder receivable	$ 6,290		$ 0
Common shares, par value per share	$ 0.0011		$ 0.0011
Common shares issued (shares)	577,956,232		574,617,195
Common shares held in treasury (shares)	171,985,981		168,997,994
Fixed maturities
Allowance for credit losses on investments	$ 5,869		$ 0
Short-term investments
Allowance for credit losses on investments	0	[1]	0
Short-term investments available for sale, at amortized cost	$ 2,276,413		$ 957,283
[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 Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2020	Jun. 30, 2019	Jun. 30, 2020	Jun. 30, 2019
Revenues
Net premiums written	$ 1,668,311	$ 1,444,898	$ 3,805,557	$ 2,970,157
Change in unearned premiums	(2,957)	18,829	(395,759)	(137,564)
Net premiums earned	1,665,354	1,463,727	3,409,798	2,832,593
Net investment income	131,485	155,038	276,638	311,987
Net realized gains (losses)	556,588	120,757	189,628	261,013
Other underwriting income	6,667	5,953	13,519	14,778
Equity in net income (loss) of investment funds accounted for using the equity method	(65,119)	32,536	(69,328)	79,403
Other income (loss)	(3,140)	1,129	5,408	2,212
Total revenues	2,291,835	1,779,140	3,825,663	3,501,986
Expenses
Losses and loss adjustment expenses	1,230,522	767,543	2,345,941	1,486,075
Acquisition expenses	254,789	210,089	502,072	407,937
Other operating expenses	209,249	198,914	443,793	400,077
Corporate expenses	17,920	18,251	38,716	36,213
Amortization of intangible assets	16,489	19,794	33,120	40,211
Interest expense	31,139	29,280	63,694	58,345
Net foreign exchange (gains) losses	39,211	4,952	(33,460)	1,427
Total expenses	1,799,319	1,248,823	3,393,876	2,430,285
Income (loss) before income taxes	492,516	530,317	431,787	1,071,701
Income tax expense	(26,127)	(44,472)	(54,072)	(90,358)
Net income (loss)	466,389	485,845	377,715	981,343
Net (income) loss attributable to noncontrolling interests	(167,568)	(16,891)	65,223	(63,861)
Net income (loss) available to Arch	298,821	468,954	442,938	917,482
Preferred dividends	(10,403)	(10,403)	(20,806)	(20,806)
Net income (loss) available to Arch common shareholders	$ 288,418	$ 458,551	$ 422,132	$ 896,676
Net income per common share and common share equivalent
Basic (per share)	$ 0.72	$ 1.14	$ 1.05	$ 2.24
Diluted (per share)	$ 0.71	$ 1.12	$ 1.03	$ 2.19
Weighted average common shares and common share equivalents outstanding
Basic (shares)	402,503,687	401,482,784	403,197,924	400,837,181
Diluted (shares)	408,119,681	410,899,483	411,005,591	409,755,250

Unaudited Consolidated Statem_2

Unaudited Consolidated Statements of Comprehensive Income - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2020	Jun. 30, 2019	Jun. 30, 2020	Jun. 30, 2019
Comprehensive Income
Net income (loss)	$ 466,389	$ 485,845	$ 377,715	$ 981,343
Unrealized appreciation (decline) in value of available-for-sale investments:
Unrealized holding gains (losses) arising during period	492,796	222,473	435,509	448,360
Reclassification of net realized (gains) losses, included in net income (loss)	(167,391)	(55,345)	(288,620)	(65,566)
Foreign currency translation adjustments	22,251	4,267	(22,438)	9,783
Comprehensive income (loss)	814,045	657,240	502,166	1,373,920
Net (income) loss attributable to noncontrolling interests	(167,568)	(16,891)	65,223	(63,861)
Other comprehensive (income) loss attributable to noncontrolling interests	(20,111)	(2,891)	12,947	(7,030)
Comprehensive income (loss) available to Arch	$ 626,366	$ 637,458	$ 580,336	$ 1,303,029

Unaudited Consolidated Statem_3

Unaudited Consolidated Statements of Changes in Shareholders' Equity - USD ($) $ in Thousands	Total	Non-cumulative preferred shares	Common shares	Additional paid-in capital	Retained earnings	Retained earningsCumulative effect of an accounting change	Retained earningsBalance at beginning of period, as adjusted	Accumulated other comprehensive income (loss), net of deferred income tax	Unrealized appreciation (decline) in value of available-for-sale securities, net of deferred income tax	Foreign currency translation adjustments, net of deferred income tax	Common shares held in treasury, at cost
Balance at beginning of period at Dec. 31, 2018		$ 780,000	$ 634	$ 1,793,781	$ 9,426,299	$ 0	$ 9,426,299	$ (178,720)	$ (114,178)	$ (64,542)	$ (2,382,167)
Common shares issued, net			4
Amortization of share-based compensation				39,515
Other changes				14,653
Net income (loss)	$ 981,343				981,343
Net (income) loss attributable to noncontrolling interests	(63,861)				(63,861)
Preferred share dividends	(20,806)				(20,806)
Unrealized holding gains (losses) during period, net of reclassification adjustment									382,794
Unrealized holding gains (losses) during period attributable to noncontrolling interests									(6,989)
Foreign currency translation adjustments	9,783									9,783
Foreign currency translation adjustments attributable to noncontrolling interests										(41)
Shares repurchased for treasury	(2,900)										(18,870)
Balance at end of period at Jun. 30, 2019	10,757,352	780,000	638	1,847,949	10,322,975			206,827	261,627	(54,800)	(2,401,037)
Non-redeemable noncontrolling interests, end of period at Jun. 30, 2019	855,347
Total shareholders’ equity at Jun. 30, 2019	11,612,699
Balance at beginning of period at Mar. 31, 2019		780,000	636	1,819,605	9,864,424	0	9,864,424	38,323	97,202	(58,879)	(2,388,392)
Common shares issued, net			2
Amortization of share-based compensation				13,607
Other changes				14,737
Net income (loss)	485,845				485,845
Net (income) loss attributable to noncontrolling interests	(16,891)				(16,891)
Preferred share dividends	(10,403)				(10,403)
Unrealized holding gains (losses) during period, net of reclassification adjustment									167,128
Unrealized holding gains (losses) during period attributable to noncontrolling interests									(2,703)
Foreign currency translation adjustments	4,267									4,267
Foreign currency translation adjustments attributable to noncontrolling interests										(188)
Shares repurchased for treasury											(12,645)
Balance at end of period at Jun. 30, 2019	10,757,352	780,000	638	1,847,949	10,322,975			206,827	261,627	(54,800)	(2,401,037)
Non-redeemable noncontrolling interests, end of period at Jun. 30, 2019	855,347
Total shareholders’ equity at Jun. 30, 2019	$ 11,612,699
Accounting Standards Update	us-gaap:AccountingStandardsUpdate201613Member
Balance at beginning of period at Dec. 31, 2019	$ 11,497,371	780,000	638	1,889,683	11,021,006	(22,452)	10,998,554	212,091	258,486	(46,395)	(2,406,047)
Common shares issued, net			4
Amortization of share-based compensation				41,210
Other changes				4,621
Net income (loss)	377,715				377,715
Net (income) loss attributable to noncontrolling interests	65,223				65,223
Preferred share dividends	(20,806)				(20,806)
Unrealized holding gains (losses) during period, net of reclassification adjustment									146,889
Unrealized holding gains (losses) during period attributable to noncontrolling interests									13,112
Foreign currency translation adjustments	(22,438)									(22,438)
Foreign currency translation adjustments attributable to noncontrolling interests										(166)
Shares repurchased for treasury	(75,500)										(88,458)
Balance at end of period at Jun. 30, 2020	11,991,825	780,000	642	1,935,514	11,420,686			349,488	418,487	(68,999)	(2,494,505)
Non-redeemable noncontrolling interests, end of period at Jun. 30, 2020	679,089
Total shareholders’ equity at Jun. 30, 2020	12,670,914
Balance at beginning of period at Mar. 31, 2020		780,000	642	1,921,487	11,132,268	$ 0	$ 11,132,268	21,944	113,149	(91,205)	(2,489,097)
Common shares issued, net			0
Amortization of share-based compensation				13,160
Other changes				867
Net income (loss)	466,389				466,389
Net (income) loss attributable to noncontrolling interests	(167,568)				(167,568)
Preferred share dividends	(10,403)				(10,403)
Unrealized holding gains (losses) during period, net of reclassification adjustment									325,405
Unrealized holding gains (losses) during period attributable to noncontrolling interests									(20,067)
Foreign currency translation adjustments	22,251									22,251
Foreign currency translation adjustments attributable to noncontrolling interests										(45)
Shares repurchased for treasury											(5,408)
Balance at end of period at Jun. 30, 2020	11,991,825	$ 780,000	$ 642	$ 1,935,514	$ 11,420,686			$ 349,488	$ 418,487	$ (68,999)	$ (2,494,505)
Non-redeemable noncontrolling interests, end of period at Jun. 30, 2020	679,089
Total shareholders’ equity at Jun. 30, 2020	$ 12,670,914

Unaudited Consolidated Statem_4

Unaudited Consolidated Statements of Cash Flows - USD ($) $ in Thousands	6 Months Ended
	Jun. 30, 2020	Jun. 30, 2019
Operating Activities
Net income (loss)	$ 377,715	$ 981,343
Adjustments to reconcile net income (loss) to net cash provided by operating activities:
Net realized (gains) losses	(194,776)	(262,935)
Equity in net income or loss of investment funds accounted for using the equity method and other income or loss	125,384	(45,720)
Amortization of intangible assets	33,120	40,211
Share-based compensation	41,912	41,537
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable	1,158,446	154,396
Unearned premiums, net of ceded unearned premiums	395,759	137,564
Premiums receivable	(463,638)	(302,050)
Deferred acquisition costs	(92,437)	(24,790)
Reinsurance balances payable	132,161	139,415
Other items, net	(192,066)	(146,447)
Net cash provided by (used for) operating activities	1,321,580	712,524
Investing Activities
Purchases of fixed maturity investments	(25,410,849)	(16,332,646)
Purchases of equity securities	(1,025,149)	(431,939)
Purchases of other investments	(501,692)	(677,063)
Proceeds from sales of fixed maturity investments	24,833,030	15,632,482
Proceeds from sales of equity securities	580,346	176,701
Proceeds from sales, redemptions and maturities of other investments	472,188	534,698
Proceeds from redemptions and maturities of fixed maturity investments	369,240	244,949
Net settlements of derivative instruments	150,471	87,701
Net (purchases) sales of short-term investments	(1,323,363)	201,520
Change in cash collateral related to securities lending	54,596	7,590
Purchases of fixed assets	(17,687)	(16,359)
Other	8,679	(174,578)
Net cash provided by (used for) investing activities	(1,810,190)	(746,944)
Financing Activities
Purchases of common shares under share repurchase program	(75,486)	(2,871)
Proceeds from common shares issued, net	(9,661)	(557)
Proceeds from borrowings	1,004,918	62,800
Repayments of borrowings	(165,000)	(27,538)
Change in cash collateral related to securities lending	(54,596)	(7,590)
Third party investment in non-redeemable noncontrolling interests	(2,867)	0
Dividends paid to redeemable noncontrolling interests	(2,540)	(8,994)
Other	(2,625)	(3,529)
Preferred dividends paid	(20,806)	(20,806)
Net cash provided by (used for) financing activities	671,337	(9,085)
Effects of exchange rate changes on foreign currency cash and restricted cash	(21,742)	1,937
Increase (decrease) in cash and restricted cash	160,985	(41,568)
Cash and restricted cash, beginning of year	903,698	724,643
Cash and restricted cash, end of period	$ 1,064,683	$ 683,075

Basis of Presentation and Recen

Basis of Presentation and Recent Accounting Pronouncements	6 Months Ended
	Jun. 30, 2020
Organization, Consolidation and Presentation of Financial Statements [Abstract]
Basis of Presentation and Recent Accounting Pronouncements	Basis of Presentation and Recent Accounting Pronouncements General Arch Capital Group Ltd. (“Arch Capital”) is a Bermuda public limited liability company which provides insurance, reinsurance and mortgage insurance on a worldwide basis through its wholly-owned subsidiaries. As used herein, the “Company” means Arch Capital and its subsidiaries. The Company’s consolidated financial statements include 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 12 . 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, 2019 (“2019 Form 10-K”), including the Company’s audited consolidated financial statements and related notes. The Company has reclassified the presentation of certain prior year information to conform to the current presentation. Such reclassifications had no effect on the Company’s net income, comprehensive income, shareholders’ equity or cash flows. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted. Recent Accounting Pronouncements Recently Issued Accounting Standards Adopted The Company adopted ASU 2018-13, “Fair Value Measurement (Topic 820): Disclosure Framework - Changes to the Disclosure Requirements for Fair Value Measurement.” The ASU modifies the disclosure requirements on fair value measurement as part of the disclosure framework project with the objective to improve the effectiveness of disclosures in the notes to the financial statements. The amendments in this update allow for removal of (1) the amount and reasons for transfer between Level 1 and Level 2 of the fair value hierarchy; (2) the policy for transfers between levels; and (3) the valuation processes for Level 3 fair value measurements. The adoption of this guidance did not have a material effect on the Company’s consolidated financial statements. The Company adopted ASU 2018-15, “Intangibles - Goodwill and Other - Internal Use Software (Subtopic 350-40).” This ASU aligns the requirements for capitalizing certain implementation costs incurred in a cloud computing arrangement that is a service contract with the requirements for capitalizing implementation costs incurred to develop or obtain internal-use software. The guidance provides flexibility in adoption, allowing for either retrospective adjustment or prospective adjustment for all implementation costs incurred after the date of adoption. The Company adopted this guidance prospectively. The adoption of this guidance did not have a material effect on the Company’s consolidated financial statements. In March 2020, the SEC amended Rule 3-10 of Regulation S-X regarding financial disclosure requirements for registered debt offerings involving subsidiaries as either issuers or guarantors and affiliates whose securities are pledged as collateral. This new guidance narrows the circumstances that require separate financial statements of subsidiary issuers and guarantors and streamlines the alternative disclosures required in lieu of those statements. The amendment is effective on January 4, 2021 with early adoption permitted. The Company elected to apply the amended requirements for the quarter ended March 31, 2020, and is no longer providing condensed consolidating financial information that resulted from the registered debt obligations of its subsidiaries, Arch Capital Group (U.S.) Inc. and Arch Capital Finance LLC., that were disclosed in Note 26 of the financial statements in the Company’s 2019 Form 10-K. The Company adopted ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326).” The ASU applies a new credit loss model (current expected credit losses) for determining credit related impairments for financial instruments measured at amortized cost, including reinsurance recoverable, contractholder receivables, and premiums receivable, and requires an entity to estimate its lifetime “expected credit loss” and record an allowance that, when deducted from the amortized cost basis of the financial asset, presents the net amount expected to be collected on the financial asset. The estimate of expected credit losses should consider historical information, current information, as well as reasonable and supportable forecasts, including estimates of prepayments. The ASU also amends the previous other-than-temporary impairment model for available-for-sale debt securities by requiring the recognition of impairments relating to credit losses through an allowance account and limits the amount of credit loss to the difference between a security’s amortized cost basis and its fair value. In addition, the length of time a security has been in an unrealized loss position will no longer impact the determination of whether a credit loss exists. The Company adopted the ASU for the quarter ending March 31, 2020 by recognizing an after-tax cumulative effect adjustment of $22.5 million to the opening balance of retained earnings as of January 1, 2020. The cumulative effect adjustment decreased retained earnings and increased the allowance for credit losses. Significant Accounting Policies The following accounting policies have been updated to reflect the Company's adoption of the new accounting guidance on credit losses. Investments The Company conducts a periodic review to identify and evaluate credit based impairments related to the Company’s available for sale investments. The Company derives estimated credit losses by comparing expected future cash flows to be collected to the amortized cost of the security. Estimates of expected future cash flows consider among other things, macroeconomic conditions as well as the financial condition, near-term and long-term prospects for the issuer, and the likelihood of the recoverability of principal and interest. Effective January 1, 2020, credit losses are recognized through an allowance account subject to reversal, rather than a reduction in amortized cost. Declines in value attributable to factors other than credit are reported in other comprehensive income while the allowance for credit loss is charged to net realized gains (losses). For available for sale investments that the Company intends to sell or for which it is more likely than not that the Company would be required to sell before an anticipated recovery in value, the full amount of the impairment is included in net realized gains (losses). The new cost basis of the investment is the previous amortized cost basis reduced by the impairment recognized in net realized gains (losses). The new cost basis is not adjusted for any subsequent recoveries in fair value. The Company reports accrued investment income separately from investment balances and has elected not to measure an allowance for credit losses for accrued investment income . Any uncollectible accrued interest income is written off in the period it is deemed uncollectible. Reinsurance Recoverables In the normal course of business, the Company’s subsidiaries cede a portion of their premium and losses through pro rata and excess of loss reinsurance agreements on a treaty or facultative basis. Reinsurance recoverables are recorded as assets, predicated on the reinsurers’ ability to meet their obligations under the reinsurance agreements. In certain instances, the Company obtains collateral, including letters of credit and trust accounts to further reduce the credit exposure on its reinsurance recoverables. The Company reports its reinsurance recoverables net of an allowance for expected credit loss. The allowance is based upon the Company’s ongoing review of amounts outstanding, the financial condition of its reinsurers, amounts and form of collateral obtained and other relevant factors. A ratings based probability-of-default and loss-given-default methodology is used to estimate the allowance for expected credit loss. Any allowance for credit losses is charged to net realized gains (losses) in the period the recoverable is recorded and revised in s ubsequent periods to reflect changes in the Company’s estimate of expected credit losses . Contractholder Receivables Certain insurance policies written by the Company’s U.S. insurance operations feature large deductibles, primarily in its construction and national accounts line of business. Under such contracts, the Company is obligated to pay the claimant for the full amount of the claim. The Company is subsequently reimbursed by the policy holder for the deductible amount. These amounts are included on a gross basis in the consolidated balance sheet as contractholder payables and contractholder receivables. In the event that the Company is unable to collect from the policyholder, the Company would be liable for such defaulted amounts. Collateral, primarily in the form of letters of credit, cash and trusts, is obtained from the policyholder to mitigate the Company’s credit risk. Contractholder receivables are reported net of an allowance for expected credit losses. The allowance is based upon the Company’s ongoing review of amounts outstanding, changes in policyholder credit standing, amounts and form of collateral obtained, and other relevant factors. A ratings based probability-of-default and loss-given-default methodology is used to estimate the allowance for expected credit losses. Any allowance for credit losses is charged to net realized gains (losses) in the period the receivable is recorded and revised in subsequent periods to reflect changes in the Company’s estimate of expected credit losses . Premiums Receivable Premiums receivable include amounts receivable from agents, brokers and insured that are both currently due and amounts not yet due on insurance, reinsurance and mortgage insurance policies. Premiums receivable balances are reported net of an allowance for expected credit losses. The Company monitors credit risk associated with premiums receivable through its ongoing review of amounts outstanding, aging of the receivable, historical loss data, and counterparty financial strength measures. The allowance also includes estimated uncollectible amounts related to dispute risk. In certain instances, credit risk may be reduced by the Company’s right to offset loss obligations or unearned premiums against premiums receivable. Any allowance for credit losses is charged to net realized gains (losses) in the period the receivable is recorded and revised in subsequent periods to reflect changes in the Company’s estimate of expected credit losses. Recently Issued Accounting Standards Not Yet Adopted In December 2019, the FASB issued ASU 2019-12, “Simplifying the Accounting for Income Taxes.” This ASU eliminates certain exceptions for recognizing deferred taxes for investments, performing intraperiod tax allocation 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 ASU is effective for fiscal years beginning after December 15, 2020 and interim periods within those fiscal years with early adoption permitted. The Company is currently evaluating the impact of the new guidance on its consolidated financial statements and does not expect this guidance to have a material effect on the Company’s consolidated financial statements. In March 2020, the FASB issued ASU 2020-04, “Facilitation of the Effects of Reference Rate Reform on Financial Reporting.” This ASU provides optional expedients and exceptions for applying GAAP to investments, derivatives, or other transactions that reference the London Interbank Offered Rate (LIBOR) or another reference rate expected to be discontinued because of reference rate reform. Along with the optional expedients, the amendments include a general principle that permits an entity to consider contract modifications due to reference reform to be an event that does not require contract re-measurement at the modification date or reassessment of a previous accounting determination. This standard may be elected over time through December 31, 2022 as reference rate reform activities occur. The Company is currently evaluating the impact of the new guidance on its consolidated financial statements and does not expect this guidance to 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 2019 Form 10-K.

Share Transactions

Share Transactions	6 Months Ended
	Jun. 30, 2020
Stockholders' Equity Note [Abstract]
Share Transactions	Share Transactions Share Repurchases The board of directors of Arch Capital has authorized the investment in Arch Capital’s common shares through a share repurchase program. Since the inception of the share repurchase program, Arch Capital has repurchased 388.9 million common shares for an aggregate purchase price of $4.04 billion . For the six months ended June 30, 2020 , Arch Capital repurchased 2.6 million shares under the share repurchase program with an aggregate purchase price of $75.5 million . Arch Capital repurchased 0.1 million shares under the share repurchase program with an aggregate purchase price of $2.9 million during the six months ended June 30, 2019 . At June 30, 2020 , $924.5 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. Depending upon results of operations, market conditions and the development of the economy, as well as other factors, generally Arch Capital will consider share repurchases on an opportunistic basis from time to time. During the 2020 second quarter, Arch Capital has not repurchased any shares under our share repurchase program and we do not expect to repurchase any shares for the remainder of 2020.

Earnings Per Common Share

Earnings Per Common Share	6 Months Ended
	Jun. 30, 2020
Earnings Per Share [Abstract]
Earnings Per Common Share	Earnings Per Common Share The following table sets forth the computation of basic and diluted earnings per common share: Three Months Ended Six Months Ended June 30, June 30, 2020 2019 2020 2019 Numerator: Net income (loss) $ 466,389 $ 485,845 $ 377,715 $ 981,343 Amounts attributable to noncontrolling interests (167,568 ) (16,891 ) 65,223 (63,861 ) Net income (loss) available to Arch 298,821 468,954 442,938 917,482 Preferred dividends (10,403 ) (10,403 ) (20,806 ) (20,806 ) Net income (loss) available to Arch common shareholders $ 288,418 $ 458,551 $ 422,132 $ 896,676 Denominator: Weighted average common shares and common share equivalents outstanding — basic 402,503,687 401,482,784 403,197,924 400,837,181 Effect of dilutive common share equivalents: Nonvested restricted shares 1,597,701 1,937,626 1,829,239 1,720,417 Stock options (1) 4,018,293 7,479,073 5,978,428 7,197,652 Weighted average common shares and common share equivalents outstanding — diluted 408,119,681 410,899,483 411,005,591 409,755,250 Earnings per common share: Basic $ 0.72 $ 1.14 $ 1.05 $ 2.24 Diluted $ 0.71 $ 1.12 $ 1.03 $ 2.19 (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 2020 second quarter and 2019 second quarter , the number of stock options excluded were 6,982,107 and 2,016,830 , respectively. For the six months ended June 30, 2020 and 2019 period, the number of stock options excluded were 2,038,758 and 2,560,755 , respectively.

