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ACGL Arch Capital

Filed: 5 Aug 21, 2:41pm

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 endedJune 30, 2021
Or
TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934
Commission file number:  001-16209

 acgl-20210630_g1.jpg
ARCH CAPITAL GROUP LTD.
(Exact name of registrant as specified in its charter)
Bermuda98-0374481
(State or other jurisdiction of incorporation or organization)(I.R.S. Employer Identification No.)
Waterloo House, Ground Floor
100 Pitts Bay Road,PembrokeHM 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 classTrading Symbol (s)Name of each exchange on which registered
Common shares, $0.0011 par value per shareACGLNASDAQ Stock Market
Depositary shares, each representing a 1/1000th interest in a 5.25% Series E preferred share
ACGLPNASDAQ Stock Market
Depositary shares, each representing a 1/1000th interest in a 5.45% Series F preferred share
ACGLONASDAQ Stock Market
Depositary shares, each representing a 1/1000th interest in a 4.55% Series G preferred shareACGLNNASDAQStock 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 July 30, 2021, there were 396,039,032 common shares, $0.0011 par value per share, of the registrant outstanding.


ARCH CAPITAL GROUP LTD.
 
INDEX TO FORM 10-Q
 
ARCH CAPITAL 12021 SECOND 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 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 22021 SECOND 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 potential replacement of LIBOR;
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 the Tax Cuts and Jobs Act of 2017; 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, 2020, 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 32021 SECOND QUARTER FORM 10-Q

ITEM 1. CONSOLIDATED FINANCIAL STATEMENTS
 Page No.
  
  
 
June 30, 2021 (unaudited) and December 31, 2020
  
For the three and six month periods ended June 30, 2021 and 2020 (unaudited)
 
For the three and six month periods ended June 30, 2021 and 2020 (unaudited)
  
 
For the three and six month periods ended June 30, 2021 and 2020 (unaudited)
  
 
For the six month periods ended June 30, 2021 and 2020 (unaudited)
  
Notes to Consolidated Financial Statements (unaudited)

ARCH CAPITAL 42021 SECOND 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 June 30, 2021, and the related consolidated statements of income, comprehensive income, and changes in shareholders’ equity for the three-month and six-month periods ended June 30, 2021 and 2020, and the consolidated statements of cash flows for the six-month periods ended June 30, 2021 and 2020, 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, 2020, 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 26, 2021, 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, 2020, 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
August 5, 2021
ARCH CAPITAL 52021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED BALANCE SHEETS
(U.S. dollars in thousands, except share data)
(Unaudited)
June 30,
2021
December 31,
2020
Assets  
Investments:  
Fixed maturities available for sale, at fair value (amortized cost: $17,764,783 and $18,143,305; net of allowance for credit losses: $2,124 and $2,397 )$18,073,779 $18,717,825 
Short-term investments available for sale, at fair value (amortized cost: $2,248,615 and $1,924,292; net of allowance for credit losses: $0 and $0)2,248,613 1,924,922 
Collateral received under securities lending, at fair value (amortized cost: $172,109 and $301,089)172,116 301,096 
Equity securities, at fair value1,693,552 1,444,830 
Other investments (portion measured at fair value: $4,071,497 and $3,824,796)4,571,497 4,324,796 
Investments accounted for using the equity method2,539,124 2,047,889 
Total investments29,298,681 28,761,358 
Cash1,234,059 906,448 
Accrued investment income96,546 103,299 
Securities pledged under securities lending, at fair value (amortized cost: $167,871 and $294,493)168,548 294,912 
Investment in operating affiliates731,810 129,291 
Premiums receivable (net of allowance for credit losses: $35,979 and $37,781)2,866,578 2,064,586 
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $11,029 and $11,636)4,314,515 4,500,802 
Contractholder receivables (net of allowance for credit losses: $4,471 and $8,638)1,882,948 1,986,924 
Ceded unearned premiums1,541,093 1,234,075 
Deferred acquisition costs1,013,657 790,708 
Receivable for securities sold309,234 92,743 
Goodwill and intangible assets667,153 692,863 
Other assets2,357,064 1,724,288 
Total assets$46,481,886 $43,282,297 
Liabilities
Reserve for losses and loss adjustment expenses$17,196,648 $16,513,929 
Unearned premiums6,011,369 4,838,965 
Reinsurance balances payable1,079,106 683,263 
Contractholder payables1,887,418 1,995,562 
Collateral held for insured obligations235,618 215,581 
Senior notes2,861,728 2,861,113 
Revolving credit agreement borrowings155,687 155,687 
Securities lending payable172,109 301,089 
Payable for securities purchased586,881 218,779 
Other liabilities1,332,843 1,510,888 
Total liabilities31,519,407 29,294,856 
Commitments and Contingencies00
Redeemable noncontrolling interests57,533 58,548 
Shareholders' Equity
Non-cumulative preferred shares1,280,000 780,000 
Common shares ($0.0011 par, shares issued: 582,654,893 and 579,000,841)647 643 
Additional paid-in capital2,028,919 1,977,794 
Retained earnings13,454,036 12,362,463 
Accumulated other comprehensive income (loss), net of deferred income tax230,048 488,895 
Common shares held in treasury, at cost (shares: 185,883,642 and 172,280,199)(3,007,578)(2,503,909)
Total shareholders' equity available to Arch13,986,072 13,105,886 
Non-redeemable noncontrolling interests918,874 823,007 
Total shareholders' equity14,904,946 13,928,893 
Total liabilities, noncontrolling interests and shareholders' equity$46,481,886 $43,282,297 
See Notes to Consolidated Financial Statements

