Item 8. FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA

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Item 8. FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA


Index to Financial Statements		Page No.

Report of Independent Registered Public Accounting Firm		84

Consolidated Balance Sheets
	At December 31, 2020 and December 31, 2019	86

Consolidated Statements of Income
	For the years ended December 31, 2020, 2019 and 2018	87

Consolidated Statements of Comprehensive Income
	For the years ended December 31, 2020, 2019 and 2018	88

Consolidated Statements of Changes in Shareholders’ Equity
	For the years ended December 31, 2020, 2019 and 2018	89

Consolidated Statements of Cash Flows
	For the years ended December 31, 2020, 2019 and 2018	90

Notes to Consolidated Financial Statements
	Note 1 - General	91
	Note 2 - Businesses Acquired	91
	Note 3 - Significant Accounting Policies	91
	Note 4 - Segment Information	100
	Note 5 - Reserve for Losses and Loss Adjustment Expenses	107
	Note 6 - Short Duration Contracts	109
	Note 7 - Allowance for Expected Credit Losses	123
	Note 8 - Reinsurance	123
	Note 9 - Investment Information	125
	Note 10 - Fair Value	130
	Note 1 1 - Derivative Instruments	137
	Note 1 2 - VIE and Noncontrolling Interests	138
	Note 1 3 - Other Comprehensive Income (Loss)	141
	Note 1 4 - Earnings Per Common Share	143
	Note 1 5 - Income Taxes	143
	Note 1 6 - Transactions with Related Parties	146
	Note 1 7 - Leases	147
	Note 1 8 - Commitments and Contingencies	147
	Note 1 9 - Debt and Financing Arrangements	148
	Note 20 - Goodwill and Intangible Assets	150
	Note 2 1 - Shareholders’ Equity	151
	Note 2 2 - Share-Based Compensation	153
	Note 2 3 - Retirement Plans	155
	Note 2 4 - Legal Proceedings	156
	Note 2 5 - Statutory Information	156
	Note 2 6 - Unaudited Condensed Quarterly Financial Information	159
	Note 27 - Subsequent Event	159


ARCH CAPITAL			83			2020 FORM 10-K

Report of Independent Registered Public Accounting Firm

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

Opinions on the Financial Statements and Internal Control over Financial Reporting

We have audited the accompanying consolidated balance sheets of Arch Capital Group Ltd. and its subsidiaries (the “Company”) as of December 31, 2020 and 2019, and the related consolidated statements of income, of comprehensive income, of changes in shareholders’ equity, and of cash flows for each of the three years in the period ended December 31, 2020, including the related notes and financial statement schedules listed in the index appearing under Item 15(a)(2) (collectively referred to as the “consolidated financial statements”). We also have audited the Company's internal control over financial reporting as of December 31, 2020, based on criteria established in Internal Control - Integrated Framework (2013) issued by the Committee of Sponsoring Organizations of the Treadway Commission (COSO).

In our opinion, the consolidated financial statements referred to above present fairly, in all material respects, the financial position of the Company as of December 31, 2020 and 2019**,** and the results of its operations and its cash flows for each of the three years in the period ended December 31, 2020, in conformity with accounting principles generally accepted in the United States of America. Also in our opinion, the Company maintained, in all material respects, effective internal control over financial reporting as of December 31, 2020, based on criteria established in Internal Control - Integrated Framework (2013) issued by the COSO.

Basis for Opinions

The Company's management is responsible for these consolidated financial statements, for maintaining effective internal control over financial reporting, and for its assessment of the effectiveness of internal control over financial reporting, included in Management's Annual Report on Internal Control Over Financial Reporting appearing under Item 9A. Our responsibility is to express opinions on the Company’s consolidated financial statements and on the Company's internal control over financial reporting based on our audits. We are a public accounting firm registered with the Public Company Accounting Oversight Board (United States) (PCAOB) and are required to be independent with respect to the Company in accordance with the U.S. federal securities laws and the applicable rules and regulations of the Securities and Exchange Commission and the PCAOB.

We conducted our audits in accordance with the standards of the PCAOB. Those standards require that we plan and perform the audits to obtain reasonable assurance about whether the consolidated financial statements are free of material misstatement, whether due to error or fraud, and whether effective internal control over financial reporting was maintained in all material respects.

Our audits of the consolidated financial statements included performing procedures to assess the risks of material misstatement of the consolidated financial statements, whether due to error or fraud, and performing procedures that respond to those risks. Such procedures included examining, on a test basis, evidence regarding the amounts and disclosures in the consolidated financial statements. Our audits also included evaluating the accounting principles used and significant estimates made by management, as well as evaluating the overall presentation of the consolidated financial statements. Our audit of internal control over financial reporting included obtaining an understanding of internal control over financial reporting, assessing the risk that a material weakness exists, and testing and evaluating the design and operating effectiveness of internal control based on the assessed risk. Our audits also included performing such other procedures as we considered necessary in the circumstances. We believe that our audits provide a reasonable basis for our opinions.

Definition and Limitations of Internal Control over Financial Reporting

A company’s internal control over financial reporting is a process designed to provide reasonable assurance regarding the reliability of financial reporting and the preparation of financial statements for external purposes in accordance with generally accepted accounting principles. A company’s internal control over financial reporting includes those policies and procedures that (i) pertain to the maintenance of records that, in reasonable detail, accurately and fairly reflect the transactions and dispositions of the assets of the company; (ii) provide reasonable assurance that transactions are recorded as necessary to permit preparation of financial statements in accordance with generally accepted accounting principles, and that receipts and expenditures of the company are being made only in accordance with authorizations of management and directors of the company; and (iii) provide reasonable assurance regarding prevention or timely detection of unauthorized acquisition, use, or disposition of the company’s assets that could have a material effect on the financial statements.


ARCH CAPITAL			84			2020 FORM 10-K

Because of its inherent limitations, internal control over financial reporting may not prevent or detect misstatements. Also, projections of any evaluation of effectiveness to future periods are subject to the risk that controls may become inadequate because of changes in conditions, or that the degree of compliance with the policies or procedures may deteriorate.

Critical Audit Matters

The critical audit matter communicated below is a matter arising from the current period audit of the consolidated financial statements that was communicated or required to be communicated to the audit committee and that (i) relates to accounts or disclosures that are material to the consolidated financial statements and (ii) involved our especially challenging, subjective, or complex judgments. The communication of critical audit matters does not alter in any way our opinion on the consolidated financial statements, taken as a whole, and we are not, by communicating the critical audit matter below, providing a separate opinion on the critical audit matter or on the accounts or disclosures to which it relates.

Valuation of Reserve for Losses and Loss Adjustment Expenses

As described in Notes 3, 5 and 6 to the consolidated financial statements, the reserve for losses and loss adjustment expenses represents estimates of future amounts required to pay losses and loss adjustment expenses for insured or reinsured events which have occurred at or before the balance sheet date. As of December 31, 2020, the Company’s total reserve for losses and loss adjustment expenses was $16.5 billion. For the insurance and reinsurance segments, management estimates ultimate losses and loss adjustment expenses using various generally accepted actuarial methods applied to known losses and other relevant information. Ultimate losses and loss adjustment expenses are generally determined by extrapolation of claim emergence and settlement patterns observed in the past that can reasonably be expected to persist into the future. Management makes a number of key assumptions in their reserving process, including estimating loss development patterns and expected loss ratios. For the mortgage segment, the lead actuarial methodology used by management is a frequency-severity method based on the inventory of pending delinquencies. The assumptions of frequency and severity reflect judgments based on historical data and experience.

The principal considerations for our determination that performing procedures relating to the valuation of the reserve for losses and loss adjustment expenses is a critical audit matter are (i) the significant judgment by management when developing their estimate, which in turn led to a high degree of auditor subjectivity and judgment in performing procedures related to the valuation of the reserve for losses and loss adjustment expenses, (ii) the significant auditor effort and judgment in evaluating audit evidence related to the aforementioned key actuarial methods and key assumptions, and (iii) the audit effort included the involvement of professionals with specialized skill and knowledge to assist in performing these procedures and evaluating the audit evidence obtained.

Addressing the matter involved performing procedures and evaluating audit evidence in connection with forming our overall opinion on the consolidated financial statements. These procedures included testing the effectiveness of controls relating to the valuation of the reserve for losses and loss adjustment expenses, including controls over the selection of key actuarial methods and development of key assumptions. These procedures also included, among others, the involvement of professionals with specialized skill and knowledge to assist in performing one or a combination of procedures, including (i) developing an independent estimate, on a test basis, of the reserve for losses and loss adjustment expenses, and comparing the independent estimate to management’s actuarially determined reserve for losses and loss adjustment expenses to evaluate the reasonableness of the reserve for losses and loss adjustment expenses and (ii) evaluating the appropriateness of the actuarial methods and reasonableness of the assumptions, related to loss development patterns, expected loss ratios, frequency, and severity used by management to determine the Company’s reserve for losses and loss adjustment expenses. Developing the independent estimate and evaluating the appropriateness of the key methods and reasonableness of the key assumptions related to loss development patterns, expected loss ratios, frequency and severity, as applicable, involved testing the completeness and accuracy of historical data provided by management.

/s/ PricewaterhouseCoopers LLP

New York, New York

February 26, 2021

We have served as the Company’s or its predecessor’s auditor since 1995.


ARCH CAPITAL			85			2020 FORM 10-K


ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES CONSOLIDATED BALANCE SHEETS (U.S. dollars in thousands, except share data)
	December 31,
	2020		2019
Assets
Investments:
Fixed maturities available for sale, at fair value (amortized cost: $18,143,305 and $16,598,808; net of allowance for credit losses: $2,397 at December 31, 2020)	$	18,717,825	$	16,894,526
Short-term investments available for sale, at fair value (amortized cost: $1,924,292 and $957,283; net of allowance for credit losses: $0 at December 31, 2020)	1,924,922		956,546
Collateral received under securities lending, at fair value (amortized cost: $301,089 and $388,366)	301,096		388,376
Equity securities, at fair value	1,444,830		838,925

Other investments (portion measured at fair value: $3,824,796 and $3,663,477)	4,324,796		3,663,477
Investments accounted for using the equity method	2,047,889		1,660,396
Total investments	28,761,358		24,402,246

Cash	906,448		726,230
Accrued investment income	103,299		117,937
Securities pledged under securities lending, at fair value (amortized cost: $294,493 and $378,738)	294,912		379,868
Premiums receivable (net of allowance for credit losses: $37,781 and $21,003)	2,064,586		1,778,717
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $11,636 and $1,364)	4,500,802		4,346,816
Contractholder receivables (net of allowance for credit losses: $8,638 and $0)	1,986,924		2,119,460
Ceded unearned premiums	1,234,075		1,234,683
Deferred acquisition costs	790,708		633,400
Receivable for securities sold	92,743		24,133
Goodwill and intangible assets	692,863		738,083
Other assets	1,853,579		1,383,788
Total assets	$	43,282,297	$	37,885,361

Liabilities
Reserve for losses and loss adjustment expenses	$	16,513,929	$	13,891,842
Unearned premiums	4,838,965		4,339,549
Reinsurance balances payable	683,263		667,072
Contractholder payables	1,995,562		2,119,460
Collateral held for insured obligations	215,581		206,698
Senior notes	2,861,113		1,871,626
Revolving credit agreement borrowings	155,687		484,287
Securities lending payable	301,089		388,366
Payable for securities purchased	218,779		87,579
Other liabilities	1,510,888		1,513,330
Total liabilities	29,294,856		25,569,809

Commitments and Contingencies
Redeemable noncontrolling interests	58,548		55,404

Shareholders’ Equity
Non-cumulative preferred shares	780,000		780,000

Common shares ($0.0011 par, shares issued: 579,000,841 and 574,617,195)	643		638
Additional paid-in capital	1,977,794		1,889,683
Retained earnings	12,362,463		11,021,006
Accumulated other comprehensive income (loss), net of deferred income tax	488,895		212,091
Common shares held in treasury, at cost (shares: 172,280,199 and 168,997,994)	(2,503,909)		(2,406,047)
Total shareholders' equity available to Arch	13,105,886		11,497,371
Non-redeemable noncontrolling interests	823,007		762,777
Total shareholders' equity	13,928,893		12,260,148
Total liabilities, noncontrolling interests and shareholders' equity	$	43,282,297	$	37,885,361

See Notes to Consolidated Financial Statements


ARCH CAPITAL			86			2020 FORM 10-K


ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES CONSOLIDATED STATEMENTS OF INCOME (U.S. dollars in thousands, except share data)
	Year Ended December 31,
	2020		2019		2018
Revenues


Net premiums earned	$	6,991,935	$	5,786,498	$	5,231,975
Net investment income	519,608		627,738		563,633
Net realized gains (losses)	823,460		363,198		(408,173)



Other underwriting income	26,784		24,861		15,073
Equity in net income of investments accounted for using the equity method	146,693		123,672		45,641
Other income (loss)	16,795		2,233		2,419
Total revenues	8,525,275		6,928,200		5,450,568

Expenses
Losses and loss adjustment expenses	4,689,599		3,133,452		2,890,106
Acquisition expenses	1,004,842		840,945		805,135
Other operating expenses	875,176		800,997		677,809
Corporate expenses	81,988		80,111		78,994
Amortization of intangible assets	69,031		82,104		105,670
Interest expense	143,456		120,872		120,484
Net foreign exchange losses (gains)	83,634		20,609		(69,402)
Total expenses	6,947,726		5,079,090		4,608,796

Income before income taxes	1,577,549		1,849,110		841,772

Income taxes:
Current tax expense (benefit)	197,662		144,361		85,863
Deferred tax expense (benefit)	(85,824)		11,449		28,088
Income tax expense	111,838		155,810		113,951

Net income	$	1,465,711	$	1,693,300	$	727,821
Net (income) loss attributable to noncontrolling interests	(60,190)		(56,981)		30,150
Net income available to Arch	1,405,521		1,636,319		757,971
Preferred dividends	(41,612)		(41,612)		(41,645)
Loss on redemption of preferred shares	—		—		(2,710)
Net income available to Arch common shareholders	$	1,363,909	$	1,594,707	$	713,616

Net income per common share and common share equivalent
Basic	$	3.38	$	3.97	$	1.76
Diluted	$	3.32	$	3.87	$	1.73

Weighted average common shares and common share equivalents outstanding
Basic	403,062,179		401,802,815		404,347,621
Diluted	410,259,455		411,609,478		412,906,478

See Notes to Consolidated Financial Statements


ARCH CAPITAL			87			2020 FORM 10-K


ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME (U.S. dollars in thousands)
	Year Ended December 31,
	2020		2019		2018
Comprehensive Income
Net income	$	1,465,711	$	1,693,300	$	727,821
Other comprehensive income (loss), net of deferred income tax
Unrealized appreciation (decline) in value of available-for-sale investments:
Unrealized holding gains (losses) arising during year	678,717		500,771		(270,057)

Reclassification of net realized (gains) losses, included in net income	(426,187)		(118,941)		144,573
Foreign currency translation adjustments	33,336		18,110		(24,830)
Comprehensive income	1,751,577		2,093,240		577,507
Net (income) loss attributable to noncontrolling interests	(60,190)		(56,981)		30,150
Other comprehensive (income) loss attributable to noncontrolling interests	(9,062)		(9,130)		3,346
Comprehensive income available to Arch	$	1,682,325	$	2,027,129	$	611,003

See Notes to Consolidated Financial Statements


ARCH CAPITAL			88			2020 FORM 10-K


ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES CONSOLIDATED STATEMENTS OF CHANGES IN SHAREHOLDERS' EQUITY (U.S. dollars in thousands)
	Year Ended December 31,
	2020		2019		2018
Non-cumulative preferred shares
Balance at beginning of year	$	780,000	$	780,000	$	872,555
Preferred shares issued	—		—		—
Preferred shares redeemed	—		—		(92,555)
Balance at end of year	780,000		780,000		780,000

Convertible non-voting common equivalent preferred shares
Balance at beginning of year	—		—		489,627

Preferred shares converted to common shares	—		—		(489,627)
Balance at end of year	—		—		—

Common shares
Balance at beginning of year	638		634		611
Common shares issued, net	5		4		23
Balance at end of year	643		638		634

Additional paid-in capital
Balance at beginning of year	1,889,683		1,793,781		1,230,617



Preferred shares converted to common shares	—		—		489,608
Amortization of share-based compensation	70,535		64,152		55,920
Other changes	17,576		31,750		17,636


Balance at end of year	1,977,794		1,889,683		1,793,781

Retained earnings
Balance at beginning of year	11,021,006		9,426,299		8,562,889
Cumulative effect of an accounting change	(22,452)		—		149,794
Balance at beginning of year, as adjusted	10,998,554		9,426,299		8,712,683
Net income	1,465,711		1,693,300		727,821
Net (income) loss attributable to noncontrolling interests	(60,190)		(56,981)		30,150
Preferred share dividends	(41,612)		(41,612)		(41,645)
Loss on redemption of preferred shares	—		—		(2,710)
Balance at end of year	12,362,463		11,021,006		9,426,299

Accumulated other comprehensive income (loss)
Balance at beginning of year	212,091		(178,720)		118,044
Unrealized appreciation (decline) in value of available-for-sale investments, net of deferred income tax:
Balance at beginning of year	258,486		(114,178)		157,400
Cumulative effect of an accounting change	—		—		(149,794)
Balance at beginning of year, as adjusted	258,486		(114,178)		7,606
Unrealized holding gains (losses) during period, net of reclassification adjustment	252,530		381,830		(125,484)
Unrealized holding gains (losses) during period attributable to noncontrolling interests	(9,721)		(9,166)		3,700

Balance at end of year	501,295		258,486		(114,178)
Foreign currency translation adjustments, net of deferred income tax:
Balance at beginning of year	(46,395)		(64,542)		(39,356)
Foreign currency translation adjustments	33,336		18,110		(24,830)
Foreign currency translation adjustments attributable to noncontrolling interests	659		37		(356)
Balance at end of year	(12,400)		(46,395)		(64,542)
Balance at end of year	488,895		212,091		(178,720)

Common shares held in treasury, at cost
Balance at beginning of year	(2,406,047)		(2,382,167)		(2,077,741)
Shares repurchased for treasury	(97,862)		(23,880)		(304,426)
Balance at end of year	(2,503,909)		(2,406,047)		(2,382,167)

Total shareholders’ equity available to Arch	13,105,886		11,497,371		9,439,827
Non-redeemable noncontrolling interests	823,007		762,777		791,560
Total shareholders’ equity	$	13,928,893	$	12,260,148	$	10,231,387

See Notes to Consolidated Financial Statements


ARCH CAPITAL			89			2020 FORM 10-K


ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES CONSOLIDATED STATEMENTS OF CASH FLOWS (U.S. dollars in thousands)
	Year Ended December 31,
	2020		2019		2018
Operating Activities
Net income	$	1,465,711	$	1,693,300	$	727,821
Adjustments to reconcile net income to net cash provided by operating activities:
Net realized (gains) losses	(844,625)		(377,967)		390,379

Equity in net income or loss of investments accounted for using the equity method and other income or loss	(47,951)		(14,013)		36,694
Amortization of intangible assets	69,031		82,104		105,670
Share-based compensation	71,262		66,417		55,776
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable	2,113,827		489,981		243,734
Unearned premiums, net of ceded unearned premiums	445,781		252,569		114,772
Premiums receivable	(318,643)		(237,752)		(211,296)
Deferred acquisition costs	(143,948)		(47,260)		(37,847)
Reinsurance balances payable	65,950		182,132		73,438

Other items, net	10,110		(41,052)		60,181
Net cash provided by operating activities	2,886,505		2,048,459		1,559,322

Investing Activities
Purchases of fixed maturity investments	(39,765,277)		(30,053,777)		(33,327,660)
Purchases of equity securities	(1,595,010)		(811,967)		(1,001,149)
Purchases of other investments	(1,808,727)		(1,470,545)		(2,014,622)
Proceeds from sales of fixed maturity investments	37,949,346		28,595,865		31,513,271
Proceeds from sales of equity securities	1,147,264		429,818		1,118,445
Proceeds from sales, redemptions and maturities of other investments	1,029,578		1,209,559		1,561,958
Proceeds from redemptions and maturities of fixed maturity investments	871,134		643,265		892,755
Net settlements of derivative instruments	179,006		59,982		44,699
Net (purchases) sales of short-term investments	(1,029,681)		39,833		485,473
Change in cash collateral related to securities lending	81,210		(62,193)		180,883

Purchases of fixed assets	(39,872)		(37,837)		(29,809)
Other	(62,197)		(348,486)		21,736
Net cash provided by (used for) investing activities	(3,043,226)		(1,806,483)		(554,020)

Financing Activities

Redemption of preferred shares	—		—		(92,555)
Purchases of common shares under share repurchase program	(83,472)		(2,871)		(282,762)
Proceeds from common shares issued, net	1,876		6,203		(7,608)
Proceeds from borrowings	1,018,793		200,083		218,259
Repayments of borrowings	(359,000)		(49,182)		(576,401)
Change in cash collateral related to securities lending	(81,210)		62,193		(180,883)
Change in third party investment in non-redeemable noncontrolling interests	(2,867)		(75,056)		—
Change in third party investment in redeemable noncontrolling interests	—		(161,882)		—
Dividends paid to redeemable noncontrolling interests	(4,945)		(12,515)		(17,989)
Other	73,715		(6,023)		(7,226)
Preferred dividends paid	(41,612)		(41,612)		(41,645)
Net cash provided by (used for) financing activities	521,278		(80,662)		(988,810)

Effects of exchange rate changes on foreign currency cash and restricted cash	22,289		17,741		(19,133)

Increase (decrease) in cash and restricted cash	386,846		179,055		(2,641)
Cash and restricted cash, beginning of year	903,698		724,643		727,284
Cash and restricted cash, end of year	$	1,290,544	$	903,698	$	724,643

Income taxes paid (received)	$	202,940	$	109,463	$	(980)
Interest paid	$	133,491	$	126,945	$	119,775

See Notes to Consolidated Financial Statements


ARCH CAPITAL			90			2020 FORM 10-K

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

1. General

Arch Capital Group Ltd. (“Arch Capital”) is a publicly listed Bermuda exempted company which provides insurance, reinsurance and mortgage insurance on a worldwide basis through its wholly owned subsidiaries.

As used herein, the “Company” means Arch Capital and its subsidiaries. Similarly, “Common Shares” means the common shares of Arch Capital. The Company’s consolidated financial statements include the results of Watford Holdings Ltd., and its wholly owned subsidiaries (“Watford”). See note 12, “Variable Interest Entity and Noncontrolling Interests”.

2. Business Acquired

Barbican Group Holdings Limited

On November 29, 2019, the Company closed the acquisition of Barbican Group Holdings Limited and its subsidiaries (collectively, “Barbican”).

The Ardonagh Group

On January 1, 2019, the Company’s U.K. insurance operations entered into a transaction with The Ardonagh Group to acquire renewal rights for a U.K. commercial lines book of business, consisting of commercial property, casualty, motor, professional liability, personal accident and travel business.

McNeil

On December 6, 2018, the Company closed the acquisition of McNeil & Co. (“McNeil”), a nationwide leader in specialized risk management and insurance programs headquartered in Cortland, New York.

3. Significant Accounting Policies

(a) Basis of Presentation

The consolidated financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America (“GAAP”) and include the accounts of Arch Capital and its subsidiaries, including Arch Reinsurance Ltd. (“Arch Re Bermuda”), Arch Reinsurance Company (“Arch Re U.S.”), Arch Capital Group (U.S.) Inc.(“Arch-U.S.”), Arch Insurance Company, Arch Specialty Insurance Company, Arch Property & Casualty Insurance Company (“Arch P&C”), Arch Indemnity Insurance Company, Arch Insurance Canada Ltd. (“Arch Insurance Canada”), Arch Reinsurance Europe Designated Activity Company (“Arch Re Europe”), Arch Mortgage Insurance

Company (“AMIC”), Arch Mortgage Guaranty Company, United Guaranty Residential Insurance Company (“UGRIC”), Arch Insurance (EU) Designated Activity Company (“Arch Insurance (EU)”), Arch Insurance (UK) Limited (“Arch Insurance (U.K.)”), Lloyd’s of London syndicate: Arch Syndicate 2012 (“Arch Syndicate 2012”) and Arch Syndicate 1955 (“Arch Syndicate 1955”) and Watford. All significant intercompany transactions and balances have been eliminated in consolidation.

The preparation of financial statements in conformity with GAAP requires management to make estimates and assumptions that affect the reported amounts of assets and liabilities and disclosure of contingent assets and liabilities at the date of the financial statements and the reported amounts of revenues and expenses during the reporting period. Actual results could differ materially from those estimates and assumptions. The Company’s principal estimates include:

The reserve for losses and loss adjustment expenses;
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses, including the provision for uncollectible amounts;
Estimates of written and earned premiums;
The valuation of the investment portfolio and assessment of allowance for credit losses;
The valuation of purchased intangible assets;
The assessment of goodwill and intangible assets for impairment; and
The valuation of deferred tax assets.

The Company has reclassified the presentation of certain prior year information to conform to the current presentation. Such reclassifications had no effect on the Company’s net income, shareholders’ equity or cash flows.

(b) Premium Revenues and Related Expenses

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

Reinsurance. Reinsurance premiums written include amounts reported by brokers and ceding companies, supplemented by the Company’s own estimates of premiums where reports have not been received. The determination of premium estimates requires a review of the Company’s experience with the ceding companies, familiarity with each market, the


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timing of the reported information, an analysis and understanding of the characteristics of each line of business, and management’s judgment of the impact of various factors, including premium or loss trends, on the volume of business written and ceded to the Company. On an ongoing basis, the Company’s underwriters review the amounts reported by these third parties for reasonableness based on their experience and knowledge of the subject class of business, taking into account the Company’s historical experience with the brokers or ceding companies. In addition, reinsurance contracts under which the Company assumes business generally contain specific provisions which allow the Company to perform audits of the ceding company to ensure compliance with the terms and conditions of the contract, including accurate and timely reporting of information. Based on a review of all available information, management establishes premium estimates where reports have not been received. Premium estimates are updated when new information is received and differences between such estimates and actual amounts are recorded in the period in which estimates are changed or the actual amounts are determined.

Reinsurance premiums written are recorded based on the type of contracts the Company writes. Premiums on the Company’s excess of loss and pro rata reinsurance contracts are estimated when the business is underwritten. For excess of loss contracts, premiums are recorded as written based on the terms of the contract. Estimates of premiums written under pro rata contracts are recorded in the period in which the underlying risks are expected to incept and are based on information provided by the brokers and the ceding companies. For multi-year reinsurance treaties which are payable in annual installments, generally, only the initial annual installment is included as premiums written at policy inception due to the ability of the reinsured to commute or cancel coverage during the term of the policy. The remaining annual installments are included as premiums written at each successive anniversary date within the multi-year term.

Reinsurance premiums written, irrespective of the class of business, are generally earned on a pro rata basis over the terms of the underlying policies or reinsurance contracts. Contracts and policies written on a “losses occurring” basis cover claims that may occur during the term of the contract or policy, which is typically 12 months. Accordingly, the premium is earned evenly over the term. Contracts which are written on a “risks attaching” basis cover claims which attach to the underlying insurance policies written during the terms of such contracts. Premiums earned on such contracts usually extend beyond the original term of the reinsurance contract, typically resulting in recognition of premiums earned over a 24-month period. Certain of the Company’s reinsurance contracts include provisions that adjust premiums or acquisition expenses based upon the experience under the contracts. Premiums written and earned, as well as related

acquisition expenses, are recorded based upon the projected experience under such contracts.

The Company also writes certain reinsurance business that is intended to provide insurers with risk management solutions that complement traditional reinsurance. Under these contracts, the Company assumes a measured amount of insurance risk in exchange for an anticipated margin, which is typically lower than on traditional reinsurance contracts. The terms and conditions of these contracts may include additional or return premiums based on loss experience, loss corridors, sublimits and caps. Examples of such business include aggregate stop-loss coverages, financial quota share coverages and multi-year retrospectively rated excess of loss coverages. If these contracts are deemed to transfer risk, they are accounted for as reinsurance. Otherwise, such contracts are accounted for under the deposit method.

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

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

Premium estimates are reviewed by management at least quarterly. Such review includes a comparison of actual reported premiums to expected ultimate premiums along with a review of the aging and collection of premium estimates. Based on management’s review, the appropriateness of the premium estimates is evaluated, and any adjustment to these estimates is recorded in the period in which it becomes known. Adjustments to premium estimates could be material


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and such adjustments could directly and significantly impact earnings favorably or unfavorably in the period they are determined because the estimated premium may be fully or substantially earned. A significant portion of amounts included as premiums receivable, which represent estimated premiums written, net of commissions, are not currently due based on the terms of the underlying contracts.