Segment Information

Segment Information	6 Months Ended
	Jun. 30, 2020
Segment Reporting [Abstract]
Segment Information	Segment Information The Company classifies its businesses into three underwriting segments — insurance, reinsurance and mortgage — and two other operating segments — ‘other’ and corporate (non-underwriting). The Company determined its reportable segments using the management approach described in accounting guidance regarding disclosures about segments of an enterprise and related information. The accounting policies of the segments are the same as those used for the preparation of the Company’s consolidated financial statements. Intersegment business is allocated to the segment accountable for the underwriting results. The Company’s insurance, reinsurance and mortgage segments each have managers who are responsible for the overall profitability of their respective segments and who are directly accountable to the Company’s chief operating decision makers, the President and Chief Executive Officer of Arch Capital, and the Chief Financial 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. 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 and income taxes. Such amounts exclude the results of the ‘other’ segment. The ‘other’ segment includes the results of Watford (see note 12 ). 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, 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) (3,140 ) — (3,140 ) 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 302,474 190,042 492,516 Income tax (expense) benefit (26,529 ) 402 (26,127 ) 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.’ Three Months Ended June 30, 2019 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 919,925 $ 545,547 $ 364,465 $ 1,829,829 $ 161,978 $ 1,937,809 Premiums ceded (292,095 ) (169,457 ) (42,857 ) (504,301 ) (42,608 ) (492,911 ) Net premiums written 627,830 376,090 321,608 1,325,528 119,370 1,444,898 Change in unearned premiums (35,388 ) (8,906 ) 31,175 (13,119 ) 31,948 18,829 Net premiums earned 592,442 367,184 352,783 1,312,409 151,318 1,463,727 Other underwriting income (loss) — 1,224 4,056 5,280 673 5,953 Losses and loss adjustment expenses (389,172 ) (240,958 ) (25,997 ) (656,127 ) (111,416 ) (767,543 ) Acquisition expenses (91,094 ) (56,785 ) (32,654 ) (180,533 ) (29,556 ) (210,089 ) Other operating expenses (109,523 ) (33,960 ) (39,819 ) (183,302 ) (15,612 ) (198,914 ) Underwriting income (loss) $ 2,653 $ 36,705 $ 258,369 297,727 (4,593 ) 293,134 Net investment income 123,038 32,000 155,038 Net realized gains (losses) 125,063 (4,306 ) 120,757 Equity in net income (loss) of investment funds accounted for using the equity method 32,536 — 32,536 Other income (loss) 1,129 — 1,129 Corporate expenses (2) (16,073 ) — (16,073 ) Transaction costs and other (2) (2,178 ) — (2,178 ) Amortization of intangible assets (19,794 ) — (19,794 ) Interest expense (23,375 ) (5,905 ) (29,280 ) Net foreign exchange gains (losses) (6,190 ) 1,238 (4,952 ) Income (loss) before income taxes 511,883 18,434 530,317 Income tax (expense) benefit (44,452 ) (20 ) (44,472 ) Net income (loss) 467,431 18,414 485,845 Amounts attributable to redeemable noncontrolling interests — (4,590 ) (4,590 ) Amounts attributable to nonredeemable noncontrolling interests — (12,301 ) (12,301 ) Net income (loss) available to Arch 467,431 1,523 468,954 Preferred dividends (10,403 ) — (10,403 ) Net income (loss) available to Arch common shareholders $ 457,028 $ 1,523 $ 458,551 Underwriting Ratios Loss ratio 65.7 % 65.6 % 7.4 % 50.0 % 73.6 % 52.4 % Acquisition expense ratio 15.4 % 15.5 % 9.3 % 13.8 % 19.5 % 14.4 % Other operating expense ratio 18.5 % 9.2 % 11.3 % 14.0 % 10.3 % 13.6 % Combined ratio 99.6 % 90.3 % 28.0 % 77.8 % 103.4 % 80.4 % Goodwill and intangible assets $ 157,440 $ — $ 475,920 $ 633,360 $ 7,650 $ 641,010 (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) 5,408 — 5,408 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 508,427 (76,640 ) 431,787 Income tax (expense) benefit (54,474 ) 402 (54,072 ) Net income (loss) 453,953 (76,238 ) 377,715 Dividends attributable to redeemable noncontrolling interests (991 ) (2,132 ) (3,123 ) Amounts attributable to nonredeemable noncontrolling interests — 68,346 68,346 Net income (loss) available to Arch 452,962 (10,024 ) 442,938 Preferred dividends (20,806 ) — (20,806 ) Net income (loss) available to Arch common shareholders $ 432,156 $ (10,024 ) $ 422,132 Underwriting Ratios Loss ratio 73.0 % 79.5 % 41.0 % 67.9 % 79.3 % 68.8 % Acquisition expense ratio 15.3 % 16.6 % 10.2 % 14.6 % 16.3 % 14.7 % Other operating expense ratio 17.7 % 8.2 % 11.7 % 13.3 % 10.3 % 13.0 % Combined ratio 106.0 % 104.3 % 62.9 % 95.8 % 105.9 % 96.5 % (1) Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total. (2) Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’ Six Months Ended June 30, 2019 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 1,861,879 $ 1,228,402 $ 720,515 $ 3,810,282 $ 348,667 $ 4,015,688 Premiums ceded (612,717 ) (401,024 ) (91,655 ) (1,104,882 ) (83,910 ) (1,045,531 ) Net premiums written 1,249,162 827,378 628,860 2,705,400 264,757 2,970,157 Change in unearned premiums (103,215 ) (113,829 ) 46,825 (170,219 ) 32,655 (137,564 ) Net premiums earned 1,145,947 713,549 675,685 2,535,181 297,412 2,832,593 Other underwriting income (loss) — 5,601 7,912 13,513 1,265 14,778 Losses and loss adjustment expenses (745,895 ) (480,768 ) (37,146 ) (1,263,809 ) (222,266 ) (1,486,075 ) Acquisition expenses (173,918 ) (111,111 ) (64,326 ) (349,355 ) (58,582 ) (407,937 ) Other operating expenses (222,919 ) (69,664 ) (79,694 ) (372,277 ) (27,800 ) (400,077 ) Underwriting income (loss) $ 3,215 $ 57,607 $ 502,431 563,253 (9,971 ) 553,282 Net investment income 244,287 67,700 311,987 Net realized gains (losses) 236,187 24,826 261,013 Equity in net income (loss) of investment funds accounted for using the equity method 79,403 — 79,403 Other income (loss) 2,212 — 2,212 Corporate expenses (2) (32,845 ) — (32,845 ) Transaction costs and other (2) (3,368 ) — (3,368 ) Amortization of intangible assets (40,211 ) — (40,211 ) Interest expense (46,857 ) (11,488 ) (58,345 ) Net foreign exchange gains (losses) (1,015 ) (412 ) (1,427 ) Income (loss) before income taxes 1,001,046 70,655 1,071,701 Income tax (expense) benefit (90,338 ) (20 ) (90,358 ) Net income (loss) 910,708 70,635 981,343 Dividends attributable to redeemable noncontrolling interests — (9,178 ) (9,178 ) Amounts attributable to nonredeemable noncontrolling interests — (54,683 ) (54,683 ) Net income (loss) available to Arch 910,708 6,774 917,482 Preferred dividends (20,806 ) — (20,806 ) Net income (loss) available to Arch common shareholders $ 889,902 $ 6,774 $ 896,676 Underwriting Ratios Loss ratio 65.1 % 67.4 % 5.5 % 49.9 % 74.7 % 52.5 % Acquisition expense ratio 15.2 % 15.6 % 9.5 % 13.8 % 19.7 % 14.4 % Other operating expense ratio 19.5 % 9.8 % 11.8 % 14.7 % 9.3 % 14.1 % Combined ratio 99.8 % 92.8 % 26.8 % 78.4 % 103.7 % 81.0 % (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)

Reserve for Losses and Loss Adj

Reserve for Losses and Loss Adjustment Expenses	6 Months Ended
	Jun. 30, 2020
Liability for Future Policy Benefits and Unpaid Claims and Claims Adjustment Expense [Abstract]
Reserve for losses and loss adjustment expenses	Reserve for Losses and Loss Adjustment Expenses The following table represents an analysis of losses and loss adjustment expenses and a reconciliation of the beginning and ending reserve for losses and loss adjustment expenses: Three Months Ended Six Months Ended June 30, June 30, 2020 2019 2020 2019 Reserve for losses and loss adjustment expenses at beginning of period $ 14,309,580 $ 12,010,041 $ 13,891,842 $ 11,853,297 Unpaid losses and loss adjustment expenses recoverable 4,070,114 2,970,159 4,082,650 2,814,291 Net reserve for losses and loss adjustment expenses at beginning of period 10,239,466 9,039,882 9,809,192 9,039,006 Net incurred losses and loss adjustment expenses relating to losses occurring in: Current year 1,274,589 805,728 2,409,031 1,563,692 Prior years (44,067 ) (38,185 ) (63,090 ) (77,617 ) Total net incurred losses and loss adjustment expenses 1,230,522 767,543 2,345,941 1,486,075 Retroactive reinsurance transactions (1) — — 60,635 (225,500 ) Net foreign exchange (gains) losses 51,157 (1,277 ) (91,416 ) (1,781 ) Net paid losses and loss adjustment expenses relating to losses occurring in: Current year (128,174 ) (61,148 ) (169,434 ) (125,488 ) Prior years (504,254 ) (539,481 ) (1,066,201 ) (966,793 ) Total net paid losses and loss adjustment expenses (632,428 ) (600,629 ) (1,235,635 ) (1,092,281 ) Net reserve for losses and loss adjustment expenses at end of period 10,888,717 9,205,519 10,888,717 9,205,519 Unpaid losses and loss adjustment expenses recoverable 4,156,157 3,024,797 4,156,157 3,024,797 Reserve for losses and loss adjustment expenses at end of period $ 15,044,874 $ 12,230,316 $ 15,044,874 $ 12,230,316 (1) During 2020 first quarter, a subsidiary of the Company entered into a reinsurance to close agreement of the 2017 and prior years of account previously covered by a third party arrangement, while in the 2019 first quarter, a subsidiary of the Company entered into a retroactive reinsurance transaction with third party reinsurer to reinsure run-off liabilities associated with certain U.S. insurance exposures. Development on Prior Year Loss Reserves 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 ( i.e. , the year in which a loss occurred) 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 ( i.e. , all premiums and losses attributable to contracts having an inception or renewal date within the given twelve-month period), 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 . 2019 Second Quarter During the 2019 second quarter , the Company recorded net favorable development on prior year loss reserves of $38.2 million , which consisted of $2.6 million from the insurance segment, $12.7 million from the reinsurance segment, $22.8 million from the mortgage segment and $0.1 million from the ‘other’ segment. The insurance segment’s net favorable development of $2.6 million , or 0.4 loss ratio points, for the 2019 second quarter consisted of $8.0 million of net favorable development in short-tailed lines, $10.4 million of net adverse development in medium-tailed lines and $4.9 million of net favorable development in long-tailed lines. Net favorable development in short-tailed lines primarily resulted from property (excluding marine) reserves across all accident years (i.e., the year in which a loss occurred). Net adverse development in medium-tailed lines primarily resulted from $15.5 million of adverse development on program business. Such amounts were partially offset by $5.1 million of net favorable development in other medium-tailed lines, including surety business and professional liability, across most accident years. Net favorable development in long-tailed lines primarily resulted from reductions in executive assurance reserves of $5.1 million , primarily from the 2008 to 2014 accident years. The reinsurance segment’s net favorable development of $12.7 million , or 3.5 loss ratio points, for the 2019 second quarter consisted of $1.8 million of net favorable development from short-tailed lines and $10.9 million of net favorable development from long-tailed and medium-tailed lines. Net favorable development in short-tailed lines primarily resulted from other specialty lines across most underwriting years (i.e., all premiums and losses attributable to contracts having an inception or renewal date within the given twelve-month period) and in property other than property catastrophe reserves from earlier underwriting years, partially offset by a small amount of adverse development from property catastrophe and property other than property catastrophe reserves in the 2015 and 2018 underwriting years. Favorable development in long-tailed and medium-tailed lines reflected reductions in casualty and marine reserves from most underwriting years. The mortgage segment’s net favorable development was $22.8 million , or 6.5 loss ratio points, for the 2019 second quarter . The 2019 second quarter development was primarily driven by continued favorable claim rates on first lien business and subrogation recoveries on second lien business. 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. Six Months Ended June 30, 2019 During the six months ended June 30, 2019 , the Company recorded net favorable development on prior year loss reserves of $77.6 million , which consisted of $7.0 million from the insurance segment, $11.0 million from the reinsurance segment, $59.4 million from the mortgage segment and $0.1 million from the ‘other’ segment. The insurance segment’s net favorable development of $7.0 million , or 0.6 loss ratio points, for the 2019 period consisted of $17.7 million of net favorable development in short-tailed lines and $6.6 million of net favorable development in long-tailed lines, partially offset by $17.3 million of net adverse development in medium-tailed lines. Net favorable development in short-tailed lines primarily resulted from property (excluding marine) reserves from the 2010 to 2018 accident years. Net favorable development in long-tailed lines reflected net reductions in executive assurance reserves of $5.7 million , primarily from the 2013 and 2015 accident years. Net adverse development in medium-tailed lines reflected $23.2 million of adverse development in program business, primarily from the 2018 accident year, and $9.7 million of adverse development on contract binding business, across most accident years. Such amounts were partially offset by $15.6 million of net favorable development in other medium-tailed lines, including professional liability, marine and surety business, across most accident years. The reinsurance segment’s net favorable development of $11.0 million , or 1.5 loss ratio points, for the 2019 period consisted of $4.3 million of net adverse development from short-tailed lines, offset by $15.3 million of net favorable development from long-tailed and medium-tailed lines. Net adverse development in short-tailed lines reflected $17.9 million from property catastrophe and property other than property catastrophe reserves, reflecting an increase in reserves on Typhoon Jebi in the 2019 first quarter of $16.0 million following receipt of updated information from cedents and additional updated industry data. Such amounts were partially offset by $10.2 million of favorable development on other specialty lines, primarily from the 2016 to 2018 underwriting years. Favorable development in long-tailed and medium-tailed lines reflected reductions in casualty reserves of $9.1 million based on varying levels of reported and paid claims activity, primarily from the 2002 to 2007 underwriting years, and favorable development in marine reserves of $6.2 million , primarily from the 2015 to 2018 underwriting years. The mortgage segment’s net favorable development was $59.4 million , or 8.8 loss ratio points, for the 2019 period. The 2019 development was primarily driven by continued lower than expected claim rates on first lien business and subrogation recoveries on second lien business.

Allowance for Expected Credit L

Allowance for Expected Credit Losses	6 Months Ended
	Jun. 30, 2020
Credit Loss [Abstract]
Allowance for expected credit losses	Allowance for Expected Credit Losses Premiums Receivable The following table provides a roll forward of the allowance for expected credit losses of the Company’s premium receivables: June 30, 2020 Premium Receivables, Net of Allowance Allowance for Expected Credit Losses Three Months Ended Balance at beginning of period $ 2,155,204 $ 27,990 Cumulative effect of accounting change (1) — Change for provision of expected credit losses (2) 8,064 Balance at end of period $ 2,203,753 $ 36,054 Six Months Ended Balance at beginning of period $ 1,778,717 $ 21,003 Cumulative effect of accounting change (1) 6,539 Change for provision of expected credit losses (2) 8,512 Balance at end of period $ 2,203,753 $ 36,054 (1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)” See note 1 . (2) Amounts deemed uncollectible are written-off in operating expenses. For the 2020 second quarter and six months ended June 30, 2020 , amounts written off totaled $1.8 million and $2.3 million , respectively. Reinsurance Recoverables The following table provides a roll forward of the allowance for expected credit losses of the Company’s reinsurance recoverables: June 30, 2020 Reinsurance Recoverables, Net of Allowance Allowance for Expected Credit Losses Three Months Ended Balance at beginning of period $ 4,303,135 $ 13,700 Cumulative effect of accounting change (1) — Change for provision of expected credit losses (105 ) Balance at end of period $ 4,363,507 $ 13,595 Six Months Ended Balance at beginning of period $ 4,346,816 $ 1,364 Cumulative effect of accounting change (1) 12,010 Change for provision of expected credit losses 221 Balance at end of period $ 4,363,507 $ 13,595 (1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)” See note 1 . At June 30, 2020 and December 31, 2019, approximately 63.1% and 61.2% of reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums) of $4.38 billion and $4.35 billion , respectively, were due from carriers which had an A.M. Best rating of “A-” or better while 36.7% and 38.8% , respectively, were from companies not rated. For items not rated, over 90% of such amount was collateralized through reinsurance trusts or letters of credit at June 30, 2020 and December 31, 2019. The largest reinsurance recoverables from any one carrier were approximately 1.8% and 1.7% , of total shareholders’ equity available to Arch at June 30, 2020 and December 31, 2019, respectively. Contractholder Receivables The following table provides a roll forward of the allowance for expected credit losses of the Company’s contractholder receivables: June 30, 2020 Contractholder Receivables, Net of Allowance Allowance for Expected Credit Losses Three Months Ended Balance at beginning of period $ 2,140,724 $ 9,038 Cumulative effect of accounting change (1) — Change for provision of expected credit losses (2,748 ) Balance at end of period $ 2,179,124 $ 6,290 Six Months Ended Balance at beginning of period $ 2,119,460 $ — Cumulative effect of accounting change (1) 6,663 Change for provision of expected credit losses (373 ) Balance at end of period $ 2,179,124 $ 6,290 (1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)” See note 1 .

Investment Information

Investment Information	6 Months Ended
	Jun. 30, 2020
Disclosure Investment Information [Abstract]
Investment Information	Investment Information At June 30, 2020 , total investable assets of $27.17 billion included $24.53 billion held by the Company and $2.64 billion attributable to Watford. Available For Sale Investments The following table summarizes the fair value and cost or amortized cost of the Company’s securities classified as available for sale: Estimated Fair Value Gross Unrealized Gains Gross Unrealized Losses Allowance for Expected Credit Losses (2) Cost or Amortized Cost June 30, 2020 Fixed maturities (1): Corporate bonds $ 7,143,600 $ 405,579 $ (34,700 ) $ (4,116 ) $ 6,776,837 Mortgage backed securities 610,839 12,417 (5,245 ) (222 ) 603,889 Municipal bonds 517,089 25,222 (542 ) (28 ) 492,437 Commercial mortgage backed securities 395,682 7,603 (8,005 ) (109 ) 396,193 U.S. government and government agencies 5,192,991 64,502 (2,708 ) — 5,131,197 Non-U.S. government securities 2,171,955 71,666 (43,928 ) — 2,144,217 Asset backed securities 1,633,481 31,410 (39,421 ) (1,394 ) 1,642,886 Total 17,665,637 618,399 (134,549 ) (5,869 ) 17,187,656 Short-term investments 2,277,866 2,087 (634 ) — 2,276,413 Total $ 19,943,503 $ 620,486 $ (135,183 ) $ (5,869 ) $ 19,464,069 December 31, 2019 Fixed maturities (1): Corporate bonds $ 6,406,591 $ 191,889 $ (12,793 ) $ 6,227,495 Mortgage backed securities 562,309 9,669 (931 ) 553,571 Municipal bonds 881,926 24,628 (2,213 ) 859,511 Commercial mortgage backed securities 733,108 14,951 (2,330 ) 720,487 U.S. government and government agencies 4,916,592 36,600 (10,134 ) 4,890,126 Non-U.S. government securities 2,078,757 48,549 (20,330 ) 2,050,538 Asset backed securities 1,683,753 24,017 (4,724 ) 1,664,460 Total 17,263,036 350,303 (53,455 ) 16,966,188 Short-term investments 956,546 811 (1,548 ) 957,283 Total $ 18,219,582 $ 351,114 $ (55,003 ) $ 17,923,471 (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. See note 1. 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 Unrealized Losses Estimated Gross Unrealized Losses Estimated Gross Unrealized Losses June 30, 2020 Fixed maturities (1): Corporate bonds $ 737,840 $ (32,848 ) $ 8,726 $ (1,852 ) $ 746,566 $ (34,700 ) Mortgage backed securities 150,547 (5,212 ) 108 (33 ) 150,655 (5,245 ) Municipal bonds 46,969 (542 ) — — 46,969 (542 ) Commercial mortgage backed securities 205,336 (7,858 ) 2,523 (147 ) 207,859 (8,005 ) U.S. government and government agencies 412,319 (2,708 ) — — 412,319 (2,708 ) Non-U.S. government securities 1,371,109 (43,928 ) — — 1,371,109 (43,928 ) Asset backed securities 721,451 (37,069 ) 32,198 (2,352 ) 753,649 (39,421 ) Total 3,645,571 (130,165 ) 43,555 (4,384 ) 3,689,126 (134,549 ) Short-term investments 1,025,993 (634 ) — — 1,025,993 (634 ) Total $ 4,671,564 $ (130,799 ) $ 43,555 $ (4,384 ) $ 4,715,119 $ (135,183 ) December 31, 2019 Fixed maturities (1): Corporate bonds $ 675,131 $ (12,350 ) $ 37,671 $ (443 ) $ 712,802 $ (12,793 ) Mortgage backed securities 102,887 (927 ) 203 (4 ) 103,090 (931 ) Municipal bonds 220,296 (2,213 ) — — 220,296 (2,213 ) Commercial mortgage backed securities 147,290 (2,302 ) 2,683 (28 ) 149,973 (2,330 ) U.S. government and government agencies 1,373,127 (10,089 ) 32,058 (45 ) 1,405,185 (10,134 ) Non-U.S. government securities 1,224,243 (20,163 ) 37,610 (167 ) 1,261,853 (20,330 ) Asset backed securities 441,522 (3,334 ) 48,313 (1,390 ) 489,835 (4,724 ) Total 4,184,496 (51,378 ) 158,538 (2,077 ) 4,343,034 (53,455 ) Short-term investments 95,777 (1,548 ) — — 95,777 (1,548 ) Total $ 4,280,273 $ (52,926 ) $ 158,538 $ (2,077 ) $ 4,438,811 $ (55,003 ) (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, 2020 , on a lot level basis, approximately 3,730 security lots out of a total of approximately 10,540 security lots were in an unrealized loss position and the largest single unrealized loss from a single lot in the Company’s fixed maturity portfolio was $1.2 million . At December 31, 2019 , on a lot level basis, approximately 2,230 security lots out of a total of approximately 9,590 security lots were in an unrealized loss position and the largest single unrealized loss from a single lot in the Company’s fixed maturity portfolio was $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, 2020 December 31, 2019 Maturity Estimated Fair Value Amortized Cost Estimated Amortized Cost Due in one year or less $ 344,032 $ 339,451 $ 428,659 $ 423,617 Due after one year through five years 9,873,345 9,645,073 10,126,403 9,996,206 Due after five years through 10 years 4,379,828 4,163,392 3,317,535 3,219,567 Due after 10 years 428,430 396,772 411,269 388,280 15,025,635 14,544,688 14,283,866 14,027,670 Mortgage backed securities 610,839 603,889 562,309 553,571 Commercial mortgage backed securities 395,682 396,193 733,108 720,487 Asset backed securities 1,633,481 1,642,886 1,683,753 1,664,460 Total (1) $ 17,665,637 $ 17,187,656 $ 17,263,036 $ 16,966,188 (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, 2020 , the fair value of the cash collateral received on securities lending was $26.6 million and the fair value of security collateral received was $447.2 million . At December 31, 2019 , the fair value of the cash collateral received on securities lending was $81.2 million , and the fair value of security collateral received was $307.2 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, 2020 U.S. government and government agencies $ 291,730 $ — $ 153,552 $ — $ 445,282 Corporate bonds 2,336 — — — 2,336 Equity securities 26,165 — — — 26,165 Total $ 320,231 $ — $ 153,552 $ — $ 473,783 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 $ 473,783 December 31, 2019 U.S. government and government agencies $ 240,332 $ — $ 115,973 $ — $ 356,305 Corporate bonds 2,570 — — — 2,570 Equity securities 29,491 — — — 29,491 Total $ 272,393 $ — $ 115,973 $ — $ 388,366 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 $ 388,366 Equity Securities, at Fair Value At June 30, 2020 , the Company held $1.26 billion of equity securities, at fair value, compared to $838.9 million at December 31, 2019 . 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 which are included in investments accounted for using the fair value option, by strategy: June 30, December 31, Term loan investments $ 1,109,031 $ 1,326,018 Lending 579,320 602,841 Credit related funds 92,970 123,020 Energy 66,667 97,402 Investment grade fixed income 133,936 151,594 Infrastructure 48,427 61,786 Private equity 72,888 49,376 Real estate 19,251 17,279 Total $ 2,122,490 $ 2,429,316 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 $ 624,382 $ 428,437 Equities 292,499 293,686 Real estate 249,822 246,851 Lending 137,270 202,690 Private equity 181,492 144,983 Infrastructure 141,972 235,033 Energy 99,865 108,716 Total $ 1,727,302 $ 1,660,396 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. Fair Value Option The following table summarizes the Company’s assets which are accounted for using the fair value option: June 30, December 31, Fixed maturities $ 923,804 $ 754,452 Other investments 2,122,490 2,429,316 Short-term investments 384,382 377,014 Equity securities 90,095 102,695 Investments accounted for using the fair value option $ 3,520,771 $ 3,663,477 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) 1,727,302 1,660,396 Investments accounted for using the fair value option (2) 178,894 188,283 Total $ 1,906,196 $ 1,848,679 (1) Aggregate unfunded commitments were $1.44 billion at June 30, 2020 , compared to $1.36 billion at December 31, 2019 . (2) Aggregate unfunded commitments were $32.3 million at June 30, 2020 , compared to $41.7 million at December 31, 2019 . Net Investment Income The components of net investment income were derived from the following sources: June 30, 2020 2019 Three Months Ended Fixed maturities $ 105,391 $ 125,018 Term loans 20,512 24,730 Equity securities 6,219 4,368 Short-term investments 3,383 3,859 Other (1) 16,460 18,523 Gross investment income 151,965 176,498 Investment expenses (20,480 ) (21,460 ) Net investment income $ 131,485 $ 155,038 Six Months Ended Fixed maturities $ 220,238 $ 254,817 Term loans 43,682 49,346 Equity securities 12,226 7,356 Short-term investments 8,279 8,038 Other (1) 35,866 39,719 Gross investment income 320,291 359,276 Investment expenses (43,653 ) (47,289 ) Net investment income $ 276,638 $ 311,987 (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, 2020 2019 Three Months Ended Available for sale securities: Gross gains on investment sales $ 232,153 $ 75,090 Gross losses on investment sales (49,824 ) (15,281 ) Change in fair value of assets and liabilities accounted for using the fair value option: Fixed maturities 68,181 11,429 Other investments 178,570 (33,780 ) Equity securities 6,664 6,414 Short-term investments 3,368 (1,392 ) Equity securities, at fair value: Net realized gains (losses) on sales during the period (18,250 ) (6,644 ) Net unrealized gains (losses) on equity securities still held at reporting date 145,686 22,632 Allowance for credit losses: Investments related 3,225 — Underwriting related (5,834 ) — Net impairment losses — (49 ) Derivative instruments (1) (836 ) 63,966 Other (6,515 ) (1,628 ) Net realized gains (losses) $ 556,588 $ 120,757 Six Months Ended Available for sale securities: Gross gains on investment sales $ 410,353 $ 118,455 Gross losses on investment sales (81,792 ) (46,937 ) Change in fair value of assets and liabilities accounted for using the fair value option: Fixed maturities (59,485 ) 42,577 Other investments (129,230 ) (15,585 ) Equity securities 1,755 10,680 Short-term investments (5,313 ) (672 ) Equity securities, at fair value: Net realized gains (losses) on sales during the period (18,789 ) 4,286 Net unrealized gains (losses) on equity securities still held at reporting date (29,880 ) 59,768 Allowance for credit losses: Investments related (6,095 ) — Underwriting related (9,104 ) — Net impairments losses (533 ) (1,358 ) Derivative instruments (1) 126,353 99,837 Other (8,612 ) (10,038 ) Net realized gains (losses) $ 189,628 $ 261,013 (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 a loss of $65.1 million related to investment funds accounted for using the equity method in the 2020 second quarter , compared to income of $32.5 million for the 2019 second quarter , and a loss of $69.3 million for the six months ended June 30, 2020 , compared to income of $79.4 million for the six months ended June 30, 2019 . In applying the equity method, investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the market value of the underlying securities in the funds). Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds. 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: June 30, 2020 Structured Securities (1) Municipal Bonds Corporate Bonds Short Term Investments Total Three Months Ended Balance at beginning of period $ 2,654 $ 23 $ 7,232 $ 29 $ 9,938 Cumulative effect of accounting change — — — — — 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 ) Write-offs charged against the allowance — — — — — Balance at end of period $ 1,726 $ 28 $ 4,115 $ — $ 5,869 Six Months Ended Balance at beginning of period $ — $ — $ — $ — $ — Cumulative effect of accounting change 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 ) Write-offs charged against the allowance — — — — — 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. 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 17, “Commitments and Contingencies,” of the notes to consolidated financial statements in the Company’s 2019 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 $ 4,633,689 $ 4,526,761 Third party agreements 2,525,173 2,278,248 Deposits with U.S. regulatory authorities 862,859 797,371 Deposits with non-U.S. regulatory authorities 189,107 119,238 Total restricted assets $ 8,210,828 $ 7,721,618 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, 2020 and December 31, 2019, Watford held $1.14 billion and $1.0 billion , 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 $ 854,259 $ 726,230 Restricted cash (included in ‘other assets’) $ 210,424 $ 177,468 Cash and restricted cash $ 1,064,683 $ 903,698