ARCH CAPITAL62021 SECOND QUARTER FORM 10-Q


ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF INCOME
(U.S. dollars in thousands, except share data)
(Unaudited)(Unaudited)
Three Months EndedSix Months Ended
June 30,June 30,
 2021202020212020
Revenues    
Net premiums earned$2,120,909 $1,665,354 4,069,331 3,409,798 
Net investment income111,613 131,485 210,469 276,638 
Net realized gains (losses)202,907 556,588 345,368 189,628 
Other underwriting income5,529 6,667 11,639 13,519 
Equity in net income (loss) of investment funds accounted for using the equity method122,186 (65,119)193,872 (69,328)
Other income (loss)6,852 33 5,111 65 
Total revenues2,569,996 2,295,008 4,835,790 3,820,320 
Expenses
Losses and loss adjustment expenses1,159,831 1,230,522 2,362,931 2,345,941 
Acquisition expenses335,143 254,789 639,624 502,072 
Other operating expenses244,943 209,249 505,976 443,793 
Corporate expenses15,951 17,920 41,335 38,716 
Amortization of intangible assets15,286 16,489 29,688 33,120 
Interest expense35,700 31,139 74,046 63,694 
Net foreign exchange (gains) losses17,775 39,211 (2,288)(33,460)
Total expenses1,824,629 1,799,319 3,651,312 3,393,876 
Income (loss) before income taxes and income (loss) from operating affiliates745,367 495,689 1,184,478 426,444 
Income tax expense(51,179)(26,127)(90,039)(54,072)
Income (loss) from operating affiliates24,476 (3,173)99,933 5,343 
Net income (loss)$718,664 $466,389 $1,194,372 $377,715 
Net (income) loss attributable to noncontrolling interests(43,178)(167,568)(80,730)65,223 
Net income (loss) available to Arch675,486 298,821 1,113,642 442,938 
Preferred dividends(11,666)(10,403)(22,069)(20,806)
Net income (loss) available to Arch common shareholders$663,820 $288,418 $1,091,573 $422,132 
Net income per common share and common share equivalent    
Basic$1.67 $0.72 $2.73 $1.05 
Diluted$1.63 $0.71 $2.68 $1.03 
Weighted average common shares and common share equivalents outstanding  
Basic397,743,402 402,503,687 399,267,183 403,197,924 
Diluted406,485,994 408,119,681 407,687,680 411,005,591 



