Item 8. FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA

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Item 8. FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA

Index to Financial StatementsPage No.
Report of Independent Registered Public Accounting Firm (PCAOB ID 238)95
Consolidated Balance Sheets
At December 31, 2022 and December 31, 202197
Consolidated Statements of Income
For the years ended December 31, 2022, 2021 and 202098
Consolidated Statements of Comprehensive Income
For the years ended December 31, 2022, 2021 and 202099
Consolidated Statements of Changes in Shareholders’ Equity
For the years ended December 31, 2022, 2021 and 2020100
Consolidated Statements of Cash Flows
For the years ended December 31, 2022, 2021 and 2020101
Notes to Consolidated Financial Statements
Note 1 - General102
Note 2 - Acquisitions102
Note 3 - Significant Accounting Policies102
Note 4 - Segment Information111
Note 5 - Reserve for Losses and Loss Adjustment Expenses118
Note 6 - Short Duration Contracts120
Note 7 - Allowance for Expected Credit Losses133
Note 8 - Reinsurance134
Note 9 - Investment Information136
Note 10 - Fair Value142
Note 11 - Derivative Instruments148
Note 12 - VIE and Noncontrolling Interests149
Note 13 - Other Comprehensive Income (Loss)151
Note 14 - Earnings Per Common Share153
Note 15 - Income Taxes153
Note 16 - Transactions with Related Parties156
Note 17 - Leases157
Note 18 - Commitments and Contingencies157
Note 19 - Debt and Financing Arrangements158
Note 20 - Goodwill and Intangible Assets160
Note 21 - Shareholders’ Equity161
Note 22 - Share-Based Compensation162
Note 23 - Retirement Plans165
Note 24 - Legal Proceedings165
Note 25 - Statutory Information165
ARCH CAPITAL942022 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, 2022 and 2021, 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, 2022, 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, 2022, 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, 2022 and 2021**,** and the results of its operations and its cash flows for each of the three years in the period ended December 31, 2022, 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, 2022, 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 CAPITAL952022 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, 2022, the Company’s total reserve for losses and loss adjustment expenses was $20.0 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 24, 2023

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

ARCH CAPITAL962022 FORM 10-K
ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES CONSOLIDATED BALANCE SHEETS (U.S. dollars in thousands, except share data)
December 31,
20222021
Assets
Investments:
Fixed maturities available for sale, at fair value (amortized cost: $21,281,863 and $17,973,823; net of allowance for credit losses: $41,355 and $2,883)$19,682,789$17,998,109
Short-term investments available for sale, at fair value (amortized cost: $1,332,996 and $1,734,738; net of allowance for credit losses: $0 and $0 )1,331,6621,734,716
Equity securities, at fair value859,9691,804,170
Other investments (portion measured at fair value: $1,644,197 and $1,973,550)1,644,1971,973,550
Investments accounted for using the equity method3,774,3103,077,611
Total investments27,292,92726,588,156
Cash855,118858,668
Accrued investment income158,68085,453
Investment in operating affiliates964,6041,135,655
Premiums receivable (net of allowance for credit losses: $35,402 and $39,958)3,624,7772,633,280
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $21,544 and $13,230)6,563,6545,880,735
Contractholder receivables (net of allowance for credit losses: $2,691 and $3,437)1,731,2931,828,691
Ceded unearned premiums1,799,1971,729,455
Deferred acquisition costs1,263,870901,841
Receivable for securities sold12,49360,179
Goodwill and intangible assets804,289944,983
Other assets2,919,6052,453,849
Total assets$47,990,507$45,100,945
Liabilities
Reserve for losses and loss adjustment expenses$20,031,943$17,757,156
Unearned premiums7,337,0026,011,942
Reinsurance balances payable1,529,9191,583,253
Contractholder payables1,733,9841,832,127
Collateral held for insured obligations249,238242,352
Senior notes2,725,4102,724,394
Payable for securities purchased95,04164,850
Other liabilities1,367,0681,329,742
Total liabilities35,069,60531,545,816
Commitments and Contingencies
Redeemable noncontrolling interests10,8299,233
Shareholders’ Equity
Non-cumulative preferred shares830,000830,000
Common shares ($0.0011 par, shares issued: 588,250,762 and 583,289,850)654648
Additional paid-in capital2,211,4442,085,075
Retained earnings15,892,06514,455,868
Accumulated other comprehensive income (loss), net of deferred income tax(1,646,170)(64,600)
Common shares held in treasury, at cost (shares: 217,904,765 and 204,365,956)(4,377,920)(3,761,095)
Total shareholders' equity available to Arch12,910,07313,545,896
Non-redeemable noncontrolling interests——
Total shareholders' equity12,910,07313,545,896
Total liabilities, noncontrolling interests and shareholders' equity$47,990,507$45,100,945

See Notes to Consolidated Financial Statements

ARCH CAPITAL972022 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,
202220212020
Revenues
Net premiums earned$9,678,077$8,082,298$6,991,935
Net investment income496,547389,118519,608
Net realized gains (losses)(662,734)379,845823,460
Other underwriting income13,22722,07326,784
Equity in net income of investments accounted for using the equity method115,856366,402146,693
Other income (loss)(26,165)10,24429
Total revenues9,614,8089,249,9808,508,509
Expenses
Losses and loss adjustment expenses5,027,5174,584,8034,689,599
Acquisition expenses1,739,5801,303,1781,004,842
Other operating expenses1,128,175998,595875,176
Corporate expenses95,48279,15781,988
Amortization of intangible assets106,20082,95569,031
Interest expense130,266139,470143,456
Net foreign exchange losses (gains)(100,905)(41,529)83,634
Total expenses8,126,3157,146,6296,947,726
Income before income taxes and income (loss) from operating affiliates1,488,4932,103,3511,560,783
Income taxes:
Current tax expense (benefit)201,216295,533197,662
Deferred tax expense (benefit)(121,255)(166,951)(85,824)
Income tax expense79,961128,582111,838
Income (loss) from operating affiliates73,891264,69316,766
Net income$1,482,423$2,239,462$1,465,711
Net (income) loss attributable to noncontrolling interests(5,490)(82,613)(60,190)
Net income available to Arch1,476,9332,156,8491,405,521
Preferred dividends(40,736)(48,343)(41,612)
Loss on redemption of preferred shares—(15,101)—
Net income available to Arch common shareholders$1,436,197$2,093,405$1,363,909
Net income per common share and common share equivalent
Basic$3.90$5.34$3.38
Diluted$3.80$5.23$3.32
Weighted average common shares and common share equivalents outstanding
Basic368,612,197391,748,715403,062,179
Diluted377,609,767400,345,936410,259,455

See Notes to Consolidated Financial Statements

ARCH CAPITAL982022 FORM 10-K
ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME (U.S. dollars in thousands)
Year Ended December 31,
202220212020
Comprehensive Income
Net income$1,482,423$2,239,462$1,465,711
Other comprehensive income (loss), net of deferred income tax
Unrealized appreciation (decline) in value of available-for-sale investments:
Unrealized holding gains (losses) arising during year(1,772,649)(386,929)678,717
Reclassification of net realized (gains) losses, included in net income247,799(116,068)(426,187)
Foreign currency translation adjustments(56,720)(64,482)33,336
Comprehensive income (loss)(99,147)1,671,9831,751,577
Net (income) loss attributable to noncontrolling interests(5,490)(82,613)(60,190)
Other comprehensive (income) loss attributable to noncontrolling interests—13,984(9,062)
Comprehensive income available to Arch (loss)$(104,637)$1,603,354$1,682,325

See Notes to Consolidated Financial Statements

ARCH CAPITAL992022 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,
202220212020
Non-cumulative preferred shares
Balance at beginning of year$830,000$780,000$780,000
Preferred shares issued—500,000—
Preferred shares redeemed—(450,000)—
Balance at end of year830,000830,000780,000
Common shares
Balance at beginning of year648643638
Common shares issued, net655
Balance at end of year654648643
Additional paid-in capital
Balance at beginning of year2,085,0751,977,7941,889,683
Issue costs on preferred shares issued—(14,179)—
Reversal of issue costs on preferred shares redeemed—15,101—
Amortization of share-based compensation87,62086,05370,535
Other changes38,74920,30617,576
Balance at end of year2,211,4442,085,0751,977,794
Retained earnings
Balance at beginning of year14,455,86812,362,46311,021,006
Cumulative effect of an accounting change——(22,452)
Balance at beginning of year, as adjusted14,455,86812,362,46310,998,554
Net income1,482,4232,239,4621,465,711
Net (income) loss attributable to noncontrolling interests(5,490)(82,613)(60,190)
Preferred share dividends(40,736)(48,343)(41,612)
Loss on redemption of preferred shares—(15,101)—
Balance at end of year15,892,06514,455,86812,362,463
Accumulated other comprehensive income (loss)
Balance at beginning of year(64,600)488,895212,091
Unrealized appreciation (decline) in value of available-for-sale investments, net of deferred income tax:
Balance at beginning of year13,486501,295258,486
Unrealized holding gains (losses) during period, net of reclassification adjustment(1,524,850)(502,997)252,530
Unrealized holding gains (losses) during period attributable to noncontrolling interests—15,188(9,721)
Balance at end of year(1,511,364)13,486501,295
Foreign currency translation adjustments, net of deferred income tax:
Balance at beginning of year(78,086)(12,400)(46,395)
Foreign currency translation adjustments(56,720)(64,482)33,336
Foreign currency translation adjustments attributable to noncontrolling interests—(1,204)659
Balance at end of year(134,806)(78,086)(12,400)
Balance at end of year(1,646,170)(64,600)488,895
Common shares held in treasury, at cost
Balance at beginning of year(3,761,095)(2,503,909)(2,406,047)
Shares repurchased for treasury(616,825)(1,257,186)(97,862)
Balance at end of year(4,377,920)(3,761,095)(2,503,909)
Total shareholders’ equity available to Arch12,910,07313,545,89613,105,886
Non-redeemable noncontrolling interests——823,007
Total shareholders’ equity$12,910,073$13,545,896$13,928,893

See Notes to Consolidated Financial Statements

ARCH CAPITAL1002022 FORM 10-K
ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES CONSOLIDATED STATEMENTS OF CASH FLOWS (U.S. dollars in thousands)
Year Ended December 31,
202220212020
Operating Activities
Net income$1,482,423$2,239,462$1,465,711
Adjustments to reconcile net income to net cash provided by operating activities:
Net realized (gains) losses651,568(427,367)(844,625)
Equity in net (income) or loss of investments accounted for using the equity method and other income or loss153,157(464,050)(47,951)
Amortization of intangible assets106,20082,95569,031
Share-based compensation87,62887,09471,262
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable1,889,0151,762,1902,113,827
Unearned premiums, net of ceded unearned premiums1,399,112936,039445,781
Premiums receivable(1,109,229)(685,214)(318,643)
Deferred acquisition costs(374,067)(263,243)(143,948)
Reinsurance balances payable(35,509)500,06565,950
Other items, net(435,071)(340,376)10,110
Net cash provided by operating activities3,815,2273,427,5552,886,505
Investing Activities
Purchases of fixed maturity investments(16,390,475)(35,451,858)(39,765,277)
Purchases of equity securities(796,998)(1,175,480)(1,595,010)
Purchases of other investments(1,720,457)(1,859,096)(1,808,727)
Proceeds from sales of fixed maturity investments11,844,00433,577,44537,949,346
Proceeds from sales of equity securities1,554,116918,1451,147,264
Proceeds from sales, redemptions and maturities of other investments1,221,0721,765,5331,029,578
Proceeds from redemptions and maturities of fixed maturity investments714,5191,628,755871,134
Net settlements of derivative instruments(68,818)(40,072)179,006
Net (purchases) sales of short-term investments467,249165,272(1,029,681)
Change in cash collateral related to securities lending——81,210
Purchase of operating affiliate—(753,916)—
Impact of the deconsolidation of the variable interest entity—(349,202)—
Purchases of fixed assets(51,672)(41,394)(39,872)
Other125,405(523,864)(62,197)
Net cash used for investing activities(3,102,055)(2,139,732)(3,043,226)
Financing Activities
Proceeds from issuance of preferred shares, net—485,821—
Redemption of preferred shares—(450,000)—
Purchases of common shares under share repurchase program(585,823)(1,234,294)(83,472)
Proceeds from common shares issued, net6,6606,4181,876
Proceeds from borrowings——1,018,793
Repayments of borrowings——(359,000)
Change in cash collateral related to securities lending——(81,210)
Third party investment in non-redeemable noncontrolling interests—15,971(2,867)
Dividends paid to redeemable noncontrolling interests—(1,907)(4,945)
Other(85,827)(3,278)73,715
Preferred dividends paid(40,736)(48,280)(41,612)
Net cash provided by (used for) financing activities(705,726)(1,229,549)521,278
Effects of exchange rate changes on foreign currency cash and restricted cash(48,889)(34,047)22,289
Increase (decrease) in cash and restricted cash(41,443)24,227386,846
Cash and restricted cash, beginning of year1,314,7711,290,544903,698
Cash and restricted cash, end of year$1,273,328$1,314,771$1,290,544
Income taxes paid (received)$254,922$286,810$202,940
Interest paid$128,425$139,301$133,491

See Notes to Consolidated Financial Statements

ARCH CAPITAL1012022 FORM 10-K

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

1. General

Arch Capital Group Ltd. (“Arch Capital” or “Arch”) 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 included the results of Somers Group Holdings Ltd. (formerly Watford Holdings Ltd.) and its wholly owned subsidiaries (“Somers”). Effective July 1, 2021, Somers is wholly owned by Greysbridge Holdings Ltd., (“Greysbridge”) and Greysbridge is owned 40% by the Company, 30% by certain investment funds managed by Kelso & Company (“Kelso”) and 30% by certain investment funds managed by Warburg Pincus LLC (“Warburg”). Based on the governing documents of Greysbridge, the Company concluded that, while it retains significant influence over Somers, Somers no longer constitutes a variable interest entity. Accordingly, effective July 1, 2021, Arch no longer consolidates the results of Somers in its consolidated financial statements and footnotes. See note 12, “Variable Interest Entity and Noncontrolling Interests”.

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. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.

2. Acquisitions

Westpac Lenders Mortgage Insurance Limited (“WLMI”)

On August 31, 2021, the Company completed the acquisition of WLMI, an Australian Prudential Regulation Authority authorized captive lenders mortgage insurance (“LMI”) provider to the Westpac Banking Corporation (“Westpac”). As part of the acquisition, WLMI retained its existing risk in force and will remain Westpac’s exclusive provider of LMI on new mortgage originations for a period of 10 years from the acquisition date. The Company was renamed Arch Lenders Mortgage Indemnity Limited (“Arch Indemnity”) and will be the Company’s primary provider of LMI to the Australian market.

Somerset Bridge Group Limited, Southern Rock Holdings Limited and affiliates (“Somerset Group”)

On August 6, 2021, the Company completed the acquisition of Somerset Group. The acquisition includes Somerset Group’s motor insurance managing general agent, distribution capabilities through direct and aggregator channels, affiliated insurer and fully integrated claims operation.

In connection with the acquisitions noted above, the Company increased its goodwill and intangible assets by $350.1 million.

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 Indemnity Insurance”), 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 (“AMG”), United Guaranty Residential Insurance Company (“UGRIC”), Arch Indemnity, Arch Insurance (EU) Designated Activity Company (“Arch Insurance (EU)”), Arch Insurance (U.K.) Limited (“Arch Insurance (U.K.)”) and the Company’s participation on Lloyd’s of London syndicates: 2012 (“Arch Syndicate 2012”) and 1955 (“Arch Syndicate 1955” and together with Arch Syndicate 2012, the Company’s “Lloyd’s Syndicates”). 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;

ARCH CAPITAL1022022 FORM 10-K

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

  • 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.