Fair Value

Fair Value	6 Months Ended
	Jun. 30, 2020
Fair Value Disclosures [Abstract]
Fair Value	Fair Value Accounting guidance regarding fair value measurements addresses how companies should measure fair value when they are required to use a fair value measure for recognition or disclosure purposes under GAAP and provides a common definition of fair value to be used throughout GAAP. It defines fair value as the price that would be received to sell an asset or paid to transfer a liability in an orderly fashion between market participants at the measurement date. In addition, it establishes a three-level valuation hierarchy for the disclosure of fair value measurements. The valuation hierarchy is based upon the transparency of inputs to the valuation of an asset or liability as of the measurement date. The level in the hierarchy within which a given fair value measurement falls is determined based on the lowest level input that is significant to the measurement (Level 1 being the highest priority and Level 3 being the lowest priority). The levels in the hierarchy are defined as follows: Level 1: Inputs to the valuation methodology are observable inputs that reflect quoted prices (unadjusted) for identical assets or liabilities in active markets Level 2: Inputs to the valuation methodology include quoted prices for similar assets and liabilities in active markets, and inputs that are observable for the asset or liability, either directly or indirectly, for substantially the full term of the financial instrument Level 3: Inputs to the valuation methodology are unobservable and significant to the fair value measurement Following is a description of the valuation methodologies used for securities measured at fair value, as well as the general classification of such securities pursuant to the valuation hierarchy. The Company reviews its securities measured at fair value and discusses the proper classification of such investments with investment advisers and others. The Company determines the existence of an active market based on its judgment as to whether transactions for the financial instrument occur in such market with sufficient frequency and volume to provide reliable pricing information. The independent pricing sources obtain market quotations and actual transaction prices for securities that have quoted prices in active markets. The Company uses quoted values and other data provided by nationally recognized independent pricing sources as inputs into its process for determining fair values of its fixed maturity investments. To validate the techniques or models used by pricing sources, the Company's review process includes, but is not limited to: (i) quantitative analysis ( e.g., comparing the quarterly return for each managed portfolio to its target benchmark, with significant differences identified and investigated); (ii) a review of the average number of prices obtained in the pricing process and the range of resulting fair values; (iii) initial and ongoing evaluation of methodologies used by outside parties to calculate fair value; (iv) a comparison of the fair value estimates to the Company’s knowledge of the current market; (v) a comparison of the pricing services' fair values to other pricing services' fair values for the same investments; and (vi) periodic back-testing, which includes randomly selecting purchased or sold securities and comparing the executed prices to the fair value estimates from the pricing service. A price source hierarchy was maintained in order to determine which price source would be used (i.e. , a price obtained from a pricing service with more seniority in the hierarchy will be used over a less senior one in all cases). The hierarchy prioritizes pricing services based on availability and reliability and assigns the highest priority to index providers. Based on the above review, the Company will challenge any prices for a security or portfolio which are considered not to be representative of fair value. The Company did not adjust any of the prices obtained from the independent pricing sources at June 30, 2020 . 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 $24.92 billion of financial assets and liabilities measured at fair value at June 30, 2020 , approximately $121.1 million , or 0.5% , were priced using non-binding broker-dealer quotes or modeled valuations. Of the $22.90 billion of financial assets and liabilities measured at fair value at December 31, 2019 , approximately $179.6 million , or 0.8% , 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 determined that exchange-traded investments in mutual funds would be included in Level 1 as their fair values are based on quoted market prices in active markets. Other investments also include term loan investments for which fair values are estimated by using quoted prices of term loan investments with similar characteristics, pricing models or matrix pricing. Such investments are generally classified within Level 2. 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. The following table presents the Company’s financial assets and liabilities measured at fair value by level at June 30, 2020 : Estimated Fair Value Measurements Using: Estimated Fair Value Quoted Prices in Active Markets for Identical Assets (Level 1) Significant Other Observable Inputs (Level 2) Significant Unobservable Inputs (Level 3) Assets measured at fair value (1): Available for sale securities: Fixed maturities: Corporate bonds $ 7,143,600 $ — $ 7,142,743 $ 857 Mortgage backed securities 610,839 — 610,621 218 Municipal bonds 517,089 — 517,089 — Commercial mortgage backed securities 395,682 — 395,682 — U.S. government and government agencies 5,192,991 5,077,056 115,935 — Non-U.S. government securities 2,171,955 — 2,171,955 — Asset backed securities 1,633,481 — 1,630,249 3,232 Total 17,665,637 5,077,056 12,584,274 4,307 Short-term investments 2,277,866 2,250,377 27,489 — Equity securities, at fair value 1,263,914 1,205,352 6,581 51,981 Derivative instruments (4) 96,909 — 96,909 — Fair value option: Corporate bonds 673,457 — 672,459 998 Non-U.S. government bonds 68,340 — 68,340 — Mortgage backed securities 14,142 — 14,142 — Municipal bonds 249 — 249 — Commercial mortgage backed securities 1,131 — 1,131 — Asset backed securities 165,890 — 165,890 — U.S. government and government agencies 595 483 112 — Short-term investments 384,382 370,286 14,096 — Equity securities 90,096 28,507 142 61,447 Other investments 1,167,345 39,493 1,081,399 46,453 Other investments measured at net asset value (2) 955,145 Total 3,520,772 438,769 2,017,960 108,898 Total assets measured at fair value $ 24,825,098 $ 8,971,554 $ 14,733,213 $ 165,186 Liabilities measured at fair value: Contingent consideration liabilities $ (1,250 ) $ — $ — $ (1,250 ) Securities sold but not yet purchased (3) (29,289 ) — (29,289 ) — Derivative instruments (4) (66,821 ) — (66,821 ) — Total liabilities measured at fair value $ (97,360 ) $ — $ (96,110 ) $ (1,250 ) (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, 2019 : Estimated Fair Value Measurements Using: Estimated Quoted Prices in Active Markets for Identical Assets (Level 1) Significant Other Observable Inputs (Level 2) Significant Unobservable Inputs (Level 3) Assets measured at fair value (1): Available for sale securities: Fixed maturities: Corporate bonds $ 6,406,591 $ — $ 6,397,740 $ 8,851 Mortgage backed securities 562,309 — 562,055 254 Municipal bonds 881,926 — 881,926 — Commercial mortgage backed securities 733,108 — 733,108 — U.S. government and government agencies 4,916,592 4,805,581 111,011 — Non-U.S. government securities 2,078,757 — 2,078,757 — Asset backed securities 1,683,753 — 1,678,791 4,962 Total 17,263,036 4,805,581 12,443,388 14,067 Short-term investments 956,546 904,804 51,742 — Equity securities, at fair value 850,283 789,596 4,798 55,889 Derivative instruments (4) 48,946 — 48,946 — Fair value option: Corporate bonds 488,402 — 487,470 932 Non-U.S. government bonds 50,465 — 50,465 — Mortgage backed securities 11,947 — 11,947 — Municipal bonds 377 — 377 — Commercial mortgage backed securities 1,134 — 1,134 — Asset backed securities 200,163 — 200,163 — U.S. government and government agencies 1,962 1,852 110 — Short-term investments 377,014 333,320 43,694 — Equity securities 102,697 43,962 641 58,094 Other investments 1,418,273 53,287 1,296,169 68,817 Other investments measured at net asset value (2) 1,011,043 Total 3,663,477 432,421 2,092,170 127,843 Total assets measured at fair value $ 22,782,288 $ 6,932,402 $ 14,641,044 $ 197,799 Liabilities measured at fair value: Contingent consideration liabilities $ (7,998 ) $ — $ — $ (7,998 ) Securities sold but not yet purchased (3) (66,257 ) — (66,257 ) — Derivative instruments (4) (39,750 ) — (39,750 ) — Total liabilities measured at fair value $ (114,005 ) $ — $ (106,007 ) $ (7,998 ) (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 Investments Equity Securities Equity Securities Contingent Consideration Liabilities 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 ) Three Months Ended June 30, 2019 Balance at beginning of period $ 302 $ 7,567 $ 2,233 $ 62,329 $ — $ — $ (68,121 ) Total gains or (losses) (realized/unrealized) Included in earnings (2) — — (49 ) (11,614 ) — — (423 ) Included in other comprehensive income 1 102 — — — — — Purchases, issuances, sales and settlements Purchases — 429 — — — — — Issuances — — — — — — — Sales — — — (74 ) — — — Settlements (13 ) (456 ) — — — — 60,719 Transfers in and/or out of Level 3 — — 23,919 44,632 56,145 51,212 — Balance at end of period $ 290 $ 7,642 $ 26,103 $ 95,273 $ 56,145 $ 51,212 $ (7,825 ) 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 ) Six Months Ended June 30, 2019 Balance at beginning of year $ 313 $ 8,141 $ 5,758 $ 62,705 $ — $ — $ (66,665 ) Total gains or (losses) (realized/unrealized) Included in earnings (2) 1,757 — (339 ) (11,316 ) — — (1,331 ) Included in other comprehensive income 5 (16 ) — — — — — Purchases, issuances, sales and settlements Purchases — 429 — — — — — Issuances — — — — — — (548 ) Sales (1,757 ) — (3,235 ) (148 ) — — — Settlements (28 ) (912 ) — (600 ) — — 60,719 Transfers in and/or out of Level 3 — — 23,919 44,632 56,145 51,212 — Balance at end of period $ 290 $ 7,642 $ 26,103 $ 95,273 $ 56,145 $ 51,212 $ (7,825 ) (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, 2020 , due to their respective short maturities. As these financial instruments are not actively traded, their respective fair values are classified within Level 2. At June 30, 2020 , the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.86 billion and had a fair value of $3.49 billion . At December 31, 2019 , the Company’s senior notes were carried at their cost, net of debt issuance costs, of $1.87 billion and had a fair value of $2.34 billion

Derivative Instruments

Derivative Instruments	6 Months Ended
	Jun. 30, 2020
Derivative Instruments and Hedging Activities Disclosure [Abstract]
Derivative Instruments	Derivative Instruments The Company’s investment strategy allows for the use of derivative instruments. The Company’s derivative instruments are recorded on its consolidated balance sheets at fair value. The Company utilizes exchange traded U.S. Treasury note, Eurodollar and other futures contracts and commodity futures to manage portfolio duration or replicate investment positions in its portfolios and the Company routinely utilizes foreign currency forward contracts, currency options, index futures contracts and other derivatives as part of its total return objective. In addition, certain of the Company’s investments are managed in portfolios which incorporate the use of foreign currency forward contracts which are intended to provide an economic hedge against foreign currency movements. In addition, the Company purchases to-be-announced mortgage backed securities (“TBAs”) as part of its investment strategy. TBAs represent commitments to purchase a future issuance of agency mortgage backed securities. For the period between purchase of a TBA and issuance of the underlying security, the Company’s position is accounted for as a derivative. The Company purchases TBAs in both long and short positions to enhance investment performance and as part of its overall investment strategy. The following table summarizes information on the fair values and notional values of the Company’s derivative instruments: Estimated Fair Value Asset Derivatives Liability Derivatives Notional Value (1) June 30, 2020 Futures contracts (2) $ 17,181 $ (5,894 ) $ 2,635,862 Foreign currency forward contracts (2) 12,366 (9,400 ) 1,073,432 TBAs (3) 5,973 — 5,740 Other (2) 67,362 (51,527 ) 3,398,053 Total $ 102,882 $ (66,821 ) December 31, 2019 Futures contracts (2) $ 10,065 $ (13,722 ) $ 4,104,559 Foreign currency forward contracts (2) 5,352 (5,327 ) 686,878 TBAs (3) 55,010 — 53,229 Other (2) 33,529 (20,701 ) 4,356,300 Total $ 103,956 $ (39,750 ) (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.’ (3) The fair value of TBAs are included in ‘fixed maturities available for sale, at fair value.’ The Company did not hold any derivatives which were designated as hedging instruments at June 30, 2020 or December 31, 2019 . 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, 2020 , asset derivatives and liability derivatives of $87.0 million and $60.3 million , respectively, were subject to a master netting agreement, compared to $97.8 million and $37.8 million , respectively, at December 31, 2019 . 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: 2020 2019 Three Months Ended Net realized gains (losses): Futures contracts $ (1,607 ) $ 66,973 Foreign currency forward contracts 3,523 (5,365 ) TBAs 264 48 Other (3,016 ) 2,310 Total $ (836 ) $ 63,966 Six Months Ended Net realized gains (losses): Futures contracts $ 94,337 $ 94,309 Foreign currency forward contracts (7,347 ) (19,074 ) TBAs 1,009 238 Other 38,354 24,364 Total $ 126,353 $ 99,837

Commitments and Contingencies

Commitments and Contingencies	6 Months Ended
	Jun. 30, 2020
Commitments and Contingencies Disclosure [Abstract]
Commitments and Contingencies	Commitments and Contingencies Senior Notes On June 30, 2020, Arch Capital completed a public offering of $1.0 billion aggregate principal amount of its 3.635 % senior notes with a scheduled maturity of June 30, 2050 (the “2050 notes”). The 2050 notes are Arch Capital’s senior unsecured obligations and rank equally with all of its existing and future senior unsecured indebtedness. Interest payments on the 2050 notes are due semi-annually in arrears on June 30 and December 30, beginning on December 30, 2020, to holders of record on the preceding June 15 or December 15, as the case may be. Interest will be calculated on the basis of a 360-day year of twelve 30-day months . Subject to conditions of redemption, Arch Capital may redeem the 2050 notes at any time and from time to time prior to December 30, 2049, in whole or in part, at a redemption price equal to the “make-whole” redemption price, plus accrued and unpaid interest thereon to, but excluding, the redemption date. Arch Capital is planning to use the net proceeds for general corporate purposes. 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 $1.77 billion at June 30, 2020 , compared to $1.69 billion at December 31, 2019 . Interest Paid Interest paid on the Company’s senior notes and other borrowings were $57.4 million for the six months ended June 30, 2020 , consistent with $60.9 million for the 2019

Leases

Leases	6 Months Ended
	Jun. 30, 2020
Leases [Abstract]
Leases	Leases In the ordinary course of business, the Company renews and enters into new leases for office property and equipment. At the lease inception date, the Company determines whether a contract contains a lease and its classification as a finance or operating lease. Primarily all of the Company’s leases are classified as operating leases. The Company’s operating leases have remaining lease terms of up to 11 years , some of which include options to extend the lease term. The Company considers these options when determining the lease term and measuring its lease liability and right-of-use asset. In addition, the Company’s lease agreements do not contain any material residual value guarantees or material restrictive covenants. Short-term operating leases with an initial term of twelve months or less were excluded on the Company's consolidated balance sheet and represent an inconsequential amount of operating lease expense. As most leases do not provide an implicit rate, the Company uses its incremental borrowing rate based on the information available at the lease commencement date in determining the present value of lease payments. Additional information regarding the Company’s operating leases is as follows: June 30, 2020 2019 Three Months Ended Operating lease costs $ 7,821 $ 7,244 Cash payments included in the measurement of lease liabilities reported in operating cash flows 5,844 7,685 Right-of-use assets obtained in exchange for new lease liabilities 435 4,420 Right-of-use assets (1) 119,494 134,061 Operating lease liability (1) 139,772 150,341 Weighted average discount rate 3.9 % 3.9 % Weighted average remaining lease term 6.1 years 6.5 years Six Months Ended Operating lease costs $ 15,812 $ 14,860 Cash payments included in the measurement of lease liabilities reported in operating cash flows 14,305 14,585 Right-of-use assets obtained in exchange for new lease liabilities 3,885 4,420 Right-of-use assets (1) 119,494 134,061 Operating lease liability (1) 139,772 150,341 Weighted average discount rate 3.9 % 3.9 % Weighted average remaining lease term 6.1 years 6.5 years (1) The right-of-use assets are included in ‘other assets’ while the operating lease liability is included in ‘other liabilities.’ The following table presents the contractual maturities of the Company's operating lease liabilities at June 30, 2020 : Years Ending December 31, 2020 (remainder) $ 15,835 2021 31,475 2022 28,341 2023 23,820 2024 17,601 2025 and thereafter 40,139 Total undiscounted lease liability $ 157,211 Less: present value adjustment (17,439 ) Operating lease liability $ 139,772

Variable Interest Entities and

Variable Interest Entities and Noncontrolling Interests	6 Months Ended
	Jun. 30, 2020
Noncontrolling Interest [Abstract]
Variable Interest Entity and Noncontrolling Interests	Variable Interest Entities and Noncontrolling Interests Watford In March 2014, the Company invested $100.0 million and acquired 2,500,000 common shares, approximately 11% of Watford’s outstanding common equity. Watford’s common shares are listed on the Nasdaq Select Global Market under the ticker symbol “WTRE”. As of June 30, 2020 , the Company owns approximately 13% of Watford’s outstanding common equity. In July 2019, Watford completed an offering of $175.0 million in aggregate principal amount of its 6.5% senior notes, due July 2, 2029 (“Watford Senior Notes”). Interest on the Watford Senior Notes is payable semi-annually in arrears on each January 2 and July 2 commencing on January 2, 2020. The $172.4 million net proceeds from the offering were used to redeem a portion of Watford’s outstanding preference shares (“Watford Preference Shares”). The Company purchased $35.0 million in aggregate principal amount of the Watford Senior Notes. Watford is considered a VIE and the Company concluded that it is the primary beneficiary of Watford. As such, the results of Watford are included in the Company’s consolidated financial statements. 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. 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, 2020 2019 Assets Investments accounted for using the fair value option $ 1,886,676 $ 1,898,091 Fixed maturities available for sale, at fair value 690,225 745,708 Equity securities, at fair value 62,443 65,338 Cash 107,653 102,437 Accrued investment income 14,364 14,025 Premiums receivable 258,178 273,657 Reinsurance recoverable on unpaid and paid losses and LAE 229,746 170,973 Ceded unearned premiums 131,919 132,577 Deferred acquisition costs 64,149 64,044 Receivable for securities sold 31,314 16,287 Goodwill and intangible assets 7,650 7,650 Other assets 63,441 60,070 Total assets of consolidated VIE $ 3,547,758 $ 3,550,857 Liabilities Reserve for losses and loss adjustment expenses $ 1,353,049 $ 1,263,628 Unearned premiums 456,170 438,907 Reinsurance balances payable 72,776 77,066 Revolving credit agreement borrowings 335,587 484,287 Senior notes 172,554 172,418 Payable for securities purchased 67,272 18,180 Other liabilities (1) 261,267 171,714 Total liabilities of consolidated VIE $ 2,718,675 $ 2,626,200 Redeemable noncontrolling interests $ 52,351 $ 52,305 (1) Includes certain borrowings related to investing activities. For the six months ended June 30, 2020 , Watford generated $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, compared to $115.9 million of cash provided by operating activities, $135.7 million of cash used for investing activities and $25.6 million of cash provided by financing activities for the six months ended June 30, 2019 . 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 87% at June 30, 2020 . 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, 2020 2019 Three Months Ended Balance, beginning of period $ 492,785 $ 838,081 Additional paid in capital attributable to noncontrolling interests 595 2,074 Amounts attributable to noncontrolling interests 165,598 12,301 Other comprehensive income (loss) attributable to noncontrolling interests 20,111 2,891 Balance, end of period $ 679,089 $ 855,347 Six Months Ended Balance, beginning of year $ 762,777 $ 791,560 Additional paid in capital attributable to noncontrolling interests 472 2,074 Repurchases attributable to non-redeemable noncontrolling interests (1) (2,867 ) — Amounts attributable to noncontrolling interests (68,346 ) 54,683 Other comprehensive income (loss) attributable to noncontrolling interests (12,947 ) 7,030 Balance, end of period $ 679,089 $ 855,347 (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. In August 2019, Watford redeemed 6,919,998 of its 9,065,200 issued and outstanding Watford Preference Shares. The Watford Preference Shares were redeemed at a total redemption price of $25.19748 per share, inclusive of all declared and unpaid dividends, with accumulation of any undeclared dividends on or after June 30, 2019. In addition, the Company received $11.5 million pursuant to the redemption of Watford Preference Shares. The following table sets forth activity in the redeemable non-controlling interests: June 30, 2020 2019 Three Months Ended Balance, beginning of period $ 55,376 $ 206,383 Accretion of preference share issuance costs 23 92 Other 587 — Balance, end of period $ 55,986 $ 206,475 Six Months Ended Balance, beginning of year $ 55,404 $ 206,292 Accretion of preference share issuance costs 46 183 Other 536 — Balance, end of period $ 55,986 $ 206,475 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, 2020 2019 Three Months Ended Amounts attributable to non-redeemable noncontrolling interests $ (165,598 ) $ (12,301 ) Amounts attributable to redeemable noncontrolling interests (1,970 ) (4,590 ) Net (income) loss attributable to noncontrolling interests $ (167,568 ) $ (16,891 ) Six Months Ended Amounts attributable to non-redeemable noncontrolling interests $ 68,346 $ (54,683 ) Amounts attributable to redeemable noncontrolling interests (3,123 ) (9,178 ) Net (income) loss attributable to noncontrolling interests $ 65,223 $ (63,861 ) 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 one month LIBOR, the basis for the contractual payments to bond holders, and short term invested trust asset yields. Maximum Exposure to Loss Bellemeade Entities (Issue Date) Total VIE Assets On-Balance Sheet (Asset) Liability Off-Balance Sheet Total Jun 30, 2020 Bellemeade 2017-1 Ltd. (Oct-17) $ 145,573 $ (295 ) $ 2,469 $ 2,174 Bellemeade 2018-1 Ltd. (Apr-18) 250,095 (1,244 ) 5,597 4,353 Bellemeade 2018-2 Ltd. (Aug-18) 272,685 (1,206 ) 4,210 3,004 Bellemeade 2018-3 Ltd. (Oct-18) 302,563 (1,883 ) 8,387 6,504 Bellemeade 2019-1 Ltd. (Mar-19) 219,256 (83 ) 10,251 10,168 Bellemeade 2019-2 Ltd. (Apr-19) 398,316 54 13,088 13,142 Bellemeade 2019-3 Ltd. (Jul-19) 528,084 (248 ) 10,649 10,401 Bellemeade 2019-4 Ltd. (Oct-19) 468,737 257 14,687 14,944 Bellemeade 2020-1 Ltd. (Jun-20) (1) 450,040 (60 ) 8,984 8,924 Total $ 3,035,349 $ (4,708 ) $ 78,322 $ 73,614 Dec 31, 2019 Bellemeade 2017-1 Ltd. (Oct-17) $ 216,429 $ (442 ) $ 2,794 $ 2,352 Bellemeade 2018-1 Ltd. (Apr-18) 328,482 (1,574 ) 5,757 4,183 Bellemeade 2018-2 Ltd. (Aug-18) 437,009 (877 ) 2,524 1,647 Bellemeade 2018-3 Ltd. (Oct-18) 426,806 (1,113 ) 3,937 2,824 Bellemeade 2019-1 Ltd. (Mar-19) 257,358 (226 ) 3,027 2,801 Bellemeade 2019-2 Ltd. (Apr-19) 525,959 (78 ) 2,579 2,501 Bellemeade 2019-3 Ltd. (Jul-19) 656,523 (585 ) 9,273 8,688 Bellemeade 2019-4 Ltd. (Oct-19) 577,267 (302 ) 12,193 11,891 Total $ 3,425,833 $ (5,197 ) $ 42,084 $ 36,887 (1) An additional $78.5 million

Other Comprehensive Income (Los

Other Comprehensive Income (Loss)	6 Months Ended
	Jun. 30, 2020
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 2020 2019 2020 2019 Unrealized appreciation on available-for-sale investments Net realized gains (losses) $ 182,329 $ 59,809 $ 328,561 $ 71,518 Provision for credit losses 3,225 (6,095 ) Other-than-temporary impairment losses — (49 ) (533 ) (1,358 ) Total before tax 185,554 59,760 321,933 70,160 Income tax (expense) benefit (18,163 ) (4,415 ) (33,313 ) (4,594 ) Net of tax $ 167,391 $ 55,345 $ 288,620 $ 65,566 Before Tax Amount Tax Expense (Benefit) Net of Tax Amount 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 Three Months Ended June 30, 2019 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ 248,074 $ 25,601 $ 222,473 Less reclassification of net realized gains (losses) included in net income 59,760 4,415 55,345 Foreign currency translation adjustments 4,409 142 4,267 Other comprehensive income (loss) $ 192,723 $ 21,328 $ 171,395 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 Six Months Ended June 30, 2019 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ 503,064 $ 54,704 $ 448,360 Less reclassification of net realized gains (losses) included in net income 70,160 4,594 65,566 Foreign currency translation adjustments 10,053 270 9,783 Other comprehensive income (loss) $ 442,957 $ 50,380 $ 392,577

Income Taxes

Income Taxes	6 Months Ended
	Jun. 30, 2020
Income Tax Disclosure [Abstract]
Income Taxes	Income Taxes The Company’s income tax provision on income before income taxes resulted in an effective tax rate of 12.5% for the six months ended June 30, 2020 , compared to 8.4% for the 2019 period. 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. For interim reporting purposes, the Company has calculated its annual effective tax rate for the full year 2020 by treating excess tax benefits in the U.S. that arise from the accounting for stock based compensation as a discrete item. The impact of the discrete item resulted in a benefit of 0.5% for the six months ended June 30, 2020 . The Company had a net deferred tax asset of $9.3 million at June 30, 2020 , compared to a net deferred tax liability of $53.5 million at December 31, 2019 . The change is primarily a result of fluctuations in the contingency reserve. In addition, the Company paid $10.4 million and $43.5 million of income taxes for the six months ended June 30, 2020 and 2019 , respectively.