See Notes to Consolidated Financial Statements

ARCH CAPITAL72021 SECOND QUARTER FORM 10-Q


ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME
(U.S. dollars in thousands)
(Unaudited)(Unaudited)
Three Months EndedSix Months Ended
June 30,June 30,
 2021202020212020
Comprehensive Income  
Net income (loss)$718,664 $466,389 $1,194,372 $377,715 
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 period78,571 492,796 (183,179)435,509 
Reclassification of net realized (gains) losses, included in net income (loss)(60,547)(167,391)(57,850)(288,620)
Foreign currency translation adjustments6,205 22,251 (22,379)(22,438)
Comprehensive income (loss)742,893 814,045 930,964 502,166 
Net (income) loss attributable to noncontrolling interests(43,178)(167,568)(80,730)65,223 
Other comprehensive (income) loss attributable to noncontrolling interests(10)(20,111)4,560 12,947 
Comprehensive income (loss) available to Arch$699,705 $626,366 $854,794 $580,336 



See Notes to Consolidated Financial Statements

ARCH CAPITAL82021 SECOND QUARTER FORM 10-Q


ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF CHANGES IN SHAREHOLDERS’ EQUITY
(U.S. dollars in thousands)
(Unaudited)(Unaudited)
Three Months EndedSix Months Ended
June 30,June 30,
 2021202020212020
Non-cumulative preferred shares  
Balance at beginning of period$780,000 $780,000 $780,000 $780,000 
Preferred shares issued500,000 500,000 
Balance at beginning and end of period$1,280,000 $780,000 $1,280,000 $780,000 
Common shares
Balance at beginning of period645 642 643 638 
Common shares issued, net
Balance at end of period647 642 647 642 
Additional paid-in capital  
Balance at beginning of period2,014,741 1,921,487 1,977,794 1,889,683 
Amortization of share-based compensation16,490 13,160 57,063 41,210 
Issue costs on preferred shares(14,179)(14,179)
Other changes11,867 867 8,241 4,621 
Balance at end of period2,028,919 1,935,514 2,028,919 1,935,514 
Retained earnings  
Balance at beginning of period12,790,216 11,132,268 12,362,463 11,021,006 
Cumulative effect of an accounting change (1)(22,452)
Balance at beginning of period, as adjusted12,790,216 11,132,268 12,362,463 10,998,554 
Net income (loss)718,664 466,389 1,194,372 377,715 
Net (income) loss attributable to noncontrolling interests(43,178)(167,568)(80,730)65,223 
Preferred share dividends(11,666)(10,403)(22,069)(20,806)
Balance at end of period13,454,036 11,420,686 13,454,036 11,420,686 
Accumulated other comprehensive income (loss), net of deferred income tax
Balance at beginning of period205,827 21,944 488,895 212,091 
Unrealized appreciation (decline) in value of available-for-sale investments, net of deferred income tax:
Balance at beginning of period246,711 113,149 501,295 258,486 
Unrealized holding gains (losses) during period, net of reclassification adjustment18,024 325,405 (241,029)146,889 
Unrealized holding gains (losses) during period attributable to noncontrolling interests(33)(20,067)4,436 13,112 
Balance at end of period264,702 418,487 264,702 418,487 
Foreign currency translation adjustments, net of deferred income tax:
Balance at beginning of period(40,884)(91,205)(12,400)(46,395)
Foreign currency translation adjustments6,205 22,251 (22,379)(22,438)
Foreign currency translation adjustments attributable to noncontrolling interests25 (45)125 (166)
Balance at end of period(34,654)(68,999)(34,654)(68,999)
Balance at end of period230,048 349,488 230,048 349,488 
Common shares held in treasury, at cost
Balance at beginning of period(2,694,957)(2,489,097)(2,503,909)(2,406,047)
Shares repurchased for treasury(312,621)(5,408)(503,669)(88,458)
Balance at end of period(3,007,578)(2,494,505)(3,007,578)(2,494,505)
Total shareholders’ equity available to Arch13,986,072 11,991,825 13,986,072 11,991,825 
Non-redeemable noncontrolling interests918,874 679,089 918,874 679,089 
Total shareholders’ equity$14,904,946 $12,670,914 $14,904,946 $12,670,914 

