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UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
WASHINGTON, D.C. 20549
 
FORM 10-Q
QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934
For the quarterly period ended March 31, 2022
Or
TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934
Commission file number: 001-16209

 acgl-20220331_g1.jpg
ARCH CAPITAL GROUP LTD.
(Exact name of registrant as specified in its charter)
Bermuda 98-0374481
(State or other jurisdiction of incorporation or organization) (I.R.S. Employer Identification No.)
Waterloo House, Ground Floor
100 Pitts Bay Road, Pembroke HM 08, Bermuda (441) 278-9250
(Address of principal executive offices) (Registrant’s telephone number, including area code)

Securities registered pursuant to Section 12(b) of the Exchange Act:
Title of each class Trading Symbol (s) Name of each exchange on which registered
Common shares, $0.0011 par value per share ACGL NASDAQ  Stock Market
Depositary shares, each representing a 1/1000th interest in a 5.45% Series F preferred share
ACGLO
NASDAQ  Stock Market
Depositary shares, each representing a 1/1000th interest in a 4.55% Series G preferred share
ACGLN
NASDAQ Stock Market
Indicate by check mark whether the registrant (1) has filed all reports required to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during the preceding 12 months (or for such shorter period that the registrant was required to file such reports), and (2) has been subject to such filing requirements for the past 90 days. Yes No
Indicate by check mark whether the registrant has submitted electronically every Interactive Data File required to be submitted pursuant to Rule 405 of Regulation S-T (§232.405 of this chapter) during the preceding 12 months (or for such shorter period that the registrant was required to submit such files). Yes No
Indicate by check mark whether the registrant is a large accelerated filer, an accelerated filer, a non-accelerated filer, a smaller reporting company, or an emerging growth company. See the definitions of “large accelerated filer,” “accelerated filer,” “smaller reporting company,” and “emerging growth company” in Rule 12b-2 of the Exchange Act.
Large Accelerated Filer Accelerated Filer Non-accelerated Filer Smaller reporting company Emerging growth company
If an emerging growth company, indicate by check mark if the Registrant has elected not to use the extended transition period for complying with any new or revised financial accounting standards provided pursuant to Section 13(a) of the Exchange Act.
Indicate by check mark whether the Registrant is a shell company (as defined in Rule 12b-2 of the Exchange Act). Yes No

As of May 2, 2022, there were 375,651,595 common shares, $0.0011 par value per share, of the registrant outstanding.


ARCH CAPITAL GROUP LTD.
 
INDEX TO FORM 10-Q
 
ARCH CAPITAL
 1
2022 FIRST QUARTER FORM 10-Q

PART I. FINANCIAL INFORMATION
Cautionary Note Regarding Forward-Looking Statements 
The Private Securities Litigation Reform Act of 1995 (“PSLRA”) provides a “safe harbor” for forward-looking statements. This report or any other written or oral statements made by or on behalf of us may include forward-looking statements, which reflect our current views with respect to future events and financial performance. All statements other than statements of historical fact included in or incorporated by reference in this report are forward-looking statements. Forward-looking statements, for purposes of the PSLRA or otherwise, can generally be identified by the use of forward-looking terminology such as “may,” “will,” “expect,” “intend,” “estimate,” “anticipate,” “believe” or “continue” and similar statements of a future or forward-looking nature or their negative or variations or similar terminology.
Forward-looking statements involve our current assessment of risks and uncertainties. Actual events and results may differ materially from those expressed or implied in these statements. Important factors that could cause actual events or results to differ materially from those indicated in such statements are discussed below and elsewhere in this report and in our periodic reports filed with the Securities and Exchange Commission (the “SEC”), and include:
our ability to successfully implement our business strategy during “soft” as well as “hard” markets;
acceptance of our business strategy, security and financial condition by rating agencies and regulators, as well as by brokers and our insureds and reinsureds;
our ability to consummate acquisitions and integrate the business we have acquired or may acquire into our existing operations;
our ability to maintain or improve our ratings, which may be affected by our ability to raise additional equity or debt financings, by ratings agencies’ existing or new policies and practices, as well as other factors described herein;
general economic and market conditions (including inflation, interest rates, unemployment, housing prices, foreign currency exchange rates, prevailing credit terms and the depth and duration of a recession, including those resulting from COVID-19) and conditions specific to the reinsurance and insurance markets in which we operate;
competition, including increased competition, on the basis of pricing, capacity (including alternative sources of capital), coverage terms, or other factors;
developments in the world’s financial and capital markets and our access to such markets;
our ability to successfully enhance, integrate and maintain operating procedures (including information technology) to effectively support our current and new business;
the loss and addition of key personnel;
material differences between actual and expected assessments for guaranty funds and mandatory pooling arrangements;
accuracy of those estimates and judgments utilized in the preparation of our financial statements, including those related to revenue recognition, insurance and other reserves, reinsurance recoverables, investment valuations, intangible assets, bad debts, income taxes, contingencies and litigation, and any determination to use the deposit method of accounting;
greater than expected loss ratios on business written by us and adverse development on claim and/or claim expense liabilities related to business written by our insurance and reinsurance subsidiaries;
the adequacy of the Company’s loss reserves;
severity and/or frequency of losses;
greater frequency or severity of unpredictable natural and man-made catastrophic events;
claims for natural or man-made catastrophic events or severe economic events in our insurance, reinsurance and mortgage businesses could cause large losses and substantial volatility in our results of operations;
the effect of climate change on our business;
the effect of contagious disease (including COVID-19) on our business;
acts of terrorism, political unrest and other hostilities or other unforecasted and unpredictable events;
ARCH CAPITAL
 2
2022 FIRST QUARTER FORM 10-Q

availability to us of reinsurance to manage our gross and net exposures and the cost of such reinsurance;
the failure of reinsurers, managing general agents, third party administrators or others to meet their obligations to us;
the timing of loss payments being faster or the receipt of reinsurance recoverables being slower than anticipated by us;
our investment performance, including legislative or regulatory developments that may adversely affect the fair value of our investments;
changes in general economic conditions, including sovereign debt concerns or downgrades of U.S. securities by credit rating agencies, which could affect our business, financial condition and results of operations;
changes in the method for determining the London Inter-bank Offered Rate (“LIBOR”) and the replacement of LIBOR with alternative benchmark rates;
the volatility of our shareholders’ equity from foreign currency fluctuations, which could increase due to us not matching portions of our projected liabilities in foreign currencies with investments in the same currencies;
changes in accounting principles or policies or in our application of such accounting principles or policies;
changes in the political environment of certain countries in which we operate or underwrite business;
a disruption caused by cyber-attacks or other technology breaches or failures on us or our business partners and service providers, which could negatively impact our business and/or expose us to litigation;
statutory or regulatory developments, including as to tax matters and insurance and other regulatory matters such as the adoption of proposed legislation that would affect Bermuda-headquartered companies and/or Bermuda-based insurers or reinsurers and/or changes in regulations or tax laws applicable to us, our subsidiaries, brokers or customers, including new guidance implementing the Tax Cuts and Jobs Act of 2017 and the possible implementation of the Organization for Economic Cooperation and Development (“OECD”) Pillar I and Pillar II initiatives; and
the other matters set forth under Item 1A “Risk Factors”, Item 7 “Management’s Discussion and Analysis of Financial Condition and Results of Operations” and other sections of our Annual Report on Form 10-K for the year ended December 31, 2021, as well as the other factors set forth in our other documents on file with the SEC, and management’s response to any of the aforementioned factors.
 