(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 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

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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 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, “Allowance 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

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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 2022, 2021 or 2020.

(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 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

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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 or 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 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’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, short-term investments 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” or “Short-term investments” in the Company's consolidated balance sheet 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

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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 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 as an unrealized loss in other comprehensive income while the allowance for credit loss is charged to net realized gains (losses) in the consolidated statement of income.

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.

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 (losses)” 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 2022, 2021, and 2020, the Company did not designate any derivative instruments as hedges under the relevant accounting guidance. See note 11, “Derivative Instruments” for additional information.

(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

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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 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

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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 business combination 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. 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

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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) Investment in Operating Affiliates

Investment in operating affiliates primarily represent the Company’s investments in which it has significant influence and which are accounted for under the equity method of accounting. In applying the equity method of accounting, investments in operating affiliates are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of net income or loss of the operating affiliate. The Company records its proportionate share of other comprehensive income or loss of the operating affiliate as a component of other comprehensive income. Adjustments are based on the most recently available financial information from the operating affiliate. Changes in the carrying value of these investments are recorded in income (loss) from operating affiliates.

(s) Funds Held Arrangements

Funds held arrangements are agreements with a third party reinsurance company, where the reinsured retains the related assets on a funds held basis. Such amounts are included in “Other assets” on the Company’s balance sheet. Investment returns produced by those assets are recorded as part of net investment income and net realized gains (losses) in the Company's consolidated results of operations. Funds held as collateral by the Company are included in “Other liabilities” and changes to the funds held liability are reflected as part of interest expense in the Company’s consolidated results of operations.

(t) Recent Accounting Pronouncements

Recently Issued Accounting Standards Adopted

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

Recently Issued Accounting Standards Not Yet Adopted

ASU 2020-04, “Facilitation of the Effects of Reference Rate Reform on Financial Reporting,” was issued in March 2020 and amended in December 2022 with ASU 2022-06, “Reference Rate Reform (Topic 848)”. 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. The amendment deferred the sunset date from December 31, 2022 to December 31, 2024. As a result, this standard can be adopted no later than December 31, 2024, with early adoption permitted. Based on its current analysis, the Company does not expect that the new guidance will have a material effect on the Company’s consolidated financial statements.

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4. Segment Information

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

The Company’s insurance, reinsurance and mortgage segments each have managers who are responsible for the overall profitability of their respective segments and who are directly accountable to the Company’s chief operating decision makers, the Chief Executive Officer of Arch Capital, 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 for middle market and large construction accounts, a comprehensive range of products for middle market accounts in specialty industries and casualty solutions for large national accounts, including loss sensitive primary insurance programs (large deductible, self-insured retention and retrospectively rated programs).

  • Excess and surplus casualty: primary and excess casualty insurance coverages written on a non-admitted basis.

  • Professional lines: directors’ and officers’ liability, errors and omissions liability, employment practices liability, fiduciary liability, crime, professional indemnity and other financial related coverages for corporate, private equity, venture capital, real estate investment trust, limited partnership, financial institution and not-for-profit clients of all sizes, cyber insurance, and medical professional and general liability

insurance coverages for the healthcare industry. The business is predominately written on a claims-made basis.

  • Programs: primarily targeting program managers with unique expertise and niche products offering some combination of general liability, commercial automobile, property, inland marine, umbrella and workers’ compensation.

  • Property, energy, marine and aviation: primary and excess general property insurance coverages, including catastrophe-exposed property coverage, for commercial clients. Coverages for marine include hull, cargo, war, specie and liability. Aviation, stand-alone terrorism and political risks are also offered. Coverage may be provided for operational and construction risk.

  • 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.

  • Warranty and lenders solutions: 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.

  • 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, commercial and transactional surety coverages.

The reinsurance segment consists of the Company’s reinsurance underwriting units which offer specialty product lines on a worldwide basis. Reinsurance agreements are typically offered on a proportional and/or excess of loss basis and provide coverage to ceding company clients for specific underlying written policies. Product lines include:

  • Casualty: provides coverage on third party liability exposures including, among others, executive assurance, professional liability, excess and umbrella liability, excess motor and healthcare business, and workers’ compensation. Business is assumed primarily on a treaty basis, with some facultative coverages also offered.

  • Marine and aviation: provides coverage for energy, hull, cargo, specie, liability and transit, and aviation business, including airline and general aviation risks. Business written may also include space business, which

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includes coverages for satellite assembly, launch and operation for commercial space programs.

*•*Other specialty: provides coverage for proportional motor reinsurance, whole account multi-line treaties, cyber, trade credit and surety, accident and health, workers’ compensation catastrophe, agriculture and political risk, among others.

  • Property catastrophe: provides protection for most types of catastrophic losses, including hurricane, earthquake, flood, tornado, hail and fire, and for other perils on a case-by-case basis. Excess of loss coverages are triggered when aggregate losses and loss adjustment expense from a single occurrence of a covered peril exceed the retention specified in the contract.

  • Property excluding property catastrophe: provides coverage for personal lines and/or commercial property exposures and principally covers buildings, structures, equipment and contents. The primary perils in this business include fire, explosion, collapse, riot, vandalism, wind, tornado, flood and earthquake. Business is assumed on either a treaty or facultative basis*.*

  • Other: includes life reinsurance business, casualty clash business and, in limited instances, non-traditional business which is intended to provide insurers with risk management solutions that complement traditional reinsurance.

The mortgage segment includes the Company’s underwriting units which offer mortgage insurance and reinsurance products on a worldwide basis. Underwriting units include:

  • U.S. primary mortgage insurance: offers private mortgage insurance through Arch Mortgage Insurance Company and United Guaranty Residential Insurance Company (combined “Arch MI U.S.”), both approved eligible mortgage insurers by Fannie Mae and Freddie Mac. Arch MI U.S. also includes AMG, which is not a government sponsored enterprise (“GSE”) approved entity.

  • U.S. credit risk transfer (“CRT”) and other: underwrites CRT transactions, which are predominantly with GSEs, and other U.S. reinsurance transactions.

  • International mortgage insurance/reinsurance: underwrites mortgage insurance and reinsurance outside of the U.S.

The corporate segment results include net investment income, net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings), equity in net income or loss of investments accounted for using the equity method, other income (loss), corporate expenses, transaction costs and other, amortization of intangible assets, interest expense, net foreign exchange gains or losses, income taxes, income or loss from operating affiliates and items related to the Company’s non-cumulative preferred shares. Such amounts exclude the results of the ‘other’ segment.

Through June 30, 2021, the ‘other’ segment included the results of Somers. In July 2021, the Company announced the completion of the previously disclosed acquisition of Somers by Greysbridge. Based on the governing documents of Greysbridge, the Company has concluded that, while it retains significant influence over Somers, Somers no longer constitutes a variable interest entity. Accordingly, effective July 1, 2021, Arch no longer consolidates the results of Somers in its consolidated financial statements. See note 12, “Variable Interest Entity and Noncontrolling Interests.”

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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, 2022
InsuranceReinsuranceMortgageSub-TotalOtherTotal
Gross premiums written (1)$6,930,864$6,948,438$1,454,971$15,326,447$—$15,326,447
Premiums ceded(1,910,222)(2,024,462)(322,400)(4,249,258)—(4,249,258)
Net premiums written5,020,6424,923,9761,132,57111,077,189—11,077,189
Change in unearned premiums(461,307)(964,595)26,790(1,399,112)—(1,399,112)
Net premiums earned4,559,3353,959,3811,159,3619,678,077—9,678,077
Other underwriting income—4,8718,35613,227—13,227
Losses and loss adjustment expenses(2,782,945)(2,568,843)324,271(5,027,517)—(5,027,517)
Acquisition expenses(885,866)(813,555)(40,159)(1,739,580)—(1,739,580)
Other operating expenses(665,472)(267,531)(195,172)(1,128,175)—(1,128,175)
Underwriting income$225,052$314,323$1,256,6571,796,032—1,796,032
Net investment income496,547—496,547
Net realized gains (losses)(662,734)—(662,734)
Equity in net income (loss) of investments accounted for using the equity method115,856—115,856
Other income (loss)(26,165)—(26,165)
Corporate expenses(94,390)—(94,390)
Transaction costs and other(1,092)—(1,092)
Amortization of intangible assets(106,200)—(106,200)
Interest expense(130,266)—(130,266)
Net foreign exchange gains (losses)100,905—100,905
Income (loss) before income taxes and income (loss) from operating affiliates1,488,493—1,488,493
Income tax expense(79,961)—(79,961)
Income (loss) from operating affiliates73,891—73,891
Net income (loss)1,482,423—1,482,423
Amounts attributable to redeemable noncontrolling interests(5,490)—(5,490)
Net income (loss) available to Arch1,476,933—1,476,933
Preferred dividends(40,736)—(40,736)
Net income (loss) available to Arch common shareholders$1,436,197$—$1,436,197
Underwriting Ratios
Loss ratio61.0%64.9%-28.0%51.9%—%51.9%
Acquisition expense ratio19.4%20.5%3.5%18.0%—%18.0%
Other operating expense ratio14.6%6.8%16.8%11.7%—%11.7%
Combined ratio95.0%92.2%-7.7%81.6%—%81.6%
Goodwill and intangible assets$228,532$144,846$430,911$804,289$—$804,289
Total investable assets$28,065,497$—$28,065,497
Total assets47,990,507—47,990,507
Total liabilities35,069,605—35,069,605

(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, 2021
InsuranceReinsuranceMortgageSub-TotalOtherTotal
Gross premiums written (1)$5,867,734$5,093,930$1,507,825$12,463,788$457,465$12,752,487
Premiums ceded(1,719,541)(1,839,556)(246,757)(3,800,153)(102,763)(3,734,150)
Net premiums written4,148,1933,254,3741,261,0688,663,635354,7029,018,337
Change in unearned premiums(521,725)(413,931)22,351(913,305)(22,734)(936,039)
Net premiums earned3,626,4682,840,4431,283,4197,750,330331,9688,082,298
Other underwriting income—3,66917,66521,33473922,073
Losses and loss adjustment expenses(2,344,365)(1,924,719)(56,677)(4,325,761)(259,042)(4,584,803)
Acquisition expenses, net(606,265)(536,754)(97,418)(1,240,437)(62,741)(1,303,178)
Other operating expenses(558,906)(212,810)(194,010)(965,726)(32,869)(998,595)
Underwriting income (loss)$116,932$169,829$952,9791,239,740(21,945)1,217,795
Net investment income346,80842,310389,118
Net realized gains (losses)299,20780,638379,845
Equity in net income (loss) of investments accounted for using the equity method366,402—366,402
Other income (loss)10,244—10,244
Corporate expenses(77,119)—(77,119)
Transaction costs and other(1,103)(935)(2,038)
Amortization of intangible assets(82,057)(898)(82,955)
Interest expense(131,060)(8,410)(139,470)
Net foreign exchange gains (losses)42,854(1,325)41,529
Income (loss) before income taxes and income (loss) from operating affiliates2,013,91689,4352,103,351
Income tax expense(128,348)(234)(128,582)
Income (loss) from operating affiliates264,693—264,693
Net income (loss)2,150,26189,2012,239,462
Amounts attributable to redeemable noncontrolling interests(2,346)(1,953)(4,299)
Amounts attributable to nonredeemable noncontrolling interests—(78,314)(78,314)
Net income (loss) available to Arch2,147,9158,9342,156,849
Preferred dividends(48,343)—(48,343)
Loss on redemption of preferred shares(15,101)—(15,101)
Net income (loss) available to Arch common shareholders$2,084,471$8,934$2,093,405
Underwriting Ratios
Loss ratio64.6%67.8%4.4%55.8%78.0%56.7%
Acquisition expense ratio16.7%18.9%7.6%16.0%18.9%16.1%
Other operating expense ratio15.4%7.5%15.1%12.5%9.9%12.4%
Combined ratio96.7%94.2%27.1%84.3%106.8%85.2%
Goodwill and intangible assets$256,434$183,523$505,026$944,983$—$944,983
Total investable assets$27,442,153$—$27,442,153
Total assets45,100,945—45,100,945
Total liabilities31,545,816—31,545,816

(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, 2020
InsuranceReinsuranceMortgageSub-TotalOtherTotal
Gross premiums written (1)$4,688,562$3,472,086$1,473,999$9,632,691$728,546$10,088,068
Premiums ceded(1,525,655)(1,014,716)(194,149)(2,732,564)(190,957)(2,650,352)
Net premiums written3,162,9072,457,3701,279,8506,900,127537,5897,437,716
Change in unearned premiums(291,487)(295,141)118,085(468,543)22,762(445,781)
Net premiums earned2,871,4202,162,2291,397,9356,431,584560,3516,991,935
Other underwriting income(31)4,45420,31624,7392,04526,784
Losses and loss adjustment expenses(2,092,453)(1,628,320)(528,344)(4,249,117)(440,482)(4,689,599)
Acquisition expenses, net(418,483)(354,048)(134,240)(906,771)(98,071)(1,004,842)
Other operating expenses(489,153)(168,011)(162,202)(819,366)(55,810)(875,176)
Underwriting income (loss)$(128,700)$16,304$593,465481,069(31,967)449,102
Net investment income401,908117,700519,608
Net realized gains (losses)813,7819,679823,460
Equity in net income (loss) of investments accounted for using the equity method146,693—146,693
Other income (loss)29—29
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 and income (loss) from operating affiliates1,496,12664,6571,560,783
Income tax expense(111,812)(26)(111,838)
Income (loss) from operating affiliates16,766—16,766
Net income1,401,08064,6311,465,711
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 Arch1,398,0837,4381,405,521
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 ratio72.9%75.3%37.8%66.1%78.6%67.1%
Acquisition expense ratio14.6%16.4%9.6%14.1%17.5%14.4%
Other operating expense ratio17.0%7.8%11.6%12.7%10.0%12.5%
Combined ratio104.5%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 assets39,791,9833,490,31443,282,297
Total liabilities26,789,1492,505,70729,294,856

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

INSURANCE SEGMENTYear Ended December 31,
202220212020
Net premiums earned (1)
Professional lines$1,314,236$942,817$655,872
Property, energy, marine and aviation772,388667,892506,182
Programs589,860506,867432,854
Travel, accident and health491,847255,590190,944
Construction and national accounts432,020416,107398,999
Excess and surplus casualty393,353318,027270,620
Warranty and lenders solutions127,222153,958114,687
Other438,409365,210301,262
Total$4,559,335$3,626,468$2,871,420
Net premiums written by underwriting location (1)
United States$3,340,038$2,813,039$2,158,415
Europe1,405,7191,125,192856,572
Other274,885209,962147,920
Total$5,020,642$4,148,193$3,162,907
REINSURANCE SEGMENTYear Ended December 31,
202220212020
Net premiums earned (1)
Other specialty$1,377,880$818,801$626,409
Property excluding property catastrophe1,091,440836,573562,208
Casualty854,543666,754549,056
Property catastrophe366,991280,738237,736
Marine and aviation159,401152,955109,624
Other109,12684,62277,196
Total$3,959,381$2,840,443$2,162,229
Net premiums written by underwriting location (1)
United States$1,246,507$828,504$687,622
Bermuda2,561,7711,557,2941,001,990
Europe and other1,115,698868,576767,758
Total$4,923,976$3,254,374$2,457,370
MORTGAGE SEGMENTYear Ended December 31,
202220212020
Net premiums earned by underwriting location
United States$815,519$970,507$1,158,563
Other343,842312,912239,372
Total$1,159,361$1,283,419$1,397,935
Net premiums written by underwriting location
United States$780,256$914,477$1,021,950
Other352,315346,591257,900
Total$1,132,571$1,261,068$1,279,850

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

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OTHER SEGMENTYear Ended December 31,
202220212020
Net premiums earned (1)
Casualty$—$138,551$245,272
Other specialty—118,356186,717
Property catastrophe—15,23523,037
Property excluding property catastrophe—6,5781,130
Marine and aviation—190429
Other—53,058103,766
Total$—$331,968$560,351
Net premiums written by underwriting location (1)
United States$—$63,403$115,471
Europe—91,49997,753
Bermuda—199,800324,365
Total$—$354,702$537,589

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

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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,
202220212020
Reserve for losses and loss adjustment expenses at beginning of year$17,757,156$16,513,929$13,891,842
Unpaid losses and loss adjustment expenses recoverable5,599,2314,314,8554,082,650
Net reserve for losses and loss adjustment expenses at beginning of year12,157,92512,199,0749,809,192
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year5,798,5284,940,9874,851,051
Prior years(771,011)(356,184)(161,452)
Total net incurred losses and loss adjustment expenses5,027,5174,584,8034,689,599
Net losses and loss adjustment expense reserves of acquired business (1)—104,176—
Retroactive reinsurance transactions (2)—(444,147)182,210
Impact of deconsolidation of Somers (3)—(1,460,611)—
Foreign exchange (gains) losses and other(290,376)1,181179,190
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year(887,464)(734,846)(661,529)
Prior years(2,254,484)(2,091,705)(1,999,588)
Total net paid losses and loss adjustment expenses(3,141,948)(2,826,551)(2,661,117)
Net reserve for losses and loss adjustment expenses at end of year13,753,11812,157,92512,199,074
Unpaid losses and loss adjustment expenses recoverable6,278,8255,599,2314,314,855
Reserve for losses and loss adjustment expenses at end of year$20,031,943$17,757,156$16,513,929

(1) Represents activity related to the Company’s acquisitions in the 2021 period. See note 2, “Acquisitions.”