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

See Notes to Consolidated Financial Statements

ARCH CAPITAL92021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF CASH FLOWS
(U.S. dollars in thousands)
(Unaudited)
Six Months Ended
June 30,
 20212020
Operating Activities  
Net income (loss)$1,194,372 $377,715 
Adjustments to reconcile net income (loss) to net cash provided by operating activities:
Net realized (gains) losses(379,049)(194,776)
Equity in net (income) or loss of investment funds accounted for using the equity method and other income or loss(181,028)125,384 
Amortization of intangible assets29,688 33,120 
Share-based compensation57,564 41,912 
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable948,505 1,158,446 
Unearned premiums, net of ceded unearned premiums838,650 395,759 
Premiums receivable(781,391)(463,638)
Deferred acquisition costs(214,893)(92,437)
Reinsurance balances payable331,461 132,161 
Other items, net(231,307)(192,066)
Net cash provided by (used for) operating activities1,612,572 1,321,580 
Investing Activities  
Purchases of fixed maturity investments(23,554,384)(25,410,849)
Purchases of equity securities(620,774)(1,025,149)
Purchases of other investments(1,033,134)(501,692)
Proceeds from sales of fixed maturity investments23,130,388 24,833,030 
Proceeds from sales of equity securities542,290 580,346 
Proceeds from sales, redemptions and maturities of other investments772,549 472,188 
Proceeds from redemptions and maturities of fixed maturity investments805,836 369,240 
Net settlements of derivative instruments17,286 150,471 
Net (purchases) sales of short-term investments(378,086)(1,323,363)
Change in cash collateral related to securities lending(826)54,596 
Purchase of operating affiliate(546,349)
Purchases of fixed assets(23,585)(17,687)
Other(204,889)8,679 
Net cash provided by (used for) investing activities(1,093,678)(1,810,190)
Financing Activities  
Proceeds from issuance of preferred shares, net485,821 
Purchases of common shares under share repurchase program(485,315)(75,486)
Proceeds from common shares issued, net185 (9,661)
Proceeds from borrowings1,004,918 
Repayments of borrowings(165,000)
Change in cash collateral related to securities lending826 (54,596)
Third party investment in non-redeemable noncontrolling interests15,971 (2,867)
Dividends paid to redeemable noncontrolling interests(1,907)(2,540)
Other27,639 (2,625)
Preferred dividends paid(20,805)(20,806)
Net cash provided by (used for) financing activities22,415 671,337 
Effects of exchange rate changes on foreign currency cash and restricted cash(13,390)(21,742)
Increase (decrease) in cash and restricted cash527,919 160,985 
Cash and restricted cash, beginning of year1,290,544 903,698 
Cash and restricted cash, end of period$1,818,463 $1,064,683 