All subsequent written and oral forward-looking statements attributable to us or persons acting on our behalf are expressly qualified in their entirety by these cautionary statements. The foregoing review of important factors should not be construed as exhaustive and should be read in conjunction with other cautionary statements that are included herein or elsewhere. We undertake no obligation to publicly update or revise any forward-looking statement, whether as a result of new information, future events or otherwise. 

ARCH CAPITAL
 3
2022 FIRST QUARTER FORM 10-Q

ITEM 1. CONSOLIDATED FINANCIAL STATEMENTS
  Page No.
   
5
March 31, 2022 (unaudited) and December 31, 2021
6
For the three month periods ended March 31, 2022 and 2021 (unaudited)
7
For the three month periods ended March 31, 2022 and 2021 (unaudited)
8
For the three month periods ended March 31, 2022 and 2021 (unaudited)
9
For the three month periods ended March 31, 2022 and 2021 (unaudited)
Notes to Consolidated Financial Statements (unaudited)

ARCH CAPITAL
 4
2022 FIRST QUARTER FORM 10-Q

Report of Independent Registered Public Accounting Firm

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

Results of Review of Interim Financial Statements

We have reviewed the accompanying consolidated balance sheet of Arch Capital Group Ltd. and its subsidiaries (the “Company”) as of March 31, 2022, and the related consolidated statements of income, comprehensive income, changes in shareholders’ equity, and the consolidated statements of cash flows for the three-month periods ended March 31, 2022 and 2021, including the related notes (collectively referred to as the “interim financial statements”). Based on our reviews, we are not aware of any material modifications that should be made to the accompanying interim financial statements for them to be in conformity with accounting principles generally accepted in the United States of America.
We have previously audited, in accordance with the standards of the Public Company Accounting Oversight Board (United States) (PCAOB), the consolidated balance sheet of the Company as of December 31, 2021, and the related consolidated statements of income, comprehensive income, changes in shareholders’ equity, and cash flows for the year then ended (not presented herein), and in our report dated February 25, 2022, we expressed an unqualified opinion on those consolidated financial statements. In our opinion, the information set forth in the accompanying consolidated balance sheet as of December 31, 2021, is fairly stated, in all material respects, in relation to the consolidated balance sheet from which it has been derived.

Basis for Review Results

These interim financial statements are the responsibility of the Company’s management. We are a public accounting firm registered with the PCAOB and are required to be independent with respect to the Company in accordance with the U.S. federal securities laws and the applicable rules and regulations of the Securities and Exchange Commission and the PCAOB. We conducted our review in accordance with the standards of the PCAOB. A review of interim financial information consists principally of applying analytical procedures and making inquiries of persons responsible for financial and accounting matters. It is substantially less in scope than an audit conducted in accordance with the standards of the PCAOB, the objective of which is the expression of an opinion regarding the financial statements taken as a whole. Accordingly, we do not express such an opinion.



/s/ PricewaterhouseCoopers LLP


New York, NY
May 4, 2022
ARCH CAPITAL
 5
2022 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED BALANCE SHEETS
(U.S. dollars in thousands, except share data)
(Unaudited)
March 31,
2022
December 31,
2021
Assets    
Investments:    
Fixed maturities available for sale, at fair value (amortized cost: $18,317,693 and $17,973,823; net of allowance for credit losses: $34,145 and $2,883 )
$ 17,648,853  $ 17,998,109 
Short-term investments available for sale, at fair value (amortized cost: $2,332,513 and $1,734,738; net of allowance for credit losses: $0 and $0)
2,332,624  1,734,716 
Equity securities, at fair value 1,002,572  1,804,170 
Other investments, at fair value 1,686,666  1,973,550 
Investments accounted for using the equity method 3,325,543  3,077,611 
Total investments 25,996,258  26,588,156 
Cash 812,917  858,668 
Accrued investment income 82,607  85,453 
Investment in operating affiliates 1,144,255  1,135,655 
Premiums receivable (net of allowance for credit losses: $39,073 and $39,958)
3,223,504  2,633,280 
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $18,483 and $13,230)
5,941,000  5,880,735 
Contractholder receivables (net of allowance for credit losses: $3,731 and $3,437)
1,810,199  1,828,691 
Ceded unearned premiums 1,951,960  1,729,455 
Deferred acquisition costs 1,001,866  901,841 
Receivable for securities sold 116,633  60,179 
Goodwill and intangible assets 926,427  944,983 
Other assets 2,670,315  2,453,849 
Total assets $ 45,677,941  $ 45,100,945 
Liabilities
Reserve for losses and loss adjustment expenses $ 18,109,107  $ 17,757,156 
Unearned premiums 6,737,779  6,011,942 
Reinsurance balances payable 1,510,906  1,583,253 
Contractholder payables 1,813,930  1,832,127 
Collateral held for insured obligations 244,502  242,352 
Senior notes 2,724,642  2,724,394 
Payable for securities purchased 176,452  64,850 
Other liabilities 1,431,271  1,329,742 
Total liabilities 32,748,589  31,545,816 
Commitments and Contingencies
Redeemable noncontrolling interests 9,763  9,233 
Shareholders' Equity
Non-cumulative preferred shares 830,000  830,000 
Common shares ($0.0011 par, shares issued: 586,115,502 and 583,289,850)
651  648 
Additional paid-in capital 2,134,241  2,085,075 
Retained earnings 14,641,484  14,455,868 
Accumulated other comprehensive income (loss), net of deferred income tax (649,445) (64,600)
Common shares held in treasury, at cost (shares: 210,384,611 and 204,365,956)
(4,037,342) (3,761,095)
Total shareholders' equity available to Arch 12,919,589  13,545,896 
Total liabilities, noncontrolling interests and shareholders' equity $ 45,677,941  $ 45,100,945 
See Notes to Consolidated Financial Statements