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

Premiums receivable include amounts receivable from agents, brokers and insured that are both currently due and amounts not yet due on insurance, reinsurance and mortgage insurance policies. Premiums receivable balances are reported net of an allowance for expected credit losses. The Company monitors credit risk associated with premiums receivable through its ongoing review of amounts outstanding, aging of the receivable, historical loss data, and counterparty financial strength measures. The allowance also includes estimated uncollectible amounts related to dispute risk. In certain instances, credit risk may be reduced by the Company’s right to offset loss obligations or unearned premiums against premiums receivable. Any allowance for credit losses is charged to net realized gains (losses) in the period the receivable is recorded and revised in subsequent periods to reflect changes in the Company’s estimate of expected credit losses. See note 7 , “Allo wance for Expected Credit Losses ” for additional information.

Acquisition Costs. Acquisition costs that are directly related and incremental to the successful acquisition or renewal of business are deferred and amortized based on the type of contract. The Company’s insurance and reinsurance operations capitalize incremental direct external costs that result from acquiring a contract but do not capitalize salaries, benefits and other internal underwriting costs. For the Company’s mortgage insurance operations, which include a substantial direct sales force, both external and certain internal direct costs are deferred and amortized. For property and casualty insurance and reinsurance contracts, deferred acquisition costs are amortized over the period in which the related premiums are earned. Consistent with mortgage insurance industry accounting practice, amortization of acquisition costs related to the mortgage insurance contracts for each underwriting year’s book of business is recorded in proportion to estimated gross profits. Estimated gross profits

are comprised of earned premiums and losses and loss adjustment expenses. For each underwriting year, the Company estimates the rate of amortization to reflect actual experience and any changes to persistency or loss development.

Deferred acquisition costs are carried at their estimated realizable value and take into account anticipated losses and loss adjustment expenses, based on historical and current experience, and anticipated investment income.

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

To assess the need for a PDR on mortgage exposures, the Company develops loss projections based on modeled loan defaults related to its current policies in force. This projection is based on recent trends in default experience, severity and rates of defaulted loans moving to claim, as well as recent trends in the rate at which loans are prepaid, and incorporates anticipated interest income. Evaluating the expected profitability of the Company’s existing mortgage insurance business and the need for a PDR for its mortgage business involves significant reliance upon assumptions and estimates with regard to the likelihood, magnitude and timing of potential losses and premium revenues.

No premium deficiency charges were recorded by the Company during 2020, 2019 or 2018.

(c) Deposit Accounting

Certain assumed reinsurance contracts that are deemed not to transfer insurance risk, are accounted for using the deposit method of accounting. However, it is possible that the Company could incur financial losses on such contracts. Management exercises significant judgment in the assumptions used in determining whether assumed contracts should be accounted for as reinsurance contracts or deposit contracts. For those contracts that contain only significant underwriting risk, the estimated profit margin is deferred and amortized over the contract period and such amount is included in the Company’s underwriting results. When the estimated profit margin is explicit, the margin is reflected as other underwriting income and any adverse financial results on such contracts are reflected as incurred losses. When the estimated profit margin is implicit, the margin is reflected as an offset to paid losses and any adverse financial results on such contracts are reflected as incurred losses. Additional


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judgments are required when applying the accounting guidance with respect to the revenue recognition criteria for contracts deemed to transfer only significant underwriting risk. For those contracts that contain only significant timing risk, an accretion rate is established at inception of the contract based on actuarial estimates whereby the deposit accounting liability is increased to the estimated amount payable over the contract term. The accretion on the deposit is based on the expected rate of return required to fund the expected future payment obligations. Periodically the Company reassesses the estimated ultimate liability and the related expected rate of return. The accretion of the deposit accounting liability as well as changes to the estimated ultimate liability and the accretion rate would be reflected as part of interest expense in the Company’s results of operations. Any negative accretion in a deposit accounting liability is shown in other underwriting income in the Company’s results of operations.

Under some of these contracts, the ceding company retains the related assets on a funds-held basis. Such amounts are included in “Other assets” on the Company’s balance sheet. Interest income produced by those assets are recorded as part of net investment income in the Company's results of operations.

(d) Retroactive Reinsurance

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

(e) Reinsurance Ceded

In the normal course of business, the Company purchases reinsurance to increase capacity and to limit the impact of individual losses and events on its underwriting results by reinsuring certain levels of risk with other insurance enterprises or reinsurers. The Company uses pro rata, excess of loss and facultative reinsurance contracts. Reinsurance ceding commissions that represent a recovery of acquisition costs are recognized as a reduction to acquisition costs while

the remaining portion is deferred. The accompanying consolidated statement of income reflects premiums and losses and loss adjustment expenses and acquisition costs, net of reinsurance ceded. See note 8, “Reinsurance” for information on the Company's reinsurance usage. Reinsurance premiums ceded and unpaid losses and loss adjustment expenses recoverable are estimated in a manner consistent with that of the original policies issued and the terms of the reinsurance contracts. If the reinsurers are unable to satisfy their obligations under the agreements, the Company’s insurance or reinsurance subsidiaries would be liable for such defaulted amounts.

Reinsurance recoverables are recorded as assets, predicated on the reinsurers’ ability to meet their obligations under the reinsurance agreements. In certain instances, the Company obtains collateral, including letters of credit and trust accounts to further reduce the credit exposure on its reinsurance recoverables. The Company reports its reinsurance recoverables net of an allowance for expected credit loss. The allowance is based upon the Company’s ongoing review of amounts outstanding, the financial condition of its reinsurers, amounts and form of collateral obtained and other relevant factors. A ratings based probability-of-default and loss-given-default methodology is used to estimate the allowance for expected credit loss. Any allowance for credit losses is charged to net realized gains (losses) in the period the recoverable is recorded and revised in subsequent periods to reflect changes in the Company’s estimate of expected credit losses. See note 7 , “Allowance for Expected Credit Losses” for additional information.

(f) Cash

Cash includes cash equivalents, which are investments with original maturities of three months or less which are not part of the investment portfolio.

(g) Restricted Cash

Restricted cash represents amounts held for the benefit of third parties and is legally or contractually restricted as to withdrawal or usage by the Company. Such amounts are included in “Other assets” on the Company’s balance sheet.

(h) Investments

The Company currently classifies substantially all of its fixed maturity investments and short-term investments as “available for sale” and, accordingly, they are carried at estimated fair value (also known as fair value) with the changes in fair value recorded as an unrealized gain or loss component of accumulated other comprehensive income in shareholders’ equity. The fair value of fixed maturity securities and equity securities is generally determined from quotations received from nationally recognized pricing


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services, or when such prices are not available, by reference to broker or underwriter bid indications. Short-term investments comprise securities due to mature within one year of the date of issue. Short-term investments include certain cash equivalents which are part of investment portfolios under the management of external and internal investment managers.

The Company 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. Such securities have been reclassified as “Securities pledged under securities lending, at fair value.” The Company maintains legal control over the securities it lends, 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. Collateral received is required at a rate of 102% or greater of the fair value of the loaned securities including accrued investment income and is monitored and maintained by the lending agent. Such collateral is reflected as “Collateral received under securities lending, at fair value.”

The Company’s investment portfolio includes certain funds that, due to their ownership structure, are accounted for by the Company using the equity method. In applying the equity method, these investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the fair value of the underlying securities in the funds). Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds. Changes in the carrying value of such investments are recorded in net income as “Equity in net income (loss) of investments accounted for using the equity method.” As such, fluctuations in the carrying value of the investments accounted for using the equity method may increase the volatility of the Company’s reported results of operations.

The Company’s investment portfolio includes equity securities that are accounted for at fair value. Such holdings primarily include publicly traded common stocks. Dividend income on equities is reflected in net investment income. Changes in fair value on equity securities are included in “Net realized gains (losses)” in the consolidated statement of income.

The Company elected to carry certain fixed maturity securities, equity securities and other investments at fair value under the fair value option afforded by accounting guidance regarding the fair value option for financial assets and liabilities. The fair value for certain of the Company’s other investments are determined using net asset values (“NAVs”) as advised by external fund managers. The NAV

is based on the fund manager’s valuation of the underlying holdings in accordance with the fund’s governing documents.

Changes in fair value of investments accounted for using the fair value option are included in “Net realized gains (losses).” The primary reasons for electing the fair value option were to address simplification and cost-benefit considerations.

The Company invests in reverse repurchase agreements that are generally treated as collateralized receivables. Receivables for reverse repurchase agreements are reflected in “Other investments” in the Company's consolidated balance sheet and may be short or long-term investments depending on their terms. These agreements are recorded at their contracted resale amount plus accrued interest, other than those that are accounted for at fair value. In reverse repurchase transactions, the Company obtains an interest in the purchased assets that are received as collateral.

The Company invests in limited partner interests and shares of limited liability companies. Such amounts are included in investments accounted for using the equity method and other investments. These investments can often have characteristics of a variable interest entity (“VIE”). A VIE refers to entities that have characteristics such as (i) insufficient equity at risk to allow the entity to finance its activities without additional financial support or (ii) instances where the equity investors, as a group, do not have the characteristic of a controlling financial interest. If the Company is determined to be the primary beneficiary, it is required to consolidate the VIE. The primary beneficiary is defined as the variable interest holder that is determined to have the controlling financial interest as a result of having both (i) the power to direct the activities of a VIE that most significantly impact the economic performance of the VIE and (ii) the obligation to absorb losses or right to receive benefits from the VIE that could potentially be significant to the VIE. At inception of the VIE as well as on an ongoing basis, the Company determines whether it is the primary beneficiary based on an analysis of the Company’s level of involvement in the VIE, the contractual terms, and the overall structure of the VIE. The Company's maximum exposure to loss with respect to these investments is limited to the investment carrying amounts reported in the Company's consolidated balance sheet and any unfunded commitment.

The Company conducts a periodic review to identify and evaluate credit based impairments related to the Company’s available for sale investments. The Company derives estimated credit losses by comparing expected future cash flows to be collected to the amortized cost of the security. Estimates of expected future cash flows consider among other things, macroeconomic conditions as well as the financial condition, near-term and long-term prospects for the issuer, and the likelihood of the recoverability of principal and interest. Effective January 1, 2020, credit losses are


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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.

Prior to January 1, 2020, the Company performed quarterly reviews of its investments to determine whether declines in fair value below the cost basis were considered other-than-temporary in accordance with applicable accounting guidance regarding the recognition and presentation of OTTI. The process of determining whether a security was other-than-temporarily impaired required judgment and involved analyzing many factors. These factors included (i) an analysis of the liquidity, business prospects and overall financial condition of the issuer, (ii) the time period in which there was a significant decline in value, (iii) the significance of the decline and (iv) the analysis of specific credit events. When there were credit-related losses associated with debt securities for which the Company did not have an intent to sell and it was more likely than not that it would not be required to sell the security before recovery of its cost basis, the amount of the OTTI related to a credit loss was recognized in earnings and the amount of the OTTI related to other factors (e.g., interest rates, market conditions, etc.) was recorded as a component of other comprehensive income (loss). The amount of the credit loss of an impaired debt security was the difference between the amortized cost and the greater of (i) the present value of expected future cash flows and (ii) the fair value of the security. In instances where no credit loss existed but it was more likely than not that the Company would have to sell the debt security prior to the anticipated recovery, the decline in fair value below amortized cost was recognized as an OTTI in earnings. In periods after the recognition of an OTTI on debt securities, the Company accounted for such securities as if they had been purchased on the measurement date of the OTTI at an amortized cost basis equal to the previous amortized cost basis less the OTTI recognized in earnings. For debt securities for which OTTI were recognized in earnings, the

difference between the new amortized cost basis and the cash flows expected to be collected would be accreted or amortized into net investment income. See note 9, “Investment Information” for additional information.

Net investment income includes interest and dividend income together with amortization of market premiums and discounts and is net of investment management and custody fees. Anticipated prepayments and expected maturities are used in applying the interest method for certain investments such as mortgage and other asset-backed securities. When actual prepayments differ significantly from anticipated prepayments, the effective yield is recalculated to reflect actual payments to date and anticipated future payments. The net investment in such securities is adjusted to the amount that would have existed had the new effective yield been applied since the acquisition of the security. Such adjustments, if any, are included in net investment income when determined.

Investment gains or losses realized on the sale of investments, except for certain fund investments, are determined on a first-in, first-out basis and are reflected in net income. Investment gains or losses realized on the sale of certain fund investments are determined on an average cost basis. Unrealized appreciation or decline in the value of available for sale securities, which are carried at fair value, is excluded from net income and recorded as a separate component of accumulated other comprehensive income, net of applicable deferred income tax.

(i) Derivative Instruments

The Company recognizes all derivative instruments, including embedded derivative instruments, at fair value in its consolidated balance sheets. The Company employs the use of derivative instruments within its operations to mitigate risks arising from assets and liabilities held in foreign currencies as well as part of its overall investment strategy. For such instruments, changes in assets and liabilities measured at fair value are recorded as “Net realized gains” in the consolidated statements of income. In addition, the Company’s derivative instruments include amounts related to underwriting activities where an insurance or reinsurance contract meets the accounting definition of a derivative instrument. For such contracts, changes in fair value are reflected in “Other underwriting income” in the consolidated statements of income as the underlying contract originates from the Company’s underwriting operations. For the periods ended 2020, 2019, and 2018, the Company did not designate any derivative instruments as hedges under the relevant accounting guidance. See note 11, “Derivative Instruments” for additional information.


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(j) Reserves for Losses and Loss Adjustment Expenses

Insurance and Reinsurance. The reserve for losses and loss adjustment expenses consists of estimates of unpaid reported losses and loss adjustment expenses and estimates for losses incurred but not reported. The reserve for unpaid reported losses and loss adjustment expenses, established by management based on reports from ceding companies and claims from insureds, excludes estimates of amounts related to losses under high deductible policies, and represents the estimated ultimate cost of events or conditions that have been reported to or specifically identified by the Company. Such reserves are supplemented by management’s estimates of reserves for losses incurred for which reports or claims have not been received. The Company’s reserves are based on a combination of reserving methods, incorporating both Company and industry loss development patterns. The Company selects the initial expected loss and loss adjustment expense ratios based on information derived by its underwriters and actuaries during the initial pricing of the business, supplemented by industry data where appropriate. Such ratios consider, among other things, rate changes and changes in terms and conditions that have been observed in the market. These estimates are reviewed regularly and, as experience develops and new information becomes known, the reserves are adjusted as necessary. Such adjustments, if any, are reflected in income in the period in which they are determined. As actual loss information has been reported, the Company has developed its own loss experience and its reserving methods include other actuarial techniques. Over time, such techniques have been given further weight in its reserving process based on the continuing maturation of the Company’s reserves. Inherent in the estimates of ultimate losses and loss adjustment expenses are expected trends in claims severity and frequency and other factors which may vary significantly as claims are settled. Accordingly, ultimate losses and loss adjustment expenses may differ materially from the amounts recorded in the accompanying consolidated financial statements. Losses and loss adjustment expenses are recorded on an undiscounted basis, except for excess workers’ compensation and employers’ liability business written by the Company’s insurance operations.

Mortgage. The reserves for mortgage guaranty insurance losses and loss adjustment expenses are the estimated claim settlement costs on notices of delinquency that have been received by the Company, as well as loan delinquencies that have been incurred but have not been reported by the lenders. Consistent with primary mortgage insurance industry accounting practice, the Company does not establish loss reserves for future claims on insured loans that are not currently delinquent (defined as two or more payments in arrears). The Company establishes loss reserves on a case-by-case basis when insured loans are reported delinquent using estimated claim rates and average claim sizes for each cohort, net of any salvage recoverable. The Company also reserves

for delinquencies that have occurred but have not yet been reported to the Company prior to the close of an accounting period. To determine this reserve, the Company estimates the number of delinquencies not yet reported using historical information regarding late reported delinquencies and applies estimated claim rates and claim sizes for the estimated delinquencies not yet reported.

The establishment of reserves across the Company’s segments is an inherently uncertain process, are necessarily based on estimates, and the ultimate net cost may vary from such estimates. The methods for making such estimates and for establishing the resulting liability are reviewed and updated using the most current information available. Any resulting adjustments, which may be material, are reflected in current operations.

(k) Contractholder Receivables and Payables and Collateral Held for Insured Obligations

Certain insurance policies written by the Company’s U.S. insurance operations feature large deductibles, primarily in its construction and national accounts line of business. Under such contracts, the Company is obligated to pay the claimant for the full amount of the claim. The Company is subsequently reimbursed by the policy holder for the deductible amount. These amounts are included on a gross basis in the consolidated balance sheet as contractholder payables and contractholder receivables. In the event that the Company is unable to collect from the policyholder, the Company would be liable for such defaulted amounts. Collateral, primarily in the form of letters of credit, cash and trusts, is obtained from the policyholder to mitigate the Company’s credit risk. In the instances where the Company receives collateral in the form of cash, the Company reflects it in “Collateral held for insured obligations.”

Contractholder receivables are reported net of an allowance for expected credit losses. The allowance is based upon the Company’s ongoing review of amounts outstanding, changes in policyholder credit standing, amounts and form of collateral obtained, and other relevant factors. A ratings based probability-of-default and loss-given-default methodology is used to estimate the allowance for expected credit losses. Any allowance for credit losses is charged to net realized gains (losses) in the period the receivable is recorded and revised in subsequent periods to reflect changes in the Company’s estimate of expected credit losses. See note 7 , “Allowance for Expected Credit Losses” for additional information.

(l) Foreign Exchange

Assets and liabilities of foreign operations whose functional currency is not the U.S. Dollar are translated at the prevailing exchange rates at each balance sheet date. Revenues and


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expenses of such foreign operations are translated at average exchange rates during the year. The net effect of the translation adjustments for foreign operations is included in accumulated other comprehensive income, net of applicable deferred income tax. Monetary assets and liabilities, such as premiums receivable and the reserve for losses and loss adjustment expenses, denominated in foreign currencies are revalued at the exchange rate in effect at the balance sheet date with the resulting foreign exchange gains and losses included in net income. Accounts that are classified as non-monetary, such as deferred acquisition costs and the unearned premium reserves, are not revalued. In the case of foreign currency denominated fixed maturity securities which are classified as “available for sale,” the change in exchange rates between the local currency in which the investments are denominated and the Company’s functional currency at each balance sheet date is included in unrealized appreciation or decline in value of securities, a component of accumulated other comprehensive income, net of applicable deferred income tax.

(m) Income Taxes

Deferred income taxes reflect the expected future tax consequences of temporary differences between the carrying amounts of assets and liabilities for financial reporting purposes and amounts used for income tax purposes. A valuation allowance is recorded if it is more likely than not that some or all of a deferred tax asset may not be realized. The Company considers future taxable income and feasible tax planning strategies in assessing the need for a valuation allowance. In the event the Company determines that it will not be able to realize all or part of its deferred income tax assets in the future, an adjustment to the deferred income tax assets would be charged to income in the period in which such determination is made. In addition, if the Company subsequently assesses that the valuation allowance is no longer needed, a benefit would be recorded to income in the period in which such determination is made. See note 15, “Income Taxes” for additional information.

The Company recognizes a tax benefit where it concludes that it is more likely than not that the tax benefit will be sustained on audit by the taxing authority based solely on the technical merits of the associated tax position. If the recognition threshold is met, the Company recognizes a tax benefit measured at the largest amount of the tax benefit that, in the Company’s judgment, is greater than 50% likely to be realized. The Company records interest and penalties related to unrecognized tax benefits in the provision for income taxes.

(n) Share-Based Payment Arrangements

The Company applies a fair value based measurement method in accounting for its share-based payment

arrangements with eligible employees and directors. Compensation expense is estimated based on the fair value of the award at the grant date and is recognized in net income over the requisite service period with a corresponding increase in shareholders’ equity. No value is attributed to awards that employees forfeit because they fail to satisfy vesting conditions. The Company’s (i) time-based awards generally vest over a three year period with one-third vesting on the first, second and third anniversaries of the grant date and (ii) performance-based awards cliff vest after each three year performance period based on achievement of the specified performance criteria. The share-based compensation expense associated with awards that have graded vesting features and vest based on service conditions only is calculated on a straight-line basis over the requisite service period for the entire award. Compensation expense recognized in connection with performance awards is based on the achievement of the specified performance and service conditions. The final measure of compensation expense recognized over the requisite service period reflects the final performance outcome. During the recognition period compensation expense is accrued based on the performance condition that is probable of achievement. For awards granted to retirement-eligible employees where no service is required for the employee to retain the award, the grant date fair value is immediately recognized as compensation expense at the grant date because the employee is able to retain the award without continuing to provide service. For employees near retirement eligibility, attribution of compensation cost is over the period from the grant date to the retirement eligibility date. These charges had no impact on the Company’s cash flows or total shareholders’ equity. See note 22, “Share-Based Compensation” for information relating to the Company’s share-based payment awards.

(o) Guaranty Fund and Other Related Assessments

Liabilities for guaranty fund and other related assessments in the Company’s insurance and reinsurance operations are accrued when the Company receives notice that an amount is payable, or earlier if a reasonable estimate of the assessment can be made.

(p) Treasury Shares

Treasury shares are common shares purchased by the Company and not subsequently canceled. These shares are recorded at cost and result in a reduction of the Company’s shareholders’ equity in its Consolidated Balance Sheets.

(q) Goodwill and Intangible Assets

Goodwill represents the excess of the purchase price of an acquisition over the fair value of the net assets acquired and is assigned to the applicable reporting unit at acquisition. Goodwill is evaluated for impairment on an annual basis.


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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

Impairment tests may be performed more frequently if the facts and circumstances indicate a possible impairment. In performing impairment tests, the Company may first assess qualitative factors to determine whether it is more likely than not (that is, more than a 50% probability) that the fair value of a reporting unit exceeds its carrying amount as a basis for determining whether it is necessary to perform goodwill impairment test described in the accounting guidance.

Indefinite-lived intangible assets, such as insurance licenses are evaluated for impairment similar to goodwill. Finite-lived intangible assets and liabilities include the value of acquired insurance and reinsurance contracts, which are estimated based on the present value of future expected cash flows and amortized in proportion to the estimated profits expected to be realized. Other finite-lived intangible assets, including customer lists, trade name and IT platforms, are amortized over their useful lives. Finite-lived intangible assets and liabilities are periodically reviewed for indicators of impairment. An impairment is recognized when the carrying amount is not recoverable from its undiscounted cash flows and is measured as the difference between the carrying amount and fair value.

If goodwill or intangible assets are impaired, such assets are written down to their fair values with the related expense recorded in the Company’s results of operations.

(r) 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.

The Company adopted ASU 2020-09, “Debt (Topic 470): Amendments to SEC Paragraphs Pursuant to SEC Release No. 33-10762.” This ASU aligns the SEC release issued in March 2020 amending 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.


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Recently Issued Accounting Standards Not Yet Adopted

ASU 2019-12, “Simplifying the Accounting for Income Taxes,” was issued in December 2019. 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.

ASU 2020-04, “Facilitation of the Effects of Reference Rate Reform on Financial Reporting,” was issued in March 2020. 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.

4. Segment Information

The Company classifies its businesses into three underwriting segments — insurance, reinsurance and mortgage — and two other operating segments — ‘other’ and corporate (non-underwriting). The Company determined its reportable segments using the management approach described in accounting guidance regarding disclosures about segments of an enterprise and related information. The accounting policies of the segments are the same as those used for the preparation of the Company’s consolidated financial statements. Intersegment business is allocated to the segment accountable for the underwriting results.

The Company’s insurance, reinsurance and mortgage segments each have managers who are responsible for the overall profitability of their respective segments and who are directly accountable to the Company’s chief operating decision makers, the Chief Executive Officer of Arch Capital, Chief Financial Officer and Treasurer of Arch Capital and the

President and Chief Underwriting Officer of Arch Capital. The chief operating decision makers do not assess performance, measure return on equity or make resource allocation decisions on a line of business basis. Management measures segment performance for its three underwriting segments based on underwriting income or loss. The Company does not manage its assets by underwriting segment, with the exception of goodwill and intangible assets, and, accordingly, investment income is not allocated to each underwriting segment.

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

Construction and national accounts: primary and excess casualty coverages to middle and large accounts in the construction industry and a wide range of products for middle and large national accounts, specializing in loss sensitive primary casualty insurance programs (including large deductible, self-insured retention and retrospectively rated programs).
Excess and surplus casualty: primary and excess casualty insurance coverages, including middle market energy business, and contract binding, which primarily provides casualty coverage through a network of appointed agents to small and medium risks.
Lenders products: collateral protection, debt cancellation and service contract reimbursement products to banks, credit unions, automotive dealerships and original equipment manufacturers and other specialty programs that pertain to automotive lending and leasing.
Professional lines: directors’ and officers’ liability, errors and omissions liability, employment practices liability, fiduciary liability, crime, professional indemnity and other financial related coverages for corporate, private equity, venture capital, real estate investment trust, limited partnership, financial institution and not-for-profit clients of all sizes and medical professional and general liability insurance coverages for the healthcare industry. The business is predominately written on a claims-made basis.
Programs: primarily package policies, underwriting workers’ compensation and umbrella liability business in support of desirable package programs, targeting program managers with unique expertise and niche products offering general liability, commercial automobile, inland marine and property business with minimal catastrophe exposure.
Property, energy, marine and aviation: primary and excess general property insurance coverages, including catastrophe-exposed property coverage, for commercial


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clients. Coverages for marine include hull, war, specie and liability. Aviation and stand-alone terrorism are also offered.

Travel, accident and health: specialty travel and accident and related insurance products for individual, group travelers, travel agents and suppliers, as well as accident and health, which provides accident, disability and medical plan insurance coverages for employer groups, medical plan members, students and other participant groups.
Other: includes alternative market risks (including captive insurance programs), excess workers’ compensation and employer’s liability insurance coverages for qualified self-insured groups, associations and trusts, and contract and commercial surety coverages, including contract bonds (payment and performance bonds) primarily for medium and large contractors and commercial surety bonds for Fortune 1000 companies and smaller transaction business programs.

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

Casualty: provides coverage to ceding company clients on third party liability and workers’ compensation exposures from ceding company clients, primarily on a treaty basis. Exposures include, among others, executive assurance, professional liability, workers’ compensation, excess and umbrella liability, excess motor and healthcare business.
Marine and aviation: provides coverage for energy, hull, cargo, specie, liability and transit, and aviation business, including airline and general aviation risks. Business written may also include space business, which includes coverages for satellite assembly, launch and operation for commercial space programs.

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

Property catastrophe: provides protection for most catastrophic losses that are covered in the underlying policies written by reinsureds, including hurricane, earthquake, flood, tornado, hail and fire, and coverage for other perils on a case-by-case basis. Property catastrophe reinsurance provides coverage on an excess

of loss basis when aggregate losses and loss adjustment expense from a single occurrence of a covered peril exceed the retention specified in the contract.

Property excluding property catastrophe: provides coverage for both personal lines and commercial property exposures and principally covers buildings, structures, equipment and contents. The primary perils in this business include fire, explosion, collapse, riot, vandalism, wind, tornado, flood and earthquake. Business is assumed on both a proportional and excess of loss basis. In addition, facultative business is written which focuses on commercial property risks on an excess of loss basis.
Other. includes life reinsurance business on both a proportional and non-proportional basis, casualty clash business and, in limited instances, non-traditional business which is intended to provide insurers with risk management solutions that complement traditional reinsurance.

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. AMIC and UGRIC (components of “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 government sponsored enterprise, or “GSE.”. Arch MI U.S. also includes Arch Mortgage Guaranty Company, which is not a GSE-approved entity.

The corporate (non-underwriting) segment results include net investment income, other income (loss), other expenses incurred by the Company, interest expense, net realized gains or losses, net impairment losses included in earnings, equity in net income or loss of investments accounted for using the equity method, net foreign exchange gains or losses, transaction costs and other, income taxes and items related to the Company’s non-cumulative preferred shares. Such amounts exclude the results of the ‘other’ segment. The ‘other’ segment includes the results of Watford (see note 12, “Variable Interest Entity and Noncontrolling Interests”). Watford has its own management and board of directors that is responsible for the overall profitability of the ‘other’ segment. For the ‘other’ segment, performance is measured based on net income or loss.