See Notes to Consolidated Financial Statements

ARCH CAPITAL102021 SECOND 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. As of June 30, 2021, the Company’s consolidated financial statements included the results of Watford Holdings Ltd. and its wholly owned subsidiaries (“Watford”). Watford is a multi-line Bermuda reinsurance company. Watford’s own management and board of directors are responsible for its results and profitability. See note 11.
Basis of Presentation
The interim consolidated financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America (“GAAP”). All significant intercompany transactions and balances have been eliminated in consolidation. The preparation of financial statements in conformity with GAAP requires management to make estimates and assumptions that affect the reported amounts of assets and liabilities and disclosure of contingent assets and liabilities at the date of the financial statements and the reported amounts of revenues and expenses during the reporting period. Actual results could differ materially from those estimates and assumptions. In the opinion of management, the accompanying unaudited interim consolidated financial statements reflect all adjustments (consisting of normally recurring accruals) necessary for a fair statement of results on an interim basis. The results of any interim period are not necessarily indicative of the results for a full year or any future periods.
Certain information and footnote disclosures normally included in financial statements prepared in accordance with GAAP have been condensed or omitted; however, management believes that the disclosures are adequate to make the information presented not misleading. This report should be read in conjunction with the Company’s Annual Report on Form 10-K for the year ended December 31, 2020 (“2020 Form 10-K”), including the Company’s audited consolidated financial statements and related notes.
The Company has reclassified the presentation of certain prior year information to conform to the current presentation, including the correct presentation of ‘income (loss) from operating affiliates’ on its consolidated statements of income for all periods presented to reclass such item from ‘other income (loss)’. The Company also changed its presentation of ‘investment in operating affiliates’ on its consolidated
balance sheet for all periods presented to reclass such item from ‘other assets’. Such reclassifications had no effect on the Company’s net income, comprehensive income, shareholders’ equity or cash flows. Management views the impact of the prior period misclassification as not material to the financial statements on a quantitative and qualitative basis. See note 7. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.
Recent Accounting Pronouncements
Recently Issued Accounting Standards Adopted
The Company adopted ASU 2019-12, “Simplifying the Accounting for Income Taxes.” This ASU eliminates certain exceptions for recognizing deferred taxes for investments, performing intraperiod tax allocations and calculating income taxes in interim periods. The ASU also clarifies the accounting for transactions that result in a step-up in the tax basis of goodwill. The adoption of this guidance did not have a material effect on the Company’s consolidated financial statements.
For information regarding additional accounting standards that the Company has not yet adopted, see note 3(r), “Significant Accounting Policies—Recent Accounting Pronouncements,” of the notes to consolidated financial statements in the Company’s 2020 Form 10-K.
2.    Share Transactions
Share Repurchases 
The board of directors of Arch Capital has authorized the investment in Arch Capital’s common shares through a share repurchase program. Since the inception of the share repurchase program, Arch Capital has repurchased 402.3 million common shares for an aggregate purchase price of $4.54 billion. For the six months ended June 30, 2021, Arch Capital repurchased 13.1 million shares under the share repurchase program with an aggregate purchase price of $485.3 million. Arch Capital repurchased 2.6 million shares under the share repurchase program with an aggregate purchase price of $75.5 million during the six months ended June 30, 2020. At June 30, 2021, $431.2 million of share repurchases were available under the program, which may be effected from time to time in open market or privately negotiated transactions through December 31, 2021. The timing and amount of the repurchase transactions under this program will depend on a variety of factors, including market conditions and corporate and regulatory considerations.
Series G Preferred Shares
In June 2021, Arch Capital completed a $500 million underwritten public offering of 20.0 million depositary shares (the “Depositary Shares”), each of which represents a