ARCH CAPITAL
6
2022 FIRST QUARTER FORM 10-Q


ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF INCOME
(U.S. dollars in thousands, except share data)
(Unaudited)
Three Months Ended
March 31,
  2022 2021
Revenues    
Net premiums earned $ 2,120,633  $ 1,948,422 
Net investment income 80,436  98,856 
Net realized gains (losses) (292,414) 142,461 
Other underwriting income 5,897  6,110 
Equity in net income (loss) of investment funds accounted for using the equity method 36,305  71,686 
Other income (loss) (9,025) (1,741)
Total revenues 1,941,832  2,265,794 
Expenses
Losses and loss adjustment expenses 1,000,835  1,203,100 
Acquisition expenses 378,159  304,481 
Other operating expenses 289,943  261,033 
Corporate expenses 32,332  25,384 
Amortization of intangible assets 27,167  14,402 
Interest expense 32,708  38,346 
Net foreign exchange (gains) losses (3,845) (20,063)
Total expenses 1,757,299  1,826,683 
Income (loss) before income taxes and income (loss) from operating affiliates 184,533  439,111 
Income tax expense (11,619) (38,860)
Income (loss) from operating affiliates 24,518  75,457 
Net income (loss) $ 197,432  $ 475,708 
Net (income) loss attributable to noncontrolling interests (1,632) (37,552)
Net income (loss) available to Arch 195,800  438,156 
Preferred dividends (10,184) (10,403)
Net income (loss) available to Arch common shareholders $ 185,616  $ 427,753 
Net income per common share and common share equivalent    
Basic $ 0.50  $ 1.07 
Diluted $ 0.48  $ 1.05 
Weighted average common shares and common share equivalents outstanding
Basic 374,243,812  400,807,895 
Diluted 384,194,363  409,223,253 



See Notes to Consolidated Financial Statements

ARCH CAPITAL
7
2022 FIRST QUARTER FORM 10-Q


ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME
(U.S. dollars in thousands)
(Unaudited)
Three Months Ended
March 31,
  2022 2021
Comprehensive Income
Net income (loss) $ 197,432  $ 475,708 
Other comprehensive income (loss), net of deferred income tax
Unrealized appreciation (decline) in value of available-for-sale investments:
Unrealized holding gains (losses) arising during period (684,355) (261,750)
Reclassification of net realized (gains) losses, included in net income (loss) 102,278  2,697 
Foreign currency translation adjustments (2,768) (28,584)
Comprehensive income (loss) (387,413) 188,071 
Net (income) loss attributable to noncontrolling interests (1,632) (37,552)
Other comprehensive (income) loss attributable to noncontrolling interests —  4,570 
Comprehensive income (loss) available to Arch $ (389,045) $ 155,089 



See Notes to Consolidated Financial Statements

ARCH CAPITAL
8
2022 FIRST QUARTER FORM 10-Q


ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF CHANGES IN SHAREHOLDERS’ EQUITY
(U.S. dollars in thousands)
(Unaudited)
Three Months Ended
March 31,
  2022 2021
Non-cumulative preferred shares
Balance at beginning and end of period $ 830,000  $ 780,000 
Common shares
Balance at beginning of period 648  643 
Common shares issued, net
Balance at end of period 651  645 
Additional paid-in capital
Balance at beginning of period 2,085,075  1,977,794 
Amortization of share-based compensation 45,368  40,573 
Other changes 3,798  (3,626)
Balance at end of period 2,134,241  2,014,741 
Retained earnings
Balance at beginning of period 14,455,868  12,362,463 
Net income (loss) 197,432  475,708 
Net (income) loss attributable to noncontrolling interests (1,632) (37,552)
Preferred share dividends (10,184) (10,403)
Balance at end of period 14,641,484  12,790,216 
Accumulated other comprehensive income (loss), net of deferred income tax
Balance at beginning of period (64,600) 488,895 
Unrealized appreciation (decline) in value of available-for-sale investments, net of deferred income tax:
Balance at beginning of period 13,486  501,295 
Unrealized holding gains (losses) during period, net of reclassification adjustment (582,077) (259,053)
Unrealized holding gains (losses) during period attributable to noncontrolling interests —  4,469 
Balance at end of period (568,591) 246,711 
Foreign currency translation adjustments, net of deferred income tax:
Balance at beginning of period (78,086) (12,400)
Foreign currency translation adjustments (2,768) (28,584)
Foreign currency translation adjustments attributable to noncontrolling interests —  100 
Balance at end of period (80,854) (40,884)
Balance at end of period (649,445) 205,827 
Common shares held in treasury, at cost
Balance at beginning of period (3,761,095) (2,503,909)
Shares repurchased for treasury (276,247) (191,048)
Balance at end of period (4,037,342) (2,694,957)
Total shareholders’ equity available to Arch 12,919,589  13,096,472 
Non-redeemable noncontrolling interests —  876,864 
Total shareholders’ equity $ 12,919,589  $ 13,973,336 


See Notes to Consolidated Financial Statements

ARCH CAPITAL
9
2022 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF CASH FLOWS
(U.S. dollars in thousands)
(Unaudited)
Three Months Ended
March 31,
  2022 2021
Operating Activities    
Net income (loss) $ 197,432  $ 475,708 
Adjustments to reconcile net income (loss) to net cash provided by operating activities:
Net realized (gains) losses 289,213  (161,007)
Equity in net (income) or loss of investment funds accounted for using the equity method and other income or loss (11,420) (135,939)
Amortization of intangible assets 27,167  14,402 
Share-based compensation 45,379  40,812 
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable 275,954  560,153 
Unearned premiums, net of ceded unearned premiums 513,507  560,035 
Premiums receivable (600,691) (608,250)
Deferred acquisition costs (96,999) (126,701)
Reinsurance balances payable (74,022) 240,206 
Other items, net (13,957) (96,574)
Net cash provided by (used for) operating activities 551,563  762,845 
Investing Activities    
Purchases of fixed maturity investments (6,727,665) (11,530,968)
Purchases of equity securities (408,615) (309,419)
Purchases of other investments (616,659) (430,961)
Proceeds from sales of fixed maturity investments 6,053,352  10,917,134 
Proceeds from sales of equity securities 1,100,256  284,986 
Proceeds from sales, redemptions and maturities of other investments 570,341  323,591 
Proceeds from redemptions and maturities of fixed maturity investments 240,753  421,042 
Net settlements of derivative instruments (2,510) 47,660 
Net (purchases) sales of short-term investments (510,752) 589,175 
Purchase of operating affiliate —  (546,349)
Purchases of fixed assets (11,770) (12,490)
Other 550  (246,590)
Net cash provided by (used for) investing activities (312,719) (493,189)
Financing Activities    
Purchases of common shares under share repurchase program (254,988) (179,266)
Proceeds from common shares issued, net (17,260) (10,008)
Third party investment in non-redeemable noncontrolling interests —  15,971 
Dividends paid to redeemable noncontrolling interests —  (948)
Other 48,859  (1,948)
Preferred dividends paid (10,184) (10,403)
Net cash provided by (used for) financing activities (233,573) (186,602)
Effects of exchange rate changes on foreign currency cash and restricted cash (3,924) (6,084)
Increase (decrease) in cash and restricted cash 1,347  76,970 
Cash and restricted cash, beginning of year 1,314,771  1,290,544 
Cash and restricted cash, end of period $ 1,316,118  $ 1,367,514 