Legal Proceedings

Legal Proceedings	6 Months Ended
	Jun. 30, 2020
Disclosure Legal Proceedings [Abstract]
Legal Proceedings	Legal Proceedings The Company, in common with the insurance industry in general, is subject to litigation and arbitration in the normal course of its business. As of June 30, 2020 , 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 Parties	6 Months Ended
	Jun. 30, 2020
Related Party Transactions [Abstract]
Transactions with related parties	Transactions with Related Parties I n 2017, the Company acquired approximately 25% of Premia Holdings Ltd. Premia Holdings Ltd. is the parent of Premia Reinsurance Ltd., a multi-line Bermuda reinsurance company (together with Premia Holdings Ltd., “Premia”). Premia’s strategy is to reinsure or acquire companies or reserve portfolios in the non-life property and casualty insurance and reinsurance run-off market. Arch Re Bermuda and certain Arch co-investors invested $100.0 million and acquired approximately 25% of Premia as well as warrants to purchase additional common equity. Arch has appointed two directors to serve on the seven person board of directors of Premia. Arch Re Bermuda is providing a 25% quota share reinsurance treaty on certain business written by Premia. In the 2019 fourth quarter, Barbican Group Holdings Limited (“Barbican”), a wholly owned subsidiary of the Company, entered into certain reinsurance and related transactions with Premia pursuant to which Premia assumed a transfer of liability for the 2018 and prior years of account of Barbican as of July 1, 2019. Barbican recorded reinsurance recoverable on unpaid and paid losses and funds held liability of $181.9 million and $169.0 million , respectively, at June 30, 2020, compared to $177.7 million and $180.0 million , respectively, at December 31, 2019. Certain directors and executive officers of the Company own common and preference shares of Watford. See note 12, “Variable Interest Entity and Noncontrolling Interests,”

Basis of Presentation and Rec_2

Basis of Presentation and Recent Accounting Pronouncements (Policies)	6 Months Ended
	Jun. 30, 2020
Organization, Consolidation and Presentation of Financial Statements [Abstract]
Basis of accounting	The interim consolidated financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America (“GAAP”). All significant intercompany transactions and balances have been eliminated in consolidation.
Use of estimates	The preparation of financial statements in conformity with GAAP requires management to make estimates and assumptions that affect the reported amounts of assets and liabilities and disclosure of contingent assets and liabilities at the date of the financial statements and the reported amounts of revenues and expenses during the reporting period. Actual results could differ materially from those estimates and assumptions. In the opinion of management, the accompanying unaudited interim consolidated financial statements reflect all adjustments (consisting of normally recurring accruals) necessary for a fair statement of results on an interim basis. The results of any interim period are not necessarily indicative of the results for a full year or any future periods.
Recent accounting pronouncements	Recently Issued Accounting Standards Adopted The Company adopted ASU 2018-13, “Fair Value Measurement (Topic 820): Disclosure Framework - Changes to the Disclosure Requirements for Fair Value Measurement.” The ASU modifies the disclosure requirements on fair value measurement as part of the disclosure framework project with the objective to improve the effectiveness of disclosures in the notes to the financial statements. The amendments in this update allow for removal of (1) the amount and reasons for transfer between Level 1 and Level 2 of the fair value hierarchy; (2) the policy for transfers between levels; and (3) the valuation processes for Level 3 fair value measurements. The adoption of this guidance did not have a material effect on the Company’s consolidated financial statements. The Company adopted ASU 2018-15, “Intangibles - Goodwill and Other - Internal Use Software (Subtopic 350-40).” This ASU aligns the requirements for capitalizing certain implementation costs incurred in a cloud computing arrangement that is a service contract with the requirements for capitalizing implementation costs incurred to develop or obtain internal-use software. The guidance provides flexibility in adoption, allowing for either retrospective adjustment or prospective adjustment for all implementation costs incurred after the date of adoption. The Company adopted this guidance prospectively. The adoption of this guidance did not have a material effect on the Company’s consolidated financial statements. In March 2020, the SEC amended Rule 3-10 of Regulation S-X regarding financial disclosure requirements for registered debt offerings involving subsidiaries as either issuers or guarantors and affiliates whose securities are pledged as collateral. This new guidance narrows the circumstances that require separate financial statements of subsidiary issuers and guarantors and streamlines the alternative disclosures required in lieu of those statements. The amendment is effective on January 4, 2021 with early adoption permitted. The Company elected to apply the amended requirements for the quarter ended March 31, 2020, and is no longer providing condensed consolidating financial information that resulted from the registered debt obligations of its subsidiaries, Arch Capital Group (U.S.) Inc. and Arch Capital Finance LLC., that were disclosed in Note 26 of the financial statements in the Company’s 2019 Form 10-K. The Company adopted ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326).” The ASU applies a new credit loss model (current expected credit losses) for determining credit related impairments for financial instruments measured at amortized cost, including reinsurance recoverable, contractholder receivables, and premiums receivable, and requires an entity to estimate its lifetime “expected credit loss” and record an allowance that, when deducted from the amortized cost basis of the financial asset, presents the net amount expected to be collected on the financial asset. The estimate of expected credit losses should consider historical information, current information, as well as reasonable and supportable forecasts, including estimates of prepayments. The ASU also amends the previous other-than-temporary impairment model for available-for-sale debt securities by requiring the recognition of impairments relating to credit losses through an allowance account and limits the amount of credit loss to the difference between a security’s amortized cost basis and its fair value. In addition, the length of time a security has been in an unrealized loss position will no longer impact the determination of whether a credit loss exists. The Company adopted the ASU for the quarter ending March 31, 2020 by recognizing an after-tax cumulative effect adjustment of $22.5 million to the opening balance of retained earnings as of January 1, 2020. The cumulative effect adjustment decreased retained earnings and increased the allowance for credit losses. Recently Issued Accounting Standards Not Yet Adopted In December 2019, the FASB issued ASU 2019-12, “Simplifying the Accounting for Income Taxes.” This ASU eliminates certain exceptions for recognizing deferred taxes for investments, performing intraperiod tax allocation 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 ASU is effective for fiscal years beginning after December 15, 2020 and interim periods within those fiscal years with early adoption permitted. The Company is currently evaluating the impact of the new guidance on its consolidated financial statements and does not expect this guidance to have a material effect on the Company’s consolidated financial statements. In March 2020, the FASB issued ASU 2020-04, “Facilitation of the Effects of Reference Rate Reform on Financial Reporting.” This ASU provides optional expedients and exceptions for applying GAAP to investments, derivatives, or other transactions that reference the London Interbank Offered Rate (LIBOR) or another reference rate expected to be discontinued because of reference rate reform. Along with the optional expedients, the amendments include a general principle that permits an entity to consider contract modifications due to reference reform to be an event that does not require contract re-measurement at the modification date or reassessment of a previous accounting determination. This standard may be elected over time through December 31, 2022 as reference rate reform activities occur. The Company is currently evaluating the impact of the new guidance on its consolidated financial statements and does not expect this guidance to 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 2019 Form 10-K.

Earnings Per Common Share (Tabl

Earnings Per Common Share (Tables)	6 Months Ended
	Jun. 30, 2020
Earnings Per Share [Abstract]
Schedule of computation of basic and diluted earnings per common share	The following table sets forth the computation of basic and diluted earnings per common share: Three Months Ended Six Months Ended June 30, June 30, 2020 2019 2020 2019 Numerator: Net income (loss) $ 466,389 $ 485,845 $ 377,715 $ 981,343 Amounts attributable to noncontrolling interests (167,568 ) (16,891 ) 65,223 (63,861 ) Net income (loss) available to Arch 298,821 468,954 442,938 917,482 Preferred dividends (10,403 ) (10,403 ) (20,806 ) (20,806 ) Net income (loss) available to Arch common shareholders $ 288,418 $ 458,551 $ 422,132 $ 896,676 Denominator: Weighted average common shares and common share equivalents outstanding — basic 402,503,687 401,482,784 403,197,924 400,837,181 Effect of dilutive common share equivalents: Nonvested restricted shares 1,597,701 1,937,626 1,829,239 1,720,417 Stock options (1) 4,018,293 7,479,073 5,978,428 7,197,652 Weighted average common shares and common share equivalents outstanding — diluted 408,119,681 410,899,483 411,005,591 409,755,250 Earnings per common share: Basic $ 0.72 $ 1.14 $ 1.05 $ 2.24 Diluted $ 0.71 $ 1.12 $ 1.03 $ 2.19 (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 2020 second quarter and 2019 second quarter , the number of stock options excluded were 6,982,107 and 2,016,830 , respectively. For the six months ended June 30, 2020 and 2019 period, the number of stock options excluded were 2,038,758 and 2,560,755 , respectively.

Segment Information (Tables)

Segment Information (Tables)	6 Months Ended
	Jun. 30, 2020
Segment Reporting [Abstract]
Analysis of underwriting income or loss by segment and reconciliation to net income available to common shareholders	The following tables summarize the Company’s underwriting income or loss by segment, together with a reconciliation of underwriting income or loss to net income available to Arch common shareholders: Three Months Ended June 30, 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) (3,140 ) — (3,140 ) 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 302,474 190,042 492,516 Income tax (expense) benefit (26,529 ) 402 (26,127 ) 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.’ Three Months Ended June 30, 2019 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 919,925 $ 545,547 $ 364,465 $ 1,829,829 $ 161,978 $ 1,937,809 Premiums ceded (292,095 ) (169,457 ) (42,857 ) (504,301 ) (42,608 ) (492,911 ) Net premiums written 627,830 376,090 321,608 1,325,528 119,370 1,444,898 Change in unearned premiums (35,388 ) (8,906 ) 31,175 (13,119 ) 31,948 18,829 Net premiums earned 592,442 367,184 352,783 1,312,409 151,318 1,463,727 Other underwriting income (loss) — 1,224 4,056 5,280 673 5,953 Losses and loss adjustment expenses (389,172 ) (240,958 ) (25,997 ) (656,127 ) (111,416 ) (767,543 ) Acquisition expenses (91,094 ) (56,785 ) (32,654 ) (180,533 ) (29,556 ) (210,089 ) Other operating expenses (109,523 ) (33,960 ) (39,819 ) (183,302 ) (15,612 ) (198,914 ) Underwriting income (loss) $ 2,653 $ 36,705 $ 258,369 297,727 (4,593 ) 293,134 Net investment income 123,038 32,000 155,038 Net realized gains (losses) 125,063 (4,306 ) 120,757 Equity in net income (loss) of investment funds accounted for using the equity method 32,536 — 32,536 Other income (loss) 1,129 — 1,129 Corporate expenses (2) (16,073 ) — (16,073 ) Transaction costs and other (2) (2,178 ) — (2,178 ) Amortization of intangible assets (19,794 ) — (19,794 ) Interest expense (23,375 ) (5,905 ) (29,280 ) Net foreign exchange gains (losses) (6,190 ) 1,238 (4,952 ) Income (loss) before income taxes 511,883 18,434 530,317 Income tax (expense) benefit (44,452 ) (20 ) (44,472 ) Net income (loss) 467,431 18,414 485,845 Amounts attributable to redeemable noncontrolling interests — (4,590 ) (4,590 ) Amounts attributable to nonredeemable noncontrolling interests — (12,301 ) (12,301 ) Net income (loss) available to Arch 467,431 1,523 468,954 Preferred dividends (10,403 ) — (10,403 ) Net income (loss) available to Arch common shareholders $ 457,028 $ 1,523 $ 458,551 Underwriting Ratios Loss ratio 65.7 % 65.6 % 7.4 % 50.0 % 73.6 % 52.4 % Acquisition expense ratio 15.4 % 15.5 % 9.3 % 13.8 % 19.5 % 14.4 % Other operating expense ratio 18.5 % 9.2 % 11.3 % 14.0 % 10.3 % 13.6 % Combined ratio 99.6 % 90.3 % 28.0 % 77.8 % 103.4 % 80.4 % Goodwill and intangible assets $ 157,440 $ — $ 475,920 $ 633,360 $ 7,650 $ 641,010 (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) 5,408 — 5,408 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 508,427 (76,640 ) 431,787 Income tax (expense) benefit (54,474 ) 402 (54,072 ) Net income (loss) 453,953 (76,238 ) 377,715 Dividends attributable to redeemable noncontrolling interests (991 ) (2,132 ) (3,123 ) Amounts attributable to nonredeemable noncontrolling interests — 68,346 68,346 Net income (loss) available to Arch 452,962 (10,024 ) 442,938 Preferred dividends (20,806 ) — (20,806 ) Net income (loss) available to Arch common shareholders $ 432,156 $ (10,024 ) $ 422,132 Underwriting Ratios Loss ratio 73.0 % 79.5 % 41.0 % 67.9 % 79.3 % 68.8 % Acquisition expense ratio 15.3 % 16.6 % 10.2 % 14.6 % 16.3 % 14.7 % Other operating expense ratio 17.7 % 8.2 % 11.7 % 13.3 % 10.3 % 13.0 % Combined ratio 106.0 % 104.3 % 62.9 % 95.8 % 105.9 % 96.5 % (1) Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total. (2) Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’ Six Months Ended June 30, 2019 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 1,861,879 $ 1,228,402 $ 720,515 $ 3,810,282 $ 348,667 $ 4,015,688 Premiums ceded (612,717 ) (401,024 ) (91,655 ) (1,104,882 ) (83,910 ) (1,045,531 ) Net premiums written 1,249,162 827,378 628,860 2,705,400 264,757 2,970,157 Change in unearned premiums (103,215 ) (113,829 ) 46,825 (170,219 ) 32,655 (137,564 ) Net premiums earned 1,145,947 713,549 675,685 2,535,181 297,412 2,832,593 Other underwriting income (loss) — 5,601 7,912 13,513 1,265 14,778 Losses and loss adjustment expenses (745,895 ) (480,768 ) (37,146 ) (1,263,809 ) (222,266 ) (1,486,075 ) Acquisition expenses (173,918 ) (111,111 ) (64,326 ) (349,355 ) (58,582 ) (407,937 ) Other operating expenses (222,919 ) (69,664 ) (79,694 ) (372,277 ) (27,800 ) (400,077 ) Underwriting income (loss) $ 3,215 $ 57,607 $ 502,431 563,253 (9,971 ) 553,282 Net investment income 244,287 67,700 311,987 Net realized gains (losses) 236,187 24,826 261,013 Equity in net income (loss) of investment funds accounted for using the equity method 79,403 — 79,403 Other income (loss) 2,212 — 2,212 Corporate expenses (2) (32,845 ) — (32,845 ) Transaction costs and other (2) (3,368 ) — (3,368 ) Amortization of intangible assets (40,211 ) — (40,211 ) Interest expense (46,857 ) (11,488 ) (58,345 ) Net foreign exchange gains (losses) (1,015 ) (412 ) (1,427 ) Income (loss) before income taxes 1,001,046 70,655 1,071,701 Income tax (expense) benefit (90,338 ) (20 ) (90,358 ) Net income (loss) 910,708 70,635 981,343 Dividends attributable to redeemable noncontrolling interests — (9,178 ) (9,178 ) Amounts attributable to nonredeemable noncontrolling interests — (54,683 ) (54,683 ) Net income (loss) available to Arch 910,708 6,774 917,482 Preferred dividends (20,806 ) — (20,806 ) Net income (loss) available to Arch common shareholders $ 889,902 $ 6,774 $ 896,676 Underwriting Ratios Loss ratio 65.1 % 67.4 % 5.5 % 49.9 % 74.7 % 52.5 % Acquisition expense ratio 15.2 % 15.6 % 9.5 % 13.8 % 19.7 % 14.4 % Other operating expense ratio 19.5 % 9.8 % 11.8 % 14.7 % 9.3 % 14.1 % Combined ratio 99.8 % 92.8 % 26.8 % 78.4 % 103.7 % 81.0 % (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_2

Reserve for Losses and Loss Adjustment Expenses (Tables)	6 Months Ended
	Jun. 30, 2020
Liability for Future Policy Benefits and Unpaid Claims and Claims Adjustment Expense [Abstract]
Analysis of losses and loss adjustment expenses and reconciliation of beginning and ending reserve balances	The following table represents an analysis of losses and loss adjustment expenses and a reconciliation of the beginning and ending reserve for losses and loss adjustment expenses: Three Months Ended Six Months Ended June 30, June 30, 2020 2019 2020 2019 Reserve for losses and loss adjustment expenses at beginning of period $ 14,309,580 $ 12,010,041 $ 13,891,842 $ 11,853,297 Unpaid losses and loss adjustment expenses recoverable 4,070,114 2,970,159 4,082,650 2,814,291 Net reserve for losses and loss adjustment expenses at beginning of period 10,239,466 9,039,882 9,809,192 9,039,006 Net incurred losses and loss adjustment expenses relating to losses occurring in: Current year 1,274,589 805,728 2,409,031 1,563,692 Prior years (44,067 ) (38,185 ) (63,090 ) (77,617 ) Total net incurred losses and loss adjustment expenses 1,230,522 767,543 2,345,941 1,486,075 Retroactive reinsurance transactions (1) — — 60,635 (225,500 ) Net foreign exchange (gains) losses 51,157 (1,277 ) (91,416 ) (1,781 ) Net paid losses and loss adjustment expenses relating to losses occurring in: Current year (128,174 ) (61,148 ) (169,434 ) (125,488 ) Prior years (504,254 ) (539,481 ) (1,066,201 ) (966,793 ) Total net paid losses and loss adjustment expenses (632,428 ) (600,629 ) (1,235,635 ) (1,092,281 ) Net reserve for losses and loss adjustment expenses at end of period 10,888,717 9,205,519 10,888,717 9,205,519 Unpaid losses and loss adjustment expenses recoverable 4,156,157 3,024,797 4,156,157 3,024,797 Reserve for losses and loss adjustment expenses at end of period $ 15,044,874 $ 12,230,316 $ 15,044,874 $ 12,230,316 (1) During 2020 first quarter, a subsidiary of the Company entered into a reinsurance to close agreement of the 2017 and prior years of account previously covered by a third party arrangement, while in the 2019 first quarter, a subsidiary of the Company entered into a retroactive reinsurance transaction with third party reinsurer to reinsure run-off liabilities associated with certain U.S. insurance exposures.

Allowance for Expected Credit_2

Allowance for Expected Credit Losses (Tables)	6 Months Ended
	Jun. 30, 2020
Credit Loss [Abstract]
Premiums receivable	The following table provides a roll forward of the allowance for expected credit losses of the Company’s premium receivables: June 30, 2020 Premium Receivables, Net of Allowance Allowance for Expected Credit Losses Three Months Ended Balance at beginning of period $ 2,155,204 $ 27,990 Cumulative effect of accounting change (1) — Change for provision of expected credit losses (2) 8,064 Balance at end of period $ 2,203,753 $ 36,054 Six Months Ended Balance at beginning of period $ 1,778,717 $ 21,003 Cumulative effect of accounting change (1) 6,539 Change for provision of expected credit losses (2) 8,512 Balance at end of period $ 2,203,753 $ 36,054 (1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)” See note 1 . (2) Amounts deemed uncollectible are written-off in operating expenses. For the 2020 second quarter and six months ended June 30, 2020 , amounts written off totaled $1.8 million and $2.3 million , respectively.
Reinsurance recoverables	The following table provides a roll forward of the allowance for expected credit losses of the Company’s reinsurance recoverables: June 30, 2020 Reinsurance Recoverables, Net of Allowance Allowance for Expected Credit Losses Three Months Ended Balance at beginning of period $ 4,303,135 $ 13,700 Cumulative effect of accounting change (1) — Change for provision of expected credit losses (105 ) Balance at end of period $ 4,363,507 $ 13,595 Six Months Ended Balance at beginning of period $ 4,346,816 $ 1,364 Cumulative effect of accounting change (1) 12,010 Change for provision of expected credit losses 221 Balance at end of period $ 4,363,507 $ 13,595 (1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)” See note 1 .
Contractholder receivables	The following table provides a roll forward of the allowance for expected credit losses of the Company’s contractholder receivables: June 30, 2020 Contractholder Receivables, Net of Allowance Allowance for Expected Credit Losses Three Months Ended Balance at beginning of period $ 2,140,724 $ 9,038 Cumulative effect of accounting change (1) — Change for provision of expected credit losses (2,748 ) Balance at end of period $ 2,179,124 $ 6,290 Six Months Ended Balance at beginning of period $ 2,119,460 $ — Cumulative effect of accounting change (1) 6,663 Change for provision of expected credit losses (373 ) Balance at end of period $ 2,179,124 $ 6,290 (1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)” See note 1 .