(2) See ‘Retroactive Reinsurance Transactions’ section.

(3) See note 12, “Variable Interest Entity and Noncontrolling Interests.”

Development on Prior Year Loss Reserves

Year Ended December 31, 2022

During 2022, the Company recorded estimated net favorable development on prior year loss reserves of $771.0 million, which consisted of net favorable development of $25.3 million from the insurance segment, $191.6 million from the reinsurance segment and $554.1 million from the mortgage segment.

The insurance segment’s net favorable development of $25.3 million, or 0.6 points of net earned premium, consisted of $55.3 million of net favorable development in short-tailed lines partially offset by $29.9 million of net adverse development from medium-tailed and long-tailed lines. Net favorable development in short-tailed lines reflected $37.4 million of favorable development in warranty and lenders solutions, primarily from the 2021 accident year (i.e., the year in which a loss occurred), and $14.8 million of favorable development related to travel and accident

business, primarily from the 2020 and 2021 accident years. Net adverse development in medium-tailed lines reflected $24.7 million of adverse development in professional liability business, primarily from the 2013 to 2015 and 2018 to 2020 accident years, and $6.4 million of adverse development in contract binding business, across most accident years, partially offset by $12.9 million of favorable development in marine business, across most accident years. Net adverse development in long-tail lines reflected $18.5 million of adverse development related to casualty business, primarily from the 2020 and 2021 accident years, and $7.3 million of adverse development on construction and national accounts, primarily from the 2017, 2020 and 2021 accident years. This is partially offset by $21.5 million of favorable development in other business, including alternative markets and excess workers’ compensation, primarily from the 2019 and prior accident years.

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The reinsurance segment’s net favorable development of $191.6 million, or 4.8 points of net earned premium, consisted of $196.2 million of net favorable development from short-tailed and medium-tailed lines, partially offset by $4.6 million of net adverse development from long-tailed lines. Net favorable development in short-tailed lines reflected $109.4 million of favorable development from property other than property catastrophe business, primarily from the 2018 to 2021 underwriting years (i.e., all premiums and losses attributable to contracts having an inception or renewal date within the given twelve-month period), $24.0 million of favorable development from property catastrophe business, primarily from the 2018 to 2020 underwriting years, and $35.0 million from other specialty business, primarily from the 2016 and 2021 underwriting years. Net favorable development in medium-tailed lines reflected $28.0 million in marine and aviation lines, across most underwriting years. Net adverse development in long-tailed lines primarily reflected $4.6 million in casualty, spread across many prior underwriting years.

The mortgage segment experienced net favorable development of $554.1 million, or 47.8 points of net earned premium, with the majority of reserve releases being on COVID-related delinquencies associated with the U.S. first lien portfolio from the 2020 and 2021 accident years. The Company’s credit risk transfer, international, second lien and student loan businesses also contributed to the favorable development.

Year Ended December 31, 2021

During 2021, the Company recorded estimated net favorable development on prior year loss reserves of $356.2 million, which consisted of net favorable development of $16.2 million from the insurance segment, $178.8 million from the reinsurance segment, $169.6 million from the mortgage segment, partially offset by $8.4 million of adverse development from the ‘other’ segment (activity prior to the deconsolidation of Somers).

The insurance segment’s net favorable development of $16.2 million, or 0.4 points of net earned premium, consisted of $109.8 million of net favorable development in short-tailed and long-tailed lines mostly offset by $93.5 million of net adverse development from medium-tailed lines. Net favorable development of $81.7 million in short-tailed lines reflected $38.9 million of favorable development from property (excluding marine), primarily from the 2018 to 2020 accident years, $26.7 million of favorable development in warranty and lenders solutions, primarily from the 2020 accident year, and $16.2 million of favorable development on travel and accident, primarily from the 2016 to 2020 accident years. Net favorable development of $28.1 million in long-tailed lines reflected favorable development in construction, national accounts and alternative markets, primarily from the

2016 to 2019 accident years, partially offset by adverse development in executive assurance, primarily from the 2015, 2017 and 2018 accident years. Net adverse development in medium-tailed lines reflected $57.6 million of adverse development in contract binding, primarily from the 2013 to 2019 accident years and $30.8 million of adverse development in professional liability, primarily from the 2018 to 2020 accident years.

The reinsurance segment’s net favorable development of $178.8 million, or 6.3 points of net earned premium, consisted of $184.1 million of net favorable development from short-tailed and medium-tailed lines, partially offset by $5.3 million of net adverse development from long-tailed lines. Net favorable development of $175.5 million in short-tailed lines reflected $123.3 million from other specialty lines, primarily from the 2014 to 2019 underwriting years, and $88.6 million of favorable development from property other than property catastrophe business, primarily from the 2015 to 2020 underwriting years. Such amounts were partially offset by adverse development of $36.4 million from property catastrophe, primarily from the 2020 underwriting year. Adverse development in long-tailed lines reflected an increase in casualty, primarily from the 2018 underwriting year.

The mortgage segment experienced net favorable development of $169.6 million, or 13.2 points of net earned premium. Approximately a third of this development came from the U.S. first lien portfolio, which benefited from improving economic conditions and rising home prices, resulting in reduced claim rate assumptions primarily associated with pre-pandemic delinquencies. Various vintage CRT contracts also experienced similar effects and contributed to the favorable development, including the effect of contracts called by the GSEs. Subrogation recoveries on second lien and student loan business and international business also contributed to the favorable development.

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

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accident years, 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, and $53.6 million from other specialty lines, across most 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 2020. Adverse development in long-tailed lines reflected an increase in casualty, 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.

Retroactive Reinsurance Transactions

In 2021, the Company entered into a retroactive reinsurance transaction with third party reinsurer to reinsure run-off liabilities associated with certain U.S. insurance exposures.

In 2021, the Company entered into a reinsurance to close with the related party, in connection with the 2018 and prior years of account for certain London syndicate business. See note 16, “Transactions with Related Parties”.

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.

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 segmentLevel of disaggregationIncluded lines of business
InsuranceProperty energy, marine and aviationProperty energy, marine and aviation
Third party occurrence businessExcess 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 businessProfessional lines
Multi-line and other specialtyPrograms; contract binding (part of excess and surplus casualty); travel, accident and health; warranty and lenders solutions; and other (contract and commercial surety coverages)
ReinsuranceCasualtyCasualty
Property catastropheProperty catastrophe
Property excluding property catastropheProperty excluding property catastrophe
Marine and aviationMarine and aviation
Other specialtyOther specialty
MortgageDirect 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) 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 and (ii) certain reinsurance business, including casualty clash and non-traditional lines. 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.

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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 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 projection 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.

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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 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 warranty and lenders solutions), 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

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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 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.

From time to time, the Company enters into loss portfolio transfer and adverse development cover reinsurance agreements accounted for as retroactive reinsurance. These agreements transfer Loss Reserves and future favorable or adverse development on certain runoff programs and certain third party occurrence business, within multi-line and other specialty 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. Unpaid loss and loss adjustment expenses recoverable at December 31, 2022 included $280.2 million related to such reinsurance agreements.

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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 reinsuranceDecember 31, 2022
Total of IBNR liabilities plus expected development on reported claimsCumulative number of reported claims
Year ended December 31,
Accident year2013 unaudited2014 unaudited2015 unaudited2016 unaudited2017 unaudited2018 unaudited2019 unaudited2020 unaudited2021 unaudited2022
2013$158,548$156,147$148,622$142,889$134,473$133,400$128,157$126,825$125,813$124,868$273,982
2014148,104145,679147,248136,050132,166134,192134,895134,803133,6051,6743,557
2015112,299109,769103,921102,44997,78991,77091,83390,8162,6544,244
2016104,002100,843105,184100,00395,98992,10887,618615,704
2017280,686246,264235,924230,413231,199225,2983,2686,287
2018180,981186,030173,693170,057170,4117,1775,048
2019179,056178,564165,477161,1564,1625,942
2020359,394329,362335,74728,3308,546
2021426,870428,71954,7467,566
2022521,750208,0808,965
Total$2,279,988
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013$32,216$84,680$110,432$119,649$121,779$125,014$122,894$124,227$124,381$124,402
201425,84953,63277,76484,06187,68198,423115,253122,165122,792
201523,56164,90076,28286,19687,87086,19087,26087,564
201624,68483,21898,30397,08994,57090,80887,232
201730,215139,849195,512211,688215,874217,764
201830,026102,285134,858142,838149,663
201926,130105,380133,911139,141
202055,619194,487251,055
202190,423267,677
2022100,476
Total1,547,766
All outstanding liabilities before 2013, net of reinsurance18,239
Liabilities for losses and loss adjustment expenses, net of reinsurance$750,461
Third party occurrence business ($000’s except claim count)
Incurred losses and allocated loss adjustment expenses, net of reinsuranceDecember 31, 2022
Total of IBNR liabilities plus expected development on reported claimsCumulative number of reported claims
Year ended December 31,
Accident year2013 unaudited2014 unaudited2015 unaudited2016 unaudited2017 unaudited2018 unaudited2019 unaudited2020 unaudited2021 unaudited2022
2013$282,852$296,668$306,572$301,622$281,637$274,246$272,385$269,297$270,110$263,430$43,14866,118
2014329,718335,587338,505342,759339,403343,904342,641343,286345,02460,26375,557
2015358,769391,570398,565391,797391,132382,427386,465379,22675,54078,507
2016389,530394,190405,803399,315374,654367,586363,45393,80078,576
2017417,097417,662422,360412,231406,857406,165114,60384,418
2018430,128452,879450,647451,164458,050156,70077,685
2019455,928487,080480,535471,279195,28384,985
2020606,640616,314640,231309,01990,795
2021621,972662,716431,30289,718
2022688,082614,36670,380
Total$4,677,656
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013$6,840$29,215$71,335$101,153$122,045$149,012$164,090$174,591$184,444$192,159
20149,20040,22671,473112,541161,935191,108211,440223,895237,135
201511,11044,51488,411139,364181,505211,510227,439249,399
201611,67941,92087,543136,759164,534194,637215,481
201713,39152,30999,806134,988165,468220,660
201816,99163,776115,049154,138198,502
201918,37573,075121,646172,948
202024,40776,567154,902
202126,23590,791
202223,981
Total1,755,958
All outstanding liabilities before 2013, net of reinsurance263,297
Liabilities for losses and loss adjustment expenses, net of reinsurance$3,184,995
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Third party claims-made business ($000’s except claim count)
Incurred losses and allocated loss adjustment expenses, net of reinsuranceDecember 31, 2022
Total of IBNR liabilities plus expected development on reported claimsCumulative number of reported claims
Year ended December 31,
Accident year2013 unaudited2014 unaudited2015 unaudited2016 unaudited2017 unaudited2018 unaudited2019 unaudited2020 unaudited2021 unaudited2022
2013$301,608$320,266$324,044$320,177$294,372$290,852$281,642$271,156$273,607$281,584$14,63914,953
2014264,273279,410298,541278,556281,271297,248291,498287,573296,15321,20615,482
2015258,740277,358276,256259,830255,207252,263267,725266,75818,19814,392
2016274,996291,258308,080314,412321,764326,960329,53429,35615,083
2017270,272285,738311,724308,172323,128316,67345,04215,198
2018272,543314,112319,646336,106347,44961,61215,934
2019289,128317,312317,363322,17893,42215,858
2020383,497413,156423,375187,24515,438
2021514,676517,975351,73615,751
2022657,664575,48418,190
Total$3,759,343
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013$19,007$87,386$137,857$179,261$197,861$216,984$238,730$245,423$246,813$253,570
201413,81463,288129,409172,722207,447229,314243,137249,307260,333
20159,05952,007100,030126,431174,084193,105216,892220,871
201610,53768,157127,203158,127205,478242,300256,705
20179,28167,529112,975143,064195,788232,508
201812,24168,244118,105158,389208,063
201912,37365,286122,046154,630
202017,07087,248151,750
202123,25390,487
202225,244
Total1,854,161
All outstanding liabilities before 2013, net of reinsurance86,120
Liabilities for losses and loss adjustment expenses, net of reinsurance$1,991,302
Multi-line and other specialty ($000’s except claim count)
Incurred losses and allocated loss adjustment expenses, net of reinsuranceDecember 31, 2022
Total of IBNR liabilities plus expected development on reported claimsCumulative number of reported claims
Year ended December 31,
Accident year2013 unaudited2014 unaudited2015 unaudited2016 unaudited2017 unaudited2018 unaudited2019 unaudited2020 unaudited2021 unaudited2022
2013$264,243$272,335$263,631$263,928$251,894$253,271$248,634$245,825$245,069$244,191$2,76186,371
2014301,548325,705318,453318,268317,197313,221310,051309,061310,9773,968130,844
2015334,684357,939356,777364,815356,657349,432347,206344,9745,632170,579
2016408,686430,976427,829416,108409,987408,004408,7168,616189,406
2017482,436501,026491,347500,947504,322512,71712,776229,570
2018512,406564,563562,848565,116564,69321,722256,621
2019566,864612,179640,262651,00438,672250,441
2020618,340569,123515,01687,261162,214
2021635,186618,581153,336113,165
2022678,479425,10789,859
Total$4,849,348
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013$86,680$150,925$180,428$213,461$225,324$234,330$236,375$237,293$238,321$238,257
2014107,726196,899234,267267,079281,195291,727293,131294,630295,896
2015138,153236,108277,850305,895320,971326,652330,431331,320
2016175,948304,743341,789362,823379,305385,314390,350
2017181,102342,385380,696423,480446,002471,978
2018211,711389,047442,643479,824508,649
2019211,970385,794486,882548,844
2020171,994309,106358,967
2021156,992334,549
2022177,092
Total3,655,902
All outstanding liabilities before 2013, net of reinsurance22,275
Liabilities for losses and loss adjustment expenses, net of reinsurance$1,215,721
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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, 2022:

Average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance
Year 1Year 2Year 3Year 4Year 5Year 6Year 7Year 8Year 9Year 10
Property, energy, marine and aviation20.3%44.2%18.4%5.2%1.5%1.1%2.0%2.2%0.3%—%
Third party occurrence business3.4%9.3%11.8%11.2%9.7%9.7%5.4%4.5%3.8%2.9%
Third party claims-made business4.1%17.2%17.2%11.4%13.6%8.8%6.4%2.0%2.1%2.4%
Multi-line and other specialty34.3%28.9%10.9%8.8%4.5%3.1%0.9%0.4%0.4%—%

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 projection 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, 2022 there were no significant backlogs related to the processing of assumed reinsurance information at our reinsurance operations.