See Notes to Consolidated Financial Statements

ARCH CAPITAL
10
2022 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

1.    Basis of Presentation and Recent Accounting Pronouncements
General
Arch Capital Group Ltd. (“Arch Capital”) is a public listed Bermuda exempted company which provides insurance, reinsurance and mortgage insurance on a worldwide basis through its wholly-owned subsidiaries. As used herein, the “Company” means Arch Capital and its subsidiaries. The Company’s consolidated financial statements through June 30, 2021 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 11.
Basis of Presentation
The interim consolidated financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America (“GAAP”). All significant intercompany transactions and balances have been eliminated in consolidation. The preparation of financial statements in conformity with GAAP requires management to make estimates and assumptions that affect the reported amounts of assets and liabilities and disclosure of contingent assets and liabilities at the date of the financial statements and the reported amounts of revenues and expenses during the reporting period. Actual results could differ materially from those estimates and assumptions. In the opinion of management, the accompanying unaudited interim consolidated financial statements reflect all adjustments (consisting of normally recurring accruals) necessary for a fair statement of results on an interim basis. The results of any interim period are not necessarily indicative of the results for a full year or any future periods.
Certain information and footnote disclosures normally included in financial statements prepared in accordance with GAAP have been condensed or omitted; however, management believes that the disclosures are adequate to make the information presented not misleading. This report should be read in conjunction with the Company’s Annual Report on Form 10-K for the year ended December 31, 2021
(“2021 Form 10-K”), including the Company’s audited consolidated financial statements and related notes.
The Company has reclassified the presentation of certain prior year information to conform to the current presentation. Such reclassifications had no effect on the Company’s net income, comprehensive income, shareholders’ equity or cash flows. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.
Recent Accounting Pronouncements
Recently Issued Accounting Standards Adopted
For information regarding additional accounting standards that the Company has not yet adopted, see note 3(s), “Significant Accounting Policies—Recent Accounting Pronouncements,” of the notes to consolidated financial statements in the Company’s 2021 Form 10-K.
2.    Share Transactions
Share-Based Compensation
During the 2022 first quarter, the Company granted 734,254 stock options, 690,772 performance share awards (“PSAs”) and units (“PSUs”) and 971,262 restricted shares and units to certain employees. The stock options were valued at the grant date using the Black-Scholes option pricing model. The weighted average grant-date fair value of the stock options, PSAs/PSUs and restricted shares and units granted during the 2022 first quarter were approximately $13.13, $49.91 and $47.54 per share, respectively. Such values are being amortized over the respective substantive vesting period.
During the 2021 first quarter, the Company granted 1,218,465 stock options, 685,104 performance share awards (“PSAs”) and units (“PSUs”) and 1,168,577 restricted shares and units to certain employees. The stock options were valued at the grant date using the Black-Scholes option pricing model. The weighted average grant-date fair value of the stock options, PSAs/PSUs and restricted shares and units granted during the 2021 first quarter were approximately $9.20, $37.38 and $35.82 per share, respectively. Such values
are being amortized over the respective substantive vesting
period.
Share Repurchases 
The board of directors of Arch Capital has authorized the investment in Arch Capital’s common shares through a share repurchase program. Since the inception of the share repurchase program, Arch Capital has repurchased 426.2 million common shares for an aggregate purchase price of $5.54 billion. For the three months ended March 31, 2022, Arch Capital repurchased 5.6 million shares under the share repurchase program with an aggregate purchase price of $255.0 million. At March 31, 2022, $927.2 million of share
ARCH CAPITAL
 11
2022 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
repurchases were available under the program, which may be effected from time to time in open market or privately negotiated transactions. 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.

3.    Earnings Per Common Share
The following table sets forth the computation of basic and diluted earnings per common share:
Three Months Ended
March 31,
  2022 2021
Numerator:
Net income (loss) $ 197,432  $ 475,708 
Amounts attributable to noncontrolling interests (1,632) (37,552)
Net income (loss) available to Arch 195,800  438,156 
Preferred dividends (10,184) (10,403)
Net income (loss) available to Arch common shareholders $ 185,616  $ 427,753 
Denominator:
Weighted average common shares and common share equivalents outstanding — basic 374,243,812  400,807,895 
Effect of dilutive common share equivalents:
Nonvested restricted shares 2,659,922  2,230,794 
Stock options (1) 7,290,629  6,184,564 
Weighted average common shares and common share equivalents outstanding — diluted 384,194,363  409,223,253 
Earnings per common share:
Basic $ 0.50  $ 1.07 
Diluted $ 0.48  $ 1.05 
(1)    Certain stock options were not included in the computation of diluted earnings per share where the exercise price of the stock options exceeded the average market price and would have been anti-dilutive or where, when applying the treasury stock method to in-the-money options, the sum of the proceeds, including unrecognized compensation, exceeded the average market price and would have been anti-dilutive. For the 2022 first quarter and 2021 first quarter, the number of stock options excluded were 769,026 and 2,400,082, respectively.
ARCH CAPITAL
 12
2022 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
4.    Segment Information
The Company classifies its businesses into three underwriting segments — insurance, reinsurance and mortgage — and two other operating segments — 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, the Chief Financial Officer and Treasurer of Arch Capital and the President and Chief Underwriting Officer of Arch Capital. The chief operating decision makers do not assess performance, measure return on equity or make resource allocation decisions on a line of business basis. Management measures segment performance for its three underwriting segments based on underwriting income or loss. The Company does not manage its assets by underwriting segment, with the exception of goodwill and intangible assets, and, accordingly, investment income is not allocated to each underwriting segment.
The insurance segment consists of the Company’s insurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include: construction and national accounts; excess and surplus casualty; lenders products; professional lines; programs; property, energy, marine and aviation; travel, accident and health; and other (consisting of alternative markets, excess workers' compensation and surety business).
The reinsurance segment consists of the Company’s reinsurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include: casualty; marine and aviation; other specialty; property catastrophe; property excluding property catastrophe (losses on a single risk, both excess of loss and pro rata); and other (consisting of life reinsurance, casualty clash and other).
The mortgage segment includes the Company’s U.S. primary mortgage insurance business, investment and services related to U.S. credit-risk transfer (“CRT”) which are predominately with government sponsored enterprises (“GSE’s”) and international mortgage insurance and reinsurance operations. Arch Mortgage Insurance Company and United Guaranty Residential Insurance Company (combined “Arch MI U.S.”) are approved as eligible mortgage insurers by Federal National Mortgage Association (“Fannie Mae”) and Federal Home Loan Mortgage Corporation (“Freddie Mac”), each a GSE. Arch MI U.S. also includes Arch Mortgage Guaranty Company, which is not a GSE-approved entity.
The corporate 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 11.