Investment Information (Tables)

Investment Information (Tables)	6 Months Ended
	Jun. 30, 2020
Disclosure Investment Information [Abstract]
Summary of fair value and cost or amortized cost of available for sale securities	The following table summarizes the fair value and cost or amortized cost of the Company’s securities classified as available for sale: Estimated Fair Value Gross Unrealized Gains Gross Unrealized Losses Allowance for Expected Credit Losses (2) Cost or Amortized Cost June 30, 2020 Fixed maturities (1): Corporate bonds $ 7,143,600 $ 405,579 $ (34,700 ) $ (4,116 ) $ 6,776,837 Mortgage backed securities 610,839 12,417 (5,245 ) (222 ) 603,889 Municipal bonds 517,089 25,222 (542 ) (28 ) 492,437 Commercial mortgage backed securities 395,682 7,603 (8,005 ) (109 ) 396,193 U.S. government and government agencies 5,192,991 64,502 (2,708 ) — 5,131,197 Non-U.S. government securities 2,171,955 71,666 (43,928 ) — 2,144,217 Asset backed securities 1,633,481 31,410 (39,421 ) (1,394 ) 1,642,886 Total 17,665,637 618,399 (134,549 ) (5,869 ) 17,187,656 Short-term investments 2,277,866 2,087 (634 ) — 2,276,413 Total $ 19,943,503 $ 620,486 $ (135,183 ) $ (5,869 ) $ 19,464,069 December 31, 2019 Fixed maturities (1): Corporate bonds $ 6,406,591 $ 191,889 $ (12,793 ) $ 6,227,495 Mortgage backed securities 562,309 9,669 (931 ) 553,571 Municipal bonds 881,926 24,628 (2,213 ) 859,511 Commercial mortgage backed securities 733,108 14,951 (2,330 ) 720,487 U.S. government and government agencies 4,916,592 36,600 (10,134 ) 4,890,126 Non-U.S. government securities 2,078,757 48,549 (20,330 ) 2,050,538 Asset backed securities 1,683,753 24,017 (4,724 ) 1,664,460 Total 17,263,036 350,303 (53,455 ) 16,966,188 Short-term investments 956,546 811 (1,548 ) 957,283 Total $ 18,219,582 $ 351,114 $ (55,003 ) $ 17,923,471 (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)
Summary of available for sale securities in a continual unrealized loss position	The following table summarizes, for all available for sale securities in an unrealized loss position, the fair value and gross unrealized loss by length of time the security has been in a continual unrealized loss position: Less than 12 Months 12 Months or More Total Estimated Gross Unrealized Losses Estimated Gross Unrealized Losses Estimated Gross Unrealized Losses June 30, 2020 Fixed maturities (1): Corporate bonds $ 737,840 $ (32,848 ) $ 8,726 $ (1,852 ) $ 746,566 $ (34,700 ) Mortgage backed securities 150,547 (5,212 ) 108 (33 ) 150,655 (5,245 ) Municipal bonds 46,969 (542 ) — — 46,969 (542 ) Commercial mortgage backed securities 205,336 (7,858 ) 2,523 (147 ) 207,859 (8,005 ) U.S. government and government agencies 412,319 (2,708 ) — — 412,319 (2,708 ) Non-U.S. government securities 1,371,109 (43,928 ) — — 1,371,109 (43,928 ) Asset backed securities 721,451 (37,069 ) 32,198 (2,352 ) 753,649 (39,421 ) Total 3,645,571 (130,165 ) 43,555 (4,384 ) 3,689,126 (134,549 ) Short-term investments 1,025,993 (634 ) — — 1,025,993 (634 ) Total $ 4,671,564 $ (130,799 ) $ 43,555 $ (4,384 ) $ 4,715,119 $ (135,183 ) December 31, 2019 Fixed maturities (1): Corporate bonds $ 675,131 $ (12,350 ) $ 37,671 $ (443 ) $ 712,802 $ (12,793 ) Mortgage backed securities 102,887 (927 ) 203 (4 ) 103,090 (931 ) Municipal bonds 220,296 (2,213 ) — — 220,296 (2,213 ) Commercial mortgage backed securities 147,290 (2,302 ) 2,683 (28 ) 149,973 (2,330 ) U.S. government and government agencies 1,373,127 (10,089 ) 32,058 (45 ) 1,405,185 (10,134 ) Non-U.S. government securities 1,224,243 (20,163 ) 37,610 (167 ) 1,261,853 (20,330 ) Asset backed securities 441,522 (3,334 ) 48,313 (1,390 ) 489,835 (4,724 ) Total 4,184,496 (51,378 ) 158,538 (2,077 ) 4,343,034 (53,455 ) Short-term investments 95,777 (1,548 ) — — 95,777 (1,548 ) Total $ 4,280,273 $ (52,926 ) $ 158,538 $ (2,077 ) $ 4,438,811 $ (55,003 ) (1) In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”
Contractual maturities of the Company's fixed maturities and fixed maturities pledged under securities lending arrangements	The contractual maturities of the Company’s fixed maturities are shown in the following table. Expected maturities, which are management’s best estimates, will differ from contractual maturities because borrowers may have the right to call or prepay obligations with or without call or prepayment penalties. June 30, 2020 December 31, 2019 Maturity Estimated Fair Value Amortized Cost Estimated Amortized Cost Due in one year or less $ 344,032 $ 339,451 $ 428,659 $ 423,617 Due after one year through five years 9,873,345 9,645,073 10,126,403 9,996,206 Due after five years through 10 years 4,379,828 4,163,392 3,317,535 3,219,567 Due after 10 years 428,430 396,772 411,269 388,280 15,025,635 14,544,688 14,283,866 14,027,670 Mortgage backed securities 610,839 603,889 562,309 553,571 Commercial mortgage backed securities 395,682 396,193 733,108 720,487 Asset backed securities 1,633,481 1,642,886 1,683,753 1,664,460 Total (1) $ 17,665,637 $ 17,187,656 $ 17,263,036 $ 16,966,188 (1) In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”
Securities lending transactions accounted for as secured borrowings, by significant investment category	The carrying value of collateral held under the Company’s securities lending transactions by significant investment category and remaining contractual maturity of the underlying agreements is as follows: Remaining Contractual Maturity of the Agreements Overnight and Continuous Less than 30 Days 30-90 Days 90 Days or More Total June 30, 2020 U.S. government and government agencies $ 291,730 $ — $ 153,552 $ — $ 445,282 Corporate bonds 2,336 — — — 2,336 Equity securities 26,165 — — — 26,165 Total $ 320,231 $ — $ 153,552 $ — $ 473,783 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 $ 473,783 December 31, 2019 U.S. government and government agencies $ 240,332 $ — $ 115,973 $ — $ 356,305 Corporate bonds 2,570 — — — 2,570 Equity securities 29,491 — — — 29,491 Total $ 272,393 $ — $ 115,973 $ — $ 388,366 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 $ 388,366
Summary of other investments	The following table summarizes the Company’s other investments which are included in investments accounted for using the fair value option, by strategy: June 30, December 31, Term loan investments $ 1,109,031 $ 1,326,018 Lending 579,320 602,841 Credit related funds 92,970 123,020 Energy 66,667 97,402 Investment grade fixed income 133,936 151,594 Infrastructure 48,427 61,786 Private equity 72,888 49,376 Real estate 19,251 17,279 Total $ 2,122,490 $ 2,429,316
Summary of investments accounted for using equity method	The following table summarizes the Company’s investments accounted for using the equity method, by strategy: June 30, December 31, Credit related funds $ 624,382 $ 428,437 Equities 292,499 293,686 Real estate 249,822 246,851 Lending 137,270 202,690 Private equity 181,492 144,983 Infrastructure 141,972 235,033 Energy 99,865 108,716 Total $ 1,727,302 $ 1,660,396
Summary of assets and liabilities accounted for using the fair value option	The following table summarizes the Company’s assets which are accounted for using the fair value option: June 30, December 31, Fixed maturities $ 923,804 $ 754,452 Other investments 2,122,490 2,429,316 Short-term investments 384,382 377,014 Equity securities 90,095 102,695 Investments accounted for using the fair value option $ 3,520,771 $ 3,663,477
Summary of investments in limited partnership interests where the Company has a variable interest	The following table summarizes investments in limited partnership interests where the Company has a variable interest by balance sheet line item: June 30, December 31, Investments accounted for using the equity method (1) 1,727,302 1,660,396 Investments accounted for using the fair value option (2) 178,894 188,283 Total $ 1,906,196 $ 1,848,679 (1) Aggregate unfunded commitments were $1.44 billion at June 30, 2020 , compared to $1.36 billion at December 31, 2019 . (2) Aggregate unfunded commitments were $32.3 million at June 30, 2020 , compared to $41.7 million at December 31, 2019 .
Components of net investment income	The components of net investment income were derived from the following sources: June 30, 2020 2019 Three Months Ended Fixed maturities $ 105,391 $ 125,018 Term loans 20,512 24,730 Equity securities 6,219 4,368 Short-term investments 3,383 3,859 Other (1) 16,460 18,523 Gross investment income 151,965 176,498 Investment expenses (20,480 ) (21,460 ) Net investment income $ 131,485 $ 155,038 Six Months Ended Fixed maturities $ 220,238 $ 254,817 Term loans 43,682 49,346 Equity securities 12,226 7,356 Short-term investments 8,279 8,038 Other (1) 35,866 39,719 Gross investment income 320,291 359,276 Investment expenses (43,653 ) (47,289 ) Net investment income $ 276,638 $ 311,987 (1)
Summary of net realized gains (losses), excluding other-than-temporary impairment provisions	Net realized gains (losses), which include changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings were as follows: June 30, 2020 2019 Three Months Ended Available for sale securities: Gross gains on investment sales $ 232,153 $ 75,090 Gross losses on investment sales (49,824 ) (15,281 ) Change in fair value of assets and liabilities accounted for using the fair value option: Fixed maturities 68,181 11,429 Other investments 178,570 (33,780 ) Equity securities 6,664 6,414 Short-term investments 3,368 (1,392 ) Equity securities, at fair value: Net realized gains (losses) on sales during the period (18,250 ) (6,644 ) Net unrealized gains (losses) on equity securities still held at reporting date 145,686 22,632 Allowance for credit losses: Investments related 3,225 — Underwriting related (5,834 ) — Net impairment losses — (49 ) Derivative instruments (1) (836 ) 63,966 Other (6,515 ) (1,628 ) Net realized gains (losses) $ 556,588 $ 120,757 Six Months Ended Available for sale securities: Gross gains on investment sales $ 410,353 $ 118,455 Gross losses on investment sales (81,792 ) (46,937 ) Change in fair value of assets and liabilities accounted for using the fair value option: Fixed maturities (59,485 ) 42,577 Other investments (129,230 ) (15,585 ) Equity securities 1,755 10,680 Short-term investments (5,313 ) (672 ) Equity securities, at fair value: Net realized gains (losses) on sales during the period (18,789 ) 4,286 Net unrealized gains (losses) on equity securities still held at reporting date (29,880 ) 59,768 Allowance for credit losses: Investments related (6,095 ) — Underwriting related (9,104 ) — Net impairments losses (533 ) (1,358 ) Derivative instruments (1) 126,353 99,837 Other (8,612 ) (10,038 ) Net realized gains (losses) $ 189,628 $ 261,013 (1) See note 9 for information on the Company’s derivative instruments.
Rollforward of the allowance for expected credit losses of securities classified as available for sale	The following table provides a roll forward of the allowance for expected credit losses of the Company’s securities classified as available for sale: June 30, 2020 Structured Securities (1) Municipal Bonds Corporate Bonds Short Term Investments Total Three Months Ended Balance at beginning of period $ 2,654 $ 23 $ 7,232 $ 29 $ 9,938 Cumulative effect of accounting change — — — — — 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 ) Write-offs charged against the allowance — — — — — Balance at end of period $ 1,726 $ 28 $ 4,115 $ — $ 5,869 Six Months Ended Balance at beginning of period $ — $ — $ — $ — $ — Cumulative effect of accounting change 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 ) Write-offs charged against the allowance — — — — — 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.
Summary of restricted assets	The following table details the value of the Company’s restricted assets: June 30, December 31, Assets used for collateral or guarantees: Affiliated transactions $ 4,633,689 $ 4,526,761 Third party agreements 2,525,173 2,278,248 Deposits with U.S. regulatory authorities 862,859 797,371 Deposits with non-U.S. regulatory authorities 189,107 119,238 Total restricted assets $ 8,210,828 $ 7,721,618
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 $ 854,259 $ 726,230 Restricted cash (included in ‘other assets’) $ 210,424 $ 177,468 Cash and restricted cash $ 1,064,683 $ 903,698

Fair Value (Tables)

Fair Value (Tables)	6 Months Ended
	Jun. 30, 2020
Fair Value Disclosures [Abstract]
Fair value hierarchy	The following table presents the Company’s financial assets and liabilities measured at fair value by level at June 30, 2020 : Estimated Fair Value Measurements Using: Estimated Fair Value Quoted Prices in Active Markets for Identical Assets (Level 1) Significant Other Observable Inputs (Level 2) Significant Unobservable Inputs (Level 3) Assets measured at fair value (1): Available for sale securities: Fixed maturities: Corporate bonds $ 7,143,600 $ — $ 7,142,743 $ 857 Mortgage backed securities 610,839 — 610,621 218 Municipal bonds 517,089 — 517,089 — Commercial mortgage backed securities 395,682 — 395,682 — U.S. government and government agencies 5,192,991 5,077,056 115,935 — Non-U.S. government securities 2,171,955 — 2,171,955 — Asset backed securities 1,633,481 — 1,630,249 3,232 Total 17,665,637 5,077,056 12,584,274 4,307 Short-term investments 2,277,866 2,250,377 27,489 — Equity securities, at fair value 1,263,914 1,205,352 6,581 51,981 Derivative instruments (4) 96,909 — 96,909 — Fair value option: Corporate bonds 673,457 — 672,459 998 Non-U.S. government bonds 68,340 — 68,340 — Mortgage backed securities 14,142 — 14,142 — Municipal bonds 249 — 249 — Commercial mortgage backed securities 1,131 — 1,131 — Asset backed securities 165,890 — 165,890 — U.S. government and government agencies 595 483 112 — Short-term investments 384,382 370,286 14,096 — Equity securities 90,096 28,507 142 61,447 Other investments 1,167,345 39,493 1,081,399 46,453 Other investments measured at net asset value (2) 955,145 Total 3,520,772 438,769 2,017,960 108,898 Total assets measured at fair value $ 24,825,098 $ 8,971,554 $ 14,733,213 $ 165,186 Liabilities measured at fair value: Contingent consideration liabilities $ (1,250 ) $ — $ — $ (1,250 ) Securities sold but not yet purchased (3) (29,289 ) — (29,289 ) — Derivative instruments (4) (66,821 ) — (66,821 ) — Total liabilities measured at fair value $ (97,360 ) $ — $ (96,110 ) $ (1,250 ) (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, 2019 : Estimated Fair Value Measurements Using: Estimated Quoted Prices in Active Markets for Identical Assets (Level 1) Significant Other Observable Inputs (Level 2) Significant Unobservable Inputs (Level 3) Assets measured at fair value (1): Available for sale securities: Fixed maturities: Corporate bonds $ 6,406,591 $ — $ 6,397,740 $ 8,851 Mortgage backed securities 562,309 — 562,055 254 Municipal bonds 881,926 — 881,926 — Commercial mortgage backed securities 733,108 — 733,108 — U.S. government and government agencies 4,916,592 4,805,581 111,011 — Non-U.S. government securities 2,078,757 — 2,078,757 — Asset backed securities 1,683,753 — 1,678,791 4,962 Total 17,263,036 4,805,581 12,443,388 14,067 Short-term investments 956,546 904,804 51,742 — Equity securities, at fair value 850,283 789,596 4,798 55,889 Derivative instruments (4) 48,946 — 48,946 — Fair value option: Corporate bonds 488,402 — 487,470 932 Non-U.S. government bonds 50,465 — 50,465 — Mortgage backed securities 11,947 — 11,947 — Municipal bonds 377 — 377 — Commercial mortgage backed securities 1,134 — 1,134 — Asset backed securities 200,163 — 200,163 — U.S. government and government agencies 1,962 1,852 110 — Short-term investments 377,014 333,320 43,694 — Equity securities 102,697 43,962 641 58,094 Other investments 1,418,273 53,287 1,296,169 68,817 Other investments measured at net asset value (2) 1,011,043 Total 3,663,477 432,421 2,092,170 127,843 Total assets measured at fair value $ 22,782,288 $ 6,932,402 $ 14,641,044 $ 197,799 Liabilities measured at fair value: Contingent consideration liabilities $ (7,998 ) $ — $ — $ (7,998 ) Securities sold but not yet purchased (3) (66,257 ) — (66,257 ) — Derivative instruments (4) (39,750 ) — (39,750 ) — Total liabilities measured at fair value $ (114,005 ) $ — $ (106,007 ) $ (7,998 ) (1) In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See note 7 , “—Securities Lending Agreements.” (2) In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets. (3) Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets. (4) See note 9 .
Rollforward of Level 3 investments	The following table presents a reconciliation of the beginning and ending balances for all financial assets and liabilities measured at fair value on a recurring basis using Level 3 inputs: Assets Liabilities s Available For Sale Fair Value Option Fair Value Structured Securities (1) Corporate Corporate Other Investments Equity Securities Equity Securities Contingent Consideration Liabilities 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 ) Three Months Ended June 30, 2019 Balance at beginning of period $ 302 $ 7,567 $ 2,233 $ 62,329 $ — $ — $ (68,121 ) Total gains or (losses) (realized/unrealized) Included in earnings (2) — — (49 ) (11,614 ) — — (423 ) Included in other comprehensive income 1 102 — — — — — Purchases, issuances, sales and settlements Purchases — 429 — — — — — Issuances — — — — — — — Sales — — — (74 ) — — — Settlements (13 ) (456 ) — — — — 60,719 Transfers in and/or out of Level 3 — — 23,919 44,632 56,145 51,212 — Balance at end of period $ 290 $ 7,642 $ 26,103 $ 95,273 $ 56,145 $ 51,212 $ (7,825 ) 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 ) Six Months Ended June 30, 2019 Balance at beginning of year $ 313 $ 8,141 $ 5,758 $ 62,705 $ — $ — $ (66,665 ) Total gains or (losses) (realized/unrealized) Included in earnings (2) 1,757 — (339 ) (11,316 ) — — (1,331 ) Included in other comprehensive income 5 (16 ) — — — — — Purchases, issuances, sales and settlements Purchases — 429 — — — — — Issuances — — — — — — (548 ) Sales (1,757 ) — (3,235 ) (148 ) — — — Settlements (28 ) (912 ) — (600 ) — — 60,719 Transfers in and/or out of Level 3 — — 23,919 44,632 56,145 51,212 — Balance at end of period $ 290 $ 7,642 $ 26,103 $ 95,273 $ 56,145 $ 51,212 $ (7,825 ) (1) Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities. (2) Gains or losses were included in net realized gains (losses).

Derivative Instruments (Tables)

Derivative Instruments (Tables)	6 Months Ended
	Jun. 30, 2020
Derivative Instruments and Hedging Activities Disclosure [Abstract]
Fair value and notional amount of derivatives	The following table summarizes information on the fair values and notional values of the Company’s derivative instruments: Estimated Fair Value Asset Derivatives Liability Derivatives Notional Value (1) June 30, 2020 Futures contracts (2) $ 17,181 $ (5,894 ) $ 2,635,862 Foreign currency forward contracts (2) 12,366 (9,400 ) 1,073,432 TBAs (3) 5,973 — 5,740 Other (2) 67,362 (51,527 ) 3,398,053 Total $ 102,882 $ (66,821 ) December 31, 2019 Futures contracts (2) $ 10,065 $ (13,722 ) $ 4,104,559 Foreign currency forward contracts (2) 5,352 (5,327 ) 686,878 TBAs (3) 55,010 — 53,229 Other (2) 33,529 (20,701 ) 4,356,300 Total $ 103,956 $ (39,750 ) (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.’ (3) The fair value of TBAs are included in ‘fixed maturities available for sale, at fair value.’
Summary of net realized gains (losses) recorded in the consolidated statements of income	Realized and unrealized contract gains and losses on the Company’s derivative instruments are reflected in ‘net realized gains (losses)’ in the consolidated statements of income, as summarized in the following table: Derivatives not designated as June 30, hedging instruments: 2020 2019 Three Months Ended Net realized gains (losses): Futures contracts $ (1,607 ) $ 66,973 Foreign currency forward contracts 3,523 (5,365 ) TBAs 264 48 Other (3,016 ) 2,310 Total $ (836 ) $ 63,966 Six Months Ended Net realized gains (losses): Futures contracts $ 94,337 $ 94,309 Foreign currency forward contracts (7,347 ) (19,074 ) TBAs 1,009 238 Other 38,354 24,364 Total $ 126,353 $ 99,837

Leases (Tables)

Leases (Tables)	6 Months Ended
	Jun. 30, 2020
Leases [Abstract]
Additional information regarding operating leases	Additional information regarding the Company’s operating leases is as follows: June 30, 2020 2019 Three Months Ended Operating lease costs $ 7,821 $ 7,244 Cash payments included in the measurement of lease liabilities reported in operating cash flows 5,844 7,685 Right-of-use assets obtained in exchange for new lease liabilities 435 4,420 Right-of-use assets (1) 119,494 134,061 Operating lease liability (1) 139,772 150,341 Weighted average discount rate 3.9 % 3.9 % Weighted average remaining lease term 6.1 years 6.5 years Six Months Ended Operating lease costs $ 15,812 $ 14,860 Cash payments included in the measurement of lease liabilities reported in operating cash flows 14,305 14,585 Right-of-use assets obtained in exchange for new lease liabilities 3,885 4,420 Right-of-use assets (1) 119,494 134,061 Operating lease liability (1) 139,772 150,341 Weighted average discount rate 3.9 % 3.9 % Weighted average remaining lease term 6.1 years 6.5 years (1) The right-of-use assets are included in ‘other assets’ while the operating lease liability is included in ‘other liabilities.’
Contractual maturities of lease liabilities	The following table presents the contractual maturities of the Company's operating lease liabilities at June 30, 2020 : Years Ending December 31, 2020 (remainder) $ 15,835 2021 31,475 2022 28,341 2023 23,820 2024 17,601 2025 and thereafter 40,139 Total undiscounted lease liability $ 157,211 Less: present value adjustment (17,439 ) Operating lease liability $ 139,772