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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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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 reinsuranceDecember 31, 2022
Total of IBNR liabilities plus expected development on reported claimsCumulative number of reported claims
Year ended December 31,
Accident year2013 unaudited2014 unaudited2015 unaudited2016 unaudited2017 unaudited2018 unaudited2019 unaudited2020 unaudited2021 unaudited2022
2013$163,425$156,619$152,392$146,230$134,204$132,701$129,120$133,401$133,687$133,094$26,542N/A
2014212,923217,991214,724227,485224,105233,922234,293230,944231,17533,255N/A
2015217,343216,759224,385231,473235,637242,554245,756247,41944,753N/A
2016208,192221,004242,089257,214264,573264,475268,07946,122N/A
2017262,894251,827267,173293,381304,194310,85852,415N/A
2018270,621284,405276,802281,852293,32056,325N/A
2019325,359334,755361,549372,66993,310N/A
2020378,668367,595349,831169,909N/A
2021434,187431,165292,696N/A
2022541,941482,552N/A
Total$3,179,551
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013$2,421$9,822$22,886$42,861$54,323$62,751$70,289$76,141$81,167$87,485
20143,88515,97340,65163,21490,530113,596133,263143,929152,586
20154,44020,20846,93370,52395,988119,096136,138151,119
20165,72025,62651,49486,362112,818131,341155,584
20176,41730,31663,922112,474136,489163,243
20187,57631,240106,443128,728154,173
201915,79857,56896,593129,766
202017,64650,38390,156
202114,63353,264
202217,638
Total1,155,014
All outstanding liabilities before 2013, net of reinsurance299,288
Liabilities for losses and loss adjustment expenses, net of reinsurance$2,323,825
Property catastrophe ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsuranceDecember 31, 2022
Total of IBNR liabilities plus expected development on reported claimsCumulative number of reported claims
Year ended December 31,
Accident year2013 unaudited2014 unaudited2015 unaudited2016 unaudited2017 unaudited2018 unaudited2019 unaudited2020 unaudited2021 unaudited2022
2013$65,372$45,962$34,959$30,518$27,974$27,248$26,415$26,543$26,344$26,221$(138)N/A
201443,80029,80124,50021,76420,02619,32619,22919,00419,045(10)N/A
201532,74817,55811,4255,5313,7793,1332,9322,56968N/A
201623,22416,58212,7499,1906,8865,9875,181877N/A
201786,41053,69949,50735,89324,23921,026(803)N/A
201873,04152,00133,42519,83110,7223,039N/A
201925,52614,25213,0934,5904,576N/A
2020260,244322,680326,26233,413N/A
2021308,014302,12429,963N/A
2022299,63673,474N/A
Total$1,017,376
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013$12,035$18,496$23,001$24,697$26,329$26,549$26,549$27,233$26,998$27,023
201413,61919,54417,90218,67918,24418,42118,55018,62918,592
2015(3,141)(2,109)1,8432,1031,6591,7451,8171,874
2016(7,039)1,7591,8702,9322,0862,4332,594
201730,62531,62137,08427,06014,21516,034
201827,4247,34418,253(10,934)(8,100)
20194,3748,84512,895(11,472)
202052,592152,075200,510
202164,408167,806
202269,969
Total484,830
All outstanding liabilities before 2013, net of reinsurance2,612
Liabilities for losses and loss adjustment expenses, net of reinsurance$535,158
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Property excluding property catastrophe ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsuranceDecember 31, 2022
Total of IBNR liabilities plus expected development on reported claimsCumulative number of reported claims
Year ended December 31,
Accident year2013 unaudited2014 unaudited2015 unaudited2016 unaudited2017 unaudited2018 unaudited2019 unaudited2020 unaudited2021 unaudited2022
2013$114,775$76,290$69,981$65,734$64,013$63,247$62,070$62,774$62,288$63,390$29N/A
2014142,092116,33198,26390,03187,76883,47681,81280,34879,307443N/A
2015213,681187,932183,709187,569186,861175,812172,189166,5803,909N/A
2016174,506144,323136,367134,362138,216135,116128,9416,208N/A
2017266,628247,462235,310227,891212,133204,1288,794N/A
2018222,932238,876234,794211,852201,4297,370N/A
2019214,513204,620194,164189,4568,407N/A
2020366,726338,712319,09736,912N/A
2021545,101497,05983,934N/A
2022742,703360,528N/A
Total$2,592,090
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013$25,943$42,418$49,433$52,614$53,400$55,272$60,777$61,640$61,665$63,228
201423,34262,41471,14476,06077,68778,06778,02977,72877,894
201575,458118,396148,887159,482164,637158,293158,537159,054
201633,23694,12197,918103,202111,039113,300114,432
201727,456124,220155,139162,933177,737181,029
201829,654107,172151,632166,598174,778
201942,919123,293149,377161,573
2020100,927207,061242,844
2021135,815269,481
2022142,938
Total1,587,251
All outstanding liabilities before 2013, net of reinsurance5,765
Liabilities for losses and loss adjustment expenses, net of reinsurance$1,010,604
Marine and aviation ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsuranceDecember 31, 2022
Total of IBNR liabilities plus expected development on reported claimsCumulative number of reported claims
Year ended December 31,
Accident year2013 unaudited2014 unaudited2015 unaudited2016 unaudited2017 unaudited2018 unaudited2019 unaudited2020 unaudited2021 unaudited2022
2013$38,167$36,765$35,669$34,293$34,207$33,453$33,001$29,434$26,728$25,695$1,012N/A
201430,56628,75726,99525,29723,30222,91921,69821,65118,511800N/A
201533,13437,01931,49931,37330,42328,12027,29925,0081,514N/A
201627,25822,62523,44819,12216,83414,89611,9524,080N/A
201728,59026,16523,61320,74919,84217,3294,178N/A
201827,61325,68024,05824,19221,0523,738N/A
201948,38354,68460,32160,6355,574N/A
202082,71675,69579,33828,621N/A
2021110,12995,58651,391N/A
2022125,68599,917N/A
Total$480,791
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013$4,751$13,054$17,678$20,580$21,557$22,803$23,176$22,941$22,912$23,648
20144,0057,79511,33512,20914,36814,79415,65015,72917,084
2015(6)13,32118,85220,62322,31821,97122,11422,297
2016(7,371)(1,739)4453,1695,7646,6567,028
20171,6506,4339,24910,89711,48811,817
20181,9936,81711,02113,33213,923
201910,53721,26128,68034,637
20209,09626,12942,203
20218,40724,108
202212,101
Total208,846
All outstanding liabilities before 2013, net of reinsurance17,999
Liabilities for losses and loss adjustment expenses, net of reinsurance$289,944
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Other specialty ($000’s)
Incurred losses and allocated loss adjustment expenses, net of reinsuranceDecember 31, 2022
Total of IBNR liabilities plus expected development on reported claimsCumulative number of reported claims
Year ended December 31,
Accident year2013 unaudited2014 unaudited2015 unaudited2016 unaudited2017 unaudited2018 unaudited2019 unaudited2020 unaudited2021 unaudited2022
2013$304,905$280,398$269,105$267,106$266,970$264,418$263,713$257,960$255,453$254,380$4,327N/A
2014328,056308,074310,153303,589298,357299,789295,270289,460287,9416,034N/A
2015271,235269,237267,079263,826263,985261,158250,103248,8486,340N/A
2016313,982310,907303,432295,116301,277296,251293,5718,371N/A
2017382,884375,347357,762357,212355,763351,47822,234N/A
2018402,372395,484390,135413,116408,90532,668N/A
2019414,049393,864387,810383,49138,889N/A
2020579,367511,136506,16457,946N/A
2021589,452590,091148,264N/A
2022924,130601,334N/A
Total$4,248,999
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
2013$81,609$155,936$188,651$209,775$222,292$229,228$237,023$237,559$240,669$243,881
201492,743181,222223,243240,680250,427263,123266,898270,529271,712
201580,453157,176190,699204,444216,683227,879230,640231,384
2016103,649196,496231,761249,699265,763271,609277,028
2017130,150245,165285,299299,405312,273322,863
2018124,996265,000303,141323,868340,061
2019116,762204,625267,972293,260
2020129,621285,729361,031
2021146,503300,025
2022175,834
Total2,817,079
All outstanding liabilities before 2013, net of reinsurance13,001
Liabilities for losses and loss adjustment expenses, net of reinsurance$1,444,921

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, 2022:

Average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance
Year 1Year 2Year 3Year 4Year 5Year 6Year 7Year 8Year 9Year 10
Casualty2.8%7.8%12.4%11.3%9.5%8.2%7.5%5.0%3.8%4.7%
Property catastrophe41.7%27.3%49.4%(115.6)%(10.7)%4.1%1.7%1.7%(0.5)%0.1%
Property excluding property catastrophe27.0%37.4%13.2%5.6%4.0%0.6%2.4%0.4%0.1%2.5%
Marine and aviation4.5%28.8%18.3%10.9%8.4%3.0%2.4%0.1%3.6%2.9%
Other specialty29.9%29.9%13.1%6.0%4.4%3.3%1.8%0.6%0.8%1.3%

Mortgage Segment

The Company’s mortgage segment includes (1) U.S. primary mortgage insurance (2) U.S. credit risk transfer and other, and (3) international mortgage insurance and reinsurance. The latter two 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 primary 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 also reserves 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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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

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 the 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 have been 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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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

The following table presents information on the mortgage segment’s short-duration insurance contracts:

U.S. primary mortgage insurance ($000’s except claim count)
Incurred losses and allocated loss adjustment expenses, net of reinsuranceDecember 31, 2022
Total of IBNR liabilities plus expected development on reported claimsCumulative number of paid claims
Year ended December 31,
Accident year2013 unaudited2014 unaudited2015 unaudited2016 unaudited2017 unaudited2018 unaudited2019 unaudited2020 unaudited2021 unaudited2022
2013$469,311$419,668$411,793$405,809$395,693$393,149$390,987$391,062$391,324$390,29929,474
2014316,095297,151279,434266,027265,992261,091262,682262,829260,55446,311
2015222,790197,238198,001194,677189,235190,913190,560188,64914,573
2016183,556170,532148,715140,608142,392141,657137,415—3,445
2017179,376132,220107,255108,181109,242102,005(1)2,516
2018132,31896,35789,12087,96271,976(4)1,718
2019108,424119,253110,36263,485741,002
2020420,003373,53378,334476299
2021144,37577,21237972
2022173,3272,1477
Total$1,543,256
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance
201341,447203,957308,956353,189373,909382,200386,853387,894387,879388,036
201420,099129,159201,925233,879247,038254,175256,285256,875257,232
201516,15992,431151,222171,337180,321183,472184,025184,955
201611,46272,201113,357127,286131,161131,717132,387
20178,62248,11278,65087,31789,75691,645
20183,96631,47850,13555,85358,687
20192,89920,10529,10234,178
20201,0404,1447,740
20214691,687
2022176
1,156,723
All outstanding liabilities before 2013, net of reinsurance10,585
Liabilities for losses and loss adjustment expenses, net of reinsurance$397,118

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, 2022:

Average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance
Year 1Year 2Year 3Year 4Year 5Year 6Year 7Year 8Year 9Year 10
U.S. Primary5.6%30.9%23.8%9.8%4.0%1.8%0.7%0.3%0.1%—%
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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

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, 2022:

December 31, 2022
Net outstanding liabilities
Insurance
Property, energy, marine and aviation$750,461
Third party occurrence business3,184,995
Third party claims-made business1,991,302
Multi-line and other specialty1,215,721
Reinsurance
Casualty2,323,825
Property catastrophe535,158
Property excluding property catastrophe1,010,604
Marine and aviation289,944
Other specialty1,444,921
Mortgage
U.S. primary397,118
Other short duration lines not included in disclosures301,222
Total for short duration lines13,445,271
Unpaid losses and loss adjustment expenses recoverable
Insurance
Property, energy, marine and aviation423,740
Third party occurrence business1,761,871
Third party claims-made business995,921
Multi-line and other specialty173,051
Reinsurance
Casualty684,663
Property catastrophe595,740
Property excluding property catastrophe206,867
Marine and aviation186,416
Other specialty656,130
Mortgage
U.S. primary37,531
Other short duration lines not included in disclosures (1)560,642
Intercompany eliminations(3,747)
Total for short duration lines6,278,825
Lines other than short duration102,283
Discounting(60,536)
Unallocated claims adjustment expenses266,100
307,847
Total gross reserves for losses and loss adjustment expenses$20,031,943

(1) Includes unpaid loss and loss adjustment expenses recoverable of $280.2 million related to the loss portfolio transfer reinsurance agreements.

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:

Year Ended December 31, 2022Premium Receivables, Net of AllowanceAllowance for Expected Credit Losses
Balance at beginning of period$2,633,280$39,958
Change for provision of expected credit losses (1)(4,556)
Balance at end of period$3,624,777$35,402
Year Ended December 31, 2021
Balance at beginning of period$2,064,586$37,781
Change for provision of expected credit losses (1)2,177
Balance at end of period$2,633,280$39,958

(1) Amounts deemed uncollectible are written-off in operating expenses. For the 2022 and 2021 periods, amounts written off totaled $11.4 million and $3.8 million, respectively.

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:

Year Ended December 31, 2022Reinsurance Recoverables, Net of AllowanceAllowance for Expected Credit Losses
Balance at beginning of period$5,880,735$13,230
Change for provision of expected credit losses8,314
Balance at end of period$6,563,654$21,544
Year Ended December 31, 2021
Balance at beginning of period$4,500,802$11,636
Change for provision of expected credit losses1,594
Balance at end of period5,880,735$13,230
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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums) at December 31, 2022 and 2021:

December 31,
20222021
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses$6,563,654$5,880,735
% due from carriers with A.M. Best rating of “A-” or better68.8%69.7%
% due from all other rated carriers0.1%0.1%
% due from all other carriers with no A.M. Best rating (1)31.1%30.2%
Largest balance due from any one carrier as % of total shareholders’ equity9.0%6.7%

(1) At December 31, 2022 and 2021 period, over 95% and 91% of such amount is collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other, respectively.