ARCH CAPITAL
 13
2022 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
The following tables summarize the Company’s underwriting income or loss by segment, together with a reconciliation of underwriting income or loss to net income available to Arch common shareholders:
Three Months Ended
March 31, 2022
  Insurance Reinsurance Mortgage Sub-Total Other Total
Gross premiums written (1) $ 1,719,605  $ 1,718,942  $ 364,839  $ 3,800,775  $ —  $ 3,800,775 
Premiums ceded (512,709) (579,818) (76,719) (1,166,635) —  (1,166,635)
Net premiums written 1,206,896  1,139,124  288,120  2,634,140  —  2,634,140 
Change in unearned premiums (180,200) (334,724) 1,417  (513,507) —  (513,507)
Net premiums earned 1,026,696  804,400  289,537  2,120,633  —  2,120,633 
Other underwriting income (loss) —  836  5,061  5,897  —  5,897 
Losses and loss adjustment expenses (600,739) (454,700) 54,604  (1,000,835) —  (1,000,835)
Acquisition expenses (195,650) (171,996) (10,513) (378,159) —  (378,159)
Other operating expenses (166,825) (69,776) (53,342) (289,943) —  (289,943)
Underwriting income (loss) $ 63,482  $ 108,764  $ 285,347  457,593  —  457,593 
Net investment income 80,436  —  80,436 
Net realized gains (losses) (292,414) —  (292,414)
Equity in net income (loss) of investment funds accounted for using the equity method 36,305  —  36,305 
Other income (loss) (9,025) —  (9,025)
Corporate expenses (2) (31,935) —  (31,935)
Transaction costs and other (2) (397) —  (397)
Amortization of intangible assets (27,167) —  (27,167)
Interest expense (32,708) —  (32,708)
Net foreign exchange gains (losses) 3,845  —  3,845 
Income (loss) before income taxes and income (loss) from operating affiliates 184,533  —  184,533 
Income tax (expense) benefit (11,619) —  (11,619)
Income (loss) from operating affiliates 24,518  —  24,518 
Net income (loss) 197,432  —  197,432 
Amounts attributable to redeemable noncontrolling interests (1,632) —  (1,632)
Net income (loss) available to Arch 195,800  —  195,800 
Preferred dividends (10,184) —  (10,184)
Net income (loss) available to Arch common shareholders $ 185,616  $ —  $ 185,616 
Underwriting Ratios
Loss ratio 58.5  % 56.5  % (18.9) % 47.2  % —  % 47.2  %
Acquisition expense ratio 19.1  % 21.4  % 3.6  % 17.8  % —  % 17.8  %
Other operating expense ratio 16.2  % 8.7  % 18.4  % 13.7  % —  % 13.7  %
Combined ratio 93.8  % 86.6  % 3.1  % 78.7  % —  % 78.7  %
Goodwill and intangible assets $ 249,423  $ 183,675  $ 493,329  $ 926,427  $ —  $ 926,427 
(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.
(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

ARCH CAPITAL
 14
2022 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
Three Months Ended
March 31, 2021
  Insurance Reinsurance Mortgage Sub-Total Other Total
Gross premiums written (1) $ 1,415,886  $ 1,471,060  $ 391,246  $ 3,277,293  $ 216,523  $ 3,397,206 
Premiums ceded (421,047) (471,948) (56,051) (948,147) (37,212) (888,749)
Net premiums written 994,839  999,112  335,195  2,329,146  179,311  2,508,457 
Change in unearned premiums (175,365) (354,212) 1,122  (528,455) (31,580) (560,035)
Net premiums earned 819,474  644,900  336,317  1,800,691  147,731  1,948,422 
Other underwriting income (loss) —  (1,198) 6,897  5,699  411  6,110 
Losses and loss adjustment expenses (535,747) (484,870) (63,689) (1,084,306) (118,794) (1,203,100)
Acquisition expenses (128,222) (118,025) (30,082) (276,329) (28,152) (304,481)
Other operating expenses (137,113) (60,514) (49,131) (246,758) (14,275) (261,033)
Underwriting income (loss) $ 18,392  $ (19,707) $ 200,312  198,997  (13,079) 185,918 
Net investment income 78,729  20,127  98,856 
Net realized gains (losses) 101,336  41,125  142,461 
Equity in net income (loss) of investment funds accounted for using the equity method 71,686  —  71,686 
Other income (loss) (1,741) —  (1,741)
Corporate expenses (2) (23,468) —  (23,468)
Transaction costs and other (2) (1,201) (715) (1,916)
Amortization of intangible assets (14,402) —  (14,402)
Interest expense (34,197) (4,149) (38,346)
Net foreign exchange gains (losses) 21,505  (1,442) 20,063 
Income (loss) before income taxes and income (loss) from operating affiliates 397,244  41,867  439,111 
Income tax (expense) benefit (38,852) (8) (38,860)
Income (loss) from operating affiliates 75,457  —  75,457 
Net income (loss) 433,849  41,859  475,708 
Amounts attributable to redeemable noncontrolling interests 117  (972) (855)
Amounts attributable to nonredeemable noncontrolling interests —  (36,697) (36,697)
Net income (loss) available to Arch 433,966  4,190  438,156 
Preferred dividends (10,403) —  (10,403)
Net income (loss) available to Arch common shareholders $ 423,563  $ 4,190  $ 427,753 
Underwriting Ratios          
Loss ratio 65.4  % 75.2  % 18.9  % 60.2  % 80.4  % 61.7  %
Acquisition expense ratio 15.6  % 18.3  % 8.9  % 15.3  % 19.1  % 15.6  %
Other operating expense ratio 16.7  % 9.4  % 14.6  % 13.7  % 9.7  % 13.4  %
Combined ratio 97.7  % 102.9  % 42.4  % 89.2  % 109.2  % 90.7  %
Goodwill and intangible assets $ 276,211  $ 17,807  $ 377,841  $ 671,859  $ 7,650  $ 679,509 

(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.
(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’