Variable Interest Entities an_2

Variable Interest Entities and Noncontrolling Interests (Tables)	6 Months Ended
	Jun. 30, 2020
Noncontrolling Interest [Abstract]
Carrying value of assets and liabilities of variable interest entity	The following table provides the carrying amount and balance sheet caption in which the assets and liabilities of Watford are reported: June 30, December 31, 2020 2019 Assets Investments accounted for using the fair value option $ 1,886,676 $ 1,898,091 Fixed maturities available for sale, at fair value 690,225 745,708 Equity securities, at fair value 62,443 65,338 Cash 107,653 102,437 Accrued investment income 14,364 14,025 Premiums receivable 258,178 273,657 Reinsurance recoverable on unpaid and paid losses and LAE 229,746 170,973 Ceded unearned premiums 131,919 132,577 Deferred acquisition costs 64,149 64,044 Receivable for securities sold 31,314 16,287 Goodwill and intangible assets 7,650 7,650 Other assets 63,441 60,070 Total assets of consolidated VIE $ 3,547,758 $ 3,550,857 Liabilities Reserve for losses and loss adjustment expenses $ 1,353,049 $ 1,263,628 Unearned premiums 456,170 438,907 Reinsurance balances payable 72,776 77,066 Revolving credit agreement borrowings 335,587 484,287 Senior notes 172,554 172,418 Payable for securities purchased 67,272 18,180 Other liabilities (1) 261,267 171,714 Total liabilities of consolidated VIE $ 2,718,675 $ 2,626,200 Redeemable noncontrolling interests $ 52,351 $ 52,305 (1) Includes certain borrowings related to investing activities.
Activity in non-redeemable noncontrolling interests	The following table sets forth activity in the non-redeemable noncontrolling interests: June 30, 2020 2019 Three Months Ended Balance, beginning of period $ 492,785 $ 838,081 Additional paid in capital attributable to noncontrolling interests 595 2,074 Amounts attributable to noncontrolling interests 165,598 12,301 Other comprehensive income (loss) attributable to noncontrolling interests 20,111 2,891 Balance, end of period $ 679,089 $ 855,347 Six Months Ended Balance, beginning of year $ 762,777 $ 791,560 Additional paid in capital attributable to noncontrolling interests 472 2,074 Repurchases attributable to non-redeemable noncontrolling interests (1) (2,867 ) — Amounts attributable to noncontrolling interests (68,346 ) 54,683 Other comprehensive income (loss) attributable to noncontrolling interests (12,947 ) 7,030 Balance, end of period $ 679,089 $ 855,347 (1) During 2020, Watford’s board of directors authorized the investment in Watford’s common shares through a share repurchase program.
Activity in redeemable noncontrolling interests	The following table sets forth activity in the redeemable non-controlling interests: June 30, 2020 2019 Three Months Ended Balance, beginning of period $ 55,376 $ 206,383 Accretion of preference share issuance costs 23 92 Other 587 — Balance, end of period $ 55,986 $ 206,475 Six Months Ended Balance, beginning of year $ 55,404 $ 206,292 Accretion of preference share issuance costs 46 183 Other 536 — Balance, end of period $ 55,986 $ 206,475
Portion of income or loss attributable to third party investors	The portion of income or loss attributable to third party investors, recorded in the Company’s consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests,’ are summarized in the table below: June 30, 2020 2019 Three Months Ended Amounts attributable to non-redeemable noncontrolling interests $ (165,598 ) $ (12,301 ) Amounts attributable to redeemable noncontrolling interests (1,970 ) (4,590 ) Net (income) loss attributable to noncontrolling interests $ (167,568 ) $ (16,891 ) Six Months Ended Amounts attributable to non-redeemable noncontrolling interests $ 68,346 $ (54,683 ) Amounts attributable to redeemable noncontrolling interests (3,123 ) (9,178 ) Net (income) loss attributable to noncontrolling interests $ 65,223 $ (63,861 )
Total assets and maximum exposure to loss associated with VIEs	The following table presents the total assets of the Bellemeade entities, as well as the Company’s maximum exposure to loss associated with these VIEs, calculated as the maximum historical observable spread between the one month LIBOR, the basis for the contractual payments to bond holders, and short term invested trust asset yields. Maximum Exposure to Loss Bellemeade Entities (Issue Date) Total VIE Assets On-Balance Sheet (Asset) Liability Off-Balance Sheet Total Jun 30, 2020 Bellemeade 2017-1 Ltd. (Oct-17) $ 145,573 $ (295 ) $ 2,469 $ 2,174 Bellemeade 2018-1 Ltd. (Apr-18) 250,095 (1,244 ) 5,597 4,353 Bellemeade 2018-2 Ltd. (Aug-18) 272,685 (1,206 ) 4,210 3,004 Bellemeade 2018-3 Ltd. (Oct-18) 302,563 (1,883 ) 8,387 6,504 Bellemeade 2019-1 Ltd. (Mar-19) 219,256 (83 ) 10,251 10,168 Bellemeade 2019-2 Ltd. (Apr-19) 398,316 54 13,088 13,142 Bellemeade 2019-3 Ltd. (Jul-19) 528,084 (248 ) 10,649 10,401 Bellemeade 2019-4 Ltd. (Oct-19) 468,737 257 14,687 14,944 Bellemeade 2020-1 Ltd. (Jun-20) (1) 450,040 (60 ) 8,984 8,924 Total $ 3,035,349 $ (4,708 ) $ 78,322 $ 73,614 Dec 31, 2019 Bellemeade 2017-1 Ltd. (Oct-17) $ 216,429 $ (442 ) $ 2,794 $ 2,352 Bellemeade 2018-1 Ltd. (Apr-18) 328,482 (1,574 ) 5,757 4,183 Bellemeade 2018-2 Ltd. (Aug-18) 437,009 (877 ) 2,524 1,647 Bellemeade 2018-3 Ltd. (Oct-18) 426,806 (1,113 ) 3,937 2,824 Bellemeade 2019-1 Ltd. (Mar-19) 257,358 (226 ) 3,027 2,801 Bellemeade 2019-2 Ltd. (Apr-19) 525,959 (78 ) 2,579 2,501 Bellemeade 2019-3 Ltd. (Jul-19) 656,523 (585 ) 9,273 8,688 Bellemeade 2019-4 Ltd. (Oct-19) 577,267 (302 ) 12,193 11,891 Total $ 3,425,833 $ (5,197 ) $ 42,084 $ 36,887 (1) An additional $78.5 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, 2020
Comprehensive Income Note Disclosure [Abstract]
Details about amounts reclassified from AOCI	The following tables present details about amounts reclassified from accumulated other comprehensive income and the tax effects allocated to each component of other comprehensive income (loss): Amounts Reclassified from AOCI Consolidated Statement of Income Three Months Ended Six Months Ended Details About Line Item That Includes June 30, June 30, AOCI Components Reclassification 2020 2019 2020 2019 Unrealized appreciation on available-for-sale investments Net realized gains (losses) $ 182,329 $ 59,809 $ 328,561 $ 71,518 Provision for credit losses 3,225 (6,095 ) Other-than-temporary impairment losses — (49 ) (533 ) (1,358 ) Total before tax 185,554 59,760 321,933 70,160 Income tax (expense) benefit (18,163 ) (4,415 ) (33,313 ) (4,594 ) Net of tax $ 167,391 $ 55,345 $ 288,620 $ 65,566
Schedule of comprehensive income (loss)	Before Tax Amount Tax Expense (Benefit) Net of Tax Amount 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 Three Months Ended June 30, 2019 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ 248,074 $ 25,601 $ 222,473 Less reclassification of net realized gains (losses) included in net income 59,760 4,415 55,345 Foreign currency translation adjustments 4,409 142 4,267 Other comprehensive income (loss) $ 192,723 $ 21,328 $ 171,395 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 Six Months Ended June 30, 2019 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ 503,064 $ 54,704 $ 448,360 Less reclassification of net realized gains (losses) included in net income 70,160 4,594 65,566 Foreign currency translation adjustments 10,053 270 9,783 Other comprehensive income (loss) $ 442,957 $ 50,380 $ 392,577

Basis of Presentation and Rec_3

Basis of Presentation and Recent Accounting Pronouncements (Details) - USD ($) $ in Thousands	6 Months Ended
	Jun. 30, 2020	Dec. 31, 2019	Jun. 30, 2019
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Accounting Standards Update	us-gaap:AccountingStandardsUpdate201613Member
Total shareholders' equity available to Arch	$ 11,991,825	$ 11,497,371	$ 10,757,352
Cumulative effect of an accounting change | Retained earnings
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Total shareholders' equity available to Arch		$ 22,500

Share Transactions - Share repu

Share Transactions - Share repurchases (Details) - USD ($) shares in Millions, $ in Millions	6 Months Ended
	Jun. 30, 2020	Jun. 30, 2019
Class of Stock [Line Items]
Treasury stock, shares acquired (shares)	2.6	0.1
Shares repurchased for treasury	$ 75.5	$ 2.9
Common shares
Class of Stock [Line Items]
Cumulative number of shares acquired since inception of share repurchase program	388.9
Aggregate purchase price of shares acquired since inception of share repurchase program	$ 4,040
Remaining authorized repurchase amount	$ 924.5

Earnings Per Common Share (Deta

Earnings Per Common Share (Details) - USD ($) $ / shares in Units, $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2020	Jun. 30, 2019	Jun. 30, 2020	Jun. 30, 2019
Numerator:
Net income (loss)		$ 466,389	$ 485,845	$ 377,715	$ 981,343
Amounts attributable to noncontrolling interests		(167,568)	(16,891)	65,223	(63,861)
Net income available to Arch		298,821	468,954	442,938	917,482
Preferred dividends		(10,403)	(10,403)	(20,806)	(20,806)
Net income available to Arch common shareholders		$ 288,418	$ 458,551	$ 422,132	$ 896,676
Denominator:
Weighted average common shares outstanding — basic		402,503,687	401,482,784	403,197,924	400,837,181
Effect of dilutive common share equivalents:
Nonvested restricted shares		1,597,701	1,937,626	1,829,239	1,720,417
Stock options	[1]	4,018,293	7,479,073	5,978,428	7,197,652
Weighted average common shares and common share equivalents outstanding — diluted		408,119,681	410,899,483	411,005,591	409,755,250
Earnings per common share:
Basic (per share)		$ 0.72	$ 1.14	$ 1.05	$ 2.24
Diluted (per share)		$ 0.71	$ 1.12	$ 1.03	$ 2.19
Stock options
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Antidilutive securities excluded from computation of earnings per common share (shares)		6,982,107	2,016,830	2,038,758	2,560,755
[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 2020 second quarter and 2019 second quarter , the number of stock options excluded were 6,982,107 and 2,016,830 , respectively. For the six months ended June 30, 2020 and 2019 period, the number of stock options excluded were 2,038,758 and 2,560,755 , respectively.

Segment Information - Summary o

Segment Information - Summary of underwriting income or loss by segment (Details) $ in Thousands		3 Months Ended			6 Months Ended
		Jun. 30, 2020USD ($)		Jun. 30, 2019USD ($)	Jun. 30, 2020USD ($)segment		Jun. 30, 2019USD ($)		Dec. 31, 2019USD ($)
Segment Reporting Information [Line Items]
Gross premiums written		$ 2,317,692		$ 1,937,809	$ 5,150,522		$ 4,015,688
Premiums ceded		(649,381)		(492,911)	(1,344,965)		(1,045,531)
Net premiums written		1,668,311		1,444,898	3,805,557		2,970,157
Change in unearned premiums		(2,957)		18,829	(395,759)		(137,564)
Net premiums earned		1,665,354		1,463,727	3,409,798		2,832,593
Other underwriting income		6,667		5,953	13,519		14,778
Losses and loss adjustment expenses		(1,230,522)		(767,543)	(2,345,941)		(1,486,075)
Acquisition expenses, net		(254,789)		(210,089)	(502,072)		(407,937)
Other operating expenses		(209,249)		(198,914)	(443,793)		(400,077)
Underwriting income (loss)		(22,539)		293,134	131,511		553,282
Net investment income		131,485		155,038	276,638		311,987
Net realized gains (losses)		556,588		120,757	189,628		261,013
Equity in net income (loss) of investment funds accounted for using the equity method		(65,119)		32,536	(69,328)		79,403
Other income (loss)		(3,140)		1,129	5,408		2,212
Corporate expenses		(16,943)		(16,073)	(35,144)		(32,845)
Transaction costs and other		(977)	[1]	(2,178)	(3,572)	[1]	(3,368)	[1]
Amortization of intangible assets		(16,489)		(19,794)	(33,120)		(40,211)
Interest expense		(31,139)		(29,280)	(63,694)		(58,345)
Net foreign exchange gains (losses)		(39,211)		(4,952)	33,460		(1,427)
Income (loss) before income taxes		492,516		530,317	431,787		1,071,701
Income tax expense		(26,127)		(44,472)	(54,072)		(90,358)
Net income (loss)		466,389		485,845	377,715		981,343
Dividends attributable to redeemable noncontrolling interests		(1,970)		(4,590)	(3,123)		(9,178)
Amounts attributable to non-redeemable noncontrolling interests		(165,598)		(12,301)	68,346		(54,683)
Net income (loss) available to Arch		298,821		468,954	442,938		917,482
Preferred dividends		(10,403)		(10,403)	(20,806)		(20,806)
Net income available to Arch common shareholders		$ 288,418		$ 458,551	$ 422,132		$ 896,676
Underwriting Ratios
Loss ratio		73.90%		52.40%	68.80%		52.50%
Acquisition expense ratio		15.30%		14.40%	14.70%		14.40%
Other operating expense ratio		12.60%		13.60%	13.00%		14.10%
Combined ratio		101.80%		80.40%	96.50%		81.00%
Goodwill and intangible assets		$ 688,490		$ 641,010	$ 688,490		$ 641,010		$ 738,083
Other
Segment Reporting Information [Line Items]
Number of segments | segment					2
Gross premiums written	[2]	157,927		161,978	$ 392,829		348,667
Premiums ceded		(52,071)		(42,608)	(100,273)		(83,910)
Net premiums written		105,856		119,370	292,556		264,757
Change in unearned premiums		25,679		31,948	(20,982)		32,655
Net premiums earned		131,535		151,318	271,574		297,412
Other underwriting income		868		673	1,001		1,265
Losses and loss adjustment expenses		(104,786)		(111,416)	(215,462)		(222,266)
Acquisition expenses, net		(22,544)		(29,556)	(44,348)		(58,582)
Other operating expenses		(14,202)		(15,612)	(27,904)		(27,800)
Underwriting income (loss)		(9,129)		(4,593)	(15,139)		(9,971)
Net investment income		30,454		32,000	62,579		67,700
Net realized gains (losses)		171,499		(4,306)	(123,352)		24,826
Equity in net income (loss) of investment funds accounted for using the equity method		0		0	0		0
Other income (loss)		0		0	0		0
Corporate expenses	[1]	0		0	0		0
Transaction costs and other	[1]	0		0	0		0
Amortization of intangible assets		0		0	0		0
Interest expense		(6,009)		(5,905)	(13,319)		(11,488)
Net foreign exchange gains (losses)		3,227		1,238	12,591		(412)
Income (loss) before income taxes		190,042		18,434	(76,640)		70,655
Income tax expense		402		(20)	402		(20)
Net income (loss)		190,444		18,414	(76,238)		70,635
Dividends attributable to redeemable noncontrolling interests		(1,036)		(4,590)	(2,132)		(9,178)
Amounts attributable to non-redeemable noncontrolling interests		(165,598)		(12,301)	68,346		(54,683)
Net income (loss) available to Arch		23,810		1,523	(10,024)		6,774
Preferred dividends		0		0	0		0
Net income available to Arch common shareholders		$ 23,810		$ 1,523	$ (10,024)		$ 6,774
Underwriting Ratios
Loss ratio		79.70%		73.60%	79.30%		74.70%
Acquisition expense ratio		17.10%		19.50%	16.30%		19.70%
Other operating expense ratio		10.80%		10.30%	10.30%		9.30%
Combined ratio		107.60%		103.40%	105.90%		103.70%
Goodwill and intangible assets		$ 7,650		$ 7,650	$ 7,650		$ 7,650
Sub-Total
Segment Reporting Information [Line Items]
Number of segments | segment					3
Gross premiums written	[2]	2,206,410		1,829,829	$ 4,904,947		3,810,282
Premiums ceded		(643,955)		(504,301)	(1,391,946)		(1,104,882)
Net premiums written		1,562,455		1,325,528	3,513,001		2,705,400
Change in unearned premiums		(28,636)		(13,119)	(374,777)		(170,219)
Net premiums earned		1,533,819		1,312,409	3,138,224		2,535,181
Other underwriting income		5,799		5,280	12,518		13,513
Losses and loss adjustment expenses		(1,125,736)		(656,127)	(2,130,479)		(1,263,809)
Acquisition expenses, net		(232,245)		(180,533)	(457,724)		(349,355)
Other operating expenses		(195,047)		(183,302)	(415,889)		(372,277)
Underwriting income (loss)		(13,410)		297,727	146,650		563,253
Net investment income		101,031		123,038	214,059		244,287
Net realized gains (losses)		385,089		125,063	312,980		236,187
Equity in net income (loss) of investment funds accounted for using the equity method		(65,119)		32,536	(69,328)		79,403
Other income (loss)		(3,140)		1,129	5,408		2,212
Corporate expenses	[1]	(16,943)		(16,073)	(35,144)		(32,845)
Transaction costs and other	[1]	(977)		(2,178)	(3,572)		(3,368)
Amortization of intangible assets		(16,489)		(19,794)	(33,120)		(40,211)
Interest expense		(25,130)		(23,375)	(50,375)		(46,857)
Net foreign exchange gains (losses)		(42,438)		(6,190)	20,869		(1,015)
Income (loss) before income taxes		302,474		511,883	508,427		1,001,046
Income tax expense		(26,529)		(44,452)	(54,474)		(90,338)
Net income (loss)		275,945		467,431	453,953		910,708
Dividends attributable to redeemable noncontrolling interests		(934)		0	(991)		0
Amounts attributable to non-redeemable noncontrolling interests		0		0	0		0
Net income (loss) available to Arch		275,011		467,431	452,962		910,708
Preferred dividends		(10,403)		(10,403)	(20,806)		(20,806)
Net income available to Arch common shareholders		$ 264,608		$ 457,028	$ 432,156		$ 889,902
Underwriting Ratios
Loss ratio		73.40%		50.00%	67.90%		49.90%
Acquisition expense ratio		15.10%		13.80%	14.60%		13.80%
Other operating expense ratio		12.70%		14.00%	13.30%		14.70%
Combined ratio		101.20%		77.80%	95.80%		78.40%
Goodwill and intangible assets		$ 680,840		$ 633,360	$ 680,840		$ 633,360
Sub-Total | Insurance
Segment Reporting Information [Line Items]
Gross premiums written	[2]	1,030,362		919,925	2,238,007		1,861,879
Premiums ceded		(358,101)		(292,095)	(736,998)		(612,717)
Net premiums written		672,261		627,830	1,501,009		1,249,162
Change in unearned premiums		15,648		(35,388)	(97,181)		(103,215)
Net premiums earned		687,909		592,442	1,403,828		1,145,947
Other underwriting income		0		0	0		0
Losses and loss adjustment expenses		(518,203)		(389,172)	(1,025,311)		(745,895)
Acquisition expenses, net		(107,671)		(91,094)	(215,008)		(173,918)
Other operating expenses		(118,757)		(109,523)	(248,406)		(222,919)
Underwriting income (loss)		$ (56,722)		$ 2,653	$ (84,897)		$ 3,215
Underwriting Ratios
Loss ratio		75.30%		65.70%	73.00%		65.10%
Acquisition expense ratio		15.70%		15.40%	15.30%		15.20%
Other operating expense ratio		17.30%		18.50%	17.70%		19.50%
Combined ratio		108.30%		99.60%	106.00%		99.80%
Goodwill and intangible assets		$ 263,086		$ 157,440	$ 263,086		$ 157,440
Sub-Total | Reinsurance
Segment Reporting Information [Line Items]
Gross premiums written	[2]	807,065		545,547	1,929,584		1,228,402
Premiums ceded		(241,971)		(169,457)	(567,310)		(401,024)
Net premiums written		565,094		376,090	1,362,274		827,378
Change in unearned premiums		(84,897)		(8,906)	(338,617)		(113,829)
Net premiums earned		480,197		367,184	1,023,657		713,549
Other underwriting income		(651)		1,224	1,469		5,601
Losses and loss adjustment expenses		(383,433)		(240,958)	(813,502)		(480,768)
Acquisition expenses, net		(90,522)		(56,785)	(170,128)		(111,111)
Other operating expenses		(38,716)		(33,960)	(84,013)		(69,664)
Underwriting income (loss)		$ (33,125)		$ 36,705	$ (42,517)		$ 57,607
Underwriting Ratios
Loss ratio		79.80%		65.60%	79.50%		67.40%
Acquisition expense ratio		18.90%		15.50%	16.60%		15.60%
Other operating expense ratio		8.10%		9.20%	8.20%		9.80%
Combined ratio		106.80%		90.30%	104.30%		92.80%
Goodwill and intangible assets		$ 2,516		$ 0	$ 2,516		$ 0
Sub-Total | Mortgage
Segment Reporting Information [Line Items]
Gross premiums written	[2]	369,144		364,465	738,089		720,515
Premiums ceded		(44,044)		(42,857)	(88,371)		(91,655)
Net premiums written		325,100		321,608	649,718		628,860
Change in unearned premiums		40,613		31,175	61,021		46,825
Net premiums earned		365,713		352,783	710,739		675,685
Other underwriting income		6,450		4,056	11,049		7,912
Losses and loss adjustment expenses		(224,100)		(25,997)	(291,666)		(37,146)
Acquisition expenses, net		(34,052)		(32,654)	(72,588)		(64,326)
Other operating expenses		(37,574)		(39,819)	(83,470)		(79,694)
Underwriting income (loss)		$ 76,437		$ 258,369	$ 274,064		$ 502,431
Underwriting Ratios
Loss ratio		61.30%		7.40%	41.00%		5.50%
Acquisition expense ratio		9.30%		9.30%	10.20%		9.50%
Other operating expense ratio		10.30%		11.30%	11.70%		11.80%
Combined ratio		80.90%		28.00%	62.90%		26.80%
Goodwill and intangible assets		$ 415,238		$ 475,920	$ 415,238		$ 475,920
[1]	Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’
[2]	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_3

Reserve for Losses and Loss Adjustment Expenses - Reconciliation of beginning and ending balances of losses and loss adjustment reserves (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2020	Jun. 30, 2019	Jun. 30, 2020	Jun. 30, 2019
Liability for Future Policy Benefits and Unpaid Claims and Claims Adjustment Expense [Abstract]
Reserve for losses and loss adjustment expenses at beginning of period		$ 14,309,580	$ 12,010,041	$ 13,891,842	$ 11,853,297
Unpaid losses and loss adjustment expenses recoverable		4,070,114	2,970,159	4,082,650	2,814,291
Net reserve for losses and loss adjustment expenses at beginning of period		10,239,466	9,039,882	9,809,192	9,039,006
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year		1,274,589	805,728	2,409,031	1,563,692
Prior years		(44,067)	(38,185)	(63,090)	(77,617)
Total net incurred losses and loss adjustment expenses		1,230,522	767,543	2,345,941	1,486,075
Retroactive reinsurance transaction	[1]	0	0	60,635	(225,500)
Net foreign exchange (gains) losses		51,157	(1,277)	(91,416)	(1,781)
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year		(128,174)	(61,148)	(169,434)	(125,488)
Prior years		(504,254)	(539,481)	(1,066,201)	(966,793)
Total net paid losses and loss adjustment expenses		(632,428)	(600,629)	(1,235,635)	(1,092,281)
Net reserve for losses and loss adjustment expenses at end of period		10,888,717	9,205,519	10,888,717	9,205,519
Unpaid losses and loss adjustment expenses recoverable		4,156,157	3,024,797	4,156,157	3,024,797
Reserve for losses and loss adjustment expenses at end of period		$ 15,044,874	$ 12,230,316	$ 15,044,874	$ 12,230,316
[1]	During 2020 first quarter, a subsidiary of the Company entered into a reinsurance to close agreement of the 2017 and prior years of account previously covered by a third party arrangement, while in the 2019 first quarter, a subsidiary of the Company entered into a retroactive reinsurance transaction with third party reinsurer to reinsure run-off liabilities associated with certain U.S. insurance exposures.

Reserve for Losses and Loss A_4

Reserve for Losses and Loss Adjustment Expenses - Prior year development (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2020	Jun. 30, 2019	Jun. 30, 2020	Jun. 30, 2019
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 44,067	$ 38,185	$ 63,090	$ 77,617
Underwriting segments | Insurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 2,500	$ 2,600	$ 3,600	$ 7,000
Percentage of prior year development	0.40%	0.40%	0.30%	0.60%
Underwriting 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	$ 8,000	$ 15,400	$ 17,700
Underwriting segments | Insurance | Short tailed lines | Property insurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	7,500		9,600
Underwriting 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)	3,500
Underwriting 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)			3,100
Underwriting 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)	(17,100)	(10,400)	(25,100)	(17,300)
Underwriting 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)	(15,500)	(6,300)	(23,200)
Underwriting segments | Insurance | Medium tailed lines | Contract binding
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(6,100)		(19,300)	(9,700)
Underwriting 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)
Underwriting segments | Insurance | Medium 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)		5,100		15,600
Underwriting 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)	19,700		28,700
Underwriting 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	4,900	13,300	6,600
Underwriting 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	5,100		5,700
Underwriting 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
Underwriting segments | Reinsurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 40,200	$ 12,700	$ 51,800	$ 11,000
Percentage of prior year development	8.40%	3.50%	5.10%	1.50%
Underwriting 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	$ 1,800	$ 65,700	$ (4,300)
Underwriting 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			(17,900)
Underwriting segments | Reinsurance | Short tailed lines | Property catastrophe and property other than property catastrophe | Typhoon Jebi
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)				(16,000)
Underwriting 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)	27,500			10,200
Underwriting 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)			67,400
Underwriting segments | Reinsurance | Short tailed and medium tailed lines | Property catastrophe
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)			21,300
Underwriting segments | Reinsurance | Short tailed and medium 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)			39,300
Underwriting 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)	10,900		15,300
Underwriting segments | Reinsurance | Medium tailed and long tailed lines | Casualty
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)				9,100
Underwriting segments | Reinsurance | Medium tailed and long tailed lines | Marine
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)				6,200
Underwriting 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)			(15,600)
Underwriting 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)	(5,800)
Underwriting segments | Mortgage
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 200	$ 22,800	$ 6,300	$ 59,400
Percentage of prior year development	0.10%	6.50%	0.90%	8.80%
Underwriting segments | Other
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 1,100	$ 100	$ 1,300	$ 100

Allowance for Expected Credit_3

Allowance for Expected Credit Losses - Premiums receivable (Details) - USD ($) $ in Thousands		3 Months Ended	6 Months Ended
		Jun. 30, 2020	Jun. 30, 2020
Credit Loss [Abstract]
Balance at beginning of period		$ 2,155,204	$ 1,778,717
Balance at end of period		2,203,753	2,203,753
Allowance for Expected Credit Losses
Balance at beginning of period		27,990	21,003
Cumulative effect of accounting change (1)	[1]	0	6,539
Change for provision of expected credit losses (2)	[2]	8,064	8,512
Balance at end of period		36,054	36,054
Write-offs charged against the allowance		$ 1,800	$ 2,300
[1]	Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”
[2]	Amounts deemed uncollectible are written-off in operating expenses. For the 2020 second quarter and six months ended June 30, 2020 , amounts written off totaled $1.8 million and $2.3 million , respectively.