ARCH CAPITAL 112021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
1/1,000th interest in a share of its 4.550% Non-Cumulative Preferred Shares, Series G, $0.01 par value and $25,000 liquidation preference per share (equivalent to $25 liquidation preference per Depositary Share) (the “Series G Preferred Shares”). Each Depositary Share, evidenced by a depositary receipt, entitles the holder, through the depositary, to a proportional fractional interest in all rights and preferences of the Series G Preferred Shares represented thereby (including any dividend, liquidation, redemption and voting rights).
Holders of Series G Preferred Shares will be entitled to receive dividend payments only when, as and if declared by the Company’s board of directors or a duly authorized committee of the board. Any such dividends will be payable from, and including, the date of original issue on a non-cumulative basis, quarterly in arrears on the last day of March, June, September and December of each year, at an annual rate of 4.550%. Dividends on the Series G Preferred Shares are not cumulative. The Company will be restricted from paying dividends on or repurchasing its common shares unless certain dividend payments are made on the Series G Preferred Shares. The Company may not declare or pay a dividend on the Series G Preferred Shares under certain circumstances, including if the Company is or, after giving effect to such payment, would be in breach of applicable individual or group solvency and liquidity requirements or applicable individual or group enhanced capital requirements ("ECR.") The Series G Preferred Shares may not be
redeemed at any time if the ECR would be breached immediately before or after giving effect to such redemption, unless the Company replaces the capital represented by preference shares to be redeemed with capital having equal or better capital treatment.
Except in specified circumstances relating to certain tax or corporate events, the Series G Preferred Shares are not redeemable prior to June 11, 2026. On and after that date, the Series G Preferred Shares will be redeemable at the Company’s option, in whole or in part, at a redemption price of $25,000 per share of the Series G Preferred Shares (equivalent to $25 per depositary share), plus any declared and unpaid dividends, without accumulation of any undeclared dividends to, but excluding, the redemption date. The Depositary Shares will be redeemed if and to the extent the related Series G Preferred Shares are redeemed by the Company. Neither the Depositary Shares nor the Series G Preferred Shares have a stated maturity, nor will they be subject to any sinking fund or mandatory redemption. The Series G Preferred Shares are not convertible into any other securities. The Series G Preferred Shares do not have voting rights, except under limited circumstances.
The Company intends to use the net proceeds from the offering of approximately $485.8 million to redeem all or a portion of its issued and outstanding Series E Non-Cumulative Preferred Shares in September 2021, and to use any remaining amounts for general corporate purposes.
3.    Earnings Per Common Share
The following table sets forth the computation of basic and diluted earnings per common share:
Three Months EndedSix Months Ended
June 30,June 30,
 2021202020212020
Numerator:
Net income (loss)$718,664 $466,389 $1,194,372 $377,715 
Amounts attributable to noncontrolling interests(43,178)(167,568)(80,730)65,223 
Net income (loss) available to Arch675,486 298,821 1,113,642 442,938 
Preferred dividends(11,666)(10,403)(22,069)(20,806)
Net income (loss) available to Arch common shareholders$663,820 $288,418 $1,091,573 $422,132 
Denominator:
Weighted average common shares and common share equivalents outstanding — basic397,743,402 402,503,687 399,267,183 403,197,924 
Effect of dilutive common share equivalents:
Nonvested restricted shares1,990,729 1,597,701 1,932,929 1,829,239 
Stock options (1)6,751,863 4,018,293 6,487,568 5,978,428 
Weighted average common shares and common share equivalents outstanding — diluted406,485,994 408,119,681 407,687,680 411,005,591 
Earnings per common share:
Basic$1.67 $0.72 $2.73 $1.05 
Diluted$1.63 $0.71 $2.68 $1.03 
(1)    Certain stock options were not included in the computation of diluted earnings per share where the exercise price of the stock options exceeded the average market price and would have been anti-dilutive or where, when applying the treasury stock method to in-the-money options, the sum of the proceeds, including unrecognized compensation, exceeded the average market price and would have been anti-dilutive. For the 2021 second quarter and 2020 second quarter, the number of stock options excluded were 1,974,849 and 6,982,107, respectively. For the six months ended June 30, 2021 and 2020 period, the number of stock options excluded were 2,395,749 and 2,038,758, respectively.