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The following tables summarize the Company’s underwriting income or loss by segment, together with a reconciliation of underwriting income or loss to net income available to Arch common shareholders, summary information regarding net premiums written and earned by major line of business and net premiums written by location:


	Year Ended December 31, 2020
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	4,688,562		$	3,472,086		$	1,473,999		$	9,632,691		$	728,546		$	10,088,068
Premiums ceded	(1,525,655)			(1,014,716)			(194,149)			(2,732,564)			(190,957)			(2,650,352)
Net premiums written	3,162,907			2,457,370			1,279,850			6,900,127			537,589			7,437,716
Change in unearned premiums	(291,487)			(295,141)			118,085			(468,543)			22,762			(445,781)
Net premiums earned	2,871,420			2,162,229			1,397,935			6,431,584			560,351			6,991,935
Other underwriting income (loss)	(31)			4,454			20,316			24,739			2,045			26,784
Losses and loss adjustment expenses	(2,092,453)			(1,628,320)			(528,344)			(4,249,117)			(440,482)			(4,689,599)
Acquisition expenses	(418,483)			(354,048)			(134,240)			(906,771)			(98,071)			(1,004,842)
Other operating expenses	(489,153)			(168,011)			(162,202)			(819,366)			(55,810)			(875,176)
Underwriting income (loss)	$	(128,700)		$	16,304		$	593,465		481,069			(31,967)			449,102

Net investment income										401,908			117,700			519,608
Net realized gains (losses)										813,781			9,679			823,460

Equity in net income (loss) of investments accounted for using the equity method										146,693			—			146,693
Other income (loss)										16,795			—			16,795
Corporate expenses										(68,492)			—			(68,492)
Transaction costs and other										(9,456)			(4,040)			(13,496)
Amortization of intangible assets										(69,031)			—			(69,031)
Interest expense										(120,214)			(23,242)			(143,456)
Net foreign exchange gains (losses)										(80,161)			(3,473)			(83,634)
Income (loss) before income taxes										1,512,892			64,657			1,577,549
Income tax expense										(111,812)			(26)			(111,838)
Net income (loss)										1,401,080			64,631			1,465,711
Amounts attributable to redeemable noncontrolling interests										(2,997)			(4,117)			(7,114)
Amounts attributable to nonredeemable noncontrolling interests										—			(53,076)			(53,076)
Net income (loss) available to Arch										1,398,083			7,438			1,405,521
Preferred dividends										(41,612)			—			(41,612)

Net income (loss) available to Arch common shareholders										$	1,356,471		$	7,438		$	1,363,909

Underwriting Ratios
Loss ratio	72.9		%	75.3		%	37.8		%	66.1		%	78.6		%	67.1		%
Acquisition expense ratio	14.6		%	16.4		%	9.6		%	14.1		%	17.5		%	14.4		%
Other operating expense ratio	17.0		%	7.8		%	11.6		%	12.7		%	10.0		%	12.5		%
Combined ratio	104.5		%	99.5		%	59.0		%	92.9		%	106.1		%	94.0		%

Goodwill and intangible assets	$	280,978		$	18,963		$	385,272		$	685,213		$	7,650		$	692,863

Total investable assets										$	26,856,295		$	2,657,612		$	29,513,907
Total assets										39,791,983			3,490,314			43,282,297
Total liabilities										26,789,149			2,505,707			29,294,856

(1) Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.


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	Year Ended December 31, 2019
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	3,907,993		$	2,323,223		$	1,466,265		$	7,695,645		$	754,881		$	8,138,960
Premiums ceded	(1,266,267)			(720,500)			(204,509)			(2,189,440)			(222,019)			(2,099,893)
Net premiums written	2,641,726			1,602,723			1,261,756			5,506,205			532,862			6,039,067
Change in unearned premiums	(244,646)			(136,334)			104,584			(276,396)			23,827			(252,569)
Net premiums earned	2,397,080			1,466,389			1,366,340			5,229,809			556,689			5,786,498
Other underwriting income	—			6,444			16,005			22,449			2,412			24,861
Losses and loss adjustment expenses	(1,615,475)			(1,011,329)			(53,513)			(2,680,317)			(453,135)			(3,133,452)
Acquisition expenses, net	(361,614)			(239,032)			(134,319)			(734,965)			(105,980)			(840,945)
Other operating expenses	(454,770)			(141,484)			(153,092)			(749,346)			(51,651)			(800,997)
Underwriting income (loss)	$	(34,779)		$	80,988		$	1,041,421		1,087,630			(51,665)			1,035,965

Net investment income										491,067			136,671			627,738
Net realized gains (losses)										348,037			15,161			363,198

Equity in net income (loss) of investments accounted for using the equity method										123,672			—			123,672
Other income (loss)										2,233			—			2,233
Corporate expenses										(65,667)			—			(65,667)
Transaction costs and other										(14,444)			—			(14,444)
Amortization of intangible assets										(82,104)			—			(82,104)
Interest expense										(93,735)			(27,137)			(120,872)
Net foreign exchange gains (losses)										(9,252)			(11,357)			(20,609)
Income (loss) before income taxes										1,787,437			61,673			1,849,110
Income tax (expense) benefit										(155,790)			(20)			(155,810)
Net income (loss)										1,631,647			61,653			1,693,300
Amounts attributable to redeemable noncontrolling interests										—			(16,909)			(16,909)
Amounts attributable to nonredeemable noncontrolling interests										—			(40,072)			(40,072)
Net income (loss) available to Arch										1,631,647			4,672			1,636,319
Preferred dividends										(41,612)			—			(41,612)

Net income (loss) available to Arch common shareholders										$	1,590,035		$	4,672		$	1,594,707

Underwriting Ratios
Loss ratio	67.4		%	69.0		%	3.9		%	51.3		%	81.4		%	54.2		%
Acquisition expense ratio	15.1		%	16.3		%	9.8		%	14.1		%	19.0		%	14.5		%
Other operating expense ratio	19.0		%	9.6		%	11.2		%	14.3		%	9.3		%	13.8		%
Combined ratio	101.5		%	94.9		%	24.9		%	79.7		%	109.7		%	82.5		%

Goodwill and intangible assets	$	289,021		$	2,516		$	438,896		$	730,433		$	7,650		$	738,083

Total investable assets										$	22,285,676		$	2,704,589		$	24,990,265
Total assets										34,374,468			3,510,893			37,885,361
Total liabilities										22,977,636			2,592,173			25,569,809


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	Year Ended December 31, 2018
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	3,262,332		$	1,912,522		$	1,360,708		$	6,534,423		$	735,015		$	6,961,004
Premiums ceded	(1,050,207)			(539,950)			(202,833)			(1,791,851)			(130,840)			(1,614,257)
Net premiums written	2,212,125			1,372,572			1,157,875			4,742,572			604,175			5,346,747
Change in unearned premiums	(6,464)			(111,356)			28,361			(89,459)			(25,313)			(114,772)
Net premiums earned	2,205,661			1,261,216			1,186,236			4,653,113			578,862			5,231,975
Other underwriting income	—			(682)			13,033			12,351			2,722			15,073
Losses and loss adjustment expenses	(1,520,680)			(846,882)			(81,289)			(2,448,851)			(441,255)			(2,890,106)
Acquisition expenses, net	(349,702)			(211,280)			(118,595)			(679,577)			(125,558)			(805,135)
Other operating expenses	(364,138)			(133,350)			(142,432)			(639,920)			(37,889)			(677,809)
Underwriting income (loss)	$	(28,859)		$	69,022		$	856,953		897,116			(23,118)			873,998

Net investment income										437,958			125,675			563,633
Net realized gains (losses)										(287,258)			(120,915)			(408,173)

Equity in net income (loss) of investments accounted for using the equity method										45,641			—			45,641
Other income (loss)										2,419			—			2,419
Corporate expenses										(58,608)			—			(58,608)
Transaction costs and other										(11,386)			(9,000)			(20,386)
Amortization of intangible assets										(105,670)			—			(105,670)
Interest expense										(101,019)			(19,465)			(120,484)
Net foreign exchange gains (losses)										58,711			10,691			69,402
Income (loss) before income taxes										877,904			(36,132)			841,772
Income tax benefit										(113,924)			(27)			(113,951)
Net income										763,980			(36,159)			727,821
Amounts attributable to redeemable noncontrolling interests										—			(18,357)			(18,357)
Amounts attributable to nonredeemable noncontrolling interests										—			48,507			48,507
Net income (loss) available to Arch										763,980			(6,009)			757,971
Preferred dividends										(41,645)			—			(41,645)
Loss on redemption of preferred shares										(2,710)			—			(2,710)
Net income (loss) available to Arch common shareholders										$	719,625		$	(6,009)		$	713,616

Underwriting Ratios
Loss ratio	68.9		%	67.1		%	6.9		%	52.6		%	76.2		%	55.2		%
Acquisition expense ratio	15.9		%	16.8		%	10.0		%	14.6		%	21.7		%	15.4		%
Other operating expense ratio	16.5		%	10.6		%	12.0		%	13.8		%	6.5		%	13.0		%
Combined ratio	101.3		%	94.5		%	28.9		%	81.0		%	104.4		%	83.6		%

Goodwill and intangible assets	$	114,012		$	—		$	513,258		$	627,270		$	7,650		$	634,920

Total investable assets										$	19,566,861		$	2,757,663		$	22,324,524
Total assets										28,845,473			3,372,856			32,218,329
Total liabilities										19,518,395			2,262,255			21,780,650


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The following tables provide summary information regarding net premiums earned by major line of business and net premiums written by underwriting location:


INSURANCE SEGMENT	Year Ended December 31,
2020			2019			2018











Net premiums earned (1)
Property, energy, marine and aviation	$	517,247		$	298,966		$	205,069
Professional Lines (2)	655,872			499,224			458,425
Programs	432,854			414,103			389,186
Construction and national accounts	387,934			325,687			322,440
Excess and surplus casualty (3)	270,620			200,615			172,424
Travel, accident and health	190,944			305,085			297,147
Lenders products	114,687			66,079			94,248
Other (4)	301,262			287,321			266,722
Total	$	2,871,420		$	2,397,080		$	2,205,661








Net premiums written by underwriting location (1)
United States	$	2,158,415		$	1,983,476		$	1,736,651
Europe	856,572			559,214			401,974
Other	147,920			99,036			73,500
Total	$	3,162,907		$	2,641,726		$	2,212,125

(1) Insurance segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions.

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

(3) Includes casualty and contract binding business.

(4) Includes alternative markets, excess workers' compensation and surety business.


REINSURANCE SEGMENT	Year Ended December 31,
2020			2019			2018









Net premiums earned (1)
Property excluding property catastrophe	$	562,208		$	362,841		$	287,788
Property catastrophe	237,736			90,934			75,249
Other Specialty (2)	626,409			478,517			474,568
Casualty (3)	549,056			429,288			347,034
Marine and aviation	109,624			48,274			39,238
Other (4)	77,196			56,535			37,339
Total	$	2,162,229		$	1,466,389		$	1,261,216



















Net premiums written by underwriting location (1)
United States	$	687,622		$	529,943		$	413,550
Bermuda	1,001,990			578,618			487,523
Europe and other	767,758			494,162			471,499
Total	$	2,457,370		$	1,602,723		$	1,372,572

(1) Reinsurance segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions.

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

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

(4) Includes life, casualty clash and other.


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MORTGAGE SEGMENT	Year Ended December 31,
2020			2019			2018
Net premiums earned by underwriting location
United States	$	1,158,563		$	1,134,849		$	1,009,765
Other	239,372			231,491			176,471
Total	$	1,397,935		$	1,366,340		$	1,186,236

Net premiums written by underwriting location
United States	$	1,021,950		$	1,032,868		$	948,323
Other	257,900			228,888			209,552
Total	$	1,279,850		$	1,261,756		$	1,157,875


OTHER SEGMENT	Year Ended December 31,
2020			2019			2018









Net premiums earned (1)
Casualty (2)	$	245,272		$	246,894		$	277,589
Other specialty (3)	186,717			185,547			204,485
Property catastrophe	23,037			13,399			10,998
Property excluding property catastrophe	1,130			3,503			2,802
Marine and aviation	429			—			—
Other (4)	103,766			107,346			82,988
Total	$	560,351		$	556,689		$	578,862

Net premiums written by underwriting location (1)
United States	$	115,471		$	127,176		$	49,800
Europe	97,753			52,065			91,635
Bermuda	324,365			353,621			462,740
Total	$	537,589		$	532,862		$	604,175

(1) Other segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions.

(2) Includes professional liability, excess motor, programs and other.

(3) Includes proportional motor and other.

(4) Includes mortgage, US programs and other.


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5. Reserve for Losses and Loss Adjustment Expenses

The following table represents an analysis of losses and loss adjustment expenses and a reconciliation of the beginning and ending reserve for losses and loss adjustment expenses:


	Year Ended December 31,
	2020		2019		2018
Reserve for losses and loss adjustment expenses at beginning of year	$	13,891,842	$	11,853,297	$	11,383,792
Unpaid losses and loss adjustment expenses recoverable	4,082,650		2,814,291		2,464,910
Net reserve for losses and loss adjustment expenses at beginning of year	9,809,192		9,039,006		8,918,882

Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year	4,851,051		3,297,037		3,162,818
Prior years	(161,452)		(163,585)		(272,712)
Total net incurred losses and loss adjustment expenses	4,689,599		3,133,452		2,890,106

Net losses and loss adjustment expense reserves of acquired business (1)	—		209,486		—

Retroactive reinsurance transactions	182,210		(225,500)		(420,404)

Foreign exchange (gains) losses and other	179,190		36,003		(143,414)

Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year	(661,529)		(621,202)		(524,048)
Prior years	(1,999,588)		(1,762,053)		(1,682,116)
Total net paid losses and loss adjustment expenses	(2,661,117)		(2,383,255)		(2,206,164)

Net reserve for losses and loss adjustment expenses at end of year	12,199,074		9,809,192		9,039,006
Unpaid losses and loss adjustment expenses recoverable	4,314,855		4,082,650		2,814,291
Reserve for losses and loss adjustment expenses at end of year	$	16,513,929	$	13,891,842	$	11,853,297

(1) Primarily related to the acquisition of Barbican. See Note 2.

Development on Prior Year Loss Reserves

Year Ended December 31, 2020

During 2020, the Company recorded estimated net favorable development on prior year loss reserves of $161.5 million, which consisted of net favorable development of $7.8 million from the insurance segment, $134.0 million from the reinsurance segment, $19.0 million from the mortgage segment, and $0.7 million from the ‘other’ segment.

The insurance segment’s net favorable development of $7.8 million, or 0.3 points of net earned premium, consisted of $83.0 million of net favorable development in short-tailed and long-tailed lines partially offset by $75.2 million of net adverse development from medium-tailed lines. Net favorable development of $33.6 million in short-tailed lines reflected $21.6 million of favorable development from property (excluding marine), primarily from the 2015 to 2018 accident years, (i.e., the year in which a loss occurred) and $8.4 million of favorable development on travel and accident, primarily from the 2019 accident year. Net favorable development of $49.4 million in long-tailed lines included $38.8 million of favorable development related to other

business, including alternative markets and excess workers’ compensation, across all accident years, and $9.3 million of favorable development related to construction business. Net adverse development in medium-tailed lines reflected $37.9 million of adverse development in surety business, primarily from the 2019 accident year, $23.1 million in contract binding business, primarily from the 2016 to 2019 accident years, and $16.0 million in program business, primarily from the 2016 to 2019 accident years.

The reinsurance segment’s net favorable development of $134.0 million, or 6.2 points of net earned premium, consisted of $155.9 million of net favorable development from short-tailed and medium-tailed lines, partially offset by $21.9 million of net adverse development from long-tailed lines. Net favorable development of $144.0 million in short-tailed lines reflected $87.7 million related to property catastrophe and property other than property catastrophe business, primarily from the 2015 to 2019 underwriting years (i.e., losses attributable to contracts having an inception or renewal date within the given twelve-month period), and $53.6 million from other specialty lines, across most underwriting years. The net reduction of loss estimates for


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the reinsurance segment’s short-tailed lines primarily resulted from varying levels of reported and paid claims activity than previously anticipated which led to decreases in certain loss ratio selections during 2020. Adverse development in long-tailed lines reflected an increase in casualty reserves, primarily from the 2012 to 2015 underwriting years.

The mortgage segment’s net favorable development of $19.0 million, or 1.4 points of net earned premium, included $16.2 million of favorable development on U.S. primary mortgage insurance business. Such development was primarily driven by subrogation recoveries on second lien business and student loan business.

Year Ended December 31, 2019

During 2019, the Company recorded estimated net favorable development on prior year loss reserves of $163.6 million, which consisted of net favorable development of $15.8 million from the insurance segment, $46.4 million from the reinsurance segment and $125.2 million from the mortgage segment, partially offset by $23.8 million of net adverse development from the ‘other’ segment.

The insurance segment’s net favorable development of $15.8 million, or 0.7 points of net earned premium, consisted of $54.9 million of net favorable development from short-tailed lines and $39.1 million of net adverse development from medium-tailed and long-tailed lines. Net favorable development in short-tailed lines primarily resulted from lenders products and property (including special risk other than marine) reserves across all accident years, partially offset by net adverse development in travel business, primarily from the 2018 accident year. Net adverse development in medium-tailed and long-tailed lines of $39.1 million was primarily due to net adverse development of $33.6 million in contract binding business, primarily from the 2013 to 2017 accident years, and $30.1 million in programs, primarily from the 2014 and 2018 accident years. Such amounts were partially offset by net favorable development of $19.3 million in professional liability business, primarily from the 2013 to 2016 accident years, and $15.8 million in surety business, primarily from the 2014 to 2016 accident years.

The reinsurance segment’s net favorable development of $46.4 million, or 3.2 points of net earned premium, consisted of $70.5 million of net favorable development from short-tailed lines and $16.0 million of net favorable development from medium-tailed lines, partially offset by $40.1 million of net adverse development from long-tailed lines. Favorable development in short-tailed lines included $33.7 million from property catastrophe and property other than property catastrophe reserves, primarily from the 2017 and 2018 underwriting years and $40.8 million in other specialty, primarily from 2016 to 2018 underwriting years. The net

reduction of loss estimates for the reinsurance segment’s short-tailed lines primarily resulted from varying levels of reported and paid claims activity than previously anticipated which led to decreases in certain loss ratio selections during 2019. Net favorable development of $16.0 million in medium-tailed lines included reductions in marine and aviation reserves, primarily from the 2011 to 2017 underwriting years. Net adverse development in long-tailed lines of $40.1 million was primarily due to net adverse development of $44.5 million in casualty business, primarily from the 2013 to 2018 underwriting years.

The mortgage segment’s net favorable development of $125.2 million, or 9.2 points of net earned premium, included $117.1 million of favorable development on U.S. primary mortgage insurance business. Such development was primarily driven by lower than expected claim rates on first lien business and subrogation recoveries on second lien business.

Year Ended December 31, 2018

During 2018, the Company recorded estimated net favorable development on prior year loss reserves of $272.7 million, which consisted of $24.4 million from the insurance segment, $138.5 million from the reinsurance segment, $107.6 million from the mortgage segment and $2.2 million from the ‘other’ segment.

The insurance segment’s net favorable development of $24.4 million, or 1.1 points of net earned premium, consisted of $48.4 million of net favorable development from short-tailed lines and $26.3 million of net favorable development from long-tailed lines, partially offset by $50.3 million of net adverse development from medium-tailed lines. Favorable development in short-tailed lines predominantly consisted of $50.1 million of net favorable development in property lines, primarily from the 2010 to 2017 accident years, partially offset by $5.0 million of adverse development on travel, accident and health business from the 2013 to 2017 accident years. Net favorable development in long-tailed lines of $26.3 million included $19.7 million of net favorable development on executive assurance business, primarily from the 2015 accident year, and $1.4 million of net favorable development in casualty business, primarily from the 2009 to 2015 accident years. Net adverse development in medium tailed lines of $50.3 million was primarily due to net adverse development in contract binding business for accident years 2013 to 2017.

The reinsurance segment’s net favorable development of $138.5 million, or 11.0 points of net earned premium, consisted of $110.4 million from short-tailed lines and $28.1 million from medium-tailed and long-tailed lines. Favorable development in short-tailed lines included $80.8 million from property catastrophe and property other than property


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catastrophe reserves, primarily from the 2008 to 2017 underwriting years. The net reduction of loss estimates for the reinsurance segment’s short-tailed lines primarily resulted from varying levels of reported and paid claims activity than previously anticipated which led to decreases in certain loss ratio selections during 2018. Net favorable development of $28.1 million in medium-tailed and long-tailed lines included reductions in casualty reserves of $12.5 million, primarily from the 2002 to 2010 underwriting years, and in marine and aviation reserves of $15.6 million, spread across most underwriting years.

The mortgage segment’s net favorable development of $107.6 million, or 9.1 points of net earned premium, included $103.4 million of favorable development on U.S. primary mortgage insurance business. Such development was primarily driven by lower than expected claim rates on first lien business and subrogation recoveries on second lien business.

Retroactive Reinsurance Transactions

In 2020, the Company entered into a reinsurance-to-close agreement related to a third party arrangement covering the 2017 and prior years of account for certain London syndicate business. In 2019, the Company entered into a retroactive reinsurance transaction with third party reinsurer to reinsure run-off liabilities associated with certain U.S. insurance exposures, which was commuted in 2020. In 2018, the Company entered into a retroactive reinsurance transaction with third party reinsurers to reinsure run-off liabilities associated with certain U.S. insurance exposures.

6. Short Duration Contracts

The Company’s reserves for losses and loss adjustment expenses primarily relate to short-duration contracts with various characteristics (e.g., type of coverage, geography, claims duration). The Company considered such information in determining the level of disaggregation for disclosures related to its short-duration contracts, as detailed in the table below:


Reportable segment	Level of disaggregation	Included lines of business
Insurance	Property energy, marine and aviation	Property energy, marine and aviation
	Third party occurrence business	Excess and surplus casualty (excluding contract binding); construction and national accounts; and other (including alternative market risks, excess workers’ compensation and employer’s liability insurance coverages)
	Third party claims-made business	Professional lines
	Multi-line and other specialty	Programs; contract binding (part of excess and surplus casualty); travel, accident and health; lenders products; and other (contract and commercial surety coverages)

Reinsurance	Casualty	Casualty
	Property catastrophe	Property catastrophe
	Property excluding property catastrophe	Property excluding property catastrophe
	Marine and aviation	Marine and aviation
	Other specialty	Other specialty

Mortgage	Direct mortgage insurance in the U.S.	Mortgage insurance on U.S. primary exposures

The Company determined the following to be insignificant for disclosure purposes: (i) amounts included in the ‘other’ segment (i.e., Watford) as described in note 12, “Variable Interest Entity and Noncontrolling Interests”; (ii) certain mortgage business, including non-U.S. primary business, second lien and student loan exposures, global mortgage reinsurance and participation in various GSE credit risk-sharing products, (iii) certain reinsurance business, including casualty clash and non-traditional lines and (iv) amounts associated with Barbican’s reserves for underwriting years 2018 and prior. Such amounts are included as reconciling items.

The Company is required to establish reserves for losses and loss adjustment expenses (“Loss Reserves”) that arise from the business the Company underwrites. Loss Reserves for the insurance, reinsurance and mortgage segments represent estimates of future amounts required to pay losses and loss adjustment expenses for insured or reinsured events which have occurred at or before the balance sheet date. Loss Reserves do not reflect contingency reserve allowances to account for future loss occurrences. Losses arising from future events will be estimated and recognized at the time the losses are incurred and could be substantial.

Insurance Segment

Loss Reserves for the insurance segment are comprised of estimated amounts for (1) reported losses (“case reserves”) and (2) incurred but not reported losses (“IBNR reserves”). Generally, claims personnel determine whether to establish a


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case reserve for the estimated amount of the ultimate settlement of individual claims. The estimate reflects the judgment of claims personnel based on general corporate reserving practices, the experience and knowledge of such personnel regarding the nature and value of the specific type of claim and, where appropriate, advice of counsel. The Company also contracts with a number of outside third party administrators in the claims process who, in certain cases, have limited authority to establish case reserves. The work of such administrators is reviewed and monitored by our claims personnel. Loss Reserves are also established to provide for loss adjustment expenses and represent the estimated expense of settling claims, including legal and other fees and the general expenses of administering the claims adjustment process. Periodically, adjustments to the case reserves may be made as additional information is reported or payments are made. IBNR reserves are established to provide for incurred claims which have not yet been reported at the balance sheet date as well as to adjust for any projected variance in case reserving. Actuaries estimate ultimate losses and loss adjustment expenses using various generally accepted actuarial methods applied to known losses and other relevant information. Like case reserves, IBNR reserves are adjusted as additional information becomes known or payments are made. The process of estimating reserves involves a considerable degree of judgment by management and, as of any given date, is inherently uncertain.

Ultimate losses and loss adjustment expenses are generally determined by extrapolation of claim emergence and settlement patterns observed in the past that can reasonably be expected to persist into the future. In forecasting ultimate losses and loss adjustment expenses with respect to any line of business, past experience with respect to that line of business is the primary resource, developed through both industry and company experience, but cannot be relied upon in isolation. Uncertainties in estimating ultimate losses and loss adjustment expenses are magnified by the length of the time lag between when a claim actually occurs and when it is reported and settled. This time lag is sometimes referred to as the “claim-tail.” During this period additional facts regarding coverages written in prior accident years, as well as about actual claims and trends, may become known and, as a result, may lead to adjustments of the related Loss Reserves. If the Company determines that an adjustment is appropriate, the adjustment is recorded in the accounting period in which such determination is made. Accordingly, should Loss Reserves need to be increased or decreased in the future from amounts currently established, future results of operations would be negatively or positively impacted respectively. The Company authorizes managing general agents, general agents and other producers to write program business on the Company’s behalf within prescribed underwriting authorities. This delegated authority process introduces additional complexity to the actuarial determination of unpaid future

losses and loss adjustment expenses. In order to monitor adherence to the underwriting guidelines given to such parties, the Company periodically performs underwriting and claims due diligence reviews.

In determining ultimate losses and loss adjustment expenses, the cost to indemnify claimants, provide needed legal defense and other services for insureds and administer the investigation and adjustment of claims are considered. These claim costs are influenced by many factors that change over time, such as expanded coverage definitions as a result of new court decisions, inflation in costs to repair or replace damaged property, inflation in the cost of medical services and legislated changes in statutory benefits, as well as by the particular, unique facts that pertain to each claim. As a result, the rate at which claims arose in the past and the costs to settle them may not always be representative of what will occur in the future. The factors influencing changes in claim costs are often difficult to isolate or quantify and developments in paid and incurred losses from historical trends are frequently subject to multiple and conflicting interpretations. Changes in coverage terms or claims handling practices may also cause future experience and/or development patterns to vary from the past. A key objective of actuaries in developing estimates of ultimate losses and loss adjustment expenses, and resulting IBNR reserves, is to identify aberrations and systemic changes occurring within historical experience and adjust for them so that the future can be projected more reliably. Because of the factors previously discussed, this process requires the substantial use of informed judgment and is inherently uncertain.

Although Loss Reserves are initially determined based on underwriting and pricing analyses, the Company’s insurance segment applies several generally accepted actuarial methods, as discussed below, on a quarterly basis to evaluate the Loss Reserves, in addition to the expected loss method, in particular for Loss Reserves from more mature accident years (the year in which a loss occurred). Each quarter, as part of the reserving process, the segments’ actuaries reaffirm that the assumptions used in the reserving process continue to form a sound basis for the projection of liabilities. If actual loss activity differs substantially from expectations based on historical information, an adjustment to Loss Reserves may be supported. The Company places more or less reliance on a particular actuarial method based on the facts and circumstances at the time the estimates of Loss Reserves are made.

These methods generally fall into one of the following categories or are hybrids of one or more of the following categories:

*•*Expected loss methods - these methods are based on the assumption that ultimate losses vary proportionately with premiums. Expected loss and loss adjustment expense


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ratios are typically developed based upon the information derived by underwriters and actuaries during the initial pricing of the business, supplemented by industry data available from organizations, such as statistical bureaus and consulting firms, where appropriate. These ratios consider, among other things, rate increases and changes in terms and conditions that have been observed in the market. Expected loss methods are useful for estimating ultimate losses and loss adjustment expenses in the early years of long-tailed lines of business, when little or no paid or incurred loss information is available, and is commonly applied when limited loss experience exists for a company.

Historical incurred loss development methods - these methods assume that the ratio of losses in one period to losses in an earlier period will remain constant in the future. These methods use incurred losses (i.e., the sum of cumulative historical loss payments plus outstanding case reserves) over discrete periods of time to estimate future losses. Historical incurred loss development methods may be preferable to historical paid loss development methods because they explicitly take into account open cases and the claims adjusters’ evaluations of the cost to settle all known claims. However, historical incurred loss development methods necessarily assume that case reserving practices are consistently applied over time. Therefore, when there have been significant changes in how case reserves are established, using incurred loss data to project ultimate losses may be less reliable than other methods.
Historical paid loss development methods - these methods, like historical incurred loss development methods, assume that the ratio of losses in one period to losses in an earlier period will remain constant. These methods use historical loss payments over discrete periods of time to estimate future losses and necessarily assume that factors that have affected paid losses in the past, such as inflation or the effects of litigation, will remain constant in the future. Because historical paid loss development methods do not use incurred losses to estimate ultimate losses, they may be more reliable than the other methods that use incurred losses in situations where there are significant changes in how incurred losses are established by a company’s claims adjusters. However, historical paid loss development methods are more leveraged (meaning that small changes in payments have a larger impact on estimates of ultimate losses) than actuarial methods that use incurred losses because cumulative loss payments take much longer to equal the expected ultimate losses than cumulative incurred amounts. In addition, and for similar reasons, historical paid loss development methods are often slow to react to situations when new or different factors arise than those that have affected paid losses in the past.
Adjusted historical paid and incurred loss development methods - these methods take traditional historical paid and incurred loss development methods and adjust them for the estimated impact of changes from the past in factors such as inflation, the speed of claim payments or the adequacy of case reserves. Adjusted historical paid and incurred loss development methods are often more reliable methods of predicting ultimate losses in periods of significant change, provided the actuaries can develop methods to reasonably quantify the impact of changes. As such, these methods utilize more judgment than historical paid and incurred loss development methods.
Bornhuetter-Ferguson (“B-F”) paid and incurred loss methods - these methods utilize actual paid and incurred losses and expected patterns of paid and incurred losses, taking the initial expected ultimate losses into account to determine an estimate of expected ultimate losses. The B-F paid and incurred loss methods are useful when there are few reported claims and a relatively less stable pattern of reported losses.