Contractholder Receivables

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

Year Ended December 31, 2022Contractholder Receivables, Net of AllowanceAllowance for Expected Credit Losses
Balance at beginning of period$1,828,691$3,437
Change for provision of expected credit losses(746)
Balance at end of period$1,731,293$2,691
Year Ended December 31, 2021
Balance at beginning of period$1,986,924$8,638
Change for provision of expected credit losses(5,201)
Balance at end of period1,828,691$3,437

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 to third parties. 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 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,
202220212020
Premiums Written
Direct$8,540,787$7,706,832$6,553,910
Assumed6,785,6605,045,6553,534,158
Ceded(4,249,258)(3,734,150)(2,650,352)
Net$11,077,189$9,018,337$7,437,716
Premiums Earned
Direct$8,057,635$7,149,794$6,361,451
Assumed5,767,7384,333,8733,213,873
Ceded(4,147,296)(3,401,369)(2,583,389)
Net$9,678,077$8,082,298$6,991,935
Losses and Loss Adjustment Expenses
Direct$3,990,768$4,266,758$4,392,392
Assumed3,559,1332,826,8202,204,323
Ceded(2,522,384)(2,508,775)(1,907,116)
Net$5,027,517$4,584,803$4,689,599
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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

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

The following table summarizes the respective coverages and retentions at December 31, 2022:

December 31, 2022
Bellemeade Entities (Issue Date)Initial Coverage at IssuanceCurrent CoverageRemaining Retention, Net
2017-1 Ltd. (1)$368,114$36,679$142,461
2018-1 Ltd. (2)374,46089,698143,592
2018-3 Ltd. (3)506,110199,237152,861
2019-1 Ltd. (4)341,790107,880118,908
2019-2 Ltd. (5)621,022325,462191,550
2019-3 Ltd. (6)700,920222,977208,931
2019-4 Ltd. (7)577,267266,124142,564
2020-2 Ltd. (8)449,167105,110237,709
2020-3 Ltd. (9)451,816250,971161,544
2020-4 Ltd. (10)337,013101,729138,131
2021-1 Ltd. (11)643,577503,267153,525
2021-2 Ltd. (12)616,017535,461138,524
2021-3 Ltd. (13)639,391616,959132,492
2022-1 Ltd. (14)316,760316,760143,577
2022-2 Ltd. (15)327,165327,165217,436
Total$7,270,589$4,005,479$2,423,805

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

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

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

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

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

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

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

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

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

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

(11) Issued in March 2021, covering in-force policies issued between September 1, 2020 and November 30, 2020. $580 million was directly funded by Bellemeade Re 2021-1 Ltd. with an additional $64 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(12) Issued in June 2021, covering in-force policies issued between December 1, 2020 and March 31, 2021. $523 million was directly funded by Bellemeade Re 2021-2 Ltd. via insurance-linked notes, with an additional $93 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(13) Issued in September 2021, covering in-force policies issued between April 1, 2021 and June 30, 2021. $508 million was directly funded by Bellemeade Re 2021-3 Ltd. via insurance-linked notes, with an additional $131 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(14) Issued in January 2022, covering in-force policies issued between July 1, 2021 and November 30, 2021. $284 million was directly funded by Bellemeade Re 2022-1 Ltd. via insurance-linked notes, with an additional $33 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(15) Issued in September 2022, covering in-force policies issued between November 1, 2021 and June 30, 2022. $201 million was directly funded by Bellemeade Re 2022-2 Ltd. via insurance-linked notes, with an additional $126 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

9. Investment Information

Available For Sale Investments

The following table summarizes the fair value and cost or amortized cost of the Company’s securities classified as available for sale:

Estimated Fair ValueGross Unrealized GainsGross Unrealized LossesAllowance for Expected Credit LossesCost or Amortized Cost
December 31, 2022
Fixed maturities:
Corporate bonds$8,020,128$55,468$(781,353)$(29,950)$8,775,963
Mortgage backed securities795,3914,933(86,587)2877,043
Municipal bonds419,1663,149(33,360)(100)449,477
Commercial mortgage backed securities1,047,275608(57,667)(3,415)1,107,749
U.S. government and government agencies5,161,19314,891(342,963)—5,489,265
Non-U.S. government securities2,312,8198,870(237,846)(1,882)2,543,677
Asset backed securities1,926,817761(106,623)(6,010)2,038,689
Total19,682,78988,680(1,646,399)(41,355)21,281,863
Short-term investments1,331,662554(1,888)—1,332,996
Total$21,014,451$89,234$(1,648,287)$(41,355)$22,614,859
December 31, 2021
Fixed maturities:
Corporate bonds$6,553,333$104,170$(69,194)$(2,037)$6,520,394
Mortgage backed securities408,4772,825(5,410)(48)411,110
Municipal bonds404,66618,724(1,409)(2)387,353
Commercial mortgage backed securities1,046,4841,740(3,117)(6)1,047,867
U.S. government and government agencies4,772,76410,076(45,967)—4,808,655
Non-U.S. government securities2,120,29454,048(34,749)(82)2,101,077
Asset backed securities2,692,0916,540(11,108)(708)2,697,367
Total17,998,109198,123(170,954)(2,883)17,973,823
Short-term investments1,734,716568(590)—1,734,738
Total$19,732,825$198,691$(171,544)$(2,883)$19,708,561
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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

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 Months12 Months or MoreTotal
Estimated Fair ValueGross Unrealized LossesEstimated Fair ValueGross Unrealized LossesEstimated Fair ValueGross Unrealized Losses
December 31, 2022
Fixed maturities:
Corporate bonds$4,822,624$(393,112)$2,559,399$(388,241)$7,382,023$(781,353)
Mortgage backed securities545,844(51,673)154,154(34,914)699,998(86,587)
Municipal bonds363,936(29,924)16,282(3,436)380,218(33,360)
Commercial mortgage backed securities598,392(34,899)445,175(22,768)1,043,567(57,667)
U.S. government and government agencies3,556,676(197,259)1,442,542(145,704)4,999,218(342,963)
Non-U.S. government securities1,702,973(153,587)541,652(84,259)2,244,625(237,846)
Asset backed securities1,148,220(65,189)512,376(41,434)1,660,596(106,623)
Total12,738,665(925,643)5,671,580(720,756)18,410,245(1,646,399)
Short-term investments236,735(1,888)——236,735(1,888)
Total$12,975,400$(927,531)$5,671,580$(720,756)$18,646,980$(1,648,287)
December 31, 2021
Fixed maturities:
Corporate bonds$3,639,582$(63,938)$98,867$(5,256)$3,738,449$(69,194)
Mortgage backed securities222,176(3,545)46,809(1,865)268,985(5,410)
Municipal bonds26,665(385)16,361(1,024)43,026(1,409)
Commercial mortgage backed securities675,603(2,805)5,908(312)681,511(3,117)
U.S. government and government agencies4,211,621(44,180)33,373(1,787)4,244,994(45,967)
Non-U.S. government securities1,511,301(31,983)62,957(2,766)1,574,258(34,749)
Asset backed securities1,667,002(9,853)33,082(1,255)1,700,084(11,108)
Total11,953,950(156,689)297,357(14,265)12,251,307(170,954)
Short-term investments284,733(590)——284,733(590)
Total$12,238,683$(157,279)$297,357$(14,265)$12,536,040$(171,544)

At December 31, 2022, on a lot level basis, approximately 9,810 security lots out of a total of approximately 12,590 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 $7.2 million. The Company believes that such securities were temporarily impaired at December 31, 2022. At December 31, 2021, on a lot level basis, approximately 4,700 security lots out of a total of approximately 10,240 security lots were in an unrealized loss position and the largest single unrealized loss from a single lot in the Company’s fixed maturity portfolio was $1.1 million.

ARCH CAPITAL1372022 FORM 10-K

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

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

December 31, 2022December 31, 2021
MaturityEstimated Fair ValueAmortized CostEstimated Fair ValueAmortized Cost
Due in one year or less$510,669$536,962$300,889$299,772
Due after one year through five years11,014,75311,714,4278,355,2558,339,387
Due after five years through 10 years3,984,4974,527,4474,689,1554,684,393
Due after 10 years403,387479,546505,758493,927
15,913,30617,258,38213,851,05713,817,479
Mortgage backed securities795,391877,043408,477411,110
Commercial mortgage backed securities1,047,2751,107,7491,046,4841,047,867
Asset backed securities1,926,8172,038,6892,692,0912,697,367
Total$19,682,789$21,281,863$17,998,109$17,973,823

Equity Securities, at Fair Value

At December 31, 2022, the Company held $860.0 million of equity securities, at fair value, compared to $1.8 billion at December 31, 2021.

Net Investment Income

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

Year Ended December 31,
202220212020
Fixed maturities$468,659$330,061$412,481
Term loans2,03834,84384,149
Equity securities22,49742,39628,958
Short-term investments29,5196,92810,840
Other (1)44,60962,89572,395
Gross investment income567,322477,123608,823
Investment expenses(70,775)(88,005)(89,215)
Net investment income$496,547$389,118$519,608

(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,
202220212020
Available for sale securities:
Gross gains on investment sales$81,161$313,886$595,941
Gross losses on investment sales(317,150)(156,791)(117,282)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities(70,951)7,95315,881
Other investments(19,498)116,78113,656
Equity securities(4,520)13,02814,629
Short-term investments(3,012)6012,279
Equity securities, at fair value :
Net realized gains (losses) on securities sold74,922122,60626,849
Net unrealized gains (losses) on equity securities still held at reporting date(267,927)48,746102,394
Allowance for credit losses:
Investments related(43,909)(2,100)(3,597)
Underwriting related(13,274)1,062(10,007)
Net impairment losses——(533)
Derivative instruments (1)(75,023)(32,390)179,675
Other (2)(3,553)(53,537)3,575
Net realized gains (losses)$(662,734)$379,845$823,460

(1) See note 11, “Derivative Instruments” for information on the Company’s derivative instruments.

(2) 2021 period reflected $33.1 million of losses related to the Company’s

deconsolidation of Somers.

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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

Other Investments

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

December 31,
20222021
Fixed maturities$554,120$416,698
Other investments1,043,1841,432,553
Short-term investments33,10197,806
Equity securities13,79226,493
Total other investments$1,644,197$1,973,550

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

December 31,
20222021
Lending405,871536,345
Investment grade fixed income271,143147,810
Term loan investments163,941484,950
Private equity123,26691,126
Energy22,62781,692
Credit related funds56,33670,278
Infrastructure—20,352
Total$1,043,184$1,432,553

Investments Accounted For Using the Equity Method

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

December 31,
20222021
Credit related funds$1,135,818$1,022,334
Private equity916,534436,042
Real estate535,238396,395
Lending531,339376,649
Infrastructure245,246230,070
Equities169,156395,090
Fixed income130,062101,890
Energy110,917119,141
Total$3,774,310$3,077,611

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.

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 $115.9 million for 2022, compared to $366.4 million for 2021 and $146.7 million for 2020. In applying the equity method, investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the market value of the underlying securities in the funds).

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

December 31,
20222021
Invested assets$74,960,738$58,508,009
Total assets88,062,99169,648,905
Total liabilities27,553,30717,944,325
Net assets$60,509,684$51,704,580
Year Ended December 31,
202220212020
Total revenues$12,305,082$11,785,949$5,762,098
Total expenses5,374,0473,238,6061,656,029
Net income (loss)$6,931,035$8,547,343$4,106,069

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.

ARCH CAPITAL1392022 FORM 10-K

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

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 these limited partnership interests represented variable interests 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,
20222021
Investments accounted for using the equity method (1)$3,774,310$3,077,611
Investments accounted for using the fair value option (2)130,466170,595
Total$3,904,776$3,248,206

(1) Aggregate unfunded commitments were $2.6 billion at December 31, 2022, consistent with $2.6 billion at December 31, 2021.

(2) Aggregate unfunded commitments were $16.7 million at December 31, 2022, compared to $18.8 million at December 31, 2021.

Investments in Operating Affiliates

Investments in which the Company has significant influence over the operating and financial policies are classified as ‘investments in operating affiliates’ on the Company’s balance sheets and are accounted for under the equity method. Such investments primarily include the Company’s investment in Coface SA (“Coface”), Greysbridge and Premia. Investments in Coface and Premia are generally recorded on a three month lag, while the Company’s investment in Greysbridge is not recorded on a lag.

In 2021, the Company completed the share purchase agreement with Natixis to purchase 29.5% of the common

equity of Coface, a France-based leader in the global trade credit insurance market. The consideration paid was €9.95 per share, or an aggregate €453 million (approximately $546 million) including related fees. Income (loss) from operating affiliates reflected a one-time gain of $74.5 million realized from the acquisition. As a result of equity method accounting rules, approximately $36 million of additional gain was deferred and will generally be recognized over the next five years. As of December 31, 2022, the Company owned approximately 29.9% of the issued shares of Coface, or 30.1% excluding treasury shares, with a carrying value of $562.9 million, compared to $630.5 million at December 31, 2021.

In July 2021, the Company announced the completion of the previously disclosed acquisition of Somers by Greysbridge for a cash purchase price of $35.00 per common share.

Effective July 1, 2021, Somers is wholly owned by Greysbridge, and Greysbridge is owned 40% by the Company, 30% by certain investment funds managed by Kelso and 30% by certain investment funds managed by Warburg. At December 31, 2022 the Company’s carrying value in Greysbridge was $305.6 million, compared to $375.7 million at December 31, 2021. The Company’s carrying value in Greysbridge at December 31, 2021 reflected aggregate purchase price of $278.9 million along with income (loss) from operating affiliates, which included a one-time gain of $95.7 million recognized from the acquisition. In addition, the ‘net realized gains (losses)’ line on the Company’s consolidated statements of income included a $33.1 million loss as a result of deconsolidation of Somers in the Company’s financial statements following the close of the transaction. See note 12, “Variable Interest Entity and Noncontrolling Interests.”

The Company recorded income from operating affiliates of $73.9 million for 2022, compared to income of $264.7 million for 2021 and $16.8 million for 2020.

ARCH CAPITAL1402022 FORM 10-K

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

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, 2022Structured Securities (1)Municipal BondsNon-U.S. Government SecuritiesCorporate BondsTotal
Balance at beginning of period$802$2$82$1,997$2,883
Additions for current-period provision for expected credit losses14,1843591,61639,47755,636
Additions (reductions) for previously recognized expected credit losses(3,184)(261)275(8,619)(11,789)
Reductions due to disposals(2,379)—(91)(2,905)(5,375)
Balance at end of period$9,423$100$1,882$29,950$41,355
Year Ended December 31, 2021
Balance at beginning of period$1,490$11$—$896$2,397
Additions for current-period provision for expected credit losses602—822,8583,542
Additions (reductions) for previously recognized expected credit losses(847)(9)—(402)(1,258)
Reductions due to disposals (2)(443)——(1,355)(1,798)
Balance at end of period$802$2$82$1,997$2,883

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

(2) Reduction for the 2021 periods primarily related to the Company’s deconsolidation of Somers.

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,
20222021
Assets used for collateral or guarantees:
Affiliated transactions$4,254,398$4,223,955
Third party agreements2,632,8922,289,631
Deposits with U.S. regulatory authorities776,342798,100
Other (1)1,037,848938,046
Total restricted assets$8,701,480$8,249,732

(1) Primarily includes Funds at Lloyds, deposits with non-U.S. regulatory authorities and other restricted assets.

Reconciliation of Cash and Restricted Cash

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

December 31,
202220212020
Cash$855,118$858,668$906,448
Restricted cash (included in ‘other assets’)418,210456,103384,096
Cash and restricted cash$1,273,328$1,314,771$1,290,544
ARCH CAPITAL1412022 FORM 10-K

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

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).

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 $23.8 billion of financial assets and liabilities measured at fair value at December 31, 2022, approximately $12.6 million, or 0.1%, were priced using non-binding broker-dealer quotes. Of the $23.8 billion of financial assets and liabilities measured at fair value at December 31, 2021, approximately $7.7 million, or 0.0%, were priced using non-binding broker-dealer quotes.

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:

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U.S. government and government agencies – valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The Company determined that all U.S. Treasuries would be classified as Level 1 securities due to observed levels of trading activity, the high number of strongly correlated pricing quotes received on U.S. Treasuries and other factors. The fair values of U.S. government agency securities are generally determined using the spread above the risk-free yield curve. As the yields for the risk-free yield curve and the spreads for these securities are observable market inputs, the fair values of U.S. government agency securities are classified within Level 2.

Corporate bonds – valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined using the spread above the risk-free yield curve. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. As the significant inputs used in the pricing process for corporate bonds are observable market inputs, the fair value of these securities are classified within Level 2. A small number of securities are included in Level 3 due to 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.

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.

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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.

Short-term investments

The Company determined that certain of its short-term investments held in highly liquid money market-type funds, Treasury bills and commercial paper would be included in Level 1 as their fair values are based on quoted market prices in active markets. The fair values of other short-term investments are generally determined using the spread above the risk-free yield curve and are classified within Level 2.