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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
5.    Reserve for Losses and Loss Adjustment Expenses
The following table represents an analysis of losses and loss adjustment expenses and a reconciliation of the beginning and ending reserve for losses and loss adjustment expenses:
Three Months Ended
March 31,
2022 2021
Reserve for losses and loss adjustment expenses at beginning of period
$ 17,757,156  $ 16,513,929 
Unpaid losses and loss adjustment expenses recoverable
5,599,231  4,314,855 
Net reserve for losses and loss adjustment expenses at beginning of period
12,157,925  12,199,074 
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year
1,142,647  1,244,772 
Prior years
(141,812) (41,672)
Total net incurred losses and loss adjustment expenses
1,000,835  1,203,100 
Retroactive reinsurance transactions (1)
—  (183,893)
Net foreign exchange (gains) losses and other
(32,640) (46,877)
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year
(70,806) (58,984)
Prior years
(656,205) (585,118)
Total net paid losses and loss adjustment expenses
(727,011) (644,102)
Net reserve for losses and loss adjustment expenses at end of period
12,399,109  12,527,302 
Unpaid losses and loss adjustment expenses recoverable
5,709,998  3,916,650 
Reserve for losses and loss adjustment expenses at end of period
$ 18,109,107  $ 16,443,952 
(1)     During the 2021 first quarter, the Company entered into a reinsurance to close and other related agreements with Premia Managing Agency Limited (“Premia”), in connection with the 2018 and prior years of account related to the acquisition of Barbican Group Holdings Limited (“Barbican”).

Development on Prior Year Loss Reserves

2022 First Quarter

During the 2022 first quarter, the Company recorded net favorable development on prior year loss reserves of $141.8 million, which consisted of $7.3 million from the insurance segment, $32.5 million from the reinsurance segment and $102.1 million from the mortgage segment.
The insurance segment’s net favorable development of $7.3 million, or 0.7 loss ratio points, for the 2022 first quarter consisted of $19.0 million of net favorable development in short-tailed lines and $11.7 million of net adverse development in medium-tailed and long-tailed lines. Net favorable development in short-tailed lines reflected $18.6 million of favorable development in lenders products, primarily from the 2021 accident year (i.e., the year in which a loss occurred). Net adverse development in medium-tailed lines included $7.2 million of adverse development in professional liability business, primarily from the 2010 to 2013, 2015 and 2019 accident years, and $6.0 million of adverse development in contract binding business, across
most accident years, partially offset by favorable development in program business of $5.0 million, primarily from the 2020 accident year. Net adverse development in long-tailed lines primarily reflected $5.8 million of unfavorable development related to casualty lines, primarily from 2019 to 2021 accident years.
The reinsurance segment’s net favorable development of $32.5 million, or 4.0 loss ratio points, for the 2022 first quarter consisted of $35.4 million of net favorable development in short-tailed and medium-tailed lines and $2.9 million of net adverse development in long-tailed lines. Net favorable development in short-tailed lines reflected $19.2 million of favorable development related to property catastrophe and property other than property catastrophe business, primarily from the 2018, 2019 and 2021 underwriting years (i.e., all premiums and losses attributable to contracts having an inception or renewal date within the given twelve-month period). Net favorable development in medium-tailed lines included $10.7 million of favorable development in marine and aviation lines, across most underwriting years. Adverse development in long-tailed lines reflected an increase in casualty reserves, primarily from the
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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
2021 underwriting year, which was partially offset by favorable development in earlier underwriting years.
The mortgage segment’s net favorable development was $102.1 million, or 35.3 loss ratio points, for the 2022 first quarter, primarily reflecting the impact of lower new delinquencies and favorable cure activity related to the U.S. first lien portfolio primarily from the 2020 accident year. The Company’s credit risk transfer, international, second lien and student loan business also contributed to the favorable development.
2021 First Quarter
During the 2021 first quarter, the Company recorded net favorable development on prior year loss reserves of $41.7 million, which consisted of $4.1 million from the insurance segment, $26.8 million from the reinsurance segment and $10.9 million from the mortgage segment, partially offset by $0.1 million unfavorable from the ‘other’ segment.
The insurance segment’s net favorable development of $4.1 million, or 0.5 loss ratio points, for the 2021 first quarter consisted of $25.0 million of net favorable development in short-tailed and $20.9 million of net adverse development in medium-tailed lines. Net favorable development in short-tailed lines reflected $14.6 million of favorable development from property (excluding marine), primarily from the 2019 and 2020 accident years, $8.0 million of favorable development in lenders products, primarily from the 2020 accident year, and $2.5 million of favorable development in travel and accident, primarily from the 2020 accident year. Net adverse development in medium-tailed lines included $10.8 million of adverse development in program business, primarily from the 2016 to 2020 accident years, $6.0 million of adverse development in professional liability business, primarily from the 2019 accident year, and $5.0 million of adverse development in surety, primarily from the 2019 accident year.
The reinsurance segment’s net favorable development of $26.8 million, or 4.2 loss ratio points, for the 2021 first quarter consisted of net favorable development in short-tailed, medium-tailed and long-tailed lines. Net favorable development of $17.5 million in short-tailed lines reflected $23.3 million of favorable development related to property other than property catastrophe business, primarily from the 2016 to 2019 underwriting years, and $16.6 million of favorable development from other specialty, primarily from the 2018 and 2019 underwriting years, partially offset by $22.5 million of net adverse development related to property catastrophe, primarily from the 2020 underwriting year. Net favorable development of $9.3 million in medium and long-tailed lines reflected favorable development in casualty across most underwriting years.
The mortgage segment’s net favorable development was $10.9 million, or 3.2 loss ratio points, for the 2021 first
quarter, primarily driven by favorable development in the credit risk transfer and international portfolios. Subrogation recoveries on second lien and student loan business also contributed.
6.    Allowance for Expected Credit Losses
Premiums Receivable
The following table provides a roll forward of the allowance for expected credit losses of the Company’s premium receivables:
Premium Receivables, Net of Allowance Allowance for Expected Credit Losses
Three Months Ended March 31, 2022
Balance at beginning of period $ 2,633,280  $ 39,958 
Change for provision of expected credit losses (1)
(885)
Balance at end of period $ 3,223,504  $ 39,073 
Three Months Ended March 31, 2021
Balance at beginning of period $ 2,064,586  $ 37,781 
Change for provision of expected credit losses (1)
(1,670)
Balance at end of period $ 2,618,175  $ 36,111 
(1)Amounts deemed uncollectible are written-off in operating expenses. For the 2022 first quarter and 2021 first quarter, amounts written off were $1.5 million and $0.1 million, respectively.