*•*Frequency-Severity methods - These methods utilize actual paid and incurred claim experience, but break the data down into its component pieces: claim counts, often expressed as a ratio to exposure or premium (frequency), and average claim size (severity). The component pieces are projected to an ultimate level and multiplied together to result in an estimate of ultimate loss. These methods are especially useful when the severity of claims can be confined to a relatively stable range of estimated ultimate average claim value.

Additional analyses - other methodologies are often used in the reserving process for specific types of claims or events, such as catastrophic or other specific major events. These include vendor catastrophe models, which are typically used in the estimation of Loss Reserves at the early stage of known catastrophic events before information has been reported to an insurer or reinsurer.

In the initial reserving process for short-tail insurance lines (consisting of property, energy, marine and aviation and other exposures including travel, accident and health and lenders products), the Company relies on a combination of the reserving methods discussed above. For catastrophe-exposed business, the reserving process also includes the usage of catastrophe models for known events and a heavy reliance on analysis of individual catastrophic events and management judgment. The development of losses on short-tail business can be unstable, especially for policies characterized by high severity, low frequency losses. As time passes, for a given accident year, additional weight is given to the paid and incurred B-F loss development methods and eventually to the historical paid and incurred loss development methods in the reserving process. The Company


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makes a number of key assumptions in their reserving process, including that historical paid and reported development patterns are stable, catastrophe models provide useful information about our exposure to catastrophic events that have occurred and underwriters’ judgment as to potential loss exposures can be relied on. The expected loss ratios used in the initial reserving process for short-tail business have varied over time due to changes in pricing, reinsurance structure, estimates of catastrophe losses, policy changes (such as attachment points, class and limits) and geographical distribution. As losses in short-tail lines are reported relatively quickly, expected loss ratios are selected for the current accident year based upon actual attritional loss ratios for earlier accident years, adjusted for rate changes, inflation, changes in reinsurance programs and expected attritional losses based on modeling. Furthermore, ultimate losses for short-tail business are known in a reasonably short period of time.

In the initial reserving process for medium-tail and long-tail insurance lines **(**consisting of third party occurrence business, third party claims made business, and other exposures including surety, programs and contract binding exposures), the Company primarily relies on the expected loss method. The development of the Company’s medium-tail and long-tail business may be unstable, especially if there are high severity major events, as a portion of the Company’s casualty business is in high excess layers. As time passes, for a given accident year, additional weight is given to the paid and incurred B-F loss development methods and historical paid and incurred loss development methods in the reserving process. The Company makes a number of key assumptions in reserving for medium-tail and long-tail lines, including that the pricing loss ratio is the best estimate of the ultimate loss ratio at the time the policy is entered into, that the loss

development patterns, which are based on a combination of company and industry loss development patterns and adjusted to reflect differences in the insurance segment’s mix of business, are reasonable and that claims personnel and underwriters analyses of our exposure to major events are assumed to be the best estimate of exposure to the known claims on those events. The expected loss ratios used in the initial reserving process for medium-tail and long-tail business for recent accident years have varied over time, in some cases significantly, from earlier accident years. As the credibility of historical experience for earlier accident years increases, the experience from these accident years will be given a greater weighting in the actuarial analysis to determine future accident year expected loss ratios, adjusted for changes in pricing, loss trends, terms and conditions and reinsurance structure.

In 2018, the Company entered into a loss portfolio transfer and adverse development cover reinsurance agreement accounted for as retroactive reinsurance. The agreement transfers Loss Reserves and future favorable or adverse development on certain runoff programs, within multi-line and other specialty business, and certain third party occurrence business (the “Covered Lines”). As incurred losses and allocated loss adjustment expenses for the Covered Lines are ceded to the reinsurer, the Company is not exposed to changes in the amount, timing and uncertainty of cash flows arising from the Covered Lines. To avoid distortion, the incurred losses and allocated loss adjustment expenses and cumulative paid losses and loss adjustment expenses for the Covered Lines are excluded entirely from the tables below. Reinsurance recoverables at December 31, 2020 included $153.1 million related to this reinsurance agreement.


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The following tables present information on the insurance segment’s short-duration insurance contracts:


Property, energy, marine and aviation ($000’s except claim count)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2020
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2011 unaudited		2012 unaudited		2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020
2011	$	269,739	$	272,897	$	231,841	$	220,231	$	210,926	$	207,814	$	200,918	$	201,198	$	197,833	$	196,436	$	689	4,219
2012			232,500		231,742		205,098		198,837		196,405		192,406		190,192		178,039		177,673		931		4,269
2013					158,718		156,344		148,800		143,046		134,620		133,544		128,301		126,968		809		4,278
2014							148,185		145,765		147,315		136,096		132,209		134,234		134,937		4,206		3,930
2015									112,333		109,799		103,944		102,469		97,809		91,788		5,249		4,618
2016											104,139		100,986		105,330		100,147		96,127		882		6,389
2017													280,695		246,272		235,932		230,421		9,327		6,752
2018															180,981		186,030		173,693		14,784		5,347
2019																	179,056		178,564		20,553		6,051
2020																			359,394		168,463		16,980
																	Total		$	1,766,001

Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2011	$	34,478	$	99,724	$	142,231	$	167,867	$	200,473	$	202,347	$	197,720	$	198,626	$	195,245	$	195,347
2012			20,522		92,855		138,431		161,255		166,965		179,371		180,734		172,611		173,460
2013					32,239		84,759		110,548		119,791		121,922		125,156		123,036		124,369
2014							25,859		53,669		77,804		84,103		87,721		98,463		115,293
2015									23,567		64,916		76,299		86,214		87,887		86,207
2016											24,728		83,321		98,420		97,218		94,703
2017													30,219		139,854		195,518		211,694
2018															30,026		102,285		134,858
2019																	26,130		105,380
2020																			55,619
									Total										1,296,930
									All outstanding liabilities before 2011, net of reinsurance										23,517
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	492,588


Third party occurrence business ($000’s except claim count)
	Incurred losses and allocated loss adjustment expenses, net of reinsurance																				December 31, 2020
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2011 unaudited		2012 unaudited		2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020
2011	$	234,068	$	240,669	$	254,181	$	258,784	$	252,615	$	253,976	$	247,052	$	239,676	$	234,782	$	235,073	$	35,138	70,924
2012			241,062		262,718		268,365		271,035		257,418		252,822		242,930		243,484		241,378		50,208		65,495
2013					282,968		296,839		306,751		301,789		281,786		274,391		272,528		269,437		60,720		66,685
2014							329,809		335,720		338,623		342,868		339,495		343,995		342,731		77,547		74,964
2015									358,858		391,666		398,670		391,904		391,231		382,518		107,083		77,257
2016											389,623		394,281		405,889		399,394		374,728		142,000		76,765
2017													417,183		417,748		422,441		412,318		195,684		82,267
2018															430,216		452,975		450,736		248,271		74,789
2019																	456,059		487,224		318,622		80,934
2020																			606,827		524,473		67,541
																	Total		$	3,802,970

Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2011	$	7,020	$	25,276	$	43,479	$	73,448	$	113,502	$	134,622	$	152,756	$	160,609	$	172,940	$	181,505
2012			6,966		30,824		58,444		83,328		108,252		129,572		143,177		154,282		162,202
2013					6,845		29,230		71,370		101,196		122,120		149,098		164,187		174,700
2014							9,209		40,263		71,519		112,591		161,993		191,168		211,503
2015									11,119		44,542		88,443		139,403		181,566		211,573
2016											11,689		41,938		87,565		136,793		164,573
2017													13,396		52,323		99,827		135,025
2018															17,002		63,798		115,076
2019																	18,392		73,120
2020																			24,439
									Total										1,453,716
									All outstanding liabilities before 2011, net of reinsurance										209,031
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	2,558,285


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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS


Third party claims-made business ($000’s except claim count)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2020
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2011 unaudited		2012 unaudited		2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020
2011	$	287,607	$	330,898	$	322,274	$	317,074	$	322,934	$	301,240	$	288,038	$	289,974	$	291,477	$	290,124	$	4,594	11,762
2012			317,360		319,961		318,161		313,622		291,010		275,388		277,388		284,875		285,236		13,772		14,760
2013					301,715		320,387		324,167		320,284		294,465		290,961		281,751		271,262		15,306		14,543
2014							264,354		279,544		298,715		278,706		281,513		297,485		291,729		29,279		13,935
2015									258,817		277,437		276,328		259,902		255,276		252,329		29,255		13,817
2016											275,119		291,377		308,195		314,515		321,850		61,156		15,734
2017													270,523		285,993		311,980		308,401		82,537		15,923
2018															272,844		314,412		319,956		123,386		14,988
2019																	289,463		317,668		186,452		18,871
2020																			383,914		327,587		21,538
																	Total		$	3,042,469

Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2011	$	13,740	$	72,365	$	130,424	$	175,139	$	208,665	$	228,450	$	240,267	$	254,300	$	269,579	$	276,887
2012			17,709		69,020		121,112		164,605		190,200		209,097		227,179		251,078		255,098
2013					19,015		87,408		137,890		179,302		197,907		217,030		238,798		245,504
2014							13,815		63,296		129,502		172,835		207,640		229,512		243,338
2015									9,061		52,019		100,048		126,452		174,108		193,130
2016											10,547		68,178		127,229		158,159		205,514
2017													9,289		67,572		113,047		143,149
2018															12,255		68,300		118,184
2019																	12,387		65,345
2020																			17,098
									Total										1,763,247
									All outstanding liabilities before 2011, net of reinsurance										97,957
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	1,377,179


Multi-line and other specialty ($000’s except claim count) (1)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2020
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2011 unaudited		2012 unaudited		2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020
2011	$	183,081	$	188,766	$	182,979	$	176,545	$	172,649	$	172,403	$	168,888	$	170,350	$	170,091	$	166,577	$	1,790	44,989
2012			253,525		264,217		258,467		256,106		255,277		247,050		247,279		244,191		244,246		2,551		55,512
2013					274,361		283,112		274,483		281,697		271,687		275,386		273,177		270,853		4,661		72,323
2014							349,754		373,978		370,442		387,082		398,240		410,366		418,512		12,232		111,727
2015									398,755		418,761		420,642		443,258		456,329		471,865		18,596		151,598
2016											482,653		504,586		514,650		516,239		537,591		28,282		177,931
2017													551,688		579,217		578,341		615,833		45,947		221,643
2018															570,069		621,534		629,299		74,894		247,622
2019																	613,638		667,415		134,996		234,383
2020																			654,302		403,044		117,814
																	Total		$	4,676,493

Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2011	$	51,312	$	103,372	$	117,927	$	136,686	$	148,049	$	151,710	$	157,199	$	159,526	$	162,460	$	162,995
2012			78,337		165,836		190,064		209,124		222,929		231,776		232,987		236,282		239,244
2013					86,791		152,773		185,611		222,086		237,898		251,698		257,744		260,374
2014							109,236		206,444		255,332		306,411		341,580		367,026		380,041
2015									142,009		250,360		304,197		350,781		380,818		409,455
2016											181,415		323,681		382,805		425,642		464,774
2017													187,606		363,275		419,454		480,336
2018															214,475		399,852		464,970
2019																	213,950		397,104
2020																			174,862
									Total										3,434,155
									All outstanding liabilities before 2011, net of reinsurance										31,453
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	1,273,791

(1) In 2019, the Company entered into a loss portfolio transfer agreement, which transferred reserves associated with certain multi-line business for accident years 2017 and prior to a third party. This loss portfolio transfer agreement was commuted in 2020, therefore the complete history of the subject business is now included in the multi-line triangles above.


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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

The following table presents the average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance, as of December 31, 2020:


	Average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance
	Year 1		Year 2		Year 3		Year 4		Year 5		Year 6		Year 7		Year 8		Year 9		Year 10
Property, energy, marine and aviation	18.6	%	41.7	%	19.6	%	7.8	%	3.9	%	3.3	%	2.3	%	(1.0)	%	(0.6)	%	0.1	%
Third party occurrence business	3.2	%	9.2	%	11.3	%	11.6	%	11.3	%	8.8	%	6.2	%	3.9	%	4.3	%	3.6	%
Third party claims-made business	4.5	%	18.7	%	18.4	%	12.9	%	12.2	%	7.1	%	5.8	%	5.2	%	3.3	%	2.5	%
Multi-line and other specialty	30.8	%	27.7	%	10.5	%	10.4	%	6.7	%	4.6	%	2.3	%	1.2	%	1.5	%	0.3	%

Reinsurance Segment

Loss Reserves for the Company’s reinsurance segment are comprised of (1) case reserves, (2) additional case reserves (“ACRs”) and (3) IBNR reserves. The Company receives reports of claims notices from ceding companies and records case reserves based upon the amount of reserves recommended by the ceding company. Case reserves may be supplemented by ACRs, which may be estimated by the Company’s claims personnel ahead of official notification from the ceding company, or when judgment regarding the size or severity of the known event differs from the ceding company. In certain instances, the Company establishes ACRs even when the ceding company does not report any liability on a known event. In addition, specific claim information reported by ceding companies or obtained through claim audits can alert the Company to emerging trends such as changing legal interpretations of coverage and liability, claims from unexpected sources or classes of business, and significant changes in the frequency or severity of individual claims. Such information is often used in the process of estimating IBNR reserves. IBNR reserves are established to provide for incurred claims which have not yet been reported at the balance sheet date as well as to adjust for any projected variance in case reserving. Actuaries estimate ultimate losses and loss adjustment expenses using various generally accepted actuarial methods applied to known losses and other relevant information. Like case reserves, IBNR reserves are adjusted as additional information becomes known or payments are made. The process of estimating Loss Reserves involves a considerable degree of judgment by management and, as of any given date, is inherently uncertain.

The estimation of Loss Reserves for the reinsurance segment is subject to the same risk factors as the estimation of Loss Reserves for the insurance segment. In addition, the inherent uncertainties of estimating such reserves are even greater for reinsurers, due primarily to the following factors: (1) the claim-tail for reinsurers is generally longer because claims are first reported to the ceding company and then to the reinsurer through one or more intermediaries, (2) the reliance on premium estimates, where reports have not been received from the ceding company, in the reserving process, (3) the potential for writing a number of reinsurance contracts with different ceding companies with the same exposure to a single loss event, (4) the diversity of loss development

patterns among different types of reinsurance contracts, (5) the necessary reliance on the ceding companies for information regarding reported claims and (6) the differing reserving practices among ceding companies.

Ultimate losses and loss adjustment expenses are generally determined by extrapolation of claim emergence and settlement patterns observed in the past that can reasonably be expected to persist into the future.As with the insurance segment, the process of estimating Loss Reserves for the reinsurance segment involves a considerable degree of judgment by management and, as of any given date, is inherently uncertain. As discussed above, such uncertainty is greater for reinsurers compared to insurers. As a result, our reinsurance operations obtain information from numerous sources to assist in the process. Pricing actuaries from the reinsurance segment devote considerable effort to understanding and analyzing a ceding company’s operations and loss history during the underwriting of the business, using a combination of ceding company and industry statistics. Such statistics normally include historical premium and loss data by class of business, individual claim information for larger claims, distributions of insurance limits provided, loss reporting and payment patterns, and rate change history. This analysis is used to project expected loss ratios for each treaty during the upcoming contract period.

As mentioned above, there can be a considerable time lag from the time a claim is reported to a ceding company to the time it is reported to the reinsurer. The lag can be several years in some cases and may be attributed to a number of reasons, including the time it takes to investigate a claim, delays associated with the litigation process, the deterioration in a claimant’s physical condition many years after an accident occurs, the case reserving approach of the ceding company, etc. In the reserving process, the Company assumes that such lags are predictable, on average, over time and therefore the lags are contemplated in the loss reporting patterns used in their actuarial methods. This means that the reinsurance segment must rely on estimates for a longer period of time than does an insurance company. Backlogs in the recording of assumed reinsurance can also complicate the accuracy of loss reserve estimation. As of December 31, 2020 there were no significant backlogs related to the processing of assumed reinsurance information at our reinsurance operations.


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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

The reinsurance segment relies heavily on information reported by ceding companies, as discussed above. In order to determine the accuracy and completeness of such information, underwriters, actuaries, and claims personnel often perform audits of ceding companies and regularly review information received from ceding companies for unusual or unexpected results. Material findings are usually discussed with the ceding companies. The Company sometimes encounters situations where they determine that a claim presentation from a ceding company is not in accordance with contract terms. In these situations, the Company attempts to resolve the dispute with the ceding company. Most situations are resolved amicably and without the need for litigation or arbitration. However, in the infrequent situations where a resolution is not possible, the Company will vigorously defend its position in such disputes.

Although Loss Reserves are initially determined based on underwriting and pricing analysis, the Company applies several generally accepted actuarial methods, as discussed above, on a quarterly basis to evaluate its Loss Reserves in addition to the expected loss method, in particular for reserves from more mature underwriting years (the year in which business is underwritten). Each quarter, as part of the reserving process, the Company’s actuaries reaffirm that the assumptions used in the reserving process continue to form a sound basis for projection of liabilities. If actual loss activity differs substantially from expectations based on historical information, an adjustment to Loss Reserves may be supported. Estimated Loss Reserves for more mature underwriting years are now based more on actual loss activity and historical patterns than on the initial assumptions based on pricing indications. More recent underwriting years rely more heavily on internal pricing assumptions. The Company places more or less reliance on a particular actuarial method based on the facts and circumstances at the time the estimates of Loss Reserves are made.

In the initial reserving process for short-tail reinsurance lines (consisting of property excluding property catastrophe and property catastrophe exposures), the Company relies on a combination of the reserving methods discussed above. For known catastrophic events, the reserving process also includes the usage of catastrophe models and a heavy reliance on analysis which includes ceding company inquiries and management judgment. The development of property losses may be unstable, especially where there is high catastrophic exposure, may be characterized by high severity, low frequency losses for excess and catastrophe-exposed business and may be highly correlated across contracts. As time passes, for a given underwriting year, additional weight is given to the paid and incurred B-F loss development methods and historical paid and incurred loss development

methods in the reserving process. The Company makes a number of key assumptions in reserving for short-tail lines, including that historical paid and reported development patterns are stable, catastrophe models provide useful information about our exposure to catastrophic events that have occurred and our underwriters’ judgment and guidance received from ceding companies as to potential loss exposures may be relied on. The expected loss ratios used in the initial reserving process for property exposures have varied over time due to changes in pricing, reinsurance structure, estimates of catastrophe losses, terms and conditions and geographical distribution. As losses in property lines are reported relatively quickly, expected loss ratios are selected for the current underwriting year incorporating the experience for earlier underwriting years, adjusted for rate changes, inflation, changes in reinsurance programs, expectations about present and future market conditions and expected attritional losses based on modeling. Due to the short-tail nature of property business, reported loss experience emerges quickly and ultimate losses are known in a reasonably short period of time.

In the initial reserving process for medium-tail and long-tail reinsurance lines (consisting of casualty, other specialty, marine and aviation and other exposures), the Company primarily relies on the expected loss method. The development of medium-tail and long-tail business may be unstable, especially if there are high severity major events, with business written on an excess of loss basis typically having a longer tail than business written on a pro rata basis. As time passes, for a given underwriting year, additional weight is given to the paid and incurred B-F loss development methods and eventually to the historical paid and incurred loss development methods in the reserving process. Our reinsurance operations make a number of key assumptions in reserving for medium-tail and long-tail lines, including that the pricing loss ratio is the best estimate of the ultimate loss ratio at the time the contract is entered into, historical paid and reported development patterns are stable and claims personnel and underwriters’ analyses of our exposure to major events are our best estimate of our exposure to the known claims on those events. The expected loss ratios used in our reinsurance operations’ initial reserving process for medium-tail and long-tail contracts have varied over time due to changes in pricing, terms and conditions and reinsurance structure. As the credibility of historical experience for earlier underwriting years increases, the experience from these underwriting years is used in the actuarial analysis to determine future underwriting year expected loss ratios, adjusted for changes in pricing, loss trends, terms and conditions and reinsurance structure.


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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

The following tables present information on the reinsurance segment’s short-duration insurance contracts:


Casualty ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2020
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2011 unaudited		2012 unaudited		2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020
2011	$	152,359	$	155,796	$	149,799	$	145,259	$	141,023	$	138,257	$	132,142	$	129,307	$	130,769	$	126,543	$	16,905	N/A
2012			145,770		143,950		139,762		127,563		117,551		111,938		120,655		123,884		122,312		28,208		N/A
2013					168,738		161,993		157,804		151,340		139,221		137,591		133,857		137,978		37,566		N/A
2014							219,506		224,801		222,220		236,505		233,033		242,792		243,067		48,039		N/A
2015									225,908		224,525		233,644		240,886		244,861		251,747		63,133		N/A
2016											217,499		229,862		254,032		268,880		275,966		65,394		N/A
2017													268,353		253,959		269,434		297,998		79,858		N/A
2018															282,010		296,507		286,944		81,666		N/A
2019																	338,581		347,126		178,981		N/A
2020																			393,328		333,679		N/A
																	Total		$	2,483,009

Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2011	$	2,353	$	11,509	$	21,684	$	38,998	$	55,027	$	64,486	$	71,457	$	76,722	$	82,728	$	87,463
2012			1,371		8,637		14,875		25,738		36,809		48,109		59,877		70,308		76,287
2013					2,549		10,050		23,209		43,263		54,797		63,415		71,150		77,089
2014							3,962		16,160		40,949		63,636		91,366		114,798		135,101
2015									4,490		20,340		47,381		71,231		97,007		120,889
2016											5,763		25,720		51,822		86,989		114,096
2017													6,441		29,414		59,377		108,591
2018															7,588		31,118		106,454
2019																	15,824		57,682
2020																			17,822
									Total										901,474
									All outstanding liabilities before 2011, net of reinsurance										303,572
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	1,885,107


Property catastrophe ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2020
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2011 unaudited		2012 unaudited		2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020
2011	$	215,493	$	195,232	$	176,170	$	162,993	$	159,174	$	158,465	$	156,150	$	152,082	$	150,971	$	150,459	$	—	N/A
2012			150,570		123,288		108,787		102,254		99,998		99,178		97,143		97,252		96,637		132		N/A
2013					69,044		49,507		37,714		33,143		30,567		29,848		28,910		29,060		(132)		N/A
2014							46,774		32,188		26,438		23,491		21,671		20,957		20,845		(10)		N/A
2015									34,895		19,282		12,724		6,643		4,746		4,102		67		N/A
2016											26,671		19,556		15,313		11,487		9,027		1,302		N/A
2017													82,521		49,340		46,354		32,747		87		N/A
2018															75,309		63,106		44,448		5,855		N/A
2019																	51,202		35,789		9,545		N/A
2020																			273,069		50,368		N/A
																	Total		$	696,183

Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2011	$	63,175	$	89,042	$	122,060	$	137,400	$	143,141	$	145,774	$	147,929	$	148,338	$	148,929	$	148,403
2012			25,850		70,843		83,929		90,834		92,993		94,122		94,732		95,419		95,521
2013					12,283		19,701		24,911		26,953		28,859		29,117		29,119		29,846
2014							13,702		20,635		19,293		20,170		19,786		19,993		20,146
2015									(3,161)		(1,825)		2,660		2,959		2,537		2,630
2016											(6,752)		2,646		3,057		4,515		3,803
2017													30,173		30,224		34,534		24,209
2018															25,505		14,232		26,189
2019																	3,878		17,393
2020																			53,495
									Total										421,635
									All outstanding liabilities before 2011, net of reinsurance										1,624
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	276,172


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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS


Property excluding property catastrophe ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2020
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2011 unaudited		2012 unaudited		2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020
2011	$	208,318	$	180,624	$	168,122	$	164,414	$	160,264	$	158,952	$	156,647	$	155,606	$	154,261	$	152,753	$	801	N/A
2012			156,980		122,552		124,408		119,838		115,425		113,201		111,722		109,122		103,596		251		N/A
2013					116,130		77,474		71,100		66,669		64,950		64,162		62,949		63,769		770		N/A
2014							144,299		118,056		99,891		91,272		88,994		84,679		82,899		2,063		N/A
2015									215,856		189,735		185,288		189,702		188,992		177,928		12,275		N/A
2016											178,103		147,154		139,032		138,008		141,789		15,986		N/A
2017													262,387		245,333		231,062		223,442		17,528		N/A
2018															223,917		241,754		238,162		18,520		N/A
2019																	219,130		209,696		32,266		N/A
2020																			387,907		167,596		N/A
																	Total		$	1,781,941

Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2011	$	47,949	$	122,137	$	142,081	$	146,626	$	148,684	$	149,788	$	150,028	$	150,302	$	151,322	$	150,417
2012			26,158		78,416		93,752		102,445		103,452		104,091		103,274		103,216		103,076
2013					26,068		43,068		50,208		53,389		54,202		56,090		61,601		62,591
2014							23,641		63,144		72,133		77,098		78,753		79,146		79,009
2015									75,725		119,578		150,207		161,447		166,632		160,271
2016											33,418		96,174		99,954		105,486		113,336
2017													25,807		118,658		148,638		156,523
2018															29,724		108,263		153,599
2019																	43,809		125,698
2020																			102,474
									Total										1,206,994
									All outstanding liabilities before 2011, net of reinsurance										6,125
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	581,072


Marine and aviation ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2020
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2011 unaudited		2012 unaudited		2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020
2011	$	39,359	$	32,956	$	35,889	$	32,436	$	28,811	$	27,213	$	27,264	$	24,871	$	23,792	$	23,517	$	1,317	N/A
2012			59,117		58,956		55,172		52,428		51,223		49,865		46,183		43,165		41,316		2,228		N/A
2013					39,538		38,509		37,545		36,101		35,993		35,248		34,806		31,087		5,039		N/A
2014							31,333		29,576		27,763		26,059		24,050		23,695		22,347		5,044		N/A
2015									34,066		37,875		31,953		31,910		30,964		28,618		4,738		N/A
2016											27,409		22,804		23,622		19,344		17,029		8,230		N/A
2017													28,868		26,407		23,878		20,853		6,783		N/A
2018															28,355		26,395		24,957		7,490		N/A
2019																	49,466		55,921		17,208		N/A
2020																			84,238		58,896		N/A
																	Total		$	349,883

Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2011	$	4,421	$	12,122	$	16,530	$	19,235	$	15,959	$	16,634	$	21,988	$	21,911	$	21,973	$	21,979
2012			2,664		11,480		27,623		33,428		35,174		36,379		37,871		38,164		38,257
2013					5,109		14,330		19,075		22,111		23,135		24,427		24,804		24,520
2014							4,373		8,221		11,872		12,748		14,939		15,376		16,253
2015									11		13,476		19,120		20,971		22,773		22,456
2016											(7,300)		(1,655)		552		3,292		5,900
2017													1,659		6,546		9,372		11,037
2018															2,006		7,087		11,384
2019																	11,015		21,930
2020																			9,339
									Total										183,055
									All outstanding liabilities before 2011, net of reinsurance										16,534
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	183,362


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Other specialty ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																					December 31, 2020
																					Total of IBNR liabilities plus expected development on reported claims		Cumulative number of reported claims
	Year ended December 31,
Accident year	2011 unaudited		2012 unaudited		2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020
2011	$	115,554	$	100,395	$	96,117	$	94,512	$	92,703	$	91,334	$	90,727	$	88,820	$	89,163	$	87,648	$	1,058	N/A
2012			231,531		219,627		209,355		203,114		200,945		203,898		202,085		196,309		187,908		4,635		N/A
2013					259,594		232,427		222,046		218,354		219,314		216,861		216,579		210,455		10,351		N/A
2014							283,138		263,653		265,417		258,595		253,373		255,341		250,825		15,127		N/A
2015									217,666		208,927		207,220		204,179		204,458		201,046		19,996		N/A
2016											231,160		228,501		222,788		217,054		223,777		18,179		N/A
2017													282,024		271,084		260,051		259,041		40,904		N/A
2018															338,298		334,567		326,027		53,316		N/A
2019																	378,545		358,997		80,438		N/A
2020																			551,374		259,496		N/A
																	Total		$	2,657,098

Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2011	$	29,717	$	59,715	$	72,298	$	77,018	$	80,642	$	82,468	$	84,815	$	85,960	$	85,643	$	85,854
2012			47,484		126,138		149,753		161,073		169,096		173,202		177,742		179,614		179,943
2013					58,962		122,813		149,617		166,100		175,892		181,279		188,746		189,147
2014							71,006		151,115		187,560		201,189		207,965		219,234		221,978
2015									56,438		118,770		143,690		150,969		160,243		168,314
2016											67,730		143,624		168,425		180,542		192,947
2017													76,847		171,632		201,378		209,005
2018															75,395		211,954		243,257
2019																	84,416		167,055
2020																			101,559
									Total										1,759,059
									All outstanding liabilities before 2011, net of reinsurance										8,956
							Liabilities for losses and loss adjustment expenses, net of reinsurance												$	906,995

The following table presents the average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance, as of December 31, 2020:


	Average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance
	Year 1		Year 2		Year 3		Year 4		Year 5		Year 6		Year 7		Year 8		Year 9		Year 10
Casualty	2.4	%	7.2	%	11.2	%	12.2	%	10.3	%	8.4	%	7.3	%	5.7	%	4.8	%	3.7	%
Property catastrophe	20.5	%	30.2	%	25.1	%	2.9	%	(1.2)	%	1.4	%	0.7	%	1.2	%	0.2	%	(0.3)	%
Property excluding property catastrophe	26.4	%	39.5	%	12.8	%	5.2	%	2.3	%	0.2	%	2.0	%	0.6	%	0.3	%	(0.6)	%
Marine and aviation	6.5	%	27.2	%	19.1	%	10.0	%	4.2	%	2.2	%	7.9	%	(0.2)	%	0.2	%	—	%
Other specialty	26.9	%	33.9	%	12.3	%	5.2	%	4.3	%	3.1	%	2.4	%	0.8	%	(0.1)	%	0.2	%

Mortgage Segment

The Company’s mortgage segment includes (1) direct mortgage insurance in the U.S., (2) direct mortgage insurance in Europe, (3) global mortgage reinsurance and (4) participation in various GSE credit risk-sharing products. The latter three categories along with second lien and student loan exposures are excluded on the basis of insignificance for the purposes of presenting disclosures related to short duration contracts.