Residential mortgage loans

The Company’s residential mortgage loans (included in ‘other assets’ in the consolidated balance sheets) include amounts related to the Company’s whole mortgage loan purchase and sell program. Fair values of residential mortgage loans are generally determined based on market prices. As significant inputs used in pricing process for these residential mortgage loans are observable market inputs, the fair value of these securities are classified within Level 2.

Other liabilities

The Company’s other liabilities include contingent and deferred consideration liabilities related to the Company’s acquisitions. Contingent consideration liabilities are remeasured at fair value at each balance sheet date with changes in fair value recognized in ‘net realized gains (losses)’. To determine the fair value of contingent consideration liabilities, the Company estimates the future payments using an income approach based on modeled inputs which include a weighted average cost of capital. Deferred consideration liabilities are measured at fair value on the transaction date. The Company determined that contingent and deferred consideration liabilities would be included within Level 3.

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The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2022:

Fair Value Measurement Using:
Estimated Fair ValueQuoted Prices in Active Markets for Identical Assets (Level 1)Significant Other Observable Inputs (Level 2)Significant Unobservable Inputs (Level 3)
Assets measured at fair value:
Available for sale securities:
Fixed maturities:
Corporate bonds$8,020,128$—$7,898,901$121,227
Mortgage backed securities795,391—795,391—
Municipal bonds419,166—419,166—
Commercial mortgage backed securities1,047,275—1,047,275—
U.S. government and government agencies5,161,1935,144,46716,726—
Non-U.S. government securities2,312,819—2,312,819—
Asset backed securities1,926,817—1,926,817—
Total19,682,7895,144,46714,417,095121,227
Short-term investments1,331,6621,197,304134,358—
Equity securities, at fair value859,969828,51328,0423,414
Derivative instruments (2)148,301—148,301—
Residential mortgage loans2,283—2,283—
Fair value option:
Corporate bonds542,755—542,755—
Non-U.S. government bonds4,315—4,315—
Asset backed securities1,652—1,652—
U.S. government and government agencies5,3985,398——
Short-term investments33,10169932,402—
Equity securities13,7929,619—4,173
Other investments196,215—162,95633,259
Other investments measured at net asset value (1)846,969
Total1,644,19715,716744,08037,432
Total assets measured at fair value$23,669,201$7,186,000$15,474,159$162,073
Liabilities measured at fair value:
Contingent consideration liabilities$(14,246)$—$—$(14,246)
Derivative instruments (2)(75,961)—(75,961)—
Total liabilities measured at fair value$(90,207)$—$(75,961)$(14,246)

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

(2) See note 11, “Derivative Instruments.”

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

Fair Value Measurement Using:
Estimated Fair ValueQuoted Prices in Active Markets for Identical Assets (Level 1)Significant Other Observable Inputs (Level 2)Significant Unobservable Inputs (Level 3)
Assets measured at fair value:
Available for sale securities:
Fixed maturities:
Corporate bonds$6,553,333$—$6,553,320$13
Mortgage backed securities408,477—408,477—
Municipal bonds404,666—404,666—
Commercial mortgage backed securities1,046,484—1,046,484—
U.S. government and government agencies4,772,7644,744,51728,247—
Non-U.S. government securities2,120,294—2,120,294—
Asset backed securities2,692,091—2,688,7443,347
Total17,998,1094,744,51713,250,2323,360
Equity securities, at fair value1,804,1701,762,86438,3882,918
Short-term investments1,734,7161,052,822681,894—
Derivative instruments (2)127,121—127,121—
Residential mortgage loans49,847—49,847—
Fair value option:
Corporate bonds388,546—388,546—
Non-U.S. government bonds23,785—23,785—
Asset backed securities4,367—4,367—
U.S. government and government agencies————
Short-term investments97,80652897,278—
Equity securities26,49321,745—4,748
Other investments310,79820,352262,46527,981
Other investments measured at net asset value (1)1,121,755
Total1,973,55042,625776,44132,729
Total assets measured at fair value$23,687,513$7,602,828$14,923,923$39,007
Liabilities measured at fair value:
Contingent consideration liabilities$(16,960)$—$—$(16,960)
Derivative instruments (2)(54,224)—(54,224)—
Total liabilities measured at fair value$(71,184)$—$(54,224)$(16,960)

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

(2) See note 11, “Derivative Instruments.”

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

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 2022 and 2021:

AssetsLiabilities
Available For SaleFair Value OptionFair Value
Structured Securities (1)Corporate BondsCorporate BondsOther InvestmentsEquity SecuritiesEquity SecuritiesOther Liabilities
Year Ended December 31, 2022
Balance at beginning of year$3,347$13$—$27,981$4,748$2,918$(16,960)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)(592)352—(781)(575)(470)(364)
Included in other comprehensive income(1)(1,095)————1,170
Purchases, issuances, sales and settlements
Purchases—150,013—12,381—969—
Issuances———————
Sales(2,051)(5,363)—(3,339)—(3)—
Settlements(703)(26,250)—(2,983)——1,908
Transfers in and/or out of Level 3—3,557—————
Balance at end of year$—$121,227$—$33,259$4,173$3,414$(14,246)
Year Ended December 31, 2021
Balance at beginning of year$3,426$13$985$67,103$68,988$42,015$(461)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)(135)—138684,9411,958—
Included in other comprehensive income133——————
Purchases, issuances, sales and settlements
Purchases———13,213—5,718(16,494)
Issuances———————
Sales (3)——(998)(53,203)(69,181)(46,773)—
Settlements(77)—————(5)
Transfers in and/or out of Level 3———————
Balance at end of year$3,347$13$—$27,981$4,748$2,918$(16,960)

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

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

(3) Sales for the 2021 period primarily relates to the Company’s deconsolidation of Somers.

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, 2022, due to their respective short maturities. As these financial instruments are not actively traded, their respective fair values are classified within Level 2.

At December 31, 2022, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.7 billion and had a fair value of $2.4 billion. At December 31, 2021, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.7 billion and had a fair value of $3.3 billion. The fair values of the senior notes were obtained

from a third party pricing service and are based on observable market inputs. As such, the fair 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:

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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, 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 annually 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 (1)Liability Derivatives (1)Notional Value (2)
December 31, 2022
Futures contracts$50,629$(16,963)$3,138,446
Foreign currency forward contracts38,891(35,446)1,136,126
Other58,781(23,552)3,591,793
Total$148,301$(75,961)
December 31, 2021
Futures contracts$34,999$(9,808)$2,826,564
Foreign currency forward contracts7,734(11,390)915,962
TBAs11,227—11,227
Other73,161(33,026)3,736,773
Total$127,121$(54,224)

(1) The fair value of asset derivatives are included in ‘other assets’ and the fair value of liability derivatives are included in ‘other liabilities.’

(2) Represents the absolute notional value of all outstanding contracts, consisting of long and short positions.

The Company did not hold any derivatives which were designated as hedging instruments at December 31, 2022 or 2021.

The Company’s derivative instruments can be traded under master netting agreements, which establish terms that apply to all derivative transactions with a counterparty. In the event of a bankruptcy or other stipulated event of default, such agreements provide that the non-defaulting party may elect to terminate all outstanding derivative transactions, in which case all individual derivative positions (loss or gain) with a counterparty are closed out and netted and replaced with a single amount, usually referred to as the termination amount, which is expressed in a single currency. The resulting single net amount, where positive, is payable to the party “in-the-money” regardless of whether or not it is the defaulting party, unless the parties have agreed that only the non-defaulting party is entitled to receive a termination payment where the net amount is positive and is in its favor.

At December 31, 2022, $147.4 million and $73.2 million, respectively, of asset derivatives and liability derivatives were subject to a master netting agreement compared to $122.3 million and $53.9 million, respectively, at December 31, 2021. The remaining derivatives included in the table above were not subject to a master netting agreement.

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

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 instrumentsYear Ended December 31,
202220212020
Net realized gains (losses):
Futures contracts$(86,634)$(15,262)$114,987
Foreign currency forward contracts6,144(39,755)49,974
TBAs(51)(233)1,129
Other5,51822,86013,585
Total$(75,023)$(32,390)$179,675

12. Variable Interest Entity and Noncontrolling Interests

Somers Holdings Ltd.

In March 2014, the Company invested $100.0 million and acquired 2,500,000 common shares of Somers. Somers was considered a VIE and the Company concluded that it was the primary beneficiary of Somers. In the 2020 fourth quarter, Arch Capital, Somers and Greysbridge, a wholly-owned subsidiary of Arch Capital, entered into an Agreement and Plan of Merger (as amended, the “Merger Agreement”). The merger and the related Greysbridge equity financing closed on July 1, 2021. Effective July 1, 2021, Somers is wholly owned by Greysbridge, and Greysbridge is owned 40% by the Company, 30% by certain investment funds managed by Kelso and 30% by certain investment funds managed by Warburg. Based on the governing documents of Greysbridge, the Company concluded that, while it retains significant influence over Somers, Somers no longer constitutes a variable interest entity. Accordingly, effective July 1, 2021, the Company no longer consolidates the results of Somers in its consolidated financial statements and footnotes. The Company classifies its investment as ‘investments in operating affiliates’ on the Company’s balance sheets and is accounted for under the equity method.

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

Year Ended December 31,
202220212020
Total cash provided by (used for):
Operating activities—46,991181,736
Investing activities—96,325258,589
Financing activities—(2,042)(335,776)

Non-redeemable noncontrolling interests

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

December 31,
20222021
Balance, beginning of year$—$823,007
Impact of deconsolidation of Somers—(918,874)
Additional paid in capital attributable to noncontrolling interests—22,113
Amounts attributable to noncontrolling interests—78,314
Other comprehensive (income) loss attributable to noncontrolling interests—(4,560)
Balance, end of year$—$—

Redeemable noncontrolling interests

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

December 31,
202220212020
Balance, beginning of year$9,233$58,548$55,404
Impact of deconsolidation of Somers—(48,919)—
Other1,596(396)3,144
Balance, end of year$10,829$9,233$58,548

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,
202220212020
Amounts attributable to non-redeemable noncontrolling interests$—$(78,314)$(53,076)
Amounts attributable to redeemable noncontrolling interests(5,490)(4,299)(7,114)
Net (income) loss attributable to noncontrolling interests$(5,490)$(82,613)$(60,190)
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Bellemeade Re

The Company has entered into aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda (the “Bellemeade Agreements”). At the time the Bellemeade Agreements were entered into, the applicability of the accounting guidance that addresses VIEs was evaluated. As a result of the evaluation of the Bellemeade Agreements, the Company concluded that these entities are VIEs. However, given that the ceding insurers do not have the unilateral power to direct those activities that are significant to their economic performance, the Company does not consolidate such entities in its consolidated financial statements.

The following table presents the total assets of the Bellemeade entities, as well as the Company’s maximum exposure to loss associated with these VIEs, calculated as the maximum historical observable spread between the benchmark index for each respective transaction and short term invested trust asset yields. The benchmark index for agreements effective prior to 2021 is based on one-month LIBOR, while the 2021 and later agreements benchmark index is based on the Secured Overnight Financing Rate (“SOFR”). SOFR is a measure of the cost of borrowing cash overnight, collateralized by U.S. Treasury securities, and is based on directly observable U.S. Treasury-backed repurchase transactions.

December 31, 2022December 31, 2021
Maximum Exposure to LossMaximum Exposure to Loss
Bellemeade Entities (Issue Date)Total VIE AssetsOn-Balance Sheet (Asset) LiabilityOff-Balance SheetTotalCoverage Remaining from Reinsurers (1)Total VIE AssetsOn-Balance Sheet (Asset) LiabilityOff-Balance SheetTotal
2017-1 Ltd. (Oct-17)$36,679$(6)$14$8$—$108,368$(159)$424$265
2018-1 Ltd. (Apr-18)89,698(153)508355—181,136(528)1,268740
2018-3 Ltd. (Oct-18)199,237(250)771521—302,563(1,018)2,4961,478
2019-1 Ltd. (Mar-19)107,880(48)593545—181,324(380)5,8075,427
2019-2 Ltd. (Apr-19)325,462(206)4,3564,150—398,316(515)3,9983,483
2019-3 Ltd. (Jul-19)222,977(104)1,2291,125—409,859(584)3,1902,606
2019-4 Ltd. (Oct-19)266,124(142)3,6403,498—411,954(462)4,7594,297
2020-2 Ltd. (Sep-20)105,110(8)492484—217,766(177)1,9841,807
2020-3 Ltd. (Nov-20)243,891532,8722,9257,079348,818(128)5,7935,665
2020-4 Ltd. (Dec-20)97,563326426744,165176,826(50)1,6301,580
2021-1 Ltd. (Mar-21)467,4692392,7432,98235,798568,986(303)3,2832,980
2021-2 Ltd. (Jun-21)458,3625812,8553,43677,099522,8072814,1244,405
2021-3 Ltd. (Sep-21)489,9272172,7042,921127,032507,873(411)3,4463,035
2022-1 Ltd. (Jan-22)283,5003991,7652,16433,260
2022-2 Ltd. (Sep-22)201,0051,1721,6162,788126,160
Total$3,594,884$1,776$26,800$28,576$410,593$4,336,596$(4,434)$42,202$37,768

(1) Coverage from a separate panel of reinsurers remaining at December 31, 2022.

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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 InvestmentsForeign Currency Translation AdjustmentsTotal
Year Ended December 31, 2022
Beginning balance$13,486$(78,086)$(64,600)
Other comprehensive income (loss) before reclassifications(1,772,649)(56,720)(1,829,369)
Amounts reclassified from accumulated other comprehensive income247,799—247,799
Net current period other comprehensive income (loss)(1,524,850)(56,720)(1,581,570)
Ending balance$(1,511,364)$(134,806)$(1,646,170)
Year Ended December 31, 2021
Beginning balance$501,295$(12,400)$488,895
Other comprehensive income (loss) before reclassifications(371,741)(65,686)(437,427)
Amounts reclassified from accumulated other comprehensive income(116,068)—(116,068)
Net current period other comprehensive income (loss)(487,809)(65,686)(553,495)
Ending balance$13,486$(78,086)$(64,600)
Year Ended December 31, 2020
Beginning balance$258,486$(46,395)$212,091
Other comprehensive income (loss) before reclassifications668,99633,995702,991
Amounts reclassified from accumulated other comprehensive income(426,187)—(426,187)
Net current period other comprehensive income (loss)242,80933,995276,804
Ending balance$501,295$(12,400)$488,895

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 IncomeAmounts Reclassified from AOCI
Details AboutLine Item That IncludesYear Ended December 31,
AOCI ComponentsReclassification202220212020
Unrealized appreciation on available-for-sale investments
Net realized gains (losses)$(235,989)$157,095$478,659
Provision for credit losses(43,909)(2,099)(3,597)
Other-than-temporary impairment losses——(533)
Total before tax(279,898)154,996474,529
Income tax (expense) benefit32,099(38,928)(48,342)
Net of tax$(247,799)$116,068$426,187
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Following are the related tax effects allocated to each component of other comprehensive income (loss):

Before TaxTax ExpenseNet of Tax
Amount(Benefit)Amount
Year Ended December 31, 2022
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period$(2,010,443)$(237,794)$(1,772,649)
Less reclassification of net realized gains (losses) included in net income(279,898)(32,099)(247,799)
Foreign currency translation adjustments(56,554)166(56,720)
Other comprehensive income (loss)$(1,787,099)$(205,529)$(1,581,570)
Year Ended December 31, 2021
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period$(406,774)$(19,845)$(386,929)
Less reclassification of net realized gains (losses) included in net income154,99638,928116,068
Foreign currency translation adjustments(64,423)59(64,482)
Other comprehensive income (loss)$(626,193)$(58,714)$(567,479)
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 income474,52948,342426,187
Foreign currency translation adjustments33,70637033,336
Other comprehensive income (loss)$313,749$27,883$285,866
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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,
202220212020
Numerator:
Net income$1,482,423$2,239,462$1,465,711
Amounts attributable to noncontrolling interests(5,490)(82,613)(60,190)
Net income available to Arch1,476,9332,156,8491,405,521
Preferred dividends(40,736)(48,343)(41,612)
Loss on redemption of preferred shares—(15,101)—
Net income available to Arch common shareholders$1,436,197$2,093,405$1,363,909
Denominator:
Weighted average common shares outstanding368,612,197391,748,715403,062,179
Effect of dilutive common share equivalents:
Nonvested restricted shares2,103,0361,996,5241,682,309
Stock options (1)6,894,5346,600,6975,514,967
Weighted average common shares and common share equivalents outstanding – diluted377,609,767400,345,936410,259,455
Earnings per common share:
Basic$3.90$5.34$3.38
Diluted$3.80$5.23$3.32

(1) Certain stock options were not included in the computation of diluted earnings per share where the exercise price of the stock options exceeded the average market price and would have been anti-dilutive or where, when applying the treasury stock method to in-the-money options, the sum of the proceeds, including unrecognized compensation, exceeded the average market price and would have been anti-dilutive. For 2022, 2021 and 2020, the number of stock options excluded were 798,053, 2,398,608 and 2,249,821, 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., or because a non-U.S. subsidiary has elected to be treated as a U.S. taxpayer. 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 successfully that Arch Capital, or its non-U.S. subsidiaries that do not elect to become U.S. taxpayers, 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

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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,
202220212020
Current expense (benefit):
United States$195,588$284,274$181,571
Non-U.S.5,62811,25916,091
201,216295,533197,662
Deferred expense (benefit):
United States(96,599)(123,261)(89,170)
Non-U.S.(24,656)(43,690)3,346
(121,255)(166,951)(85,824)
Income tax expense$79,961$128,582$111,838

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

Year Ended December 31,
202220212020
Income (Loss) Before Income Taxes:
Bermuda$985,828$1,518,616$1,114,117
United States400,865643,239409,893
Other175,691206,18753,539
Total$1,562,384$2,368,042$1,577,549

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 2022 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 (12.5%), Australia (30.0%), Hong Kong (16.5%) and the Netherlands (25.8%).