Allowance for Expected Credit_4

Allowance for Expected Credit Losses - Reinsurance recoverables (Details) - USD ($) $ in Thousands		3 Months Ended	6 Months Ended
		Jun. 30, 2020	Jun. 30, 2020
Credit Loss [Abstract]
Balance at beginning of period		$ 4,303,135	$ 4,346,816
Balance at end of period		4,363,507	4,363,507
Allowance for Expected Credit Losses
Balance at beginning of period		13,700	1,364
Cumulative effect of accounting change (1)	[1]	0	12,010
Change for provision of expected credit losses		(105)	221
Balance at end of period		$ 13,595	$ 13,595
[1]	Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”

Allowance for Expected Credit_5

Allowance for Expected Credit Losses - Ceded credit risk (Details) - USD ($) $ in Millions	6 Months Ended	12 Months Ended
	Jun. 30, 2020	Dec. 31, 2019
Ceded Credit Risk [Line Items]
Reinsurance recoverable on unpaid and paid losses and LAE	$ 4,380	$ 4,350
Reinsurance recoverable | Credit concentration risk | AM Best A minus Or Better Rating
Ceded Credit Risk [Line Items]
Concentration risk percentage	63.10%	61.20%
Reinsurance recoverable | Credit concentration risk | Not Rated
Ceded Credit Risk [Line Items]
Concentration risk percentage	36.70%	38.80%
Reinsurance recoverable | Credit concentration risk | Not Rated | Reinsurance trusts or letters of credit
Ceded Credit Risk [Line Items]
Concentration risk percentage	90.00%
Stockholders' equity | Reinsurer concentration risk
Ceded Credit Risk [Line Items]
Concentration risk percentage	1.80%	1.70%

Allowance for Expected Credit_6

Allowance for Expected Credit Losses - Contractholder receivables (Details) - USD ($) $ in Thousands		3 Months Ended	6 Months Ended
		Jun. 30, 2020	Jun. 30, 2020
Credit Loss [Abstract]
Balance at beginning of period		$ 2,140,724	$ 2,119,460
Balance at end of period		2,179,124	2,179,124
Allowance for Expected Credit Losses
Balance at beginning of period		9,038	0
Cumulative effect of accounting change (1)	[1]	0	6,663
Change for provision of expected credit losses		(2,748)	(373)
Balance at end of period		$ 6,290	$ 6,290
[1]	Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”

Investment Information - Summar

Investment Information - Summary of available for sale securities (Details) - USD ($) $ in Thousands		Jun. 30, 2020		Mar. 31, 2020	Dec. 31, 2019
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		$ 17,207,731			$ 16,894,526
Estimated Fair Value		2,277,866			956,546
Estimated Fair Value		19,943,503			18,219,582
Gross Unrealized Gains		620,486			351,114
Gross Unrealized Losses		(135,183)			(55,003)
Allowance for expected credit losses		(5,869)		$ (9,938)	0
Amortized cost		16,733,493			16,598,808
Cost		2,276,413			957,283
Cost or Amortized Cost		19,464,069			17,923,471
Fixed maturities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	[1]	17,665,637			17,263,036
Gross Unrealized Gains	[1]	618,399			350,303
Gross Unrealized Losses	[1]	(134,549)			(53,455)
Allowance for expected credit losses	[1],[2]	(5,869)
Amortized cost	[1]	17,187,656			16,966,188
Fixed maturities | Corporate bonds
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		7,143,600			6,406,591
Gross Unrealized Gains	[1]	405,579			191,889
Gross Unrealized Losses	[1]	(34,700)			(12,793)
Allowance for expected credit losses	[1],[2]	(4,116)
Amortized cost	[1]	6,776,837			6,227,495
Fixed maturities | Mortgage backed securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		610,839			562,309
Gross Unrealized Gains	[1]	12,417			9,669
Gross Unrealized Losses	[1]	(5,245)			(931)
Allowance for expected credit losses	[1],[2]	(222)
Amortized cost	[1]	603,889			553,571
Fixed maturities | Municipal bonds
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		517,089			881,926
Gross Unrealized Gains	[1]	25,222			24,628
Gross Unrealized Losses	[1]	(542)			(2,213)
Allowance for expected credit losses	[1],[2]	(28)
Amortized cost	[1]	492,437			859,511
Fixed maturities | Commercial mortgage backed securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		395,682			733,108
Gross Unrealized Gains	[1]	7,603			14,951
Gross Unrealized Losses	[1]	(8,005)			(2,330)
Allowance for expected credit losses	[1],[2]	(109)
Amortized cost	[1]	396,193			720,487
Fixed maturities | US government and government agencies
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		5,192,991			4,916,592
Gross Unrealized Gains	[1]	64,502			36,600
Gross Unrealized Losses	[1]	(2,708)			(10,134)
Allowance for expected credit losses	[1],[2]	0
Amortized cost	[1]	5,131,197			4,890,126
Fixed maturities | Non-US government securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		2,171,955			2,078,757
Gross Unrealized Gains	[1]	71,666			48,549
Gross Unrealized Losses	[1]	(43,928)			(20,330)
Allowance for expected credit losses	[1],[2]	0
Amortized cost	[1]	2,144,217			2,050,538
Fixed maturities | Asset backed securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		1,633,481			1,683,753
Gross Unrealized Gains	[1]	31,410			24,017
Gross Unrealized Losses	[1]	(39,421)			(4,724)
Allowance for expected credit losses	[1],[2]	(1,394)
Amortized cost	[1]	1,642,886			1,664,460
Short-term investments
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		2,277,866			956,546
Gross Unrealized Gains		2,087			811
Gross Unrealized Losses		(634)			(1,548)
Allowance for expected credit losses		0	[2]	$ (29)	0
Cost		$ 2,276,413			$ 957,283
[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 Thousands		Jun. 30, 2020	Dec. 31, 2019
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months		$ 4,671,564	$ 4,280,273
Estimated Fair Value - 12 Months or More		43,555	158,538
Estimated Fair Value		4,715,119	4,438,811
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months		(130,799)	(52,926)
Gross Unrealized Losses - 12 Months or More		(4,384)	(2,077)
Gross Unrealized Losses		(135,183)	(55,003)
Fixed maturities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	[1]	3,645,571	4,184,496
Estimated Fair Value - 12 Months or More	[1]	43,555	158,538
Estimated Fair Value	[1]	3,689,126	4,343,034
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(130,165)	(51,378)
Gross Unrealized Losses - 12 Months or More	[1]	(4,384)	(2,077)
Gross Unrealized Losses	[1]	(134,549)	(53,455)
Fixed maturities | Corporate bonds
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	[1]	737,840	675,131
Estimated Fair Value - 12 Months or More	[1]	8,726	37,671
Estimated Fair Value	[1]	746,566	712,802
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(32,848)	(12,350)
Gross Unrealized Losses - 12 Months or More	[1]	(1,852)	(443)
Gross Unrealized Losses	[1]	(34,700)	(12,793)
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]	150,547	102,887
Estimated Fair Value - 12 Months or More	[1]	108	203
Estimated Fair Value	[1]	150,655	103,090
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(5,212)	(927)
Gross Unrealized Losses - 12 Months or More	[1]	(33)	(4)
Gross Unrealized Losses	[1]	(5,245)	(931)
Fixed maturities | Municipal bonds
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	[1]	46,969	220,296
Estimated Fair Value - 12 Months or More	[1]	0	0
Estimated Fair Value	[1]	46,969	220,296
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(542)	(2,213)
Gross Unrealized Losses - 12 Months or More	[1]	0	0
Gross Unrealized Losses	[1]	(542)	(2,213)
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]	205,336	147,290
Estimated Fair Value - 12 Months or More	[1]	2,523	2,683
Estimated Fair Value	[1]	207,859	149,973
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(7,858)	(2,302)
Gross Unrealized Losses - 12 Months or More	[1]	(147)	(28)
Gross Unrealized Losses	[1]	(8,005)	(2,330)
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]	412,319	1,373,127
Estimated Fair Value - 12 Months or More	[1]	0	32,058
Estimated Fair Value	[1]	412,319	1,405,185
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(2,708)	(10,089)
Gross Unrealized Losses - 12 Months or More	[1]	0	(45)
Gross Unrealized Losses	[1]	(2,708)	(10,134)
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]	1,371,109	1,224,243
Estimated Fair Value - 12 Months or More	[1]	0	37,610
Estimated Fair Value	[1]	1,371,109	1,261,853
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(43,928)	(20,163)
Gross Unrealized Losses - 12 Months or More	[1]	0	(167)
Gross Unrealized Losses	[1]	(43,928)	(20,330)
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]	721,451	441,522
Estimated Fair Value - 12 Months or More	[1]	32,198	48,313
Estimated Fair Value	[1]	753,649	489,835
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(37,069)	(3,334)
Gross Unrealized Losses - 12 Months or More	[1]	(2,352)	(1,390)
Gross Unrealized Losses	[1]	(39,421)	(4,724)
Short-term investments
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months		1,025,993	95,777
Estimated Fair Value - 12 Months or More		0	0
Estimated Fair Value		1,025,993	95,777
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months		(634)	(1,548)
Gross Unrealized Losses - 12 Months or More		0	0
Gross Unrealized Losses		$ (634)	$ (1,548)
[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 Thousands		Jun. 30, 2020	Dec. 31, 2019
Estimated Fair Value
Estimated Fair Value		$ 17,207,731	$ 16,894,526
Amortized Cost
Amortized cost		16,733,493	16,598,808
Fixed maturities
Estimated Fair Value
Due in one year or less		344,032	428,659
Due after one year through five years		9,873,345	10,126,403
Due after five years through 10 years		4,379,828	3,317,535
Due after 10 years		428,430	411,269
Single maturity date		15,025,635	14,283,866
Estimated Fair Value	[1]	17,665,637	17,263,036
Amortized Cost
Due in one year or less		339,451	423,617
Due after one year through five years		9,645,073	9,996,206
Due after five years through 10 years		4,163,392	3,219,567
Due after 10 years		396,772	388,280
Single maturity date		14,544,688	14,027,670
Amortized cost	[1]	17,187,656	16,966,188
Fixed maturities | Mortgage backed securities
Estimated Fair Value
Securities without single maturity date		610,839	562,309
Estimated Fair Value		610,839	562,309
Amortized Cost
Securities without single maturity date		603,889	553,571
Amortized cost	[1]	603,889	553,571
Fixed maturities | Commercial mortgage backed securities
Estimated Fair Value
Securities without single maturity date		395,682	733,108
Estimated Fair Value		395,682	733,108
Amortized Cost
Securities without single maturity date		396,193	720,487
Amortized cost	[1]	396,193	720,487
Fixed maturities | Asset backed securities
Estimated Fair Value
Securities without single maturity date		1,633,481	1,683,753
Estimated Fair Value		1,633,481	1,683,753
Amortized Cost
Securities without single maturity date		1,642,886	1,664,460
Amortized cost	[1]	$ 1,642,886	$ 1,664,460
[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 Thousands	Jun. 30, 2020	Dec. 31, 2019
Disclosure Investment Information [Abstract]
Fair value of cash collateral received on securities lending	$ 26,600	$ 81,200
Fair value of non-cash collateral received on securities lending	447,200	307,200
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	473,783	388,366
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9	0	0
Amounts related to securities lending not included in offsetting disclosure in note 9	473,783	388,366
US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	445,282	356,305
Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	2,336	2,570
Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	26,165	29,491
Overnight and continuous
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	320,231	272,393
Overnight and continuous | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	291,730	240,332
Overnight and continuous | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	2,336	2,570
Overnight and continuous | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	26,165	29,491
Less than 30 days
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
Less than 30 days | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
Less than 30 days | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
Less than 30 days | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
30 - 90 days
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	153,552	115,973
30 - 90 days | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	153,552	115,973
30 - 90 days | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
30 - 90 days | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
90 days or more
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
90 days or more | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
90 days or more | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
90 days or more | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	$ 0	$ 0

Investment Information - Other

Investment Information - Other investments (Details) - Fair value option - USD ($) $ in Thousands	Jun. 30, 2020	Dec. 31, 2019
Schedule Of Other Investments [Line Items]
Other investments	$ 2,122,490	$ 2,429,316
Term loan investments
Schedule Of Other Investments [Line Items]
Other investments	1,109,031	1,326,018
Lending
Schedule Of Other Investments [Line Items]
Other investments	579,320	602,841
Credit related funds
Schedule Of Other Investments [Line Items]
Other investments	92,970	123,020
Energy
Schedule Of Other Investments [Line Items]
Other investments	66,667	97,402
Investment grade fixed income
Schedule Of Other Investments [Line Items]
Other investments	133,936	151,594
Infrastructure
Schedule Of Other Investments [Line Items]
Other investments	48,427	61,786
Private equity
Schedule Of Other Investments [Line Items]
Other investments	72,888	49,376
Real estate
Schedule Of Other Investments [Line Items]
Other investments	$ 19,251	$ 17,279

Investment Information - Equity

Investment Information - Equity method investments (Details) - USD ($) $ in Thousands	Jun. 30, 2020	Dec. 31, 2019
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	$ 1,727,302	$ 1,660,396
Credit related funds
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	624,382	428,437
Equity securities
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	292,499	293,686
Real estate
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	249,822	246,851
Lending
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	137,270	202,690
Private equity
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	181,492	144,983
Infrastructure
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	141,972	235,033
Energy
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	$ 99,865	$ 108,716

Investment Information - Fair v

Investment Information - Fair value option (Details) - USD ($) $ in Thousands	Jun. 30, 2020	Dec. 31, 2019
Fair Value, Option, Quantitative Disclosures [Line Items]
Investments accounted for using the fair value option	$ 3,520,771	$ 3,663,477
Fixed maturities
Fair Value, Option, Quantitative Disclosures [Line Items]
Investments accounted for using the fair value option	923,804	754,452
Other investments
Fair Value, Option, Quantitative Disclosures [Line Items]
Investments accounted for using the fair value option	2,122,490	2,429,316
Short-term investments
Fair Value, Option, Quantitative Disclosures [Line Items]
Investments accounted for using the fair value option	384,382	377,014
Equity securities
Fair Value, Option, Quantitative Disclosures [Line Items]
Investments accounted for using the fair value option	$ 90,095	$ 102,695

Investment Information - Limite

Investment Information - Limited partnership interests (Details) - USD ($) $ in Thousands		Jun. 30, 2020	Dec. 31, 2019
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss		$ 1,906,196	$ 1,848,679
Aggregate unfunded commitments		1,770,000	1,690,000
Equity method investments
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss	[1]	1,727,302	1,660,396
Aggregate unfunded commitments		1,440,000	1,360,000
Fair value option
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss	[2]	178,894	188,283
Aggregate unfunded commitments		$ 32,300	$ 41,700
[1]	Aggregate unfunded commitments were $1.44 billion at June 30, 2020 , compared to $1.36 billion at December 31, 2019 .
[2]	Aggregate unfunded commitments were $32.3 million at June 30, 2020 , compared to $41.7 million at December 31, 2019 .

Investment Information - Net in

Investment Information - Net investment income (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2020	Jun. 30, 2019	Jun. 30, 2020	Jun. 30, 2019
Net investment income:
Gross investment income		$ 151,965	$ 176,498	$ 320,291	$ 359,276
Investment expenses		(20,480)	(21,460)	(43,653)	(47,289)
Net investment income		131,485	155,038	276,638	311,987
Fixed maturities
Net investment income:
Gross investment income		105,391	125,018	220,238	254,817
Term loans
Net investment income:
Gross investment income		20,512	24,730	43,682	49,346
Equity securities
Net investment income:
Gross investment income		6,219	4,368	12,226	7,356
Short-term investments
Net investment income:
Gross investment income		3,383	3,859	8,279	8,038
Other
Net investment income:
Gross investment income	[1]	$ 16,460	$ 18,523	$ 35,866	$ 39,719
[1]	Includes income distributions from investment funds and other items.

Investment Information - Net re

Investment Information - Net realized gains and losses (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2020	Jun. 30, 2019	Jun. 30, 2020	Jun. 30, 2019
Available for sale securities:
Available for sale securities, gross gains on investment sales		$ 232,153	$ 75,090	$ 410,353	$ 118,455
Available for sale securities, gross losses on investment sales		(49,824)	(15,281)	(81,792)	(46,937)
Equity securities, at fair value:
Net realized gains (losses) on sales during the period		(18,250)	(6,644)	(18,789)	4,286
Net unrealized gains (losses) on equity securities still held at reporting date		145,686	22,632	(29,880)	59,768
Allowance for credit losses:
Allowance for credit losses - investment related		(1,000)		(10,349)
Allowance for credit losses - underwriting related		(5,834)	0	(9,104)	0
Net impairment losses		0	(49)	(533)	(1,358)
Derivative instruments	[1]	(836)	63,966	126,353	99,837
Other		(6,515)	(1,628)	(8,612)	(10,038)
Net realized gains (losses)		556,588	120,757	189,628	261,013
Fixed maturities
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		68,181	11,429	(59,485)	42,577
Allowance for credit losses:
Allowance for credit losses - investment related		3,225	0	(6,095)	0
Other investments
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		178,570	(33,780)	(129,230)	(15,585)
Equity securities
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		6,664	6,414	1,755	10,680
Short-term investments
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		$ 3,368	$ (1,392)	$ (5,313)	$ (672)
[1]	See note 9 for information on the Company’s derivative instruments.

Investment Information - Allowa

Investment Information - Allowance for expected credit losses (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2020	Jun. 30, 2019	Jun. 30, 2020	Jun. 30, 2019
Allowance for expected credit losses
Balance at beginning of period		$ 9,938		$ 0
Cumulative effect of accounting change		0		634
Additions for current-period provision for expected credit losses		1,000		10,349
Additions (reductions) for previously recognized expected credit losses		(4,232)		(4,255)
Reductions due to disposals		(837)		(859)
Write-offs charged against the allowance		0		0
Balance at end of period		5,869		5,869
Fixed maturities
Allowance for expected credit losses
Balance at beginning of period				0
Additions for current-period provision for expected credit losses		(3,225)	$ 0	6,095	$ 0
Balance at end of period		5,869		5,869
Fixed maturities | Structured securities
Allowance for expected credit losses
Balance at beginning of period		2,654		0
Cumulative effect of accounting change		0		517
Additions for current-period provision for expected credit losses		695		2,841
Additions (reductions) for previously recognized expected credit losses		(1,304)		(1,306)
Reductions due to disposals		(319)		(326)
Write-offs charged against the allowance		0		0
Balance at end of period		1,726		1,726
Fixed maturities | Municipal bonds
Allowance for expected credit losses
Balance at beginning of period		23		0
Cumulative effect of accounting change		0		0
Additions for current-period provision for expected credit losses		44		67
Additions (reductions) for previously recognized expected credit losses		(25)		(25)
Reductions due to disposals		(14)		(14)
Write-offs charged against the allowance		0		0
Balance at end of period		28		28
Fixed maturities | Corporate bonds
Allowance for expected credit losses
Balance at beginning of period		7,232		0
Cumulative effect of accounting change		0		117
Additions for current-period provision for expected credit losses		290		7,441
Additions (reductions) for previously recognized expected credit losses		(2,903)		(2,924)
Reductions due to disposals		(504)		(519)
Write-offs charged against the allowance		0		0
Balance at end of period		4,115		4,115
Short-term investments
Allowance for expected credit losses
Balance at beginning of period		29		0
Cumulative effect of accounting change		0		0
Additions for current-period provision for expected credit losses		(29)		0
Additions (reductions) for previously recognized expected credit losses		0		0
Reductions due to disposals		0		0
Write-offs charged against the allowance		0		0
Balance at end of period	[1]	$ 0		$ 0
[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.

Investment Information - Restri

Investment Information - Restricted assets (Details) - USD ($) $ in Thousands	Jun. 30, 2020	Dec. 31, 2019
Restricted Assets [Line Items]
Restricted assets	$ 8,210,828	$ 7,721,618
Collateral or guarantees - affiliated transactions
Restricted Assets [Line Items]
Restricted assets	4,633,689	4,526,761
Collateral or guarantees - third party agreements
Restricted Assets [Line Items]
Restricted assets	2,525,173	2,278,248
Deposits with US regulatory authorities
Restricted Assets [Line Items]
Restricted assets	862,859	797,371
Deposits with non-US regulatory authorities
Restricted Assets [Line Items]
Restricted assets	189,107	119,238
Watford Holdings Ltd
Restricted Assets [Line Items]
Assets pledged as collateral	$ 1,140,000	$ 1,000,000

Investment Information - Cash a

Investment Information - Cash and restricted cash (Details) - USD ($) $ in Thousands	Jun. 30, 2020	Dec. 31, 2019	Jun. 30, 2019	Dec. 31, 2018
Disclosure Investment Information [Abstract]
Cash	$ 854,259	$ 726,230
Restricted cash (included in ‘other assets’)	210,424	177,468
Cash and restricted cash	$ 1,064,683	$ 903,698	$ 683,075	$ 724,643

Investment Information - Narrat

Investment Information - Narrative (Details) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2020USD ($)lots	Jun. 30, 2019USD ($)	Jun. 30, 2020USD ($)lots	Jun. 30, 2019USD ($)	Dec. 31, 2019USD ($)lots
Narrative items:
Investable assets	$ 27,170,000		$ 27,170,000
Equity in net (loss) income of investment funds accounted for using the equity method	$ (65,119)	$ 32,536	$ (69,328)	$ 79,403
Continuous unrealized loss, qualitative disclosures:
Number of positions in an unrealized loss position (lots) | lots	3,730		3,730		2,230
Total number of positions (lots) | lots	10,540		10,540		9,590
Largest single loss	$ 1,200		$ 1,200		$ 900
Equity securities, at fair value	1,257,317		$ 1,257,317		$ 838,925
Minimum
Narrative items:
Time lag for reporting			1 month
Maximum
Narrative items:
Time lag for reporting			3 months
Underwriting segments
Narrative items:
Investable assets	24,530,000		$ 24,530,000
Equity in net (loss) income of investment funds accounted for using the equity method	(65,119)	32,536	(69,328)	79,403
Other
Narrative items:
Investable assets	2,640,000		2,640,000
Equity in net (loss) income of investment funds accounted for using the equity method	$ 0	$ 0	$ 0	$ 0