For direct mortgage insurance business, the Company establishes case reserves for loans that have been reported as delinquent by loan servicers as well as those that are delinquent but not reported (IBNR reserves). The Company’s U.S. mortgage insurance operations also reserve for the expenses of adjusting claims related to these delinquencies. The trigger that creates a case reserve estimate is that an insured loan is reported to us as being two payments in arrears. The actuarial reviews and documentation created in the reserving process are completed in accordance with

generally accepted actuarial standards. The selected assumptions reflect actuarial judgment based on the analysis of historical data and experience combined with information concerning current underwriting, economic, judicial, regulatory and other influences on ultimate claim settlements.

Because the reserving process requires the Company to forecast future conditions, it is inherently uncertain and requires significant judgment and estimation. The use of different estimates would result in the establishment of different reserve levels. Additionally, changes in estimates are likely to occur from period to period as economic conditions change, and the ultimate liability may vary significantly from the estimates used. Major risk factors include (but are not limited to) changes in home prices and borrower equity, which can limit the borrower’s ability to sell the property and satisfy the outstanding loan balance, and changes in unemployment, which can affect the borrower’s income and ability to make mortgage payments. The unique nature of the COVID-19 pandemic, with no historical


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precedent, adds further uncertainty to current reserve estimates.

The lead actuarial methodology used by the Company is a frequency-severity method based on the inventory of pending delinquencies. Each month the loan servicers report the delinquency status of each insured loan. Using the frequency-severity method allows the Company to take advantage of its knowledge of the number of delinquent loans and the coverage provided (“risk size”) on those loans by directly relating the reserves to these amounts. The delinquencies are grouped into homogeneous cohorts for analysis, reflecting product type and age of delinquency. A claim rate is then developed for each cohort which represents the frequency with which the delinquencies become claims. The claim frequency rates are based on an analysis of the patterns of emerging cure counts and claim counts, the foreclosure status of the pending delinquencies, the product and geographical mix of the delinquencies and our view of future economic and claim conditions, which include trends in home prices and unemployment. Claim rates can vary materially by age of delinquency, depending on the mix of delinquencies and economic conditions.

Claim size severity estimates are determined by examining the risk sizes on the delinquent loans and estimating the portion of risk that will be paid, as well as any expenses. This is done based on a review of historical development patterns, an assessment of economic conditions and the level of equity the borrowers may have in their homes, as well as considering economic conditions and loss mitigation opportunities. Mortgage insurance is generally not subject to large claim sizes, as with some other lines of insurance. A claim size over $250,000 is rare, and this helps reduce the volatility of claim size estimates.

The claim rate and claim size assumptions generate case reserves for the population of reported delinquencies. The reserve for unreported delinquencies (included in IBNR reserves) is estimated by looking at historical patterns of reporting. Claim rates and claim sizes can then be assigned to estimated unreported delinquencies using assumptions made in the establishment of case reserves.

Mortgage insurance Loss Reserves are short-tail, in the sense that the vast majority of delinquencies are resolved within two years of being reported. Due to the forbearances and foreclosure moratoriums associated with COVID-19, settlement timelines may be extended. While reserves are initially analyzed by reserve cohort, as described above, they are also rolled up by underwriting year to ensure that reserve assumptions are consistent with the performance of the underwriting year. The accuracy of prior reserve assumptions is also checked in hindsight to determine if adjustments to the assumptions are needed.

Loss Reserves for the Company’s mortgage reinsurance business and GSE credit-risk sharing transactions are comprised of case reserves and IBNR reserves. The Company’s mortgage reinsurance operations receive reports of delinquent loans and claims notices from ceding companies and record case reserves based upon the amount of reserves recommended by the ceding company. In addition, specific claim and delinquency information reported by ceding companies is used in the process of estimating IBNR reserves.


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The tables below include the acquired business of United Guaranty Corporation (“UGC”) (including UGRIC), across all periods presented. Consistent with prior practice, the Company provides accident years 2012 and forward in the disclosures below. The following table presents information on the mortgage segment’s short-duration insurance contracts:


Direct mortgage insurance business in the U.S. ($000’s except claim count)
Incurred losses and allocated loss adjustment expenses, net of reinsurance																			December 31, 2020
																				Total of IBNR liabilities plus expected development on reported claims	Cumulative number of paid claims
Year ended December 31,
Accident year	2012 unaudited		2013 unaudited		2014 unaudited		2015 unaudited		2016 unaudited		2017 unaudited		2018 unaudited		2019 unaudited		2020
2012	$	520,835	$	480,592	$	475,317	$	469,238	$	467,296	$	459,467	$	458,065	$	456,286	$	456,331		5	15,083
2013			469,311		419,668		411,793		405,809		395,693		393,149		390,987		391,062			3	9,471
2014					316,095		297,151		279,434		266,027		265,992		261,091		262,682			7	6,290
2015							222,790		197,238		198,001		194,677		189,235		190,913			4	4,543
2016									183,556		170,532		148,715		140,608		142,392			7	3,411
2017											179,376		132,220		107,255		108,181			630	2,429
2018													132,318		96,357		89,120			1,281	1,512
2019															108,424		119,253			2,921	566
2020																	420,003			15,879	32
															Total		$	2,179,937

Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2012	(106,065)		186,605		327,605		395,695		426,024		441,577		448,151		452,348		453,587
2013			41,447		203,957		308,956		353,189		373,909		382,200		386,853		387,894
2014					20,099		129,159		201,925		233,879		247,038		254,175		256,285
2015							16,159		92,431		151,222		171,337		180,321		183,472
2016									11,462		72,201		113,357		127,286		131,161
2017											8,622		48,112		78,650		87,317
2018													3,966		31,478		50,135
2019															2,899		20,105
2020																	1,040
																	1,570,996
									All outstanding liabilities before 2012, net of reinsurance								14,504
							Liabilities for losses and loss adjustment expenses, net of reinsurance										$	623,445

The following table presents the average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance, as of December 31, 2020:


Average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance
	Year 1		Year 2		Year 3		Year 4		Year 5		Year 6		Year 7		Year 8		Year 9
U.S. Primary	3.0	%	39.0	%	27.8	%	11.1	%	4.9	%	2.5	%	1.1	%	0.6	%	0.3	%

Other Segment

Loss Reserves for the ‘other’ segment (i.e., Watford) are comprised of case reserves, ACRs and IBNR reserves. For all business assumed by Watford, the Company acts as reinsurance underwriting manager, provides actuarial and risk management services and recommends a level of Loss Reserves to Watford. 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 common and preferred shares and counterparty credit risk (mitigated by collateral) arising from the reinsurance transactions. The estimation of Loss Reserves for Watford is subject to the same risk factors as the estimation of Loss Reserves for the Company’s insurance, reinsurance

and mortgage segments as described earlier. Watford performs its own reserve reviews and sets its reserves independently. As noted previously, the Company determined that amounts in the ‘other’ segment are insignificant for the purposes of these footnote disclosures.

For the year ended December 31, 2020, the Company did not make any significant changes in its methodologies or assumptions as described above (a) to determine the presented amounts of IBNR reserves, (b) for expected development on case reserves.

The Company measures claim frequency information on an individual claim count basis. Claim counts are provided for the insurance and mortgage segments, where reliable


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information is available. For insurance business, any claim which is reported to the Company is included in the count, even if it is subsequently settled without liability to the Company. The Company does not include claim count information for losses from U.S. insurance pool business where individual loss information is unavailable and impracticable to obtain. For mortgage business, only delinquencies which subsequently become claims are included in the claim count. For reinsurance business, claim counts are not provided. A significant amount of the Company’s reinsurance business is written on a proportional basis, for which individual loss information is typically unavailable and impracticable to obtain.

For the year ended December 31, 2020, the Company did not make any significant changes in its methodologies or assumptions as described above to calculate the cumulative claim frequency.

The following table represents a reconciliation of the disclosures of net incurred and paid loss development tables to the reserve for losses and loss adjustment expenses at December 31, 2020:


	December 31, 2020
Net outstanding liabilities
Insurance
Property, energy, marine and aviation	$	492,588
Third party occurrence business	2,558,285
Third party claims-made business	1,377,179
Multi-line and other specialty	1,273,791
Reinsurance
Casualty	1,885,107
Property catastrophe	276,172
Property excluding property catastrophe	581,072
Marine and aviation	183,362
Other specialty	906,995
Mortgage
U.S. primary	623,445
Other short duration lines not included in disclosures (1)	1,765,397
Total for short duration lines	11,923,393

Unpaid losses and loss adjustment expenses recoverable
Insurance
Property, energy, marine and aviation	331,817
Third party occurrence business	1,272,034
Third party claims-made business	808,238
Multi-line and other specialty	246,915
Reinsurance
Casualty	536,809
Property catastrophe	266,946
Property excluding property catastrophe	70,108
Marine and aviation	63,781
Other specialty	317,011
Mortgage
U.S. primary	52,016
Other short duration lines not included in disclosures (2)	1,090,486
Intercompany eliminations	(718,507)
Total for short duration lines	4,337,654

Lines other than short duration	75,369
Discounting	(23,326)
Unallocated claims adjustment expenses	200,839
	252,882

Total gross reserves for losses and loss adjustment expenses	$	16,513,929

(1) Includes net outstanding liabilities of $1.2 billion for the ‘other’ segment.

(2) Includes unpaid loss and loss adjustment expenses recoverable of $153.1 million related to the loss portfolio transfer reinsurance agreement.


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7. Allowance for Expected Credit Losses

Premiums Receivable

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


	December 31, 2020
	Premium Receivables, Net of Allowance		Allowance for Expected Credit Losses









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)			10,239

Balance at end of period	$	2,064,586	$	37,781

(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)” See note 3.

(2) Amounts deemed uncollectible are written-off in operating expenses. For the 2020 period, amounts written off totaled $2.8 million.

Reinsurance Recoverables

The Company monitors the financial condition of its reinsurers and attempts to place coverages only with substantial, financially sound carriers. Although the Company has not experienced any material credit losses to date, an inability of its reinsurers or retrocessionaires to meet their obligations to it over the relevant exposure periods for any reason could have a material adverse effect on its financial condition and results of operations.

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


	December 31, 2020
	Reinsurance Recoverables, Net of Allowance		Allowance for Expected Credit Losses









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			(1,738)


Balance at end of period	$	4,500,802	$	11,636

(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)” See note 3.

The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums) at December 31, 2020 and 2019:


	December 31,
	2020			2019
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	$	4,500,802		$	4,346,816
% due from carriers with A.M. Best rating of “A-” or better	63.9		%	61.2		%

% due from all other carriers with no A.M. Best rating (1)	36.1		%	38.8		%
Largest balance due from any one carrier as % of total shareholders’ equity	1.8		%	1.7		%

(1) Over 94% of such amount is collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other.

Contractholder Receivables

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


	December 31, 2020
	Contractholder Receivables, Net of Allowance		Allowance for Expected Credit Losses









Balance at beginning of period	$	2,119,460	$	0
Cumulative effect of accounting change (1)			6,663
Change for provision of expected credit losses			1,975


Balance at end of period	$	1,986,924	$	8,638

(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)” See note 3.

8. Reinsurance

In the normal course of business, the Company’s insurance subsidiaries cede a portion of their premium through pro rata and excess of loss reinsurance agreements on a treaty or facultative basis. The Company’s reinsurance subsidiaries participate in “common account” retrocessional arrangements for certain pro rata treaties. Such arrangements reduce the effect of individual or aggregate losses to all companies participating on such treaties, including the reinsurers, such as the Company’s reinsurance subsidiaries, and the ceding company. In addition, the Company’s reinsurance subsidiaries may purchase retrocessional coverage as part of their risk management program. The Company’s mortgage subsidiaries cede a portion of their premium through quota share arrangements and enter into various aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies. Reinsurance recoverables are recorded as assets, predicated on the reinsurers’ ability to meet their obligations under the reinsurance agreements. If the reinsurers are unable to satisfy their obligations under the


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agreements, the Company’s insurance or reinsurance subsidiaries would be liable for such defaulted amounts.

The effects of reinsurance on the Company’s written and earned premiums and losses and loss adjustment expenses with unaffiliated reinsurers were as follows:


	Year Ended December 31,
	2020		2019		2018
Premiums Written
Direct	$	6,553,910	$	5,681,523	$	4,838,902
Assumed	3,534,158		2,457,437		2,122,102
Ceded	(2,650,352)		(2,099,893)		(1,614,257)
Net	$	7,437,716	$	6,039,067	$	5,346,747

Premiums Earned
Direct	$	6,361,451	$	5,447,829	$	4,799,842
Assumed	3,213,873		2,337,950		1,988,038
Ceded	(2,583,389)		(1,999,281)		(1,555,905)
Net	$	6,991,935	$	5,786,498	$	5,231,975

Losses and Loss Adjustment Expenses
Direct	$	4,392,392	$	2,953,072	$	2,472,133
Assumed	2,204,323		1,602,528		1,307,317
Ceded	(1,907,116)		(1,422,148)		(889,344)
Net	$	4,689,599	$	3,133,452	$	2,890,106

Bellemeade Re

The Company has entered into various aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda (the “Bellemeade Agreements”). For the respective coverage periods, the Company will retain the first layer of the respective aggregate losses and the special purpose reinsurance companies will provide second layer coverage up to the outstanding coverage amount. The Company will then retain losses in excess of the outstanding coverage limit. The aggregate excess of loss reinsurance coverage decreases over a ten-year period as the underlying covered mortgages amortize.

The following table summarizes the respective coverages and retentions at December 31, 2020:


			December 31, 2020
	Initial Coverage at Issuance		Current Coverage		Remaining Retention, Net
Bellemeade 2017-1 Ltd. (1)	368,114		145,573		125,953
Bellemeade 2018-1 Ltd. (2)	374,460		250,095		123,690
Bellemeade 2018-2 Ltd. (3)	653,278		108,395		305,606
Bellemeade 2018-3 Ltd. (4)	506,110		302,563		129,874
Bellemeade 2019-1 Ltd. (5)	341,790		219,256		116,530
Bellemeade 2019-2 Ltd. (6)	621,022		398,316		162,457
Bellemeade 2019-3 Ltd. (7)	700,920		528,084		181,036
Bellemeade 2019-4 Ltd. (8)	577,267		468,737		118,102
Bellemeade 2020-1 Ltd. (9)	528,540		308,458		754,782
Bellemeade 2020-2 Ltd. (10)	449,167		449,167		239,278
Bellemeade 2020-3 Ltd. (11)	451,816		451,816		171,580
Bellemeade 2020-4 Ltd. (12)	337,013		337,013		147,466
Total	$	5,909,497	$	3,967,473	$	2,576,354

(1) Issued in October 2017, covering in-force policies issued between January 1, 2017 and June 30, 2017.

(2) Issued in April 2018, covering in-force policies issued between July 1, 2017 and December 31, 2017.

(3) Issued in August 2018, covering in-force policies issued between April 1, 2013 and December 31, 2015.

(4) Issued in October 2018, covering in-force policies issued between January 1, 2018 and June 30, 2018.

(5) Issued in March 2019, covering in-force policies primarily issued between 2005 to 2008 under United Guaranty Residential Insurance Company (“UGRIC”); as well as policies issued through 2015 under both UGRIC and Arch Mortgage Insurance Company.

(6) Issued in April 2019, covering in-force policies issued between July 1, 2018 and December 31, 2018.

(7) Issued in July 2019, covering in-force policies issued in 2016.

(8) Issued in October 2019, covering in-force policies issued between January 1, 2019 and June 30, 2019.

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

(10) Issued in September 2020, covering in-force policies issued between January 1, 2020 and May 31, 2020. $423 million was directly funded by Bellemeade 2020-2 Ltd. with an additional $26 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(11) Issued in November 2020, covering in-force policies issued between June 1, 2020 and August 31, 2020. $418 million was directly funded by Bellemeade 2020-3 Ltd. with an additional $34 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(12) Issued in December 2020, covering in-force policies issued between July 1, 2019 and December 31, 2019. $321 million was directly funded by Bellemeade 2020-4 Ltd. with an additional $16 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

See Note 12, “Variable Interest Entity and Noncontrolling Interests.”


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9. Investment Information

At December 31, 2020, total investable assets of $29.5 billion included $26.9 billion held by the Company and $2.7 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
December 31, 2020
Fixed maturities (1):
Corporate bonds	$	7,856,571	$	414,247	$	(34,388)	$	(896)	$	7,477,608
Mortgage backed securities	630,001		8,939		(5,028)		(278)		626,368
Municipal bonds	494,522		27,291		(3,835)		(11)		471,077
Commercial mortgage backed securities	389,900		8,722		(2,954)		(122)		384,254
U.S. government and government agencies	5,557,077		22,612		(12,611)		—		5,547,076
Non-U.S. government securities	2,433,733		153,891		(8,060)		—		2,287,902
Asset backed securities	1,634,804		19,225		(10,715)		(1,090)		1,627,384
Total	18,996,608		654,927		(77,591)		(2,397)		18,421,669


Short-term investments	1,924,922		2,693		(2,063)		—		1,924,292
Total	$	20,921,530	$	657,620	$	(79,654)	$	(2,397)	$	20,345,961

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 3.


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The following table summarizes, for all available for sale securities in an unrealized loss position, the fair value and gross unrealized loss by length of time the security has been in a continual unrealized loss position:


	Less than 12 Months				12 Months or More				Total
	Estimated Fair Value		Gross Unrealized Losses		Estimated Fair Value		Gross Unrealized Losses		Estimated Fair Value		Gross Unrealized Losses
December 31, 2020
Fixed maturities (1):
Corporate bonds	$	747,442	$	(33,086)	$	3,934	$	(1,302)	$	751,376	$	(34,388)
Mortgage backed securities	284,619		(4,788)		3,637		(240)		288,256		(5,028)
Municipal bonds	67,937		(3,835)		—		—		67,937		(3,835)
Commercial mortgage backed securities	126,624		(2,916)		2,655		(38)		129,279		(2,954)
U.S. government and government agencies	1,285,907		(12,611)		—		—		1,285,907		(12,611)
Non-U.S. government securities	543,844		(7,658)		2,441		(402)		546,285		(8,060)
Asset backed securities	634,470		(9,110)		57,737		(1,605)		692,207		(10,715)
Total	3,690,843		(74,004)		70,404		(3,587)		3,761,247		(77,591)


Short-term investments	97,920		(2,063)		—		—		97,920		(2,063)
Total	$	3,788,763	$	(76,067)	$	70,404	$	(3,587)	$	3,859,167	$	(79,654)

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 and reinvested and included the fixed maturities pledged. See “—Securities Lending Agreements.”

At December 31, 2020, on a lot level basis, approximately 2,320 security lots out of a total of approximately 11,180 security lots were in an unrealized loss position and the largest single unrealized loss from a single lot in the Company’s fixed maturity portfolio was $0.9 million. The Company believes that such securities were temporarily impaired at December 31, 2020. 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.


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The contractual maturities of the Company’s fixed maturities and fixed maturities pledged under securities lending agreements are shown in the following table. Expected maturities, which are management’s best estimates, will differ from contractual maturities because borrowers may have the right to call or prepay obligations with or without call or prepayment penalties.


	December 31, 2020				December 31, 2019
Maturity	Estimated Fair Value		Amortized Cost		Estimated Fair Value		Amortized Cost
Due in one year or less	$	348,200	$	339,951	$	428,659	$	423,617
Due after one year through five years	10,629,959		10,340,819		10,126,403		9,996,206
Due after five years through 10 years	4,881,564		4,654,754		3,317,535		3,219,567
Due after 10 years	482,180		448,139		411,269		388,280
	16,341,903		15,783,663		14,283,866		14,027,670
Mortgage backed securities	630,001		626,368		562,309		553,571
Commercial mortgage backed securities	389,900		384,254		733,108		720,487
Asset backed securities	1,634,804		1,627,384		1,683,753		1,664,460
Total (1)	$	18,996,608	$	18,421,669	$	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 and reinvested and included the fixed maturities pledged. 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 to 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 December 31, 2020, the fair value of the cash collateral received on securities lending was nil and the fair value of security collateral received was $301.1 million. 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 Company’s securities lending transactions were accounted for as secured borrowings with significant investment categories as follows:


	Remaining Contractual Maturity of the Agreements
	Overnight and Continuous		Less than 30 Days		30-90 Days		90 Days or More		Total
December 31, 2020
U.S. government and government agencies	$	142,317	$	—	$	139,290	$	—	$	281,607
Corporate bonds	3,021		—		—		—		3,021
Equity securities	16,461		—		—		—		16,461
Total	$	161,799	$	—	$	139,290	$	—	$	301,089
Gross amount of recognized liabilities for securities lending in offsetting disclosure in Note 11									—
Amounts related to securities lending not included in offsetting disclosure in Note 11									$	301,089

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 11									—
Amounts related to securities lending not included in offsetting disclosure in Note 11									$	388,366


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Equity Securities, at Fair Value

At December 31, 2020, the Company held $1.4 billion of equity securities, at fair value, compared to $838.9 million at December 31, 2019. Pursuant to applicable accounting guidance, changes in fair value on equity securities are recorded through net income effective January 1, 2018.

Other Investments

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


	December 31,
	2020		2019
Fixed maturities	$	843,354	$	754,452
Other investments	2,331,885		2,429,316
Short-term investments	557,008		377,014
Equity securities	92,549		102,695
Investments accounted for using the fair value option	3,824,796		3,663,477

Other investable assets (1)	500,000		—
Total other investments	$	4,324,796	$	3,663,477

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

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


	December 31,
	2020		2019
Term loan investments	1,231,731		1,326,018
Lending	572,636		602,841
Credit related funds	90,780		123,020
Energy	65,813		97,402
Investment grade fixed income	138,646		151,594
Infrastructure	165,516		61,786
Private equity	48,750		49,376
Real estate	18,013		17,279
Total	$	2,331,885	$	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:


	December 31,
	2020		2019
Credit related funds	$	740,060	$	428,437
Equities	343,058		293,686
Real estate	258,518		246,851
Lending	179,629		202,690
Private equity	235,289		144,983
Infrastructure	175,882		235,033
Energy	115,453		108,716
Total	$	2,047,889	$	1,660,396

In applying the equity method, investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the fair value of the underlying securities in the funds). Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds.

A summary of financial information for the Company’s investment funds accounted for using the equity method is as follows:


	December 31,
	2020		2019
Invested assets	$	44,131,377	$	26,383,370
Total assets	49,078,464		28,039,181
Total liabilities	6,054,189		3,595,695
Net assets	$	43,024,275	$	24,443,486


	Year Ended December 31,
	2020		2019		2018
Total revenues	$	5,762,098	$	164,669	$	4,565,354
Total expenses	1,656,029		528,762		1,135,602
Net income (loss)	$	4,106,069	$	(364,093)	$	3,429,752

Certain of the Company’s other investments and investments accounted for using the equity method are in investment funds for which the Company has the option to redeem at agreed upon values as described in each investment fund’s subscription agreement. Depending on the terms of the various subscription agreements, investments in investment funds may be redeemed daily, monthly, quarterly or on other terms. Two common redemption restrictions which may impact the Company’s ability to redeem these investment funds are gates and lockups. A gate is a suspension of redemptions which may be implemented by the general partner or investment manager of the fund in order to defer, in whole or in part, the redemption request in the event the aggregate amount of redemption requests exceeds a predetermined percentage of the investment fund's net assets which may otherwise hinder the general partner or investment manager's ability to liquidate holdings in an orderly fashion in order to generate the cash necessary to fund extraordinarily large redemption payouts. A lockup period is the initial amount of time an investor is contractually required to hold the security before having the ability to redeem. If the investment funds are eligible to be redeemed, the time to redeem such fund can take weeks or months following the notification.

Limited Partnership Interests

In the normal course of its activities, the Company invests in limited partnerships as part of its overall investment strategy. Such amounts are included in ‘investments accounted for using the equity method’ and ‘investments accounted for using the fair value option.’ The Company determined that


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these limited partnership interests represented variable interests in the funds because the general partner did not have a significant interest in the funds. The Company’s maximum exposure to loss with respect to these investments is limited to the investment carrying amounts reported in the Company’s consolidated balance sheet and any unfunded commitment.

The following table summarizes investments in limited partnership interests where the Company has a variable interest by balance sheet item:


	December 31,
	2020		2019
Investments accounted for using the equity method (1)	$	2,047,889	$	1,660,396
Investments accounted for using the fair value option (2)	184,720		188,283
Total	$	2,232,609	$	1,848,679

(1) Aggregate unfunded commitments were $1.8 billion at December 31, 2020, compared to $1.4 billion at December 31, 2019.

(2) Aggregate unfunded commitments were $35.6 million at December 31, 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:


	Year Ended December 31,
	2020		2019		2018
Fixed maturities	$	412,481	$	505,399	$	470,912
Term loans	84,149		98,949		87,926
Equity securities	28,958		15,857		13,154
Short-term investments	10,840		15,820		18,793
Other (1)	72,395		80,618		64,942
Gross investment income	608,823		716,643		655,727
Investment expenses	(89,215)		(88,905)		(92,094)
Net investment income	$	519,608	$	627,738	$	563,633

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

Net Realized Gains (Losses)

Net realized gains (losses) were as follows:


	Year Ended December 31,
	2020		2019		2018
Available for sale securities:
Gross gains on investment sales	$	595,941	$	235,655	$	69,299
Gross losses on investment sales	(117,282)		(104,612)		(223,123)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	15,881		41,910		(90,898)
Other investments	13,656		(35,734)		(90,778)
Equity securities	14,629		15,869		(5,984)
Short-term investments	2,279		3,801		(461)
Equity securities, at fair value (1):
Net realized gains (losses) on securities sold	26,849		11,313		(40,117)
Net unrealized gains (losses) on equity securities still held at reporting date	102,394		97,768		(22,828)
Allowance for credit losses:(3)
Investments related	(3,597)		—		—
Underwriting related	(10,007)		—		—
Net impairment losses	(533)		(3,165)		(2,829)
Derivative instruments (2)	179,675		119,741		15,636
Other	3,575		(19,348)		(16,090)
Net realized gains (losses)	$	823,460	$	363,198	$	(408,173)

(1) Effective January 1, 2018, changes in fair value on equity securities are recorded through net income.

(2) See Note 11 for information on the Company’s derivative instruments.

(3) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)” See note 3.

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

The Company recorded equity in net income related to investments accounted for using the equity method of $146.7 million for 2020, compared to $123.7 million for 2019 and $45.6 million for 2018. 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.


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Allowance for Expected Credit Losses

The following table provides a roll forward of the allowance for expected credit losses of the Company’s securities classified as available for sale:


	Year Ended December 31, 2020
	Structured Securities (1)		Municipal Bonds		Corporate Bonds		Total
Balance at beginning of period	$	—	$	—	$	—	$	—
Cumulative effect of accounting change (2)	517		—		117		634
Additions for current-period provision for expected credit losses	2,942		67		7,644		10,653
Additions (reductions) for previously recognized expected credit losses	(1,398)		6		(5,638)		(7,030)
Reductions due to disposals	(571)		(62)		(1,227)		(1,860)
Write-offs charged against the allowance	—		—		—		—
Balance at end of period	$	1,490	$	11	$	896	$	2,397

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

(2) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)” See note 3.