Reinsurance Recoverables
The following table provides a roll forward of the allowance for expected credit losses of the Company’s reinsurance recoverables:
Reinsurance Recoverables, Net of Allowance Allowance for Expected Credit Losses
Three Months Ended March 31, 2022
Balance at beginning of period $ 5,880,735  $ 13,230 
Change for provision of expected credit losses 5,253 
Balance at end of period $ 5,941,000  $ 18,483 
Three Months Ended March 31, 2021
Balance at beginning of period $ 4,500,802  $ 11,636 
Change for provision of expected credit losses (764)
Balance at end of period $ 4,041,076  $ 10,872 
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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums):
March 31,
December 31
2022 2021
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses $ 5,941,000 $ 5,880,735
% due from carriers with A.M. Best rating of “A-” or better 69.5  % 69.7  %
% due from all other rated carriers 0.1  % 0.1  %
% due from all other carriers with no A.M. Best rating (1) 30.4  % 30.2  %
Largest balance due from any one carrier as % of total shareholders’ equity 7.2  % 6.7  %
(1)    At March 31, 2022 and December 31, 2021 over 93% and 91% of such amount were collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other, respectively.
Contractholder Receivables
The following table provides a roll forward of the allowance for expected credit losses of the Company’s contractholder receivables:
Contract-holder Receivables, Net of Allowance Allowance for Expected Credit Losses
Three Months Ended March 31, 2022
Balance at beginning of period $ 1,828,691  $ 3,437 
Change for provision of expected credit losses 294 
Balance at end of period $ 1,810,199  $ 3,731 
Three Months Ended March 31, 2021
Balance at beginning of period $ 1,986,924  $ 8,638 
Change for provision of expected credit losses (2,785)
Balance at end of period 1,919,655  $ 5,853 

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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
7.    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
Value
Gross
Unrealized
Gains
Gross
Unrealized
Losses
Allowance for Expected Credit Losses Cost or
Amortized
Cost
March 31, 2022
Fixed maturities:
Corporate bonds $ 7,231,686  $ 31,393  $ (356,464) $ (26,509) $ 7,583,266 
Mortgage backed securities 416,138  1,717  (28,430) (797) 443,648 
Municipal bonds 370,470  4,169  (10,900) (106) 377,307 
Commercial mortgage backed securities 1,066,365  751  (15,862) (256) 1,081,732 
U.S. government and government agencies 4,716,790  10,031  (178,836) —  4,885,595 
Non-U.S. government securities 2,169,714  42,121  (92,040) (532) 2,220,165 
Asset backed securities 1,677,690  1,128  (43,473) (5,945) 1,725,980 
Total 17,648,853  91,310  (726,005) (34,145) 18,317,693 
Short-term investments 2,332,624  758  (647) —  2,332,513 
Total $ 19,981,477  $ 92,068  $ (726,652) $ (34,145) $ 20,650,206 
December 31, 2021
Fixed maturities:
Corporate bonds $ 6,553,333  $ 104,170  $ (69,194) $ (2,037) $ 6,520,394 
Mortgage backed securities 408,477  2,825  (5,410) (48) 411,110 
Municipal bonds 404,666  18,724  (1,409) (2) 387,353 
Commercial mortgage backed securities 1,046,484  1,740  (3,117) (6) 1,047,867 
U.S. government and government agencies 4,772,764  10,076  (45,967) —  4,808,655 
Non-U.S. government securities 2,120,294  54,048  (34,749) (82) 2,101,077 
Asset backed securities 2,692,091  6,540  (11,108) (708) 2,697,367 
Total 17,998,109  198,123  (170,954) (2,883) 17,973,823 
Short-term investments 1,734,716  568  (590) —  1,734,738 
Total $ 19,732,825  $ 198,691  $ (171,544) $ (2,883) $ 19,708,561 

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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
The following table summarizes, for all available for sale securities in an unrealized loss position, the fair value and gross unrealized loss by length of time the security has been in a continual unrealized loss position:
  Less than 12 Months 12 Months or More Total
Estimated
Fair
Value
Gross
Unrealized
Losses
Estimated
Fair
Value
Gross
Unrealized
Losses
Estimated
Fair
Value
Gross
Unrealized
Losses
March 31, 2022
Fixed maturities:
Corporate bonds $ 5,798,556  $ (305,661) $ 513,866  $ (50,803) $ 6,312,422  $ (356,464)
Mortgage backed securities 328,090  (21,714) 68,490  (6,716) 396,580  (28,430)
Municipal bonds 203,717  (9,578) 14,759  (1,322) 218,476  (10,900)
Commercial mortgage backed securities 942,203  (15,815) 1,654  (47) 943,857  (15,862)
U.S. government and government agencies 4,201,416  (173,754) 80,735  (5,082) 4,282,151  (178,836)
Non-U.S. government securities 2,045,013  (82,107) 98,575  (9,933) 2,143,588  (92,040)
Asset backed securities 1,450,006  (41,196) 110,116  (2,277) 1,560,122  (43,473)
Total 14,969,001  (649,825) 888,195  (76,180) 15,857,196  (726,005)
Short-term investments 420,157  (647) —  —  420,157  (647)
Total $ 15,389,158  $ (650,472) $ 888,195  $ (76,180) $ 16,277,353  $ (726,652)
December 31, 2021
Fixed maturities:
Corporate bonds $ 3,639,582  $ (63,938) $ 98,867  $ (5,256) $ 3,738,449  $ (69,194)
Mortgage backed securities 222,176  (3,545) 46,809  (1,865) 268,985  (5,410)
Municipal bonds 26,665  (385) 16,361  (1,024) 43,026  (1,409)
Commercial mortgage backed securities 675,603  (2,805) 5,908  (312) 681,511  (3,117)
U.S. government and government agencies 4,211,621  (44,180) 33,373  (1,787) 4,244,994  (45,967)
Non-U.S. government securities 1,511,301  (31,983) 62,957  (2,766) 1,574,258  (34,749)
Asset backed securities 1,667,002  (9,853) 33,082  (1,255) 1,700,084  (11,108)
Total 11,953,950  (156,689) 297,357  (14,265) 12,251,307  (170,954)
Short-term investments 284,733  (590) —  —  284,733  (590)
Total $ 12,238,683  $ (157,279) $ 297,357  $ (14,265) $ 12,536,040  $ (171,544)
At March 31, 2022, on a lot level basis, approximately 6,550 security lots out of a total of approximately 9,060 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 $3.6 million. 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.