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,
202220212020
Expected income tax expense (benefit) computed on pre-tax income at weighted average income tax rate$110,337$158,269$111,947
Addition (reduction) in income tax expense (benefit) resulting from:
Investment income(12,762)(23,572)(1,824)
State taxes, net of U.S. federal tax benefit10,65020,9785,027
Dividend withholding taxes10,55912,2117,105
Change in valuation allowance(22,726)(40,425)13,190
Base eroding tax7,694——
Share based compensation(9,159)(5,339)(2,533)
Tax credits(9,736)——
Intercompany loan write-off(3,544)—(22,083)
Other(1,352)6,4601,009
Income tax expense (benefit)$79,961$128,582$111,838

The effect of a change in tax laws or rates on deferred tax 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,
20222021
Deferred income tax assets:
Net operating loss$76,665$87,960
Discounting of net loss reserves77,55672,001
Net unearned premium reserve96,58175,483
Compensation liabilities55,26928,062
Foreign tax credit carryforward16,73820,058
Bad debt reserves17,36510,252
Depreciation and amortization141,409115,041
Lease liability26,68121,453
Net unrealized decline of investments192,949—
Lloyds year of account deferral1,385—
Other, net14,450703
Deferred tax assets before valuation allowance717,048431,013
Valuation allowance(6,968)(43,953)
Deferred tax assets net of valuation allowance710,080387,060
Deferred income tax liabilities:
Deposit accounting liability(2,658)(1,578)
Goodwill and intangibles(38,905)(70,549)
Lloyds year of account deferral—(12,514)
Contingency reserve(43,870)(49,486)
Deferred policy acquisition costs(63,708)(25,612)
Investment related(9,225)(7,492)
Net unrealized appreciation of investments—(8,377)
Right-of-use asset(20,781)(17,406)
Total deferred tax liabilities(179,147)(193,014)
Net deferred income tax assets$530,933$194,046

The Company provides a valuation allowance to reduce the net value of certain deferred tax assets to an amount which management expects to more likely than not be realized. As of December 31, 2022, the Company’s valuation allowance was $7.0 million, compared to $44.0 million at December 31, 2021. The valuation allowance at December 31, 2022, was primarily attributable to valuation allowances on the Company’s Ireland and Hong Kong operations and certain other deferred tax assets relating to tax attributes that have a limited use.

At December 31, 2022, the Company’s net operating loss carryforwards and tax credits were as follows:

Year Ended December 31,
2022Expiration
Operating Loss Carryforwards
United Kingdom$198,571No expiration
Ireland61,685No expiration
Australia32,333No expiration
Hong Kong28,080No expiration
Netherlands60No expiration
United States (1)23,7662029 - 2038
Tax Credits
U.K. foreign tax credits13,907No expiration
U.S. foreign tax credits2,8302029 - 2032

(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 $7.0 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 $12.4 million at December 31, 2022, compared to $31.6 million at December 31, 2021.

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, 2022, 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,
20222021
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, its subsidiaries and branches file income tax returns in various federal, state and local jurisdictions. The following table details open tax years that are potentially subject to examination by local tax authorities, in the following major jurisdictions:

JurisdictionTax Years
United States2015-2022
United Kingdom2020-2022
Ireland2018-2022
Canada2018-2022
Switzerland2018-2022
Denmark2018-2022
Australia2018-2022

As of December 31, 2022, the Company’s current income tax payable (included in “Other liabilities”) was $40.6 million.

Inflation Reduction Act of 2022.

On August 16, 2022, the U.S. government enacted the Inflation Reduction Act of 2022, which among other things implements a 15% minimum tax on book income of certain large corporations, a 1% excise tax on net stock repurchases and several tax incentives to promote clean energy. The effective date of these provisions is January 1, 2023. Based on its current analysis of the provisions, the Company does not expect that this legislation will have a material effect on the Company’s consolidated financial statements.

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. During 2022, Arch Re Bermuda entered into certain reinsurance transactions with Premia which generated net premiums written and earned of $121.1 million and $119.9 million, respectively, compared to $40.4 million of net premiums written and earned in 2021. At December 31, 2022, Arch Re Bermuda recorded a funds held asset from Premia of $118.7 million, compared to $53.5 million at December 31, 2021.

In the 2021 first quarter, as part of the Company’s acquisition of Barbican, the Company entered into an agreement with Premia Managing Agency Limited for the reinsurance to close of Syndicate 1955’s 2018 underwriting year of account into Premia Syndicate 1884’s 2021 underwriting year of account. The reinsurance to close covers legacy business underwritten by Syndicate 1955 on the underwriting 2018 and prior years of account and under the agreement, approximately $380 million of net liabilities was transferred to Syndicate 1884, with an effective date of January 1, 2021. The Company had no reinsurance recoverable on unpaid and paid losses or funds held liability at December 31, 2022 and December 31, 2021.

In July 2021, following consummation of the Merger Agreement and the related Greysbridge equity financing, pursuant to which Somers became wholly owned by Greysbridge, and Greysbridge is owned 40% by the Company, 30% by certain funds managed by Kelso and 30% by certain funds managed by Warburg. During the 2022 and 2021 period, the Company entered into certain reinsurance transactions with Somers. The Company’s net premiums written was reduced by $519.4 million and $379.1 million, for the 2022 and 2021 periods, respectively (which included reinsurance transactions as well as those entered into in conjunction with the Merger Agreement). In addition, Somers paid certain acquisition costs and administrative fees to the Company. At December 31, 2022, the Company recorded a reinsurance recoverable on unpaid and paid losses from Somers of $1.2 billion and a reinsurance balance payable to Somers of $413.8 million. At December 31, 2021,

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reinsurance recoverable on unpaid and paid losses from Somers was $902.8 million, with a reinsurance balance payable to Somers of $258.4 million. See note 12, “Variable Interest Entity and Noncontrolling Interests.”

The Company has a put/call option that was entered into in connection with the Greysbridge equity financing, whereby beginning January 1, 2024 the Company will have a call right (but not the obligation) and Warburg and Kelso will each have a put right (but not the obligation) to buy/sell one third of their initial shares annually at the tangible book value per share of Greysbridge for the most recently ended fiscal quarter.

As of December 31, 2022, the Company owns $35.0 million in aggregate principal amount of Somers 6.5% senior notes, due July 2, 2029.

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,
20222021
Operating lease costs$33,571$31,691
Sublease income (1)$(988)$—
Cash payments included in the measurement of lease liabilities reported in operating cash flows$26,051$32,094
Right-of-use assets obtained in exchange for new lease liabilities$42,841$22,686
Right-of-use assets (2)$123,083$106,836
Operating lease liability (2)$151,890$126,711
Weighted average discount rate4.2%3.9%
Weighted average remaining lease term6.6 years5.9 years

(1) The sublease income primarily relates to office property in Raleigh, North Carolina.

(2) 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, 2022:

Years Ending December 31,
2023$31,861
202430,091
202524,651
202621,939
202717,859
2028 and thereafter48,522
Total undiscounted lease liability$174,923
Less: present value adjustment(23,033)
Operating lease liability$151,890

Rental expense was approximately $38.9 million, $39.1 million and $37.4 million for 2022, 2021 and 2020, respectively.

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

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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 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:

BrokerYear Ended December 31,
202220212020
Marsh & McLennan Companies and its subsidiaries17.3%18.3%13.3%
Aon Corporation and its subsidiaries13.8%12.2%12.0%

No other broker and no one insured or reinsured accounted for more than 10% of gross premiums written for 2022, 2021 and 2020.

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, 2022 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 $2.9 billion and $3.0 billion at December 31, 2022 and 2021, 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 $150.1 million and $114.1 million at December 31, 2022 and 2021, respectively.

Employment and Other Arrangements

At December 31, 2022, 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, 2022 and 2021 were as follows:

Carrying Amount at
InterestPrincipalDecember 31,
(Fixed)Amount20222021
2034 notes (1)7.350%300,000297,618297,488
2043 notes (2)5.144%500,000495,188495,063
2026 notes (3)4.011%500,000498,073497,633
2046 notes (4)5.031%450,000445,582445,490
2050 notes (5)3.635%1,000,000988,949988,720
$2,750,000$2,725,410$2,724,394

(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 (“2050 notes”).

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.

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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.

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.

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 on June 30 and December 30 of each year. Arch Capital may redeem the 2050 notes at any time and from time to time, in whole or in part, at a “make-whole” redemption price.

Letter of Credit and Revolving Credit Facilities

In the normal course of its operations, the Company enters into agreements with financial institutions to obtain secured and unsecured credit facilities. On April 7, 2022, Arch Capital and certain of its subsidiaries amended its existing credit agreement into a $925.0 million facility (the “Credit Facility”) with a syndication of lenders. The Credit Facility, as amended, consists of a $425.0 million secured facility for letters of credit (the “Secured Facility”) and a $500.0 million unsecured facility for revolving loans and letters of credit (the “Unsecured Facility”). Obligations of each borrower under the Secured Facility for letters of credit are secured by cash and eligible securities of such borrower held in collateral accounts. Commitments under the Credit Facility may be increased up to, but not exceeding, an aggregate of $1.25 billion. Arch Capital has a one-time option to convert

any or all outstanding revolving loans of Arch Capital and/or Arch-U.S. to term loans with the same terms as the revolving loans except that any prepayments may not be re-borrowed. Arch-U.S. guarantees the obligations of Arch Capital, and Arch Capital guarantees the obligations of Arch-U.S. Borrowings of revolving loans may be made at a variable rate based on SOFR. Secured letters of credit are available for issuance on behalf of certain Arch Capital subsidiaries. At December 31, 2022, the Secured Facility had $323.1 million of letters of credit outstanding and remaining capacity of $101.9 million, and the Unsecured Facility had no outstanding revolving loans or letters of credit, with remaining capacity of $500.0 million.

The Credit Facility contains certain restrictive and maintenance covenants customary for facilities of this type, including restrictions on indebtedness, minimum consolidated tangible net worth, maximum leverage 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, 2022.

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.

In addition, certain of Arch Capital’s subsidiaries had outstanding secured and unsecured letters of credit through other facilities of $24.6 million and $400.0 million respectively, which were issued in the normal course of business (“LOC Facilities”). The principal purpose of the LOC Facilities is to issue, as required, evergreen standby letters of credit in favor of primary insurance or reinsurance counterparties with which certain of Arch Capital’s subsidiaries has entered into reinsurance arrangements. This is required to ensure that such counterparties are permitted to take credit for reinsurance obtained in United States jurisdictions where such subsidiaries are not licensed or otherwise admitted as an insurer, as required under insurance regulations in the United States, and to comply with requirements of Lloyd’s of London in connection with qualifying quota share and other arrangements. The amount of letters of credit issued is driven by, among other things, the timing and payment of catastrophe losses, loss development of existing reserves, the payment pattern of such reserves, the further expansion of business and the loss experience of such business.

When issued, all secured letters of credit are secured by a portion of the investment portfolio. At December 31, 2022, these letters of credit were secured by investments with a fair value of $465.2 million. The Company had no outstanding revolving credit agreement borrowings at December 31, 2022 and 2021.

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

Federal Home Loan Bank Membership

Certain subsidiaries of the Company are members of Federal Home Loan Banks (“FHLBs”). Members may borrow from the FHLBs at competitive rates subject to certain conditions. Conditions include maintaining sufficient collateral deposits for funding and a requirement to hold stock in the FHLBs related to both membership and outstanding advances. At December 31, 2022 the Company had no advances outstanding under the FHLB program, compared to $80.0 million of advances outstanding under the FHLB program, which was secured by investments with a fair value of $80.2 million at December 31, 2021. Advances outstanding under the FHLB program are included in ‘other liabilities’ on the Company’s balance sheet.

20. Goodwill and Intangible Assets

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

GoodwillIntangible assets (indefinite life)Intangible assets (finite life)Total
Net balance at Dec. 31, 2020$314,629$79,219$299,015$692,863
Acquisitions (1)31,677—318,459350,136
Amortization——(82,955)(82,955)
Impact of deconsolidation of Somers (2)—(7,650)—(7,650)
Foreign currency movements and other adjustments(1,441)(212)(5,758)(7,411)
Net balance at Dec. 31, 2021344,86571,357528,761944,983
Acquisitions (1)8,389——8,389
Amortization——(106,200)(106,200)
Foreign currency movements and other adjustments(11,181)(2,576)(29,126)(42,883)
Net balance at Dec. 31, 2022$342,073$68,781$393,435$804,289
Gross balance at Dec. 31, 2022$351,231$70,246$1,102,298$1,523,775
Accumulated amortization——(678,020)(678,020)
Foreign currency movements and other adjustments(9,158)(1,465)(30,843)(41,466)
Net balance at Dec. 31, 2022$342,073$68,781$393,435$804,289

(1) See note 2, “Acquisitions.”

(2) See note 12, “Variable Interest Entity and Noncontrolling Interests.”

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

Gross BalanceAccumulated AmortizationForeign Currency Translation Adjustment and OtherNet Balance
Dec. 31, 2022
Acquired insurance contracts$451,505$(426,202)$339$25,642
Operating platform52,674(50,302)22,374
Distribution relationships602,518(207,908)(31,110)363,500
Goodwill351,231—(9,158)342,073
Insurance licenses48,331——48,331
Syndicate capacity21,915—(1,465)20,450
Unfavorable service contract(9,533)9,533——
Other5,134(3,141)(74)1,919
Total$1,523,775$(678,020)$(41,466)$804,289
Dec. 31, 2021
Acquired insurance contracts$451,505$(409,592)$339$42,252
Operating platform52,674(48,838)563,892
Distribution relationships602,518(120,302)(2,207)480,009
Goodwill342,842—2,023344,865
Insurance licenses48,331——48,331
Syndicate capacity21,915—1,11123,026
Unfavorable service contract(9,533)9,435—(98)
Other5,134(2,542)1142,706
Total$1,515,386$(571,839)$1,436$944,983

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

2023$91,605
202473,366
202541,060
202632,091
202729,268
2028 and thereafter126,045
Total$393,435

The estimated remaining useful lives of these assets range from one to fourteen years at December 31, 2022.