Fair Value - Fair Value Hierarc

Fair Value - Fair Value Hierarchy (Details) - Recurring - USD ($) $ in Thousands		Jun. 30, 2020	Dec. 31, 2019
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		$ 8,971,554	$ 6,932,402
Liabilities measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Contingent consideration liability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Securities sold but not yet purchased
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value	[1]	0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	5,077,056	4,805,581
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]	5,077,056	4,805,581
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,250,377	904,804
Quoted Prices in Active Markets for Identical Assets (Level 1) | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,205,352	789,596
Quoted Prices in Active Markets for Identical Assets (Level 1) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		438,769	432,421
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		483	1,852
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		370,286	333,320
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		28,507	43,962
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Other investments fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		39,493	53,287
Significant Other Observable Inputs (Level 2)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		14,733,213	14,641,044
Liabilities measured at fair value		(96,110)	(106,007)
Significant Other Observable Inputs (Level 2) | Contingent consideration liability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		0	0
Significant Other Observable Inputs (Level 2) | Securities sold but not yet purchased
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value	[1]	(29,289)	(66,257)
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		(66,821)	(39,750)
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]	12,584,274	12,443,388
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]	7,142,743	6,397,740
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]	610,621	562,055
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]	517,089	881,926
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]	395,682	733,108
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]	115,935	111,011
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]	2,171,955	2,078,757
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]	1,630,249	1,678,791
Significant Other Observable Inputs (Level 2) | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		27,489	51,742
Significant Other Observable Inputs (Level 2) | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		6,581	4,798
Significant Other Observable Inputs (Level 2) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		96,909	48,946
Significant Other Observable Inputs (Level 2) | Fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,017,960	2,092,170
Significant Other Observable Inputs (Level 2) | Fair value option | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		672,459	487,470
Significant Other Observable Inputs (Level 2) | Fair value option | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		14,142	11,947
Significant Other Observable Inputs (Level 2) | Fair value option | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		249	377
Significant Other Observable Inputs (Level 2) | Fair value option | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,131	1,134
Significant Other Observable Inputs (Level 2) | Fair value option | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		112	110
Significant Other Observable Inputs (Level 2) | Fair value option | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		68,340	50,465
Significant Other Observable Inputs (Level 2) | Fair value option | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		165,890	200,163
Significant Other Observable Inputs (Level 2) | Fair value option | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		14,096	43,694
Significant Other Observable Inputs (Level 2) | Fair value option | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		142	641
Significant Other Observable Inputs (Level 2) | Fair value option | Other investments fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,081,399	1,296,169
Significant Unobservable Inputs (Level 3)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		165,186	197,799
Liabilities measured at fair value		(1,250)	(7,998)
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		(1,250)	(7,998)
Significant Unobservable Inputs (Level 3) | Securities sold but not yet purchased
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value	[1]	0	0
Significant Unobservable Inputs (Level 3) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fixed maturities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	4,307	14,067
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]	857	8,851
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]	218	254
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]	3,232	4,962
Significant Unobservable Inputs (Level 3) | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		51,981	55,889
Significant Unobservable Inputs (Level 3) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		108,898	127,843
Significant Unobservable Inputs (Level 3) | Fair value option | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		998	932
Significant Unobservable Inputs (Level 3) | Fair value option | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		61,447	58,094
Significant Unobservable Inputs (Level 3) | Fair value option | Other investments fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		46,453	68,817
Estimated Fair Value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		24,825,098	22,782,288
Liabilities measured at fair value		(97,360)	(114,005)
Estimated Fair Value | Contingent consideration liability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(1,250)	(7,998)
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]	(29,289)	(66,257)
Estimated Fair Value | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(66,821)	(39,750)
Estimated Fair Value | Fixed maturities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		17,665,637	17,263,036
Estimated Fair Value | Fixed maturities | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		7,143,600	6,406,591
Estimated Fair Value | Fixed maturities | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		610,839	562,309
Estimated Fair Value | Fixed maturities | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		517,089	881,926
Estimated Fair Value | Fixed maturities | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		395,682	733,108
Estimated Fair Value | Fixed maturities | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		5,192,991	4,916,592
Estimated Fair Value | Fixed maturities | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,171,955	2,078,757
Estimated Fair Value | Fixed maturities | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,633,481	1,683,753
Estimated Fair Value | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,277,866	956,546
Estimated Fair Value | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,263,914	850,283
Estimated Fair Value | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		96,909	48,946
Estimated Fair Value | Fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		3,520,772	3,663,477
Estimated Fair Value | Fair value option | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		673,457	488,402
Estimated Fair Value | Fair value option | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		14,142	11,947
Estimated Fair Value | Fair value option | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		249	377
Estimated Fair Value | Fair value option | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,131	1,134
Estimated Fair Value | Fair value option | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		595	1,962
Estimated Fair Value | Fair value option | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		68,340	50,465
Estimated Fair Value | Fair value option | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		165,890	200,163
Estimated Fair Value | Fair value option | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		384,382	377,014
Estimated Fair Value | Fair value option | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		90,096	102,697
Estimated Fair Value | Fair value option | Other investments fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,167,345	1,418,273
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]	$ 955,145	$ 1,011,043
[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 Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2020	Jun. 30, 2019	Jun. 30, 2020	Jun. 30, 2019
Contingent consideration liability
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		$ (7,967)	$ (68,121)	$ (7,998)	$ (66,665)
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	(18)	(423)	(72)	(1,331)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0	0	0
Purchases, issuances, sales and settlements
Purchases		0	0	0	0
Issuances		0	0	0	(548)
Sales		0	0	0	0
Settlements		6,735	60,719	6,820	60,719
Transfers in and/or out of Level 3		0	0	0	0
Balance at end of period		(1,250)	(7,825)	(1,250)	(7,825)
Available for sale | Structured securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period	[2]	3,846	302	5,216	313
Total gains or (losses) (realized/unrealized) - included in earnings	[1],[2]	(64)	0	(55)	1,757
Total gains or (losses) (realized/unrealized) - included in other comprehensive income	[2]	(287)	1	(309)	5
Purchases, issuances, sales and settlements
Purchases	[2]	0	0	0	0
Issuances	[2]	0	0	0	0
Sales	[2]	0	0	0	(1,757)
Settlements	[2]	(45)	(13)	(1,402)	(28)
Transfers in and/or out of Level 3	[2]	0	0	0	0
Balance at end of period	[2]	3,450	290	3,450	290
Available for sale | Corporate bonds
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		1,980	7,567	8,851	8,141
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	0	0	7	0
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		(1,123)	102	(6,539)	(16)
Purchases, issuances, sales and settlements
Purchases		0	429	0	429
Issuances		0	0	0	0
Sales		0	0	0	0
Settlements		0	(456)	(1,462)	(912)
Transfers in and/or out of Level 3		0	0	0	0
Balance at end of period		857	7,642	857	7,642
Fair value option | Corporate bonds
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		965	2,233	932	5,758
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	0	(49)	0	(339)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0	0	0
Purchases, issuances, sales and settlements
Purchases		33	0	66	0
Issuances		0	0	0	0
Sales		0	0	0	(3,235)
Settlements		0	0	0	0
Transfers in and/or out of Level 3		0	23,919	0	23,919
Balance at end of period		998	26,103	998	26,103
Fair value option | Other investments
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		54,620	62,329	68,817	62,705
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	(987)	(11,614)	(1,014)	(11,316)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0	0	0
Purchases, issuances, sales and settlements
Purchases		3	0	24	0
Issuances		0	0	0	0
Sales		(7,183)	(74)	(24,358)	(148)
Settlements		0	0	0	(600)
Transfers in and/or out of Level 3		0	44,632	2,984	44,632
Balance at end of period		46,453	95,273	46,453	95,273
Fair value option | Equity securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		60,015	0	58,094	0
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	1,432	0	3,353	0
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0	0	0
Purchases, issuances, sales and settlements
Purchases		0	0	0	0
Issuances		0	0	0	0
Sales		0	0	0	0
Settlements		0	0	0	0
Transfers in and/or out of Level 3		0	56,145	0	56,145
Balance at end of period		61,447	56,145	61,447	56,145
Equity securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		55,632	0	55,889	0
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	11,799	0	8,078	0
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0	0	0
Purchases, issuances, sales and settlements
Purchases		0	0	3,464	0
Issuances		0	0	0	0
Sales		(15,450)	0	(15,450)	0
Settlements		0	0	0	0
Transfers in and/or out of Level 3		0	51,212	0	51,212
Balance at end of period		$ 51,981	$ 51,212	$ 51,981	$ 51,212
[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 Thousands	Jun. 30, 2020	Dec. 31, 2019
Fair Value Disclosures [Abstract]
Total assets and liabilities measured at fair value	$ 24,920,000	$ 22,900,000
Total assets and liabilities measured at fair value priced using non-binding broker quotes	$ 121,100	$ 179,600
Total assets and liabilities measured at fair value priced using non-binding broker quotes (percentage)	0.50%	0.80%
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Senior notes	$ 2,860,733	$ 1,871,626
Estimated fair value of senior notes	$ 3,490,000	$ 2,340,000

Derivative Instruments (Details

Derivative Instruments (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2020	Jun. 30, 2019	Jun. 30, 2020	Jun. 30, 2019	Dec. 31, 2019
Derivative offsetting [Abstract]
Derivative assets subject to master netting agreements		$ 87,000		$ 87,000		$ 97,800
Derivative liabilities subject to master netting agreements		60,300		60,300		37,800
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments	[1]	(836)	$ 63,966	126,353	$ 99,837
Not designated as hedging instrument
Derivative [Line Items]
Asset derivatives - fair value		102,882		102,882		103,956
Liability derivatives - fair value		(66,821)		(66,821)		(39,750)
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(836)	63,966	126,353	99,837
Not designated as hedging instrument | Futures contracts
Derivative [Line Items]
Net derivatives - notional value	[2],[3]	2,635,862		2,635,862		4,104,559
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(1,607)	66,973	94,337	94,309
Not designated as hedging instrument | Futures contracts | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[3]	17,181		17,181		10,065
Not designated as hedging instrument | Futures contracts | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[3]	(5,894)		(5,894)		(13,722)
Not designated as hedging instrument | Foreign currency forward contracts
Derivative [Line Items]
Net derivatives - notional value	[2],[3]	1,073,432		1,073,432		686,878
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		3,523	(5,365)	(7,347)	(19,074)
Not designated as hedging instrument | Foreign currency forward contracts | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[3]	12,366		12,366		5,352
Not designated as hedging instrument | Foreign currency forward contracts | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[3]	(9,400)		(9,400)		(5,327)
Not designated as hedging instrument | TBAs
Derivative [Line Items]
Net derivatives - notional value	[2],[4]	5,740		5,740		53,229
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		264	48	1,009	238
Not designated as hedging instrument | TBAs | Fixed maturities available for sale
Derivative [Line Items]
Asset derivatives - fair value	[4]	5,973		5,973		55,010
Liability derivatives - fair value	[4]	0		0		0
Not designated as hedging instrument | Other
Derivative [Line Items]
Net derivatives - notional value	[2],[3]	3,398,053		3,398,053		4,356,300
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(3,016)	$ 2,310	38,354	$ 24,364
Not designated as hedging instrument | Other | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[3]	67,362		67,362		33,529
Not designated as hedging instrument | Other | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[3]	$ (51,527)		$ (51,527)		$ (20,701)
[1]	See note 9 for information on the Company’s derivative instruments.
[2]	Represents the absolute notional value of all outstanding contracts, consisting of long and short positions.
[3]	The fair value of asset derivatives are included in ‘other assets’ and the fair value of liability derivatives are included in ‘other liabilities.’
[4]	The fair value of TBAs are included in ‘fixed maturities available for sale, at fair value.’

Commitments and Contingencies (

Commitments and Contingencies (Details) - USD ($) $ in Millions	6 Months Ended
	Jun. 30, 2020	Jun. 30, 2019	Dec. 31, 2019
Debt Instrument [Line Items]
Investment commitments	$ 1,770		$ 1,690
Interest expense on senior notes and other borrowings	57.4	$ 60.9
Senior notes | 3.535% Senior Notes due 2050
Debt Instrument [Line Items]
Senior notes, face amount	$ 1,000
Senior notes, stated percentage	3.635%
Description of interest rate terms	Interest will be calculated on the basis of a 360-day year of twelve 30-day months
Maturity date of senior notes	Jun. 30, 2050

Leases - Additional information

Leases - Additional information (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2020	Jun. 30, 2019	Jun. 30, 2020	Jun. 30, 2019
Lessee, Lease, Description [Line Items]
Operating lease costs		$ 7,821	$ 7,244	$ 15,812	$ 14,860
Cash payments included in the measurement of lease liabilities reported in operating cash flows		5,844	7,685	14,305	14,585
Right-of-use assets obtained in exchange for new lease liabilities		435	$ 4,420	3,885	$ 4,420
Lease liability		$ 139,772		$ 139,772
Weighted average discount rate		3.90%	3.90%	3.90%	3.90%
Weighted average remaining lease term in years		6 years 1 month 6 days	6 years 6 months	6 years 1 month 6 days	6 years 6 months
Maximum
Lessee, Lease, Description [Line Items]
Operating lease term		11 years		11 years
Other assets
Lessee, Lease, Description [Line Items]
Right-of-use assets	[1]	$ 119,494	$ 134,061	$ 119,494	$ 134,061
Other liabilities
Lessee, Lease, Description [Line Items]
Lease liability	[1]	$ 139,772	$ 150,341	$ 139,772	$ 150,341
[1]	The right-of-use assets are included in ‘other assets’ while the operating lease liability is included in ‘other liabilities.’

Leases - Contractual maturities

Leases - Contractual maturities and future minimum rental payments (Details) $ in Thousands	Jun. 30, 2020USD ($)
Contractual maturities of operating lease liabilities
2020 (remainder)	$ 15,835
2021	31,475
2022	28,341
2023	23,820
2024	17,601
2025 and thereafter	40,139
Total undiscounted lease liability	157,211
Less: present value adjustment	(17,439)
Operating lease liability	$ 139,772

Variable Interest Entities an_3

Variable Interest Entities and Noncontrolling Interests - Variable interest entity (Details) - USD ($) $ in Thousands	Jul. 02, 2019	Mar. 31, 2014	Jun. 30, 2020	Jun. 30, 2019
Variable Interest Entity [Line Items]
Net cash used for operating activities			$ 1,321,580	$ 712,524
Net cash used for investing activities			(1,810,190)	(746,944)
Net cash provided by financing activities			$ 671,337	(9,085)
Variable Interest Entity, Primary Beneficiary | Watford Holdings Ltd
Variable Interest Entity [Line Items]
Initial investment contribution amount		$ 100,000
Number of shares acquired		2,500,000
Ownership percentage		11.00%	13.00%
Senior notes, face amount	$ 175,000
Senior notes, stated percentage	6.50%
Proceeds from issuance of senior notes	$ 172,400
Senior notes acquired	$ 35,000
Net cash used for operating activities			$ 87,300	115,900
Net cash used for investing activities			78,000	(135,700)
Net cash provided by financing activities			$ (153,800)	$ 25,600

Variable Interest Entities an_4

Variable Interest Entities and Noncontrolling Interests - Carrying amount of assets and liabilities of variable interest entity (Details) - USD ($) $ in Thousands		Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018
Variable Interest Entity [Line Items]
Investments accounted for using the fair value option		$ 3,520,771		$ 3,663,477
Fixed maturities available for sale, at fair value		17,207,731		16,894,526
Equity securities, at fair value		1,257,317		838,925
Cash		854,259		726,230
Accrued investment income		102,064		117,937
Premiums receivable		2,203,753	$ 2,155,204	1,778,717
Reinsurance recoverable on unpaid and paid losses and LAE		4,363,507	4,303,135	4,346,816
Ceded unearned premiums		1,364,603		1,234,683
Deferred acquisition costs		714,531		633,400
Receivable for securities sold		167,281		24,133
Goodwill and intangible assets		688,490		738,083	$ 641,010
Other assets		1,632,756		1,383,788
Total assets		41,199,648		37,885,361
Reserve for losses and loss adjustment expenses		15,044,874	14,309,580	13,891,842	12,230,316	$ 12,010,041	$ 11,853,297
Unearned premiums		4,827,445		4,339,549
Reinsurance balances payable		793,467		667,072
Revolving credit agreement borrowings		335,587		484,287
Senior notes		2,860,733		1,871,626
Payable for securities purchased		275,257		87,579
Other liabilities		1,467,739		1,513,330
Total liabilities		28,472,748		25,569,809
Redeemable noncontrolling interests		55,986		55,404
Watford Holdings Ltd
Variable Interest Entity [Line Items]
Redeemable noncontrolling interests		55,986	$ 55,376	55,404	$ 206,475	$ 206,383	$ 206,292
Variable Interest Entity, Primary Beneficiary | Watford Holdings Ltd
Variable Interest Entity [Line Items]
Investments accounted for using the fair value option		1,886,676		1,898,091
Fixed maturities available for sale, at fair value		690,225		745,708
Equity securities, at fair value		62,443		65,338
Cash		107,653		102,437
Accrued investment income		14,364		14,025
Premiums receivable		258,178		273,657
Reinsurance recoverable on unpaid and paid losses and LAE		229,746		170,973
Ceded unearned premiums		131,919		132,577
Deferred acquisition costs		64,149		64,044
Receivable for securities sold		31,314		16,287
Goodwill and intangible assets		7,650		7,650
Other assets		63,441		60,070
Total assets		3,547,758		3,550,857
Reserve for losses and loss adjustment expenses		1,353,049		1,263,628
Unearned premiums		456,170		438,907
Reinsurance balances payable		72,776		77,066
Revolving credit agreement borrowings		335,587		484,287
Senior notes		172,554		172,418
Payable for securities purchased		67,272		18,180
Other liabilities	[1]	261,267		171,714
Total liabilities		2,718,675		2,626,200
Redeemable noncontrolling interests		$ 52,351		$ 52,305
[1]	Includes certain borrowings related to investing activities.

Variable Interest Entities an_5

Variable Interest Entities and Noncontrolling Interests - Non-redeemable noncontrolling interests (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2020	Jun. 30, 2019	Jun. 30, 2020	Jun. 30, 2019
Noncontrolling Interest [Line Items]
Non-redeemable noncontrolling interests, beginning of period				$ 762,777
Amounts attributable to noncontrolling interests		$ 165,598	$ 12,301	(68,346)	$ 54,683
Other comprehensive (income) loss attributable to noncontrolling interests		20,111	2,891	(12,947)	7,030
Non-redeemable noncontrolling interests, end of period		679,089	855,347	679,089	855,347
Watford Holdings Ltd
Noncontrolling Interest [Line Items]
Non-redeemable noncontrolling interests, beginning of period		492,785	838,081	762,777	791,560
Additional paid in capital attributable to noncontrolling interests		595	2,074	472	2,074
Repurchases attributable to non-redeemable noncontrolling interests	[1]			(2,867)	0
Amounts attributable to noncontrolling interests		165,598	12,301	(68,346)	54,683
Other comprehensive (income) loss attributable to noncontrolling interests		20,111	2,891	(12,947)	7,030
Non-redeemable noncontrolling interests, end of period		$ 679,089	$ 855,347	$ 679,089	$ 855,347
Noncontrolling shareholders | Common shares | Watford Holdings Ltd
Noncontrolling Interest [Line Items]
Noncontrolling interest, ownership percentage by noncontrolling owners		87.00%		87.00%
[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 Thousands	Aug. 01, 2019	Jun. 30, 2020	Jun. 30, 2019	Jun. 30, 2020	Jun. 30, 2019	Jul. 31, 2019	Mar. 31, 2014
Redeemable Noncontrolling Interest [Line Items]
Redeemable noncontrolling interests, beginning of period				$ 55,404
Redeemable noncontrolling interests, end of period		$ 55,986		55,986
Watford Holdings Ltd
Redeemable Noncontrolling Interest [Line Items]
Redeemable noncontrolling interests, beginning of period		55,376	$ 206,383	55,404	$ 206,292
Accretion of preference share issuance costs		23	92	46	183
Other		587	0	536	0
Redeemable noncontrolling interests, end of period		55,986	$ 206,475	55,986	$ 206,475
Cumulative redeemable preference shares | Watford Holdings Ltd
Redeemable Noncontrolling Interest [Line Items]
Par value per share							$ 0.01
Liquidation preference per share							25
Issue price per share							$ 24.50
Variable Interest Entity, Primary Beneficiary | Watford Holdings Ltd
Redeemable Noncontrolling Interest [Line Items]
Preference shares, number of shares issued						9,065,200
Number of preference shares redeemed	6,919,998
Preferred shares, redemption price	$ 25.19748
Preference shares redeemed	$ 11,500
Redeemable noncontrolling interests, beginning of period				52,305
Redeemable noncontrolling interests, end of period		$ 52,351		$ 52,351

Variable Interest Entities an_7

Variable Interest Entities and Noncontrolling Interests - Income or loss attributable to third party investors (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2020	Jun. 30, 2019	Jun. 30, 2020	Jun. 30, 2019
Noncontrolling Interest [Abstract]
Amounts attributable to non-redeemable noncontrolling interests	$ (165,598)	$ (12,301)	$ 68,346	$ (54,683)
Dividends attributable to redeemable noncontrolling interests	(1,970)	(4,590)	(3,123)	(9,178)
Net (income) loss attributable to noncontrolling interests	$ (167,568)	$ (16,891)	$ 65,223	$ (63,861)

Variable Interest Entities an_8

Variable Interest Entities and Noncontrolling Interests - Other variable interest entity disclosures (Details) - USD ($) $ in Thousands	Jun. 30, 2020	Dec. 31, 2019
Variable Interest Entity [Line Items]
Total VIE Assets	$ 41,199,648	$ 37,885,361
Maximum Exposure to Loss	1,906,196	1,848,679
Variable Interest Entity, Not Primary Beneficiary
Variable Interest Entity [Line Items]
Total VIE Assets	3,035,349	3,425,833
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability	(4,708)	(5,197)
Maximum Exposure to Loss - Off-Balance Sheet	78,322	42,084
Maximum Exposure to Loss	73,614	36,887
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2017-1 Ltd. (Oct-17)
Variable Interest Entity [Line Items]
Total VIE Assets	145,573	216,429
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability	(295)	(442)
Maximum Exposure to Loss - Off-Balance Sheet	2,469	2,794
Maximum Exposure to Loss	2,174	2,352
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-1 Ltd. (Apr-18)
Variable Interest Entity [Line Items]
Total VIE Assets	250,095	328,482
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability	(1,244)	(1,574)
Maximum Exposure to Loss - Off-Balance Sheet	5,597	5,757
Maximum Exposure to Loss	4,353	4,183
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-2 Ltd. (Aug-18)
Variable Interest Entity [Line Items]
Total VIE Assets	272,685	437,009
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability	(1,206)	(877)
Maximum Exposure to Loss - Off-Balance Sheet	4,210	2,524
Maximum Exposure to Loss	3,004	1,647
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-3 Ltd. (Oct-18)
Variable Interest Entity [Line Items]
Total VIE Assets	302,563	426,806
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability	(1,883)	(1,113)
Maximum Exposure to Loss - Off-Balance Sheet	8,387	3,937
Maximum Exposure to Loss	6,504	2,824
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-1 Ltd. (Mar-19)
Variable Interest Entity [Line Items]
Total VIE Assets	219,256	257,358
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability	(83)	(226)
Maximum Exposure to Loss - Off-Balance Sheet	10,251	3,027
Maximum Exposure to Loss	10,168	2,801
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-2 Ltd. (Apr-19)
Variable Interest Entity [Line Items]
Total VIE Assets	398,316	525,959
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability	54	(78)
Maximum Exposure to Loss - Off-Balance Sheet	13,088	2,579
Maximum Exposure to Loss	13,142	2,501
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-3 Ltd. (Jul-19)
Variable Interest Entity [Line Items]
Total VIE Assets	528,084	656,523
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability	(248)	(585)
Maximum Exposure to Loss - Off-Balance Sheet	10,649	9,273
Maximum Exposure to Loss	10,401	8,688
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-4 Ltd. (Oct-19)
Variable Interest Entity [Line Items]
Total VIE Assets	468,737	577,267
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability	257	(302)
Maximum Exposure to Loss - Off-Balance Sheet	14,687	12,193
Maximum Exposure to Loss	14,944	$ 11,891
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-1 Ltd. (Jun-20)
Variable Interest Entity [Line Items]
Total VIE Assets	450,040
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability	(60)
Maximum Exposure to Loss - Off-Balance Sheet	8,984
Maximum Exposure to Loss	8,924
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-1 Ltd. (Jun-20) | Funded by directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage, Amount	$ 78,500

Other Comprehensive Income (L_3

Other Comprehensive Income (Loss) - Amounts reclassified from accumulated other comprehensive income (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2020	Jun. 30, 2019	Jun. 30, 2020	Jun. 30, 2019
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
Provision for credit losses	$ (1,000)		$ (10,349)
Other-than-temporary impairment losses	0	$ (49)	(533)	$ (1,358)
Income (loss) before income taxes	492,516	530,317	431,787	1,071,701
Income tax expense	(26,127)	(44,472)	(54,072)	(90,358)
Net of tax	298,821	468,954	442,938	917,482
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)	182,329	59,809	328,561	71,518
Provision for credit losses	3,225		(6,095)
Other-than-temporary impairment losses	0	(49)	(533)	(1,358)
Income (loss) before income taxes	185,554	59,760	321,933	70,160
Income tax expense	(18,163)	(4,415)	(33,313)	(4,594)
Net of tax	$ 167,391	$ 55,345	$ 288,620	$ 65,566

Other Comprehensive Income (L_4

Other Comprehensive Income (Loss) - Components of other comprehensive income (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2020	Jun. 30, 2019	Jun. 30, 2020	Jun. 30, 2019
Before tax amount:
Unrealized holding gains (losses) arising during period, before tax	$ 555,576	$ 248,074	$ 492,125	$ 503,064
Less reclassification of net realized gains included in net income, before tax	185,554	59,760	321,933	70,160
Foreign currency translation adjustments, before tax	22,595	4,409	(22,829)	10,053
Other comprehensive income (loss), before tax	392,617	192,723	147,363	442,957
Tax expense (benefit):
Unrealized holding gains (losses) arising during period, tax	62,780	25,601	56,616	54,704
Less reclassification of net realized gains included in net income, tax	18,163	4,415	33,313	4,594
Foreign currency translation adjustments, tax	344	142	(391)	270
Other comprehensive income (loss), tax	44,961	21,328	22,912	50,380
Net of tax amount:
Unrealized holding gains (losses) arising during period, net of tax	492,796	222,473	435,509	448,360
Less reclassification of net realized gains included in net income, net of tax	167,391	55,345	288,620	65,566
Foreign currency translation adjustments, net of tax	22,251	4,267	(22,438)	9,783
Net current period other comprehensive income (loss)	$ 347,656	$ 171,395	$ 124,451	$ 392,577

Income Taxes (Details)

Income Taxes (Details) - USD ($) $ in Millions	6 Months Ended
	Jun. 30, 2020	Jun. 30, 2019	Dec. 31, 2019
Income Tax Disclosure [Abstract]
Effective tax rate on income before income taxes (percentage)	12.50%	8.40%
Tax benefit on share-based compensation	0.50%
Net deferred tax asset	$ 9.3
Net deferred tax liability			$ 53.5
Income taxes paid	$ 10.4	$ 43.5

Transactions With Related Par_2

Transactions With Related Parties (Details) $ in Thousands	6 Months Ended		12 Months Ended
	Jun. 30, 2020USD ($)director	Jun. 30, 2019USD ($)	Dec. 31, 2017USD ($)	Mar. 31, 2020USD ($)	Dec. 31, 2019USD ($)
Related Party Transaction [Line Items]
Purchases of other investments	$ 501,692	$ 677,063
Reinsurance recoverable on unpaid and paid losses and LAE	$ 4,363,507			$ 4,303,135	$ 4,346,816
Premia Holdings Ltd.
Related Party Transaction [Line Items]
Percentage ownership			25.00%
Number of directors appointed by Arch to the Board | director	2
Number of directors on the Board | director	7
Purchases of other investments			$ 100,000
Premia Holdings Ltd. | Barbican Group Holdings Limited
Related Party Transaction [Line Items]
Reinsurance recoverable on unpaid and paid losses and LAE	$ 181,900				177,700
Funds held liability	$ 169,000				$ 180,000