Restricted Assets

The Company is required to maintain assets on deposit, which primarily consist of fixed maturities, with various regulatory authorities to support its underwriting operations. The Company’s subsidiaries maintain assets in trust accounts as collateral for transactions with affiliated companies and also have investments in segregated portfolios primarily to provide collateral or guarantees for letters of credit to third parties

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


	December 31,
	2020		2019
Assets used for collateral or guarantees:
Affiliated transactions	$	4,643,334	$	4,526,761
Third party agreements	3,083,324		2,278,248
Deposits with U.S. regulatory authorities	827,552		797,371
Deposits with non-U.S. regulatory authorities	179,099		119,238
Total restricted assets	$	8,733,309	$	7,721,618

In addition, Watford maintains a secured credit facility 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 December 31, 2020 and December 31, 2019, Watford held $954.6 million 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:


	December 31,
	2020		2019		2018
Cash	$	906,448	$	726,230	$	646,556
Restricted cash (included in ‘other assets’)	384,096		177,468		78,087
Cash and restricted cash	$	1,290,544	$	903,698	$	724,643

10. Fair Value

Accounting guidance regarding fair value measurements addresses how companies should measure fair value when they are required to use a fair value measure for recognition or disclosure purposes under GAAP and provides a common definition of fair value to be used throughout GAAP. It defines fair value as the price that would be received to sell an asset or paid to transfer a liability in an orderly fashion between market participants at the measurement date. In addition, it establishes a three-level valuation hierarchy for the disclosure of fair value measurements. The valuation hierarchy is based upon the transparency of inputs to the valuation of an asset or liability as of the measurement date. The level in the hierarchy within which a given fair value measurement falls is determined based on the lowest level input that is significant to the measurement (Level 1 being the highest priority and Level 3 being the lowest priority).


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The levels in the hierarchy are defined as follows:

Level 1: Inputs to the valuation methodology are observable inputs that reflect quoted prices (unadjusted) for identical assets or liabilities in active markets

Level 2: Inputs to the valuation methodology include quoted prices for similar assets and liabilities in active markets, and inputs that are observable for the asset or liability, either directly or indirectly, for substantially the full term of the financial instrument

Level 3: Inputs to the valuation methodology are unobservable and significant to the fair value measurement

Following is a description of the valuation methodologies used for securities measured at fair value, as well as the general classification of such securities pursuant to the valuation hierarchy. The Company reviews its securities measured at fair value and discusses the proper classification of such investments with investment advisers and others.

The Company determines the existence of an active market based on its judgment as to whether transactions for the financial instrument occur in such market with sufficient frequency and volume to provide reliable pricing information. The independent pricing sources obtain market quotations and actual transaction prices for securities that have quoted prices in active markets. The Company uses quoted values and other data provided by nationally recognized independent pricing sources as inputs into its process for determining fair values of its fixed maturity investments. To validate the techniques or models used by pricing sources, the Company's review process includes, but is not limited to: (i) quantitative analysis (e.g., comparing the quarterly return for each managed portfolio to its target benchmark, with significant differences identified and investigated); (ii) a review of the prices obtained in the pricing process and the range of resulting fair values; (iii) initial and ongoing evaluation of methodologies used by outside parties to calculate fair value; (iv) a comparison of the fair value estimates to the Company’s knowledge of the current market; (v) a comparison of the pricing services' fair values to other pricing services' fair values for the same investments; and (vi) periodic back-testing, which includes randomly selecting purchased or sold securities and comparing the executed prices to the fair value estimates from the pricing service. A price source hierarchy was maintained in order to determine which price source would be used (i.e., a price obtained from a pricing service with more seniority in the hierarchy will be used over a less senior one in all cases). The hierarchy prioritizes pricing services based on availability and reliability and assigns the highest priority to index providers. Based on the above review, the

Company will challenge any prices for a security or portfolio which are considered not to be representative of fair value.

In certain circumstances, when fair values are unavailable from these independent pricing sources, quotes are obtained directly from broker-dealers who are active in the corresponding markets. Such quotes are subject to the validation procedures noted above. Of the $26.5 billion of financial assets and liabilities measured at fair value at December 31, 2020, approximately $150.1 million, or 0.6%, were priced using non-binding broker-dealer quotes. Of the $22.9 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.

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


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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.

Mortgage-backed securities — valuations provided by independent pricing services, substantially all through pricing vendors and index providers with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models (including Option Adjusted Spread) which use spreads to determine the expected average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. The pricing services also review prepayment speeds and other indicators, when applicable. As the significant inputs used in the pricing process for mortgage-backed securities are observable market inputs, the fair value of these securities are classified within Level 2.
Municipal bonds — valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The fair values of these securities are generally determined using spreads obtained from broker-dealers who trade in the relevant security market, trade prices and the new issue market. As the significant inputs used in the pricing process for municipal bonds are observable market inputs, the fair value of these securities are classified within Level 2.
Commercial mortgage-backed securities — valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models which use spreads to determine the appropriate average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. As the significant inputs used in the pricing process for commercial mortgage-backed securities are observable market inputs, the fair value of these securities are classified within Level 2.
Non-U.S. government securities — valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The fair values of these securities are generally based on international indices or valuation models which include daily observed yield curves, cross-currency basis index spreads and country credit spreads. As the significant inputs used in the pricing process for non-U.S. government securities are observable market inputs, the fair value of these securities are classified within Level 2.
Asset-backed securities — valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models (including Option Adjusted Spread) which use spreads to determine the appropriate average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. As the significant inputs used in the pricing process for asset-backed securities are observable market inputs, the fair value of these securities are classified within Level 2. A small number of securities are included in Level 3 due to a low level of transparency on the inputs used in the pricing process.

Equity securities

The Company determined that exchange-traded equity securities would be included in Level 1 as their fair values are based on quoted market prices in active markets. Other equity securities are included in Level 2 of the valuation hierarchy. A small number of securities are included in Level 3 due to the lack of an available independent price source for such securities. As the significant inputs used to price these securities are unobservable, the fair value of such securities are classified as Level 3.

Other investments

The Company determined that exchange-traded investments would be included in Level 1 as their fair values are based on quoted market prices in active markets. Other investments also include term loan investments for which fair values are estimated by using quoted prices of term loan investments with similar characteristics, pricing models or matrix pricing. Such investments are generally classified within Level 2. A small number of securities are included in Level 3 due to the lack of an available independent price source for such securities.

Derivative instruments

The Company’s futures contracts, foreign currency forward contracts, interest rate swaps and other derivatives trade in the over-the-counter derivative market. The Company uses the market approach valuation technique to estimate the fair value for these derivatives based on significant observable market inputs from third party pricing vendors, non-binding broker-dealer quotes and/or recent trading activity. As the significant inputs used in the pricing process for these derivative instruments are observable market inputs, the fair value of these securities are classified within Level 2.


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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.

Contingent consideration liabilities

Contingent consideration liabilities (included in ‘other liabilities’ in the consolidated balance sheets) include amounts related to the Company’s 2014 acquisition of CMG Mortgage Insurance Company and its affiliated mortgage insurance companies (the “CMG Entities”) and other acquisitions. Such amounts are remeasured at fair value at each balance sheet date with changes in fair value recognized in ‘net realized gains (losses).’ To determine the fair value of contingent consideration liabilities, the Company estimates future payments using an income approach based on modeled inputs which include a weighted average cost of capital. The Company determined that contingent consideration liabilities would be included within Level 3.


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


			Fair Value Measurement Using:
	Estimated Fair Value		Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Assets measured at fair value (1):
Available for sale securities:
Fixed maturities:
Corporate bonds	$	7,856,571	$	—	$	7,856,558	$	13
Mortgage backed securities	630,001		—		630,001		—
Municipal bonds	494,522		—		494,522		—
Commercial mortgage backed securities	389,900		—		389,900		—
U.S. government and government agencies	5,557,077		5,463,356		93,721		—
Non-U.S. government securities	2,433,733		—		2,433,733		—
Asset backed securities	1,634,804		—		1,631,378		3,426
Total	18,996,608		5,463,356		13,529,813		3,439

Short-term investments	1,924,922		1,920,565		4,357		—

Equity securities, at fair value	1,460,959		1,401,653		17,291		42,015





Derivative instruments (4)	177,383		—		177,383		—

Fair value option:
Corporate bonds	651,294		—		650,309		985
Non-U.S. government bonds	35,263		—		35,263		—
Mortgage backed securities	3,282		—		3,282		—

Commercial mortgage backed securities	1,090		—		1,090		—
Asset backed securities	152,151		—		152,151		—
U.S. government and government agencies	274		164		110		—
Short-term investments	557,008		420,131		136,877		—
Equity securities	92,549		23,373		188		68,988
Other investments	1,134,229		51,149		1,015,977		67,103
Other investments measured at net asset value (2)	1,197,656
Total	3,824,796		494,817		1,995,247		137,076

Total assets measured at fair value	$	26,384,668	$	9,280,391	$	15,724,091	$	182,530

Liabilities measured at fair value:
Contingent consideration liabilities	$	(461)	$	—	$	—	$	(461)
Securities sold but not yet purchased (3)	(21,679)		—		(21,679)		—
Derivative instruments (4)	(108,705)		—		(108,705)		—
Total liabilities measured at fair value	$	(130,845)	$	—	$	(130,384)	$	(461)

(1) In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See Note 9.

(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 11.


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The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2019:


			Fair Value Measurement Using:
	Estimated Fair Value		Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Assets measured at fair value (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

Equity securities, at fair value	850,283		789,596		4,798		55,889

Short-term investments	956,546		904,804		51,742		—





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)

(4) See Note 11.


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The following table presents a reconciliation of the beginning and ending balances for all financial assets and liabilities measured at fair value on a recurring basis using Level 3 inputs for 2020 and 2019:




			Assets										Liabilities
	Available For Sale				Fair Value Option						Fair Value
	Structured Securities (1)		Corporate Bonds		Corporate Bonds		Other Investments		Equity Securities		Equity Securities			Contingent Consideration Liabilities
Year Ended December 31, 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)	—		(5,865)		(13)		(314)		10,894		8,214			(72)
Included in other comprehensive income	(169)		397		—		—		—		—			—
Purchases, issuances, sales and settlements
Purchases	—		—		66		52,449		—		4,030			—
Issuances	—		—		—		—		—		—			—
Sales	—		—		—		(56,833)		—		(26,118)			—
Settlements	(1,413)		(1,462)		—		—		—		—			7,609
Transfers in and/or out of Level 3	(208)		(1,908)		—		2,984		—		—			—
Balance at end of year	$	3,426	$	13	$	985	$	67,103	$	68,988	$	42,015		$	(461)

Year Ended December 31, 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)	1,760		2		(162)		(8,119)		1,949		(3,418)			(1,478)
Included in other comprehensive income	3		(267)		—		—		—		—			—
Purchases, issuances, sales and settlements
Purchases	—		881		—		3,746		—		36,077			—
Issuances	—		—		—		—		—		—			(548)
Sales	(1,757)		—		(28,583)		(20,495)		—		(27,982)			—
Settlements	(552)		(1,766)		—		(600)		—		—			60,693
Transfers in and/or out of Level 3	5,449		1,860		23,919		31,580		56,145		51,212			—
Balance at end of year	$	5,216	$	8,851	$	932	$	68,817	$	58,094	$	55,889		$	(7,998)

(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 December 31, 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 December 31, 2020, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.9 billion and had a fair value of $3.7 billion. At December 31, 2019, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $1.9 billion and had a fair value of $2.3 billion. The fair values of the senior notes were obtained from a third party pricing service and are based on observable

market inputs. As such, the fair value of the senior notes is classified within Level 2.

Fair Value Measurements on a Non-Recurring Basis

The Company measures the fair value of certain assets on a non-recurring basis, generally quarterly, annually, or when events or changes in circumstances indicate that the carrying amount of the assets may not be recoverable. These assets include investments accounted for using the equity method, certain other investments, goodwill and intangible assets, and long-lived assets. The Company uses a variety of techniques to measure the fair value of these assets when appropriate, as described below:

Investments accounted for using the equity method. When the Company determines that the carrying value of these assets may not be recoverable, the Company records the assets at fair value with the loss recognized in income. In such cases,


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the Company measures the fair value of these assets using the techniques discussed above in “—Fair Value Measurements on a Recurring Basis.”

Goodwill and Intangible Assets. The Company tests goodwill and intangible assets for impairment whenever events or changes in circumstances indicate the carrying amount may not be recoverable. When the Company determines goodwill and intangible assets may be impaired, the Company uses techniques including discounted expected future cash flows, to measure fair value.

Long-Lived Assets. The Company tests its long-lived assets for impairment whenever events or changes in circumstances indicate the carrying amount of a long-lived asset may not be recoverable.

11. Derivative Instruments

The Company’s investment strategy allows for the use of derivative instruments. The Company’s derivative instruments are recorded on its consolidated balance sheets at fair value. The Company utilizes exchange traded U.S. Treasury note, Eurodollar and other futures contracts and commodity futures to manage portfolio duration or replicate investment positions in its portfolios and the Company routinely utilizes foreign currency forward contracts, currency options, index futures contracts and other derivatives as part of its total return objective. In addition, certain of the Company’s investments are managed in portfolios which incorporate the use of foreign currency forward contracts which are intended to provide an economic hedge against foreign currency movements.

In addition, the Company purchases to-be-announced mortgage backed securities (“TBAs”) as part of its investment strategy. TBAs represent commitments to purchase a future issuance of agency mortgage backed securities. For the period between purchase of a TBA and issuance of the underlying security, the Company’s position is accounted for as a derivative. The Company purchases TBAs in both long and short positions to enhance investment performance and as part of its overall investment strategy.

The following table summarizes information on the fair values and notional values of the Company’s derivative instruments:


	Estimated Fair Value
	Asset Derivatives		Liability Derivatives		Notional Value (1)
December 31, 2020
Futures contracts (2)	$	11,046	$	(4,496)	$	3,099,796
Foreign currency forward contracts (2)	52,716		(6,202)		1,656,729
TBAs (3)	—		—		—
Other (2)	113,621		(98,007)		5,763,919
Total	$	177,383	$	(108,705)

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 December 31, 2020 or 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.

At December 31, 2020, $138.8 million and $93.0 million, respectively, of asset derivatives and liability derivatives 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 table above were not subject to a master netting agreement.


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Realized and unrealized contract gains and losses on the Company’s derivative instruments are reflected in net realized gains (losses) in the consolidated statements of income, as summarized in the following table:


Derivatives not designated as hedging instruments		Year Ended December 31,
	2020			2019			2018
Net realized gains (losses):
Futures contracts		$	114,987		$	114,123		$	48,443
Foreign currency forward contracts		49,974			(9,499)			(21,770)
TBAs		1,129			463			(133)
Other		13,585			14,654			(10,904)
Total		$	179,675		$	119,741		$	15,636

12. Variable Interest Entity and Noncontrolling Interests

Watford Holdings Ltd.

In March 2014, Watford raised approximately $1.1 billion of capital consisting of $907.3 million in common equity ($895.6 million net of issuance costs) and $226.6 million in preference equity ($219.2 million net of issuance costs and discount). The Company invested $100.0 million and acquired 2,500,000 common shares. Watford’s common shares are listed on the Nasdaq Select Global Market under the ticker symbol “WTRE”. As of December 31, 2020, the Company owned approximately 13% of Watford’s outstanding common equity and, as of February 16, 2021, Arch Re Bermuda owned approximately 10.3% of Watford’s common equity.

Subsidiaries of the Company act as Watford’s reinsurance and insurance underwriting managers. HPS Investment Partners, LLC (“HPS”) manages Watford’s non-investment grade credit portfolios, and the Company manages Watford’s investment grade portfolios, each under separate long term services agreements. Maamoun Rajeh and Nicolas Papadopoulo, both officers of the Company, serve on the board of directors of Watford.

The Company concluded that Watford is a VIE and that the Company is the primary beneficiary. The Company includes the results of Watford in its consolidated financial statements. The Company concluded that Watford should be reflected in a separate operating segment (‘other’) and provides the income statement and total investable assets, total assets and total liabilities of Watford within Note 4.

Because Watford is an independent company, the assets of Watford can be used only to settle obligations of Watford and Watford is solely responsible for its own liabilities and commitments. The Company’s financial exposure to Watford is limited to its investment in Watford’s senior notes, common shares and preferred shares and counterparty credit

risk (mitigated by collateral) arising from the reinsurance transactions.

In the 2020 fourth quarter, Arch Capital, Watford Holdings Ltd. and Greysbridge Ltd., a wholly-owned subsidiary of Arch Capital, entered into an Agreement and Plan of Merger (as amended, the “Merger Agreement”) pursuant to which, among other things, Arch Capital agreed to acquire all of the common shares of Watford Holdings Ltd. not owned by Arch for a cash purchase price of $35.00 per common share. Arch Capital has assigned its rights under the Merger Agreement to Greysbridge Holdings Ltd., a wholly-owned subsidiary of Arch Capital (“Greysbridge”). The transaction is expected to close in the first half of 2021 and remains subject to customary closing conditions, including regulatory and shareholder approvals. Upon closing of the transaction, Watford will be wholly owned by Greysbridge and Greysbridge will be owned 40% by Arch Re Bermuda, 30% by certain investment funds managed by Kelso & Company and 30% by certain investment funds managed by Warburg Pincus LLC.


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


	December 31,
	2020		2019
Assets
Investments accounted for using the fair value option (1)	$	1,790,385	$	1,898,091
Fixed maturities available for sale, at fair value	655,249		745,708
Equity securities, at fair value	52,410		65,338
Cash	211,451		102,437
Accrued investment income	14,679		14,025
Premiums receivable	224,377		273,657
Reinsurance recoverable on unpaid and paid losses and LAE	286,590		170,973
Ceded unearned premiums	122,339		132,577
Deferred acquisition costs, net	53,705		64,044
Receivable for securities sold	37,423		16,287
Goodwill and intangible assets	7,650		7,650
Other assets	75,801		60,070
Total assets of consolidated VIE	$	3,532,059	$	3,550,857

Liabilities
Reserves for losses and loss adjustment expenses	$	1,519,583	$	1,263,628
Unearned premiums	407,714		438,907
Reinsurance balances payable	63,269		77,066
Revolving credit agreement borrowings	155,687		484,287
Senior notes	172,689		172,418
Payable for securities purchased	25,881		18,180
Other liabilities	193,494		171,714
Total liabilities of consolidated VIE	$	2,538,317	$	2,626,200

Redeemable noncontrolling interests	$	52,398	$	52,305

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

The following table summarizes Watford’s cash flow from operating, investing and financing activities.


	Year Ended December 31,
	2020	2019	2018
Total cash provided by (used for):
Operating activities	181,736	239,284	229,315
Investing activities	258,589	(140,620)	(285,281)
Financing activities	(335,776)	(61,433)	(2,406)

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 December 31, 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:


	December 31,
	2020		2019
Balance, beginning of year	$	762,777	$	791,560
Additional paid in capital attributable to noncontrolling interests	1,334		(2,929)
Repurchases attributable to non-redeemable noncontrolling interests (1)	(2,867)		(75,056)
Amounts attributable to noncontrolling interests	53,076		40,072
Other amounts attributable to noncontrolling interests	(375)		—
Other comprehensive (income) loss attributable to noncontrolling interests	9,062		9,130
Balance, end of year	$	823,007	$	762,777

(1) During 2020 and 2019, 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. Holders of the Watford Preference Shares will be entitled to receive, if declared by Watford’s board, quarterly cash dividends on the last day of March, June, September, and December. Dividends accrued from the closing date to June 30, 2019 at a fixed rate of 8.5% per annum. From June 30, 2019 and subsequent, dividends will accrue based on a floating rate equal to the 3 month U.S. dollar LIBOR (with a 1% floor) plus a margin based on the difference between the fixed rate and the 5 year mid swap rate to the floating rate. 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. Because the redemption features are not solely within the control of Watford, the Company accounts for the redeemable noncontrolling interests in the Watford Preference Shares in the mezzanine section of its consolidated balance sheets.

On August 1, 2019, Watford redeemed 6,919,998 of its 9,065,200 issued and outstanding preference shares (“Watford Preference Shares”) at a total redemption price of $25.19748 per share, inclusive of all declared and unpaid dividends. The Company received $11.5 million pursuant to the redemption of Watford Preference Shares.


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Preferred dividends on the Watford Preference Shares, including the accretion of the discount and issuance costs, was $4.4 million for 2020, compared to $17.8 million for 2019 and $19.6 million for 2018.

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


	December 31,
	2020		2019		2018
Balance, beginning of year	$	55,404	$	206,292	$	205,922
Redemption of noncontrolling interests	—		(157,709)		—

Accretion of preference share issuance costs	93		244		370
Other	3,051		6,577		—
Balance, end of year	$	58,548	$	55,404	$	206,292

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


	December 31,
	2020		2019		2018
Amounts attributable to non-redeemable noncontrolling interests	$	(53,076)	$	(40,072)	$	48,507
Amounts attributable to redeemable noncontrolling interests	(7,114)		(16,909)		(18,357)
Net (income) loss attributable to noncontrolling interests	$	(60,190)	$	(56,981)	$	30,150

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
Dec 31, 2020
Bellemeade 2017-1 Ltd. (Oct-17)	$	145,573	$	(245)	$	844	$	599
Bellemeade 2018-1 Ltd. (Apr-18)	250,095		(903)		2,245		1,342
Bellemeade 2018-2 Ltd. (Aug-18)	108,395		(138)		280		142
Bellemeade 2018-3 Ltd. (Oct-18)	302,563		(1,320)		3,262		1,942
Bellemeade 2019-1 Ltd. (Mar-19)	219,256		(1,361)		8,461		7,100
Bellemeade 2019-2 Ltd. (Apr-19)	398,316		(730)		5,201		4,471
Bellemeade 2019-3 Ltd. (Jul-19)	528,084		(861)		5,079		4,218
Bellemeade 2019-4 Ltd. (Oct-19)	468,737		(890)		6,676		5,786
Bellemeade 2020-1 Ltd. (Jun-20) (1)	275,068		(178)		1,012		834
Bellemeade 2020-2 Ltd. (Sep-20) (2)	423,420		(556)		6,839		6,283
Bellemeade 2020-3 Ltd. (Nov-20) (3)	418,158		(631)		9,605		8,974
Bellemeade 2020-4 Ltd. (Dec-20) (4)	321,393		(156)		6,816		6,660
Total	$	3,859,058	$	(7,969)	$	56,320	$	48,351
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 $79 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

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

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

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

See Note 8, “Reinsurance.”


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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

13. Other Comprehensive Income (Loss)

The following table presents the changes in each component of AOCI, net of noncontrolling interests:


	Unrealized Appreciation on Available-For-Sale Investments		Foreign Currency Translation Adjustments		Total
Year Ended December 31, 2020
Beginning balance	$	258,486	$	(46,395)	$	212,091

Other comprehensive income (loss) before reclassifications	668,996		33,995		702,991
Amounts reclassified from accumulated other comprehensive income	(426,187)		—		(426,187)
Net current period other comprehensive income (loss)	242,809		33,995		276,804
Ending balance	$	501,295	$	(12,400)	$	488,895

Year Ended December 31, 2019
Beginning balance	$	(114,178)	$	(64,542)	$	(178,720)

Other comprehensive income (loss) before reclassifications	491,605		18,147		509,752
Amounts reclassified from accumulated other comprehensive income	(118,941)		—		(118,941)
Net current period other comprehensive income (loss)	372,664		18,147		390,811
Ending balance	$	258,486	$	(46,395)	$	212,091

Year Ended December 31, 2018
Beginning balance	$	157,400	$	(39,356)	$	118,044
Cumulative effect of an accounting change	(149,794)		—		(149,794)
Other comprehensive income (loss) before reclassifications	(266,357)		(25,186)		(291,543)
Amounts reclassified from accumulated other comprehensive income	144,573		—		144,573
Net current period other comprehensive income (loss)	(121,784)		(25,186)		(146,970)
Ending balance	$	(114,178)	$	(64,542)	$	(178,720)

The following tables present details about amounts reclassified from accumulated other comprehensive income and the tax effects allocated to each component of other comprehensive income (loss):


	Consolidated Statement of Income	Amounts Reclassified from AOCI
Details About	Line Item That Includes	Year Ended December 31,
AOCI Components	Reclassification	2020		2019		2018
Unrealized appreciation on available-for-sale investments
	Net realized gains (losses)	$	478,659	$	131,043	$	(153,822)
	Provision for credit losses	(3,597)
	Other-than-temporary impairment losses	(533)		(3,165)		(2,829)
	Total before tax	474,529		127,878		(156,651)
	Income tax (expense) benefit	(48,342)		(8,937)		12,078
	Net of tax	$	426,187	$	118,941	$	(144,573)


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Following are the related tax effects allocated to each component of other comprehensive income (loss):


	Before Tax		Tax Expense		Net of Tax
	Amount		(Benefit)		Amount
Year Ended December 31, 2020
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	754,572	$	75,855	$	678,717

Less reclassification of net realized gains (losses) included in net income	474,529		48,342		426,187
Foreign currency translation adjustments	33,706		370		33,336
Other comprehensive income (loss)	$	313,749	$	27,883	$	285,866

Year Ended December 31, 2019
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	562,576	$	61,805	$	500,771

Less reclassification of net realized gains (losses) included in net income	127,878		8,937		118,941
Foreign currency translation adjustments	18,463		353		18,110
Other comprehensive income (loss)	$	453,161	$	53,221	$	399,940

Year Ended December 31, 2018
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(294,267)	$	(24,210)	$	(270,057)

Less reclassification of net realized gains (losses) included in net income	(156,651)		(12,078)		(144,573)
Foreign currency translation adjustments	(25,006)		(176)		(24,830)
Other comprehensive income (loss)	$	(162,622)	$	(12,308)	$	(150,314)


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14. Earnings Per Common Share

The calculation of basic earnings per common share is computed by dividing income available to Arch common shareholders by the weighted average number of Common Shares and common share equivalents outstanding. The following table sets forth the computation of basic and diluted earnings per common share:


	Year Ended December 31,
	2020		2019		2018
Numerator:
Net income	$	1,465,711	$	1,693,300	$	727,821
Amounts attributable to noncontrolling interests	(60,190)		(56,981)		30,150
Net income available to Arch	1,405,521		1,636,319		757,971
Preferred dividends	(41,612)		(41,612)		(41,645)
Loss on redemption of preferred shares	—		—		(2,710)
Net income available to Arch common shareholders	$	1,363,909	$	1,594,707	$	713,616

Denominator:
Weighted average common shares outstanding	403,062,179		401,802,815		401,036,376
Series D preferred securities (1)	—		—		3,311,245
Weighted average common shares outstanding – basic	403,062,179		401,802,815		404,347,621
Effect of dilutive common share equivalents:
Nonvested restricted shares	1,682,309		1,673,770		1,474,207
Stock options (2)	5,514,967		8,132,893		7,084,650
Weighted average common shares and common share equivalents outstanding – diluted	410,259,455		411,609,478		412,906,478

Earnings per common share:
Basic	$	3.38	$	3.97	$	1.76
Diluted	$	3.32	$	3.87	$	1.73

(1) The company has determined that, based on a review of the terms, features and rights of the Company’s non-voting common equivalent preferred shares compared to the rights of the Company’s common shareholders, the underlying common shares that the convertible securities convert to were common share equivalents at the time of their issuance.

(2) 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 2020, 2019 and 2018, the number of stock options excluded were 2,249,821, 1,302,017 and 5,673,821, respectively.

15. Income Taxes

Arch Capital is incorporated under the laws of Bermuda and, under current Bermuda law, is not obligated to pay any taxes in Bermuda based upon income or capital gains. The Company has received a written undertaking from the Minister of Finance in Bermuda under the Exempted Undertakings Tax Protection Act 1966 that, in the event that any legislation is enacted in Bermuda imposing any tax computed on profits, income, gain or appreciation on any capital asset, or any tax in the nature of estate duty or inheritance tax, such tax will not be applicable to Arch Capital or any of its operations until March 31, 2035. This undertaking does not, however, prevent the imposition of taxes on any person ordinarily resident in Bermuda or any company in respect of its ownership of real property or leasehold interests in Bermuda.

Arch Capital and its non-U.S. subsidiaries will be subject to U.S. federal income tax only to the extent that they derive U.S. source income that is subject to U.S. withholding tax or income that is effectively connected with the conduct of a trade or business within the U.S. and is not exempt from U.S. tax under an applicable income tax treaty with the U.S. Arch Capital and its non-U.S. subsidiaries will be subject to a withholding tax on dividends from U.S. investments and interest from certain U.S. payors (subject to reduction by any applicable income tax treaty). Arch Capital and its non-U.S. subsidiaries intend to conduct their operations in a manner that will not cause them to be treated as engaged in a trade or business in the United States and, therefore, will not be required to pay U.S. federal income taxes (other than U.S. excise taxes on insurance and reinsurance premium and withholding taxes on dividends and certain other U.S. source investment income). However, because there is uncertainty as to the activities which constitute being engaged in a trade or business within the United States, there can be no assurances that the U.S. Internal Revenue Service will not contend


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successfully that Arch Capital or its non-U.S. subsidiaries are engaged in a trade or business in the United States. If Arch Capital or any of its non-U.S. subsidiaries were subject to U.S. income tax, Arch Capital’s shareholders’ equity and earnings could be materially adversely affected. Arch Capital has subsidiaries and branches that operate in various jurisdictions around the world that are subject to tax in the jurisdictions in which they operate. The significant jurisdictions in which Arch Capital’s subsidiaries and branches are subject to tax are the United States, United Kingdom, Ireland, Canada, Switzerland, Australia and Denmark.