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

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,
202220212020
Common Shares:
Shares issued and outstanding, beginning of year583,289,850579,000,841574,617,195
Shares issued (1)3,517,3992,669,2292,646,164
Restricted shares issued, net of cancellations1,443,5131,619,7801,737,482
Shares issued and outstanding, end of year588,250,762583,289,850579,000,841
Common shares in treasury, end of year(217,904,765)(204,365,956)(172,280,199)
Shares issued and outstanding, end of year370,345,997378,923,894406,720,642

(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.

Share Repurchase Program

The Board of Directors of Arch Capital (the “Board”) has authorized the investment in Arch Capital’s common shares through a share repurchase program. At December 31, 2022, $1.0 billion 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, 2024. 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.

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, 2022, Arch Capital held 217.9 million shares for an aggregate cost of $4.4 billion in treasury, at cost.

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

Year Ended December 31,
202220212020
Aggregate cost of shares repurchased$585,823$1,234,294$83,472
Shares repurchased12,891,40531,486,8302,850,102
Average price per share repurchased$45.44$39.20$29.29

Since the inception of the share repurchase program through December 31, 2022, Arch Capital has repurchased approximately 433.6 million common shares for an aggregate purchase price of $5.9 billion.

Series G Preferred Shares

In June 2021, Arch Capital completed a $500 million underwritten public offering of 20.0 million depositary shares

(the “Depositary Shares”), each of which represents a 1/1,000th interest in a share of its 4.55% Non-Cumulative Preferred Shares, Series G, $0.01 par value and $25,000 liquidation preference per share (equivalent to $25 liquidation preference per Depositary Share) (the “Series G Preferred Shares”). Each Depositary Share, evidenced by a depositary receipt, entitles the holder, through the depositary,

to a proportional fractional interest in all rights and preferences of the Series G Preferred Shares represented thereby (including any dividend, liquidation, redemption and voting rights).

Holders of Series G Preferred Shares will be entitled to receive dividend payments only when, as and if declared by the Board or a duly authorized committee of the Board. Any such dividends will be payable from, and including, the date of original issue on a noncumulative basis, quarterly in arrears on the last day of March, June, September and December of each year, at an annual rate of 4.55%. Dividends on the Series G Preferred Shares are not cumulative. The Company will be restricted from paying dividends on or repurchasing its common shares unless certain dividend payments are made on the Series G Preferred Shares. The Company may not declare or pay a dividend on the Series G Preferred Shares under certain circumstances, including if the Company is or, after giving effect to such payment, would be in breach of applicable individual or group solvency and liquidity requirements or applicable individual or group enhanced capital requirements (“ECR”). The Series G Preferred Shares may not be redeemed at any time if the ECR would be breached immediately before or after giving effect to such redemption, unless the Company replaces the capital represented by preference shares to be redeemed with capital having equal or better capital treatment.

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Except in specified circumstances relating to certain tax or corporate events, the Series G Preferred Shares are not redeemable prior to June 11, 2026. On and after that date, the

Series G Preferred Shares will be redeemable at the Company’s option, in whole or in part, at a redemption price of $25,000 per share of the Series G Preferred Shares (equivalent to $25 per depositary share), plus any declared and unpaid dividends, without accumulation of any undeclared dividends to, but excluding, the redemption date. The Depositary Shares will be redeemed if and to the extent the related Series G Preferred Shares are redeemed by the Company. Neither the Depositary Shares nor the Series G Preferred Shares have a stated maturity, nor will they be subject to any sinking fund or mandatory redemption. The Series G Preferred Shares are not convertible into any other securities. The Series G Preferred Shares do not have voting rights, except under limited circumstances. The net proceeds from the Series G Preferred Share offerings were used to redeem the Company’s outstanding 5.25% Series E Non-Cumulative Preferred Shares.

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 the Board 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 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

In September, 2021, Arch Capital redeemed all outstanding 5.25% Series E 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 2022 Long-Term Incentive and Share Award Plan (“the 2022 Plan”) became effective as of May 4, 2022 following approval by shareholders of the Company. The 2022 Plan provides for the issuance of stock options, stock appreciation rights, restricted shares, restricted share units payable in common shares or cash, dividend equivalents, performance shares and performance units and other share-based awards to Arch Capital’s eligible employees and directors. The number of common shares reserved for grants under the 2022 Plan, subject to anti-dilution adjustments in the event of certain changes in Arch Capital’s capital structure, is 9,000,000; provided that no more than 6,000,000 common

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shares may be issued as incentive stock options under Section 422 of the Code. The 2022 Plan will terminate as to future awards on February 25, 2032. At December 31, 2022, 9,000,000 shares are available for future issuance.

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, 2022, 4,577,991 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, 2022, 504,872 shares are available for future issuance.

Upon shareholder approval on May 6, 2016, the Amended and Restated Arch Capital Group Ltd. 2007 Employee Share 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, 2022, 1,041,837 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,
202220212020
Dividend yield—%—%—%
Expected volatility24.0%24.2%16.6%
Risk free interest rate2.0%1.0%1.2%
Expected option life6.0 years6.0 years6.0 years

A summary of stock option and SAR activity under the Company’s Long Term Incentive and Share Award Plans during 2022 is presented below:

Year Ended December 31, 2022
Number of Options / SARsWeighted Average Exercise PriceWeighted Average Contractual TermAggregate Intrinsic Value
Outstanding, beginning of year17,083,160$25.06
Granted784,963$47.46
Exercised(3,412,371)$16.91
Forfeited or expired(34,851)$39.96
Outstanding, end of year14,420,901$28.174.37$499,051
Exercisable, end of year12,433,470$26.203.77$454,769

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 2022, the Company received proceeds of $17.2 million from the exercise of stock options and recognized a tax benefit of $8.7 million from the exercise of stock options and SARs.

Year Ended December 31,
202220212020
Weighted average grant date fair value$13.26$9.22$8.14
Aggregate intrinsic value of Options/SARs exercised$113,409$47,074$59,723
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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 2022 is presented below:

Restricted Common SharesRestricted Unit Awards
Unvested Shares:
Unvested balance, beginning of year2,070,837699,866
Granted914,694174,699
Vested(744,096)(330,144)
Forfeited(75,881)(27,128)
Unvested balance, end of year2,165,554517,293
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year$36.35$33.29
Granted$47.45$47.50
Vested$38.21$34.38
Forfeited$41.13$37.51
Unvested balance, end of year$40.23$37.17

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,
202220212020
Restricted shares and restricted unit awards granted1,089,3931,261,7731,535,330
Weighted average grant date fair value$47.45$36.12$37.55
Aggregate fair value of vested restricted share and unit awards$78,129$65,477$39,703

The aggregate intrinsic value of restricted units outstanding at December 31, 2022 was $32.5 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, and can vary between 0% and 200%. 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,
202220212020
Expected volatility38.1%37.5%18.1%
Risk free interest rate1.7%0.3%1.1%
Performance SharesPerformance Units
Unvested Shares:
Unvested balance, beginning of year1,861,76029,770
Granted669,74221,030
Performance adjustment (1) (2)(54,904)8,921
Vested(583,544)(19,695)
Forfeited(10,138)(316)
Unvested balance, end of year1,882,91639,710
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year$38.93$38.71
Granted$49.91$49.91
Performance adjustment (1) (2)$36.07$35.83
Vested$36.07$35.83
Forfeited$49.91$49.91
Unvested balance, end of year$43.75$45.33

(1) The performance adjustment represents the difference between the number of performance shares granted and earned, which vested following the end of the performance period. The performance shares were granted at the maximum level of achievement.

(2) The performance adjustment represents the change in PSUs, which vested following the end of the performance period. The performance units were granted at the target level of achievement.

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

Year Ended December 31,
202220212020
Performance awards690,772685,104557,204
Weighted average grant date fair value$49.91$37.38$44.17

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,
202220212020
Pre-Tax
Stock options and SARs$11,891$12,316$11,744
Restricted share and unit awards50,27846,81741,284
Performance awards21,51023,69614,729
ESPP3,9933,7512,135
Total$87,672$86,580$69,892
After-Tax
Stock options and SARs$10,726$10,927$10,388
Restricted share and unit awards42,34639,34934,599
Performance awards19,79421,92013,380
ESPP3,6603,4711,978
Total$76,526$75,667$60,345
December 31, 2022
Stock Options and SARsRestricted Common Shares and UnitsPerformance Common Shares and Units
Unrecognized compensation cost related to unvested awards$6,357$42,096$7,520
Weighted average recognition period (years)0.751.000.48

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 2022, 2021 and 2020, the Company expensed $67.0 million, $60.4 million and $52.0 million, respectively, related to these retirement plans.

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, 2022, the Company was not a party to any litigation or arbitration which is expected by management to have a material adverse effect on the Company’s results of operations and financial condition and liquidity.

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, 2022 and 2021:

December 31,
20222021
Actual capital and surplus (1):
Bermuda$19,546,128$17,528,510
Ireland968,443958,200
United States6,194,9545,600,652
United Kingdom1,018,092902,002
Canada68,63770,063
Australia284,998283,693
Required capital and surplus:
Bermuda$6,449,878$5,661,301
Ireland815,194794,933
United States1,748,5431,717,646
United Kingdom543,104563,164
Canada47,82542,513
Australia175,885214,022

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

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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 2022, 2021 and 2020 was as follows:

Year Ended December 31,
202220212020
Statutory net income (loss):
Bermuda$1,729,925$2,370,746$1,579,889
Ireland(52,757)25,19118,397
United States219,524345,790143,271
United Kingdom56,81835,2864,078
Canada9,2156,985(1,049)
Australia38,53811,874(8,601)

Bermuda

The Company’s Bermuda insurance and reinsurance subsidiaries are subject to the Bermuda Insurance Act 1978 and related regulations, each as amended (the “Insurance Act”). Arch Re Bermuda, the Company’s principal reinsurance and insurance subsidiary, is registered as a Class 4 insurer and long-term insurer while Arch Group Reinsurance Ltd. (“AGRL”) is registered as a Class 3A general business insurer and provides affiliated quota share reinsurance covering certain U.S. business. The Insurance Act requires that both entities maintain minimum statutory capital and surplus equal to the greater of a minimum solvency margin and the enhanced capital requirement (“ECR”) as determined by the Bermuda Monetary Authority (“BMA”). The ECR 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, 2022 and 2021, the actual and required capital and surplus were based on the economic balance sheet requirements.

Under the Insurance Act, Arch Re Bermuda and AGRL are restricted with respect to the payment of dividends. Each entity 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 $3.7 billion to Arch Capital during 2023 without providing an affidavit to the BMA. Dividends or distributions, if any, made by AGRL would result in an increase in available capital at Arch-U.S.

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 plan, Arch Insurance (EU) received approval from the Central Bank of Ireland (“CBI”) 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 CBI and must comply with Irish insurance acts and regulations as well as with directions and guidance issued by the CBI. Arch Re Europe and Arch Insurance (EU) are required to maintain a minimum level of capital. At December 31, 2022 and 2021, 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.

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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 $255.4 million of dividends during 2023 subject to the approval of the Commissioner of the Delaware Department of Insurance.

AMIC and UGRIC are approved as eligible mortgage insurers by Fannie Mae and Freddie Mac, subject to maintaining certain requirements (“eligible mortgage insurers”). In April 2015, the GSEs published their original comprehensive, requirements, known as the Private Mortgage Insurer Eligibility Requirements or “PMIERs.” Revised and restated in September 2018, and clarified thereafter by the Guidance Letters 2020-1 and 2021-1 issued by the GSEs in 2020 and 2021, respectively, the PMIERs apply to the Company’s eligible mortgage insurers, but do not apply to AMG, which is not GSE-approved.

The amount of assets required to satisfy the revised financial requirements of the PMIERs may be affected by many factors, including macro-economic conditions, the size and composition of our mortgage insurance portfolio, 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 regulation by their domiciliary and primary regulators, the Wisconsin Office of the Commissioner of Insurance (“Wisconsin OCI”) for AMIC and AMG, the North Carolina Department of Insurance (“NC DOI”) for UGRIC, 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. Each company is subject to the statutory requirements of their domiciliary regulator as to payment of dividends and return of capital; the GSEs may also impart limitations on the Company’s eligible mortgage insurers, such as required minimum assets. Under respective state law, the Company’s U.S. mortgage subsidiaries can declare a maximum of approximately $156.5 million of ordinary dividends in 2023, however, dividend capacity is limited by the respective companies unassigned surplus amounts. Such dividends would increase the available capital at Arch U.S. MI Holdings Inc., a subsidiary of Arch-U.S.

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.

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 require mortgage insurers to maintain a “minimum policyholder position” calculated in accordance with their respective regulations. Policyholders' position consists primarily of statutory policyholders' surplus plus the contingency loss reserves.

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. In May 2004, Arch Insurance (U.K.) was granted the relevant permissions for the classes of insurance business which it underwrites in the U.K. AMAL currently manages Arch Syndicate 2012 and Arch Syndicate 1955 pursuant to its authorizations by the U.K. regulators and Lloyd’s. All U.K. companies are also subject to a range of statutory provisions, including the laws and regulations of the Companies Act 2006 (as amended) (the “U.K. Companies Act”).

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, 2022 and 2021, these requirements were met.

As corporate members of Lloyd’s, AMAL (as managing agent of the Company’s Lloyd’s Syndicates) 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 and letters of credit 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

ARCH CAPITAL1672022 FORM 10-K

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

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. Under the Insurance Companies Act (Canada), approval of the Minister of Finance (Canada) is required in connection with certain acquisitions of shares of, or control of, Canadian insurance companies such as Arch Insurance Canada, and notice to and/or approval of OSFI is required in connection with the payment of dividends by or redemption of shares by Canadian insurance companies such as Arch Insurance Canada.

Australia

The Australian Prudential Regulation Authority (“APRA”) is an independent statutory authority responsible for prudential supervision of institutions across banking, insurance and superannuation and promotes financial stability in Australia. Arch Indemnity has been authorized to conduct monoline lenders’ mortgage insurance business in Australia since June 2002 and was acquired by Arch Capital on August 30, 2021 and since that date is the primary provider of lenders’ mortgage insurance for the group. Arch Indemnity has also been licensed by the Australian Securities and Investments Commission (“ASIC”) since March 2011 to engage in credit activities in Australia. Arch LMI Pty Ltd. (“Arch LMI”) was formerly authorized by APRA in January 2019 to conduct monoline lenders’ mortgage insurance business in Australia; however, in December 2022, we converted Arch LMI to a services company for our Australian lenders mortgage insurance operations and the company relinquished its APRA authorization. Major regulatory requirements that are applicable to Arch Indemnity in general as an insurance provider and financial institution in Australia include requirements and compliance with minimum capital levels; risk management strategy; corporate governance standards, privacy legislation on the collection, use and storage of personal information; cyber security obligations imposed by APRA and ASIC; modern slavery legislation; anti-money laundering and counter-terrorism legislation. At December 31, 2022 and 2021, these requirements were met.

Arch Capital also conducts property and casualty insurance business in Australia through the Company’s Lloyd’s platform. This insurance business is managed by and distributed through local coverholders and is subject to Lloyd’s Supervision. In addition, the business is subject to local Australian prudential regulatory oversight by APRA, and additional separate financial services market conduct regulation by the Australian Securities and Investments Commission.

ARCH CAPITAL1682022 FORM 10-K

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