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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
The contractual maturities of the Company’s fixed maturities are shown in the following table. Expected maturities, which are management’s best estimates, will differ from contractual maturities because borrowers may have the right to call or prepay obligations with or without call or prepayment penalties.
March 31, 2022 December 31, 2021
Maturity Estimated
Fair
Value
Amortized
Cost
Estimated
Fair
Value
Amortized
Cost
Due in one year or less $ 313,167  $ 311,780  $ 300,889  $ 299,772 
Due after one year through five years 9,592,143  9,884,149  8,355,255  8,339,387 
Due after five years through 10 years 4,107,319  4,353,470  4,689,155  4,684,393 
Due after 10 years 476,031  516,934  505,758  493,927 
  14,488,660  15,066,333  13,851,057  13,817,479 
Mortgage backed securities 416,138  443,648  408,477  411,110 
Commercial mortgage backed securities 1,066,365  1,081,732  1,046,484  1,047,867 
Asset backed securities 1,677,690  1,725,980  2,692,091  2,697,367 
Total $ 17,648,853  $ 18,317,693  $ 17,998,109  $ 17,973,823 
Equity Securities, at Fair Value
At March 31, 2022, the Company held $1.0 billion of equity securities, at fair value, compared to $1.8 billion at December 31, 2021. Such holdings include publicly traded common stocks primarily in the consumer cyclical and non-cyclical, technology, communication and financial sectors and exchange-traded funds in fixed income, equity and other sectors.
Other Investments, at Fair Value
The following table summarizes the Company’s other investments and other investable assets:
March 31,
2022
December 31,
2021
Fixed maturities $ 426,187  $ 416,698 
Other investments 1,226,808  1,432,553 
Short-term investments 12,371  97,806 
Equity securities 21,300  26,493 
Total $ 1,686,666  $ 1,973,550 
The following table summarizes the Company’s other investments, as detailed in the previous table, by strategy:
March 31,
2022
December 31,
2021
Lending $ 472,099  $ 536,345 
Investment grade fixed income 350,217  147,810 
Term loan investments 160,945  484,950 
Private equity 98,471  91,126 
Energy 81,693  81,692 
Credit related funds 63,383  70,278 
Infrastructure —  20,352 
Total $ 1,226,808  $ 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:
March 31,
2022
December 31,
2021
Credit related funds $ 1,067,549  $ 1,022,334 
Private equity 602,802  436,042 
Real estate 444,755  396,395 
Lending 409,736  376,649 
Equities 360,906  395,090 
Infrastructure 226,430  230,070 
Energy 107,842  119,141 
Fixed income 105,523  101,890 
Total $ 3,325,543  $ 3,077,611 
Certain of the Company’s other investments are in investment funds for which the Company has the option to redeem at agreed upon values as described in each investment fund’s subscription agreement. Depending on the terms of the various subscription agreements, investments in investment funds may be redeemed daily, monthly, quarterly or on other terms. Two common redemption restrictions which may impact the Company’s ability to redeem these investment funds are gates and lockups. A gate is a suspension of redemptions which may be implemented by the general partner or investment manager of the fund in order to defer, in whole or in part, the redemption request in the event the aggregate amount of redemption requests exceeds a predetermined percentage of the investment fund’s net assets which may otherwise hinder the general partner or investment manager’s ability to liquidate holdings in an orderly fashion in order to generate the cash necessary to fund extraordinarily large redemption payouts. A lockup period is the initial amount of time an investor is contractually required to hold the security before having the ability to redeem. If the investment funds are eligible to be
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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
redeemed, the time to redeem such fund can take weeks or months following the notification.
Limited Partnership Interests
In the normal course of its activities, the Company invests in limited partnerships as part of its overall investment strategy. Such amounts are included in ‘investments accounted for using the equity method’ and ‘investments accounted for using the fair value option.’ The Company has determined that it is not required to consolidate these investments because it is not the primary beneficiary of the funds. The Company’s maximum exposure to loss with respect to these investments is limited to the investment carrying amounts reported in the Company’s consolidated balance sheet and any unfunded commitment.
The following table summarizes investments in limited partnership interests where the Company has a variable interest by balance sheet line item:
March 31,
2022
December 31,
2021
Investments accounted for using the equity method (1) 3,325,543  3,077,611 
Investments accounted for using the fair value option (2) 146,718  170,595 
Total $ 3,472,261  $ 3,248,206 
(1)    Aggregate unfunded commitments were $2.7 billion at March 31, 2022, compared to $2.6 billion at December 31, 2021.
(2)    Aggregate unfunded commitments were $21.3 million at March 31, 2022, compared to $18.8 million at December 31, 2021.
Net Investment Income
The components of net investment income were derived from the following sources:
March 31,
  2022 2021
Three Months Ended
Fixed maturities $ 82,053  $ 90,626 
Term loans 1,617  14,728 
Equity securities 6,238  5,650 
Short-term investments 2,575  607 
Other (1) 10,459  14,355 
Gross investment income 102,942  125,966 
Investment expenses (22,506) (27,110)
Net investment income $ 80,436  $ 98,856 
(1)    Includes income distributions from investment funds and other items.
Net Realized Gains (Losses)
Net realized gains (losses), which include changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings were as follows:
March 31,
  2022 2021
Three Months Ended
Available for sale securities:    
Gross gains on investment sales $ 19,707  $ 65,002 
Gross losses on investment sales (108,347) (62,998)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities (30,589) 16,553 
Other investments 4,389  46,855 
Equity securities (3,313) 2,065 
Short-term investments (149) 736 
Equity securities, at fair value:
Net realized gains (losses) on sales during the period 65,211  37,849 
Net unrealized gains (losses) on equity securities still held at reporting date (176,195) 19,708 
Allowance for credit losses:
Investments related (31,722) (1,648)
Underwriting related (4,286) 5,268 
Derivative instruments (1) (23,711) 36,116 
Other (3,409) (23,045)
Net realized gains (losses) $ (292,414) $ 142,461 
(1)    See note 9 for information on the Company’s derivative instruments.

Equity in Net Income (Loss) of Investment Funds Accounted for Using the Equity Method
The Company recorded $36.3 million of equity in net income related to investment funds accounted for using the equity method in the 2022 first quarter, compared to income of $71.7 million for the 2021 first quarter. In applying the equity method, investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the market value of the underlying securities in the funds). Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds.
Investments in Operating Affiliates
Investments in which the Company has significant influence over the operating and financial policies are classified as ‘investments in operating affiliates’ on the Company’s balance sheets and are accounted for under the equity method. Such investments primarily include the Company’s investment in Coface 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.
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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
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 of March 31, 2022, the Company owned approximately 29.86% of the issued shares of Coface, or 30.09% excluding treasury shares, with a carrying value of $646.0 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 March 31, 2022 the Company’s carrying value in Greysbridge was $362.2 million, compared to $375.7 million at December 31, 2021, which reflected the Company’s 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.
Income from operating affiliates for the 2022 first quarter was $24.5 million, compared to an income of $75.5 million, for the 2021 first quarter.
Allowance for Expected Credit Losses
The following table provides a roll forward of the allowance for expected credit losses of the Company’s securities classified as available for sale:
Structured Securities (1) Municipal
Bonds
Corporate
Bonds
Total
Three Months Ended March 31, 2022
Balance at beginning of period $ 802  $ $ 2,079  $ 2,883