The components of income taxes attributable to operations were as follows:


	Year Ended December 31,
	2020		2019		2018
Current expense (benefit):
United States	$	181,571	$	139,407	$	73,078
Non-U.S.	16,091		4,954		12,785
	197,662		144,361		85,863
Deferred expense (benefit):
United States	(89,170)		11,849		19,544
Non-U.S.	3,346		(400)		8,544
	(85,824)		11,449		28,088
Income tax expense	$	111,838	$	155,810	$	113,951

The Company’s income or loss before income taxes was earned in the following jurisdictions:


	Year Ended December 31,
	2020		2019		2018
Income (Loss) Before Income Taxes:
Bermuda	$	1,114,117	$	1,122,952	$	388,492
United States	409,893		701,480		440,823
Other	53,539		24,678		12,457
Total	$	1,577,549	$	1,849,110	$	841,772

The expected tax provision computed on pre-tax income or loss at the weighted average tax rate has been calculated as the sum of the pre-tax income in each jurisdiction multiplied by that jurisdiction’s applicable statutory tax rate. The 2020 applicable statutory tax rates by jurisdiction were as follows: Bermuda (0.0%), United States (21.0 %), United Kingdom (19.0 %), Ireland (12.5 %), Denmark (22.0 %), Canada (26.5 %), Gibraltar (10.0 %), Australia (30.0 %), Hong Kong (16.5 %) and the Netherlands (16.5 %).

A reconciliation of the difference between the provision for income taxes and the expected tax provision at the weighted average tax rate follows:


	Year Ended December 31,
	2020		2019		2018
Expected income tax expense (benefit) computed on pre-tax income at weighted average income tax rate	$	111,947	$	149,799	$	91,529
Addition (reduction) in income tax expense (benefit) resulting from:
Tax-exempt investment income	(1,824)		(3,091)		(4,790)
Meals and entertainment	547		1,134		1,060
State taxes, net of U.S. federal tax benefit	5,027		3,314		2,086
Foreign branch taxes	2,094		1,231		5,428
Prior year adjustment	3,983		632		(2,522)
Foreign exchange gains & losses	(1,736)		436		1,293
Changes in applicable tax rate	—		—		(128)
Dividend withholding taxes	7,105		6,510		6,594
Change in valuation allowance	13,190		1,628		18,396
Contingent consideration	9		190		740
Share based compensation	(2,533)		(6,592)		(5,356)

Intercompany loan write-off	(22,083)		—		—
Other	(3,888)		619		(379)
Income tax expense (benefit)	$	111,838	$	155,810	$	113,951

The effect of a change in tax laws or rates on deferred taxes assets and liabilities is recognized in income in the period in which such change is enacted.

Deferred income tax assets and liabilities reflect temporary differences based on enacted tax rates between the carrying amounts of assets and liabilities for financial reporting and income tax purposes.


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Significant components of the Company’s deferred income tax assets and liabilities were as follows:


	December 31,
	2020		2019
Deferred income tax assets:
Net operating loss	$	67,142	$	30,836
Uncrystallized losses	2,926		1,565
AMT credit carryforward	—		1,323
Discounting of net loss reserves	74,247		52,582

Net unearned premium reserve	66,368		64,269
Compensation liabilities	27,351		21,693
Foreign tax credit carryforward	19,160		9,521
Interest expense	622		—
Goodwill and intangible assets	14,450		11,644

Bad debt reserves	1,864		5,983
Lease liability	23,604		26,438
Net unrealized foreign exchange gains	165		598

Other, net	1,725		206
Deferred tax assets before valuation allowance	299,624		226,658
Valuation allowance	(88,255)		(48,219)
Deferred tax assets net of valuation allowance	211,369		178,439
Deferred income tax liabilities:
Depreciation and amortization	(495)		(1,215)

Deposit accounting liability	(1,751)		(2,169)
Contingency reserve	(64,593)		(132,831)
Deferred policy acquisition costs	(42,045)		(29,847)

Net unrealized appreciation of investments	(66,681)		(38,764)
Right-of-use asset	(19,239)		(23,416)
Other, net	(843)		(3,680)
Total deferred tax liabilities	(195,647)		(231,922)
Net deferred income tax assets (liabilities)	$	15,722	$	(53,483)

The Company provides a valuation allowance to reduce certain deferred tax assets to an amount which management expects to more likely than not be realized. As of December 31, 2020, the Company’s valuation allowance was $88.3 million, compared to $48.2 million at December 31, 2019. The valuation allowance in both periods was primarily attributable to valuation allowance on the Company’s U.K. Canadian and Australian operations and certain other deferred tax assets relating to loss carryforwards that have a limited use.

At December 31, 2020, the Company’s net operating loss carryforwards and tax credits were as follows:


	Year Ended December 31,
	2020		Expiration
Operating Loss Carryforwards
United Kingdom	$	237,277	No expiration
Ireland	11,336		No expiration
Australia	37,995		No expiration
Hong Kong	21,094		No expiration
Denmark	23		No expiration
United States (1)	27,425		2029 - 2038

Tax Credits
U.K. foreign tax credits	19,160		No expiration
U.S. refundable AMT credits	0		No expiration

(1) On January 30, 2014, the Company’s U.S. mortgage operations underwent an ownership change for U.S. federal income tax purposes as a result of the Company’s acquisition of the CMG Entities. As a result of this ownership change, a limitation has been imposed upon the utilization of approximately $8.3 million of the Company’s existing U.S. net operating loss carryforwards. Utilization is limited to approximately $0.6 million per year in accordance with Section 382 of the Internal Revenue Code of 1986 as amended (“the Code”).

The Company’s U.S. mortgage operations are eligible for a tax deduction, subject to certain limitations, under Section 832(e) of the Code for amounts required by state law or regulation to be set aside in statutory contingency reserves. The deduction is allowed only to the extent that the Company purchases non-interest bearing U.S. Mortgage Guaranty Tax and Loss Bonds (“T&L Bonds”) issued by the U.S. Treasury Department in an amount equal to the tax benefit derived from deducting any portion of the statutory contingency reserves. T&L Bonds are reflected in ‘other assets’ on the Company’s balance sheet and totaled approximately $88.1 million at December 31, 2020, compared to $207.0 million at December 31, 2019.

Deferred income tax liabilities have not been accrued with respect to the undistributed earnings of the Company's U.S., U.K. and Ireland subsidiaries as it is the Company’s intention that all such earnings will be indefinitely reinvested. If the earnings were to be distributed, as dividends or otherwise, such amounts may be subject to withholding tax in the jurisdiction of the paying entity. The Company no longer intends to indefinitely reinvest earnings from the Company's Canada subsidiary, however, no income or withholding taxes have been accrued as the Canada subsidiary does not have positive cumulative earnings and profits and therefore a distribution from this particular subsidiary would not be subject to income taxes or withholding taxes. Potential tax implications of repatriation from the Company’s unremitted earnings that are indefinitely reinvested are driven by facts at the time of distribution. Therefore it is not practicable to estimate the income tax liabilities that might be incurred if


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such earnings were remitted. Distributions from the U.K. or Ireland would not be subject to withholding tax and no deferred income tax liability would need to be accrued.

The Company recognizes interest and penalties relating to unrecognized tax benefits in the provision for income taxes. As of December 31, 2020, the Company’s total unrecognized tax benefits, including interest and penalties, were $2.0 million. If recognized, the full amount of the unrecognized tax benefit would impact the consolidated effective tax rate. A reconciliation of the beginning and ending amount of unrecognized tax benefits is as follows:


	December 31,
	2020		2019
Balance at beginning of year	$	2,008	$	2,008
Additions based on tax positions related to the current year	—		—
Additions for tax positions of prior years	—		—
Reductions for tax positions of prior years	—		—
Settlements	—		—
Balance at end of year	$	2,008	$	2,008

The Company or its subsidiaries or branches files income tax returns in the U.S. federal jurisdiction and various state, local and foreign jurisdictions. The following table details open tax years that are potentially subject to examination by local tax authorities, in the following major jurisdictions:


Jurisdiction						Tax Years
United States						2015-2020
United Kingdom						2019-2020
Ireland						2016-2020
Canada						2016-2020
Switzerland						2017-2020
Denmark						2016-2020
Australia						2016-2020

As of December 31, 2020, the Company’s current income tax payable (included in “Other liabilities”) was $9.2 million.

16. Transactions with Related Parties

In 2017, the Company acquired approximately 25% of Premia Holdings Ltd. Premia Holdings Ltd. is the parent of Premia Reinsurance Ltd., a multi-line Bermuda reinsurance company (together with Premia Holdings Ltd., “Premia”). Premia’s strategy is to reinsure or acquire companies or reserve portfolios in the non-life property and casualty insurance and reinsurance run-off market. Arch Re Bermuda and certain Arch co-investors invested $100.0 million and acquired approximately 25% of Premia as well as warrants to purchase additional common equity. Arch has appointed two directors to serve on the seven person board of directors of Premia. Arch Re Bermuda is providing a 25% quota share reinsurance treaty on certain business written by Premia.

In the 2019 fourth quarter, Barbican entered into certain reinsurance and related transactions with Premia pursuant to which Premia assumed a transfer of liability for the 2018 and prior years of account of Barbican as of July 1, 2019. Barbican recorded reinsurance recoverable on unpaid and paid losses and funds held liability of $199.8 million and $149.6 million, respectively at December 31, 2020, compared to $177.7 million and $180.0 million, respectively, at December 31, 2019.

In the 2020 fourth quarter, Arch Capital and Arch Re Bermuda entered into agreements pursuant to which Arch Re Bermuda, together with certain co-investors, expect to acquire all of the common shares of Watford Holdings Ltd, subject to customary closing conditions including regulatory and shareholder approval. See note 12, “Variable Interest Entity and Noncontrolling Interests.”

Certain directors and executive officers of the Company own common and preference shares of Watford. See note 12, “Variable Interest Entity and Noncontrolling Interests,” for information about Watford.


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17. Leases

In the ordinary course of business, the Company renews and enters into new leases for office property and equipment. At the lease inception date, the Company determines whether a contract contains a lease and its classification as a finance or operating lease. Primarily all of the Company’s leases are classified as operating leases. The Company’s operating leases have remaining lease terms of up to 10 years, some of which include options to extend the lease term. The Company considers these options when determining the lease term and measuring its lease liability and right-of-use asset. In addition, the Company’s lease agreements do not contain any material residual value guarantees or material restrictive covenants.

Short-term operating leases with an initial term of twelve months or less were excluded on the Company's consolidated balance sheet and represent an inconsequential amount of operating lease expense.

As most leases do not provide an implicit rate, the Company uses its incremental borrowing rate based on the information available at the lease commencement date in determining the present value of lease payments.

Additional information regarding the Company’s operating leases is as follows:






















	December 31,
	2020			2019
Operating lease costs	$	31,826		$	30,478
Cash payments included in the measurement of lease liabilities reported in operating cash flows	$	30,365		$	27,521
Right-of-use assets obtained in exchange for new lease liabilities	$	12,060		$	7,445
Right-of-use assets (1)	$	115,911		$	131,661
Operating lease liability (1)	$	136,015		$	150,519
Weighted average discount rate	3.9		%	3.9		%
Weighted average remaining lease term	5.8 years			6.4 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 December 31, 2020:


Years Ending December 31,
2021	$	32,309
2022	30,357
2023	25,828
2024	19,480
2025	13,017
2026 and thereafter	31,318
Total undiscounted lease liability	152,309
Less: present value adjustment	(16,294)
Operating lease liability	136,015

All of these leases are for the rental of office space, with expiration terms that range from 2021 to 2030. Rental expense was approximately $31.8 million, $30.5 million and $27.6 million for 2020, 2019 and 2018, respectively.

At December 31, 2020, the Company has entered into certain financing lease agreements. The future lease payments for the Company’s financing leases are expected to be $2.1 million for 2021.

18. Commitments and Contingencies

Concentrations of Credit Risk

The creditworthiness of a counterparty is evaluated by the Company, taking into account credit ratings assigned by independent agencies. The credit approval process involves an assessment of factors, including, among others, the counterparty, country and industry credit exposure limits. Collateral may be required, at the discretion of the Company, on certain transactions based on the creditworthiness of the counterparty.

The areas where significant concentrations of credit risk may exist include unpaid losses and loss adjustment expenses recoverable, contractholder receivables, ceded unearned premiums, paid losses and loss adjustment expenses recoverable net of reinsurance balances payable, investments and cash and cash equivalent balances. A credit exposure exists with respect to reinsurance recoverables as they may become uncollectible. The Company manages its credit risk in its reinsurance relationships by transacting with reinsurers that it considers financially sound and, if necessary, the Company may hold collateral in the form of funds, trust accounts and/or irrevocable letters of credit. This collateral can be drawn on for amounts that remain unpaid beyond specified time periods on an individual reinsurer basis. In addition, certain insurance policies written by the Company’s insurance operations feature large deductibles, primarily in its construction and national accounts lines of business. Under such contracts, the Company is obligated to pay the claimant for the full amount of the claim. The Company is


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subsequently reimbursed by the policyholder for the deductible amount. These amounts are included on a gross basis in the consolidated balance sheet in contractholder payables and contractholder receivables, respectively. In the event that the Company is unable to collect from the policyholder, the Company would be liable for such defaulted amounts. Collateral, primarily in the form of letters of credit, cash and trusts, is obtained from the policyholder to mitigate the Company’s credit risk. In the instances where the company receives collateral in the form of cash, the Company records a related liability in “Collateral held for insured obligations.”

In addition, the Company underwrites a significant amount of its business through brokers and a credit risk exists should any of these brokers be unable to fulfill their contractual obligations with respect to the payments of insurance and reinsurance balances owed to the Company. The following table summarizes the percentage of the Company’s gross premiums written generated from or placed by the largest brokers:


Broker		Year Ended December 31,
	2020			2019			2018

Marsh & McLennan Companies and its subsidiaries		13.3	%		9.6	%		9.3	%
Aon Corporation and its subsidiaries		12.0	%		12.2	%		11.4	%

No other broker and no one insured or reinsured accounted for more than 10% of gross premiums written for 2020, 2019 and 2018.

The Company’s available for sale investment portfolio is managed in accordance with guidelines that have been tailored to meet specific investment strategies, including standards of diversification, which limit the allowable holdings of any single issue. There were no investments in any entity in excess of 10% of the Company’s shareholders’ equity at December 31, 2020 other than investments issued or guaranteed by the United States government or its agencies.

Investment Commitments

The Company’s investment commitments, which are primarily related to agreements entered into by the Company to invest in funds and separately managed accounts when called upon, were approximately $2.1 billion and $1.7 billion at December 31, 2020 and 2019, respectively.

Purchase Obligations

The Company has also entered into certain agreements which commit the Company to purchase goods or services, primarily related to software and computerized systems. Such purchase obligations were approximately $73.0 million and $55.6 million at December 31, 2020 and 2019, respectively.

Employment and Other Arrangements

At December 31, 2020, the Company has entered into employment agreements with certain of its executive officers. Such employment arrangements provide for compensation in the form of base salary, annual bonus, share-based awards, participation in the Company’s employee benefit programs and the reimbursements of expenses.

19. Debt and Financing Arrangements

The Company’s senior notes payable at December 31, 2020 and 2019 were as follows:


					Carrying Amount at
	Interest		Principal		December 31,
	(Fixed)		Amount		2020		2019
2034 notes (1)	7.350	%	300,000		297,367		297,254
2043 notes (2)	5.144	%	500,000		494,944		494,831
2026 notes (3)	4.011	%	500,000		497,211		496,806
2046 notes (4)	5.031	%	450,000		445,402		445,317
2050 notes (5)	3.635	%	1,000,000		988,500		—
Watford notes (6)	6.500	%	140,000		137,689		137,418
			$	2,890,000	$	2,861,113	$	1,871,626

(1) Senior notes of Arch Capital issued on May 4, 2004 and due May 1, 2034 (“2034 notes”).

(2) Senior notes of Arch-U.S., a wholly-owned subsidiary of Arch Capital, issued on December 13, 2013 and due November 1, 2043 (“2043 notes”), fully and unconditionally guaranteed by Arch Capital.

(3) Senior notes of Arch Capital Finance LLC (“Arch Finance”), a wholly-owned finance subsidiary of Arch Capital, issued on December 8, 2016 and due December 15, 2026 (“2026 notes”), fully and unconditionally guaranteed by Arch Capital.

(4) Senior notes of Arch Finance issued on December 8, 2016 and due December 15, 2046 (“2046 notes”), fully and unconditionally guaranteed by Arch Capital

(5) Senior notes of Arch Capital issued on June 30, 2020 and due June 30, 2050.

(6) Senior notes of Watford issued on July 2, 2019 and due July 2, 2029, reflecting the elimination of amounts owned by Arch-U.S.

The 2034 notes are Arch Capital’s senior unsecured obligations and rank equally with all of its existing and future senior unsecured indebtedness. Interest payments on the 2034 notes are due on May 1st and November 1st of each year. Arch Capital may redeem the 2034 notes at any time and from time to time, in whole or in part, at a “make-whole” redemption price.

The 2043 notes are unsecured and unsubordinated obligations of Arch-U.S. and Arch Capital, respectively, and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch-U.S. and Arch Capital, respectively. Interest payments on the 2043 notes are due on May 1st and November 1st of each year. Arch-U.S. may redeem the 2043 notes at any time and from time to time, in whole or in part, at a “make-whole” redemption price.


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The 2026 notes are unsecured and unsubordinated obligations of Arch Finance and Arch Capital, respectively, and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch Finance and Arch Capital, respectively. Interest payments on the 2026 notes are due on June 15th and December 15th of each year. Arch Finance may redeem the 2026 notes at any time and from time to time, in whole or in part, at a “make-whole” redemption price.

The 2046 notes are unsecured and unsubordinated obligations of Arch Finance and Arch Capital, respectively, and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch Finance and Arch Capital, respectively. Interest payments on the 2046 notes are due on June 15th and December 15th of each year. Arch Finance may redeem the 2046 notes at any time and from time to time, in whole or in part, at a “make-whole” redemption price.

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.

On July 2, 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 will be paid semi-annually in arrears on each January 2 and July 2, commencing January 2, 2020. The $172.3 million net proceeds from the offering were used to redeem a portion of Watford Preference Shares. The Company purchased $35.0 million in aggregate principal amount of the Watford Senior Notes.

Letter of Credit and Revolving Credit Facilities

In the normal course of its operations, the Company enters into agreements with financial institutions to obtain secured and unsecured credit facilities.

On December 17, 2019, Arch Capital and certain of its subsidiaries entered into a $750.0 million five-year credit facility (the “Credit Facility”) with a syndication of lenders.

The Credit Facility consists of a $250.0 million secured facility for letters of credit (the “Secured Facility”) and a $500.0 million unsecured facility for revolving loans and letters of credit (the “Unsecured Facility”). Obligations of each borrower under the Secured Facility for letters of credit are secured by cash and eligible securities of such borrower held in collateral accounts. Commitments under the Credit Facility may be increased up to, but not exceeding, an aggregate of $1.3 billion. Arch Capital has a one-time option to convert any or all outstanding revolving loans of Arch Capital and/or Arch-U.S. to term loans with the same terms as the revolving loans except that any prepayments may not be re-borrowed. Arch-U.S. guarantees the obligations of Arch Capital, and Arch Capital guarantees the obligations of Arch-U.S. Borrowings of revolving loans may be made at a variable rate based on LIBOR or an alternative base rate at the option of Arch Capital. Arch Capital and its lenders may agree on a LIBOR successor rate at the appropriate time to address the replacement of LIBOR. Secured letters of credit are available for issuance on behalf of certain Arch Capital subsidiaries. The Credit Facility is structured such that each party that requests a letter of credit or borrowing does so only for itself and its own obligations.

The Credit Facility contains certain restrictive covenants customary for facilities of this type, including restrictions on indebtedness, consolidated tangible net worth, minimum shareholders’ equity levels and minimum financial strength ratings. Arch Capital and its subsidiaries which are party to the agreement were in compliance with all covenants contained therein at December 31, 2020.

Commitments under the Credit Facility will expire on December 17, 2024, and all loans then outstanding must be repaid. Letters of credit issued under the Unsecured Facility will not have an expiration date later than December 17, 2025.

Under the $250.0 million secured letter of credit facility, Arch Capital’s subsidiaries had $218.4 million of letters of credit outstanding and remaining capacity of $31.6 million at December 31, 2020. In addition, certain of Arch Capital’s subsidiaries had outstanding secured and unsecured letters of credit of $250.0 million and $26.2 million respectively, which were issued in the normal course of business.

When issued, all secured letters of credit are secured by a portion of the investment portfolio. At December 31, 2020, these letters of credit were secured by investments with a fair value of $262.4 million.

Watford has access to a $100 million secured letter of credit facility expiring on May 16, 2021, a $50 million unsecured letter of credit facility which auto extends on September 17, 2021 and a $440 million secured credit facility expiring on November 30, 2021 that provides for borrowings and the


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issuance of letters of credit not to exceed $220 million. Borrowings of revolving loans may be made by Watford at a variable rate based on LIBOR or an alternative base rate at the option of Watford. At December 31, 2020, Watford had $126.0 million in outstanding letters of credit under the facilities and $155.7 million of borrowings outstanding under the secured credit facility, backed by Watford’s investment portfolio. Watford was in compliance with all covenants contained in these credit facilities at December 31, 2020. 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 the reinsurance transactions.

The Company’s outstanding revolving credit agreement borrowings were as follows:


		Year Ended December 31,
	2020			2019
Arch Capital		$	—		$	—
Watford		155,687			484,287
Total		$	155,687		$	484,287

20. Goodwill and Intangible Assets

The following table shows an analysis of goodwill and intangible assets:


	Goodwill		Intangible assets (indefinite life)		Intangible assets (finite life)		Total
Net balance at Dec. 31, 2018	$	249,620	$	61,874	$	323,426	$	634,920
Acquisitions	74,780		24,431		82,482		181,693
Amortization	—		—		(82,104)		(82,104)
Impairment (1)	—		(1,000)		—		(1,000)
Foreign currency movements and other adjustments	2,151		606		1,817		4,574
Net balance at Dec. 31, 2019	326,551		85,911		325,621		738,083
Acquisitions (2)	—		—		39,178		39,178
Amortization	—		—		(69,031)		(69,031)
Impairment	—		—		—		—
Foreign currency movements and other adjustments	(11,922)		(6,692)		3,247		(15,367)
Net balance at Dec. 31, 2020	$	314,629	$	79,219	$	299,015	$	692,863

Gross balance at Dec. 31, 2020	$	318,043	$	77,896	$	784,921	$	1,180,860
Accumulated amortization	—		—		(489,828)		(489,828)
Foreign currency movements and other adjustments	(3,414)		1,323		3,922		1,831
Net balance at Dec. 31, 2020	$	314,629	$	79,219	$	299,015	$	692,863

(1) The impairment to the indefinite-lived intangible assets during the year ended December 31, 2019 of $1.0 million related to insurance licenses from the acquisition of UGC.

(2) Certain amounts for the Company’s 2020 acquisitions are considered provisional.


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The following table presents the components of goodwill and intangible assets:


	Gross Balance		Accumulated Amortization		Foreign Currency Translation Adjustment and Other		Net Balance
Dec. 31, 2020
Acquired insurance contracts	$	451,505	$	(381,349)	$	284	$	70,440
Operating platform	52,674		(44,347)		60		8,387
Distribution relationships	285,141		(71,383)		3,450		217,208
Goodwill	318,043		—		(3,414)		314,629
Insurance licenses	55,981		—		—		55,981
Syndicate capacity	21,915		—		1,324		23,239
Unfavorable service contract	(9,533)		9,147		—		(386)
Other	5,134		(1,896)		127		3,365
Total	$	1,180,860	$	(489,828)	$	1,831	$	692,863

Dec. 31, 2019
Acquired insurance contracts	$	452,470	$	(336,559)	$	310	$	116,221
Operating platform	52,674		(39,571)		(259)		12,844
Distribution relationships	243,838		(50,542)		212		193,508
Goodwill	331,448		—		(4,897)		326,551
Insurance licenses	63,390		—		—		63,390
Syndicate capacity	21,915		—		605		22,520
Unfavorable service contract	(9,533)		8,657		—		(876)
Other	5,134		(1,279)		70		3,925
Total	$	1,161,336	$	(419,294)	$	(3,959)	$	738,083

The estimated remaining amortization expense for the Company’s intangible assets with finite lives is as follows:


2021	$	56,269
2022	42,211
2023	40,014
2024	34,985
2025	19,919
2026 and thereafter	105,617
Total	$	299,015

The estimated remaining useful lives of these assets range from one to sixteen years at December 31, 2020.

Other than the impairments described above, the Company’s annual impairment reviews for goodwill and intangible assets

did not result in the recognition of impairment losses for 2020 and 2019.

21. Shareholders’ Equity

Authorized and Issued

The authorized share capital of Arch Capital consists of 1.8 billion Common Shares, par value of $0.0011 per share, and 50 million Preferred Shares, par value of $0.01 per share.

Common Shares

The following table presents a roll-forward of changes in Arch Capital’s issued and outstanding Common Shares:


	Year Ended December 31,
	2020	2019	2018
Common Shares:
Shares issued and outstanding, beginning of year	574,617,195	570,737,283	549,872,226
Shares issued (1)	2,646,164	2,835,994	2,757,506
Conversion of Series D preferred shares (2)	—	—	17,022,600
Restricted shares issued, net of cancellations	1,737,482	1,043,918	1,084,951
Shares issued and outstanding, end of year	579,000,841	574,617,195	570,737,283
Common shares in treasury, end of year	(172,280,199)	(168,997,994)	(168,282,449)
Shares issued and outstanding, end of year	406,720,642	405,619,201	402,454,834

(1) Includes shares issued from the exercise of stock options and stock appreciation rights, the vesting of restricted share units and shares issued from the employee share purchase plan.

(2) Such shares represent common shares that were issued upon conversion of the non-voting common equivalent preference shares issued in connection with the AIG acquisition.

Three-For-One Common Share Split

In May 2018, shareholders approved a proposal to amend the memorandum of association by sub-dividing the authorized common shares of Arch Capital to effect a three-for-one split of Arch Capital’s common shares. The share split changed the Company’s authorized common shares to 1.8 billion common shares (600 million previously), with a par value of $.0011 per share ($.0033 previously). Information pertaining to the composition of the Company’s shareholders’ equity accounts, shares and earnings per share has been retroactively restated in the accompanying financial statements and notes to the consolidated financial statements to reflect the share split.


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Share Repurchase Program

The board of directors of Arch Capital has authorized the investment in Arch Capital’s common shares through a share repurchase program. At December 31, 2020, $916.5 million of share repurchases were available under the program. Repurchases under the program may be effected from time to time in open market or privately negotiated transactions through December 31, 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. See note 27 , “Subsequent Event s ”.

Repurchases of Arch Capital’s common shares in connection with the share repurchase plan and other share-based transactions were held in the treasury under the cost method, and the cost of the common shares acquired is included in ‘Common shares held in treasury, at cost.’ At December 31, 2020, Arch Capital held 172.3 million shares for an aggregate cost of $2.5 billion in treasury, at cost.

The Company’s repurchases under the share repurchase program were as follows:


	Year Ended December 31,
	2020		2019		2018
Aggregate cost of shares repurchased	$	83,472	$	2,871	$	282,762
Shares repurchased	2,850,102		110,598		10,559,850
Average price per share repurchased	$	29.29	$	25.96	$	26.78

Since the inception of the share repurchase program through December 31, 2020, Arch Capital has repurchased approximately 389.2 million common shares for an aggregate purchase price of $4.1 billion.

Convertible Non-Voting Common Equivalent Preferred Shares

On December 31, 2016, the Company completed the acquisition of all of the outstanding shares of capital stock of UGC. Based upon a formula set forth in the Stock Purchase Agreement, AIG received 1,276,282 of Arch Capital’s Series D convertible non-voting common equivalent preferred shares (“Series D Preferred Shares”). Each Series D Preferred Share converts to 10 shares of Arch Capital fully paid non-assessable common stock.

The Company determined, based on a review of the terms features and rights of the Series D preferred shares compared to the rights of the Company’s common shareholders, the underlying 38,288,460 common shares that the convertible securities convert to were common share equivalents at the time of their issuance*.*

In June 2017, Arch Capital completed an underwritten public secondary offering of 21,265,860 common shares by AIG following transfer of 708,862 Series D Preferred Shares. In March 2018, Arch Capital completed an underwritten public secondary offering of 17,022,600 common shares by AIG following transfer of 567,420 Series D Preferred Shares. Proceeds from the sale of common shares pursuant to the public offering were received by AIG. At December 31, 2020 and 2018, no Series D Preferred Shares were outstanding.

Series F Preferred Shares

In August 2017 and November 2017, Arch Capital completed combined $330 million of underwritten public offerings ($230 million in August 2017 and $100 million in November 2017) of 13.2 million depositary shares (the “Series F Depositary Shares”), each of which represents a 1/1,000th interest in a share of its 5.45% Non-Cumulative Preferred Shares, Series F, with a $0.01 par value and $25,000 liquidation preference per share (equivalent to $25 liquidation preference per Series F Depositary Share) (the “Series F Preferred Shares”). Each Series F Depositary Share, evidenced by a depositary receipt, entitles the holder, through the depositary, to a proportional fractional interest in all rights and preferences of the Series F Preferred Shares represented thereby (including any dividend, liquidation, redemption and voting rights).

Holders of Series F Preferred Shares will be entitled to receive dividend payments only when, as and if declared by our board of directors or a duly authorized committee of the board. Any such dividends will be payable from, and including, the date of original issue on a noncumulative basis, quarterly in arrears on the last day of March, June, September and December of each year, at an annual rate of 5.45%. Dividends on the Series F Preferred Shares are not cumulative. The Company will be restricted from paying dividends on or repurchasing its common shares unless certain dividend payments are made on the Series F Preferred Shares.

Except in specified circumstances relating to certain tax or corporate events, the Series F Preferred Shares are not redeemable prior to August 17, 2022 (the fifth anniversary of the issue date). On and after that date, the Series F Preferred Shares will be redeemable at the Company’s option, in whole or in part, at a redemption price of $25,000 per share of the Series F Preferred Shares (equivalent to $25 per depositary share), plus any declared and unpaid dividends, without accumulation of any undeclared dividends to, but excluding, the redemption date. The Series F Depositary Shares will be redeemed if and to the extent the related Series F Preferred Shares are redeemed by the Company. Neither the Series F Depositary Shares nor the Series F Preferred Shares have a stated maturity, nor will they be subject to any sinking fund or mandatory redemption. The Series F Preferred Shares are


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not convertible into any other securities. The Series F Preferred Shares will not have voting rights, except under limited circumstances. The net proceeds from the Series F Preferred Share offerings were used to redeem the Company’s outstanding 6.75% Series C Non-Cumulative Preferred Shares.

Series E Preferred Shares

On September 29, 2016, Arch Capital completed a $450 million underwritten public offering of 18.0 million depositary shares (the “Series E Depositary Shares”), each of which represents a 1/1,000th interest in a share of its 5.25% Non-Cumulative Preferred Shares, Series E, with a $0.01 par value and $25,000 liquidation preference per share (equivalent to $25 liquidation preference per Series E Depositary Share) (the “Series E Preferred Shares”). Each Series E Depositary Share, evidenced by a depositary receipt, entitles the holder, through the depositary, to a proportional fractional interest in all rights and preferences of the Series E Preferred Shares represented thereby (including any dividend, liquidation, redemption and voting rights).

Holders of Series E Preferred Shares will be entitled to receive dividend payments only when, as and if declared by our board of directors or a duly authorized committee of the board. Any such dividends will be payable from, and including, the date of original issue on a non-cumulative basis, quarterly in arrears on the last day of March, June, September and December of each year, at an annual rate of 5.25%. Dividends on the Series E Preferred Shares are not cumulative. The Company will be restricted from paying dividends on or repurchasing its common shares unless certain dividend payments are made on the Series E preferred shares.

Except in specified circumstances relating to certain tax or corporate events, the Series E Preferred Shares are not redeemable prior to September 29, 2021 (the fifth anniversary of the issue date). On and after that date, the Series E Preferred Shares will be redeemable at the Company’s option, in whole or in part, at a redemption price of $25,000 per share of the Series E Preferred Shares (equivalent to $25 per Series E Depositary Share), plus any declared and unpaid dividends, without accumulation of any undeclared dividends to, but excluding, the redemption date. The Series E Depositary Shares will be redeemed if and to the extent the related Series E Preferred Shares are redeemed by the Company. Neither the Series E Depositary Shares nor the Series E Preferred Shares have a stated maturity, nor will they be subject to any sinking fund or mandatory redemption. The Series E Preferred Shares are not convertible into any other securities. The Series E Preferred Shares will not have voting rights, except under limited circumstances.

Series C Preferred Shares

On January 2, 2018, Arch Capital redeemed all outstanding 6.75% Series C non-cumulative preferred shares. The preferred shares were redeemed at a redemption price equal to $25 per share, plus all declared and unpaid dividends to (but excluding) the redemption date. In accordance with GAAP, following the redemption, original issuance costs related to such shares have been removed from additional paid-in capital and recorded as a “loss on redemption of preferred shares.” Such adjustment had no impact on total shareholders’ equity or cash flows.

22. Share-Based Compensation

Long Term Incentive and Share Award Plans

The Company utilizes share-based compensation plans for officers, other employees and directors of Arch Capital and its subsidiaries to provide competitive compensation opportunities, to encourage long-term service, to recognize individual contributions and reward achievement of performance goals and to promote the creation of long-term value for shareholders by aligning the interests of such persons with those of shareholders.

The 2018 Long-Term Incentive and Share Award Plan (the “2018 Plan”) became effective as of May 9, 2018 following approval by shareholders of the Company. The 2018 Plan provides for the issuance of restricted stock units, performance units, restricted shares, performance shares, stock options and stock appreciation rights and other equity-based awards to our employees and directors. The 2018 Plan authorizes the issuance of 34,500,000 common shares and will terminate as to future awards on February 28, 2028. At December 31, 2020, 17,284,108 shares are available for future issuance.

The 2015 Long Term Incentive and Share Award Plan (the (“2015 Plan”) authorizes the issuance of 12,900,000 common shares and became effective as of May 7, 2015 following approval by shareholders of the Company. The 2015 Plan provides for the issuance of share-based awards to our employees and directors and will terminate as to future awards on February 26, 2025. At December 31, 2020, 555,759 shares are available for future issuance.

The 2012 Long Term Incentive and Share Award Plan (the “2012 Plan”) became effective as of May 9, 2012 following approval by shareholders of the Company. The 2012 Plan authorizes the issuance of 22,301,772 common shares and will terminate as to future awards on February 28, 2022. At December 31, 2020, 502,994 shares are available for grant under the 2012 Plan.

Upon shareholder approval on May 6, 2016, the Amended and Restated Arch Capital Group Ltd. 2007 Employee Share


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Purchase Plan (the “ESPP”) became effective and a total of 4,689,777 common shares were reserved for issuance. The purpose of the ESPP is to give employees of Arch Capital and its subsidiaries an opportunity to purchase common shares through payroll deductions, thereby encouraging employees to share in the economic growth and success of Arch Capital and its subsidiaries. The ESPP is designed to qualify as an “employee share purchase plan” under Section 423 of the Code. At December 31, 2020, 2,267,676 shares remain available for issuance.

Stock Options and Stock Appreciation Rights

The Company generally issues stock options and SARs to eligible employees, with exercise prices equal to the fair market values of the Company’s Common Shares on the grant dates. Such grants generally vest over a three year period with one-third vesting on the first, second and third anniversaries of the grant date.

The grant date fair value is determined using the Black-Scholes option valuation model. The expected life assumption is based on an expected term analysis, which incorporates the Company’s historical exercise experience. Expected volatility is based on the Company’s daily historical trading data of its common shares. The table below summarizes the assumptions used.


	Year Ended December 31,
	2020		2019		2018
Dividend yield	—	%	—	%	—	%
Expected volatility	16.6 %		18.1	%	21.3	%
Risk free interest rate	1.2 %		2.5	%	2.8	%
Expected option life	6.0 years		6.0 years		6.0 years

A summary of stock option and SAR activity under the Company’s Long Term Incentive and Share Award Plans during 2020 is presented below:


	Year Ended December 31, 2020
	Number of Options / SARs	Weighted Average Exercise Price		Weighted Average Contractual Term	Aggregate Intrinsic Value
Outstanding, beginning of year	18,853,018	$	20.94
Granted	1,121,833	$	42.34
Exercised	(1,981,216)	$	10.92
Forfeited or expired	(154,302)	$	30.13
Outstanding, end of year	17,839,333	$	23.32	4.74	$	234,659
Exercisable, end of year	15,132,810	$	21.30	4.10	$	223,908

The aggregate intrinsic value of stock options and SARs exercised represents the difference between the exercise price of the stock options and SARs and the closing market price of the Company’s common shares on the exercise dates. During 2020, the Company received proceeds of $5.0 million from the exercise of stock options and recognized a tax benefit of $3.0 million from the exercise of stock options and SARs.


	Year Ended December 31,
	2020		2019		2018
Weighted average grant date fair value	$	8.14	$	7.90	$	7.50
Aggregate intrinsic value of Options/SARs exercised	$	59,723	$	51,350	$	43,468

Restricted Common Shares and Restricted Units

The Company also issues restricted share and unit awards to eligible employees and directors, for which the fair value is equal to the fair market values of the Company’s Common Shares on the grant dates. Restricted share and unit awards generally vest over a three year period with one-third vesting on the first, second and third anniversaries of the grant date.

A summary of restricted share and restricted unit activity under the Company’s Long Term Incentive and Share Award Plans for 2020 is presented below:


	Restricted Common Shares		Restricted Unit Awards
Unvested Shares:
Unvested balance, beginning of year	1,045,921		1,563,012
Granted	1,328,033		207,297
Vested	(697,090)		(620,905)
Forfeited	(41,019)		(27,685)
Unvested balance, end of year	1,635,845		1,121,719

Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year	$	31.02	$	30.07
Granted	$	37.58	$	37.32
Vested	$	30.86	$	29.99
Forfeited	$	33.91	$	30.76
Unvested balance, end of year	$	36.34	$	31.43


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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

The following table presents the weighted average grant date fair value of restricted shares and restricted unit awards granted and the aggregate fair value of restricted shares and unit awards vesting in each year.


	Year Ended December 31,
	2020		2019		2018
Restricted shares and restricted unit awards granted	1,535,330		1,195,741		1,563,287
Weighted average grant date fair value	$	37.55	$	32.89	$	26.86
Aggregate fair value of vested restricted share and unit awards	$	39,703	$	46,262	$	39,898

The aggregate intrinsic value of restricted units outstanding at December 31, 2020 was $40.5 million.

Performance Awards

The Company also issues performance share and unit awards (“performance awards”) to eligible employees, which are earned based on the achievement of pre-established threshold, target and maximum goals over three-year performance periods. Final payouts depend on the level of achievement along with each employees continued service through the vest date. The grant date fair value of the performance awards is measured using a Monte Carlo simulation model, which incorporated the assumptions summarized in the table below. Expected volatility is based on the Company’s daily historical trading data of its common shares. The cumulative compensation expense recognized and unrecognized as of any reporting period date represents the adjusted estimate of performance shares and units that will ultimately be awarded, valued at their original grant date fair values.


	Year Ended December 31,
	2020	2019	2018
Expected volatility	18.1 %	17.1 %	16.2 %
Risk free interest rate	1.1 %	2.5 %	2.6 %


	Performance Shares		Performance Units
Unvested Shares:
Unvested balance, beginning of year	1,400,914		23,767
Granted	548,906		8,298
Vested	—		—
Forfeited	(98,438)		—
Unvested balance, end of year	1,851,382		32,065

Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year	$	30.29	$	29.75
Granted	$	44.17	$	44.17
Vested	$	—	$	—
Forfeited	$	30.01	$	—
Unvested balance, end of year	$	34.42	$	33.48

The following table presents the weighted average grant date fair values of performance awards granted.


	Year Ended December 31,
	2020		2019		2018
Performance awards	557,204		696,360		743,513
Weighted average grant date fair value	$	44.17	$	36.05	$	24.77

The issuance of share-based awards and amortization thereon has no effect on the Company’s consolidated shareholders’ equity.

Share-Based Compensation Expense

The following tables present pre-tax and after-tax share-based compensation expense recognized as well as the unrecognized compensation cost associated with unvested awards and the weighted average period over which it is expected to be recognized.


	Year Ended December 31,
	2020		2019		2018
Pre-Tax
Stock options and SARs	$	11,744	$	12,866	$	16,272
Restricted share and unit awards	41,284		38,988		34,025
Performance awards	14,729		8,949		4,414
ESPP	2,135		3,045		1,224
Total	$	69,892	$	63,848	$	55,935

After-Tax
Stock options and SARs	$	10,388	$	11,450	$	14,894
Restricted share and unit awards	34,599		32,999		29,044
Performance awards	13,380		8,295		4,127
ESPP	1,978		2,758		1,114
Total	$	60,345	$	55,502	$	49,179


	December 31, 2020
	Stock Options and SARs		Restricted Common Shares and Units		Performance Common Shares and Units
Unrecognized compensation cost related to unvested awards	$	9,333	$	52,726	$	9,450
Weighted average recognition period (years)	1.02		1.48		0.66

23. Retirement Plans

For purposes of providing employees with retirement benefits, the Company maintains defined contribution retirement plans. Contributions are based on the participants’ eligible compensation. For 2020, 2019 and 2018, the Company expensed $52.0 million, $44.8 million and $40.8 million, respectively, related to these retirement plans.


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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

24. Legal Proceedings

The Company, in common with the insurance industry in general, is subject to litigation and arbitration in the normal course of its business. As of December 31, 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.

25. Statutory Information

The Company’s insurance and reinsurance subsidiaries are subject to insurance and/or reinsurance laws and regulations in the jurisdictions in which they operate. These regulations include certain restrictions on the amount of dividends or other distributions available to shareholders without prior approval of the insurance regulatory authorities.

The actual and required statutory capital and surplus for the Company’s principal operating subsidiaries at December 31, 2020 and 2019:


	December 31,
	2020		2019
Actual capital and surplus (1):
Bermuda	$	16,193,415	$	13,511,729
Ireland	883,337		721,439
United States	4,904,840		4,440,848
United Kingdom	967,440		748,276
Canada	64,286		61,351

Required capital and surplus:
Bermuda	$	6,431,413	$	5,492,968
Ireland	701,161		542,703
United States	1,644,324		1,697,640
United Kingdom	601,662		349,328
Canada	37,441		32,763

(1)Such amounts include ownership interests in affiliated insurance and reinsurance subsidiaries.

There were no state-prescribed or permitted regulatory accounting practices for any of the Company’s insurance or reinsurance entities that resulted in reported statutory surplus that differed from that which would have been reported under the prescribed practices of the respective regulatory authorities, including the National Association of Insurance Commissioners. The differences between statutory financial statements and statements prepared in accordance with GAAP vary by jurisdiction, however, with the primary differences being that statutory financial statements may not reflect deferred acquisition costs, certain net deferred tax assets, goodwill and intangible assets, unrealized appreciation or depreciation on debt securities and certain unauthorized reinsurance recoverables and include contingency reserves.

The statutory net income (loss) for the Company’s principal operating subsidiaries for 2020, 2019 and 2018 was as follows:


	Year Ended December 31,
	2020		2019		2018
Statutory net income (loss):
Bermuda	$	1,665,261	$	1,876,416	$	919,554
Ireland	18,397		26,367		29,223
United States	143,271		481,188		292,831
United Kingdom	4,078		(17,423)		(18,467)
Canada	(1,049)		(1,023)		2,525

Bermuda

The Company has two Bermuda based subsidiaries: Arch Re Bermuda, a Class 4 general business insurer and Class C long-term insurer, and Watford, a Class 4 general business insurer. Under the Bermuda Insurance Act 1978 (the “Insurance Act”), these subsidiaries are required to maintain minimum statutory capital and surplus equal to the greater of a minimum solvency margin and the enhanced capital requirement as determined by the Bermuda Monetary Authority (“BMA”). The enhanced capital requirement is calculated based on the Bermuda Solvency Capital Requirement model, a risk-based model that takes into account the risk characteristics of different aspects of the company’s business. At December 31, 2020 and 2019, all such requirements were met.

The ability of these subsidiaries to pay dividends is limited under Bermuda law and regulations. Under the Insurance Act, Arch Re Bermuda is restricted with respect to the payment of dividends. Arch Re Bermuda is prohibited from declaring or paying in any financial year dividends of more than 25% of its total statutory capital and surplus (as shown on its previous financial year’s statutory balance sheet) unless it files, at least seven days before payment of such dividends, with the BMA an affidavit stating that it will continue to meet the required margins following the declaration of those dividends. Accordingly, Arch Re Bermuda can pay approximately $3.8 billion to Arch Capital during 2021 without providing an affidavit to the BMA.

Ireland

The Company has three Irish subsidiaries: Arch Re Europe, an authorized life and non-life reinsurer, Arch Insurance (EU), an authorized non-life insurer and Arch Underwriting Europe, a registered insurance and reinsurance intermediary. Irish authorized reinsurers and insurers, such as Arch Re Europe, Arch Insurance (EU) and Irish intermediaries, such as Arch Underwriters Europe, are also subject to the general body of Irish laws and regulations including the provisions of the Companies Act 2014. As part of the Company’s Brexit

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

plan, Arch Insurance (EU) received approval from the Central Bank of Ireland (“CBOI”) to expand the nature of its business in 2019 commenced writing insurance lines in the European Economic Area in 2020, and the Part VII Transfer was completed at the end of December 2020. Arch Re Europe, Arch Insurance (EU) and Arch Underwriters Europe are subject to the supervision of the CBOI and must comply with Irish insurance acts and regulations as well as with directions and guidance issued by the CBOI. Arch Re Europe and Arch Insurance (EU) are required to maintain a minimum level of capital. At December 31, 2020 and 2019, these requirements were met.

The amount of dividends these subsidiaries are permitted to declare is limited to accumulated, realized profits, so far as not previously utilized by distribution or capitalization, less its accumulated, realized losses, so far as not previously written off in a reduction or reorganization of capital duly made. The solvency and capital requirements must still be met following any distribution. Dividends or distributions, if any, made by Arch Re Europe would result in an increase in available capital at Arch Re Bermuda.

United States

The Company’s U.S. insurance and reinsurance subsidiaries are subject to insurance laws and regulations in the jurisdictions in which they operate. The ability of the Company’s regulated insurance subsidiaries to pay dividends or make distributions is dependent on their ability to meet applicable regulatory standards. These regulations include restrictions that limit the amount of dividends or other distributions, such as loans or cash advances, available to shareholders without prior approval of the insurance regulatory authorities.

Dividends or distributions, if any, made by Arch Re U.S. would result in an increase in available capital at Arch-U.S., the Company’s U.S. holding company. Arch Re U.S. can declare a maximum of approximately $147.6 million of dividends during 2021 subject to the approval of the Commissioner of the Delaware Department of Insurance.

AMIC and UGRIC have each been approved as an eligible mortgage insurer by Fannie Mae and Freddie Mac, subject to maintaining certain ongoing requirements (“eligible mortgage insurers”). In April 2015, the GSEs published comprehensive, revised requirements, known as the Private Mortgage Insurer Eligibility Requirements or “PMIERs.” As clarified and revised by the Guidance Letters issued by the GSEs in December 2016 and March 2017, the PMIERs apply to the Company’s eligible mortgage insurers, but do not apply to Arch Mortgage Guaranty Company, which is not GSE-approved.

The amount of assets required to satisfy the revised financial requirements of the PMIERs at any point in time will be affected by many factors, including macro-economic conditions, the size and composition of our eligible mortgage insurers’ mortgage insurance portfolio at the point in time, and the amount of risk ceded to reinsurers that may be deducted in our calculation of “minimum required assets.”

The Company’s U.S. mortgage insurance subsidiaries are subject to detailed regulation by their domiciliary and primary regulators, the Wisconsin Office of the Commissioner of Insurance (“Wisconsin OCI”) for Arch Mortgage Insurance Company and Arch Mortgage Guaranty Company, the North Carolina Department of Insurance (“NC DOI”) for United Guaranty Residential Insurance Company, and by state insurance departments in each state in which they are licensed. As mandated by state insurance laws, mortgage insurers are generally mono-line companies restricted to writing a single type of insurance business, such as mortgage insurance business. Each company is subject to either Wisconsin or North Carolina statutory requirements as to payment of dividends. Generally, both Wisconsin and North Carolina law precludes any dividend before giving at least 30 days’ notice to the Wisconsin OCI or NC DOI, as applicable, and prohibits paying any dividend unless it is fair and reasonable to do so. In addition, the state regulators and the GSEs limit or restrict our eligible mortgage insurers’ ability to pay stockholder dividends or otherwise return capital to shareholders. Under respective states law, our U.S. mortgage subsidiaries can declare a maximum of approximately $143.1 million of ordinary dividends in 2021, however, dividend capacity is limited by the respective companies unassigned surplus amounts. In certain instances, approval by the GSEs would be required for dividends or other forms of return of capital to shareholders due to the requirements under PMIERs, including the minimum required assets imposed on our eligible mortgage insurers by the GSEs. Such dividend would result in an increase in available capital at Arch U.S. MI Holdings Inc., a subsidiary of Arch-U.S. The ability of the Company’s U.S. mortgage insurance subsidiaries to pay dividends is subject to prior notifications and approval through June 30, 2021, pursuant the GSEs’ PMIERs guidance related to COVID-19.

Mortgage insurance companies licensed in Wisconsin or North Carolina are required to establish contingency loss reserves for purposes of statutory accounting in an amount equal to at least 50% of net earned premiums. These amounts generally cannot be withdrawn for a period of 10 years and are separate liabilities for statutory accounting purposes, which affects the ability to pay dividends. However, with prior regulatory approval, a mortgage insurance company may make early withdrawals from the contingency reserve when incurred losses exceed 35% of net premiums earned in a calendar year.


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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

Under Wisconsin and North Carolina law, as well as that of 14 other states, a mortgage insurer must maintain a minimum amount of statutory capital relative to its risk in force in order for the mortgage insurer to continue to write new business. While formulations of minimum capital vary in certain jurisdictions, the most common measure applied allows for a maximum risk-to-capital ratio of 25 to 1. Wisconsin and North Carolina both require a mortgage insurer to maintain a “minimum policyholder position” calculated in accordance with their respective regulations. Policyholders' position consists primarily of statutory policyholders' surplus plus the statutory contingency reserve, less ceded reinsurance. While the statutory contingency reserve is reported as a liability on the statutory balance sheet, for risk-to-capital ratio calculations, it is included as capital for purposes of statutory capital.

United Kingdom

The Prudential Regulation Authority (“PRA”) and the Financial Conduct Authority (“FCA”) regulate insurance and reinsurance companies and the FCA regulates firms carrying on insurance mediation activities operating in the U.K., both under the Financial Services and Markets Act 2000. The Company’s U.K. insurance operations are conducted through Arch Insurance (U.K.), Lloyds syndicates: Arch Syndicate 2012 and Arch Syndicate 1955. Arch Managing Agency Limited (“AMAL”) is the managing agent of Arch Syndicate 2012 and Arch Syndicate 1955. Arch Syndicate 2012 and Arch Syndicate 1955 provide access to Lloyd’s extensive distribution network and worldwide licenses. AMAL also acts as managing agent for third party members of Arch Syndicate 1955. All U.K. companies are also subject to a range of statutory provisions, including the laws and regulations of the Companies Acts 2006 (as amended) (the “U.K. Companies Acts”).

Arch Insurance (U.K.) and AMAL must maintain a margin of solvency at all times under the Solvency II Directive from the European Insurance and Occupational Pensions Authority. The regulations stipulate that insurers are required to maintain the minimum capital requirement and solvency capital requirement at all times. At December 31, 2020 and 2019, our subsidiaries were in compliance with these requirements.

As corporate members of Lloyd’s, AMAL (as managing agent of Arch Syndicate 2012 and Arch Syndicate 1955) and each syndicate’s respective corporate members are subject to the oversight of the Council of Lloyd’s. The capital required to support a Syndicate’s underwriting capacity, or funds at Lloyd’s, is assessed annually and is determined by Lloyd’s in accordance with the capital adequacy rules established by the PRA. The Company has provided capital to support the underwriting of Arch Syndicate 2012 and Arch Syndicate

1955 in the form of pledged assets provided by Arch Re Bermuda. The amount which the Company provides as funds at Lloyd’s is not available for distribution to the Company for the payment of dividends. Lloyd’s is supervised by the PRA and required to implement certain rules prescribed by the PRA under the Lloyd’s Act of 1982 regarding the operation of the Lloyd’s market. With respect to managing agents and corporate members, Lloyd’s prescribes certain minimum standards relating to management and control, solvency and other requirements and monitors managing agents’ compliance with such standards.

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

Canada

Arch Insurance Canada and the Canadian branch of Arch Re U.S. (“Arch Re Canada”) are subject to federal, as well as provincial and territorial, regulation in Canada. The Office of the Superintendent of Financial Institutions (“OSFI”) is the federal regulatory body that, under the Insurance Companies Act (Canada), regulates federal Canadian and non-Canadian insurance companies operating in Canada. Arch Insurance Canada and Arch Re Canada are subject to regulation in the provinces and territories in which they underwrite insurance/reinsurance, and the primary goal of insurance/reinsurance regulation at the provincial and territorial levels is to govern the market conduct of insurance/reinsurance companies. Arch Insurance Canada is licensed to carry on insurance business by OSFI and in each province and territory. Arch Re Canada is licensed to carry-on reinsurance business by OSFI and in the provinces of Ontario and Quebec.

Under the Insurance Companies Act (Canada), Arch Insurance Canada is required to maintain an adequate amount of capital in Canada, calculated in accordance with a test promulgated by OSFI called the Minimum Capital Test (“MCT”), and Arch Re Canada is required to maintain an adequate margin of assets over liabilities in Canada, calculated in accordance with a test promulgated by OSFI called the Branch Adequacy of Assets Test. Dividends or distributions, if any, made by Arch Insurance Canada would result in an increase in available capital at Arch Insurance Company (see “—United States” section).


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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

26. Unaudited Condensed Quarterly Financial Information

The following table summarizes the 2020 and 2019 unaudited condensed quarterly financial information:


	Fourth Quarter		Third Quarter		Second Quarter		First Quarter
Year Ended December 31, 2020
Net premiums written	$	1,758,015	$	1,874,144	$	1,668,311	$	2,137,246
Net premiums earned	1,811,045		1,771,092		1,665,354		1,744,444
Net investment income	114,458		128,512		131,485		145,153
Net realized gains (losses)	353,333		280,499		556,588		(366,960)

Underwriting income (loss)	220,987		96,604		(22,539)		154,050
Net income (loss) attributable to Arch	543,544		419,039		298,821		144,117
Preferred dividends	(10,403)		(10,403)		(10,403)		(10,403)
Net income (loss) available to Arch common shareholders	533,141		408,636		288,418		133,714
Net income (loss) per common share -- basic	$	1.32	$	1.01	$	0.72	$	0.33
Net income (loss) per common share -- diluted	$	1.30	$	1.00	$	0.71	$	0.32

Year Ended December 31, 2019
Net premiums written	$	1,455,453	$	1,613,457	$	1,444,898	$	1,525,259
Net premiums earned	1,515,882		1,438,023		1,463,727		1,368,866
Net investment income	154,263		161,488		155,038		156,949
Net realized gains (losses)	40,830		61,355		120,757		140,256

Underwriting income (loss)	251,421		231,262		293,134		260,148
Net income (loss) attributable to Arch	326,384		392,453		468,954		448,528
Preferred dividends	(10,403)		(10,403)		(10,403)		(10,403)
Net income (loss) available to Arch common shareholders	315,981		382,050		458,551		438,125
Net income (loss) per common share -- basic	$	0.78	$	0.95	$	1.14	$	1.09
Net income (loss) per common share -- diluted	$	0.76	$	0.92	$	1.12	$	1.07

27. Subsequent Events

Coface

On February 10, 2021, the Company announced that it had completed the share purchase agreement with Natixis to purchase a 29.5% stake in Coface, a France-based leader in the global trade credit insurance market. The consideration paid was €9.95 per share, or an aggregate €453 million including related fees. In connection with our minority stake in Coface, the Company has four representatives on the Coface Board of Directors.

Share Repurchases

From January 1 to February 24, 2021, the Company repurchased approximately 4.6 million common shares for an aggregate purchase price of $154.9 million. At February 24, 2021 approximately $761.6 million of repurchases were available under the share repurchase program.

Reinsurance to Close

As part of the Company’s acquisition of Barbican, on February 18, 2021, the Company entered into an agreement with Premia Managing Agency Limited for the Reinsurance to Close (“RITC”) of Syndicate 1955’s 2018 underwriting year of account into Premia Syndicate 1884’s 2021 underwriting year of account. The RITC covers legacy business underwritten by Syndicate 1955 on the underwriting 2018 and prior years of account and under the agreement, approximately $380 million of net liabilities transferred to Syndicate 1884, with an effective date of January 1, 2021.

Texas Winter Storm

In February 2021, a winter storm struck Texas and other parts of the southern U.S., resulting in significant insured losses. It is too early to reasonably estimate losses for this recent event given the significant unknowns, the early stage of the damage assessment process and the unusual nature of the event.


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Table of C ontents

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