ARCH CAPITAL 122021 SECOND 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 3 underwriting segments — insurance, reinsurance and mortgage — and 2 other operating segments — ‘other’ and corporate (non-underwriting). The Company determined its reportable segments using the management approach described in accounting guidance regarding disclosures about segments of an enterprise and related information. The accounting policies of the segments are the same as those used for the preparation of the Company’s consolidated financial statements. Intersegment business is allocated to the segment accountable for the underwriting results.
The Company’s insurance, reinsurance and mortgage segments each have managers who are responsible for the overall profitability of their respective segments and who are directly accountable to the Company’s chief operating decision makers, the Chief Executive Officer of Arch Capital, the Chief Financial Officer and Treasurer of Arch Capital and the President and Chief Underwriting Officer of Arch Capital. The chief operating decision makers do not assess performance, measure return on equity or make resource allocation decisions on a line of business basis. Management measures segment performance for its three underwriting segments based on underwriting income or loss. The Company does not manage its assets by underwriting segment, with the exception of goodwill and intangible assets, and, accordingly, investment income is not allocated to each underwriting segment.
The insurance segment consists of the Company’s insurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include: construction and national accounts; excess and surplus casualty; lenders products; professional lines; programs; property, energy, marine and aviation; travel, accident and health; and other (consisting of alternative markets, excess workers' compensation and surety business).
The reinsurance segment consists of the Company’s reinsurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include: casualty; marine and aviation; other specialty; property catastrophe; property excluding property catastrophe (losses on a single risk, both excess of loss and pro rata); and other (consisting of life reinsurance, casualty clash and other).
The mortgage segment includes the Company’s U.S. and international mortgage insurance and reinsurance operations as well as government sponsored enterprise (“GSE”) credit-risk sharing transactions. Arch Mortgage Insurance Company and United Guaranty Residential Insurance Company (combined “Arch MI U.S.”) are approved as eligible mortgage insurers by Federal National Mortgage Association (“Fannie Mae”) and Federal Home Loan Mortgage Corporation (“Freddie Mac”), each a GSE. Arch MI U.S. also includes Arch Mortgage Guaranty Company, which is not a GSE-approved entity.
The corporate (non-underwriting) segment results include net investment income, other income (loss), corporate expenses, transaction costs and other, interest expense, items related to the Company’s non-cumulative preferred shares, net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings), equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses, income or loss from operating affiliates and income taxes. Such amounts exclude the results of the ‘other’ segment.
The ‘other’ segment includes the results of Watford (see note 11). For the ‘other’ segment, performance is measured based on net income or loss.
ARCH CAPITAL 132021 SECOND 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
June 30, 2021
 InsuranceReinsuranceMortgageSub-TotalOtherTotal
Gross premiums written (1)$1,368,867 $1,358,020 $391,511 $3,117,505 $240,942 $3,286,291 
Premiums ceded(405,312)(433,288)(55,665)(893,372)(65,551)(886,767)
Net premiums written963,555 924,732 335,846 2,224,133 175,391 2,399,524 
Change in unearned premiums(98,128)(187,708)(1,625)(287,461)8,846 (278,615)
Net premiums earned865,427 737,024 334,221 1,936,672 184,237 2,120,909 
Other underwriting income (loss)1,053 4,148 5,201 328 5,529 
Losses and loss adjustment expenses(545,880)(463,823)(9,880)(1,019,583)(140,248)(1,159,831)
Acquisition expenses(136,852)(133,585)(30,117)(300,554)(34,589)(335,143)
Other operating expenses(133,342)(44,695)(48,312)(226,349)(18,594)(244,943)
Underwriting income (loss)$49,353 $95,974 $250,060 395,387 (8,866)386,521 
Net investment income89,430 22,183 111,613 
Net realized gains (losses)163,394 39,513 202,907 
Equity in net income (loss) of investment funds accounted for using the equity method122,186 122,186 
Other income (loss)6,852 6,852 
Corporate expenses (2)(17,175)(17,175)
Transaction costs and other (2)1,444 (220)1,224 
Amortization of intangible assets(14,388)(898)(15,286)
Interest expense(31,439)(4,261)(35,700)
Net foreign exchange gains (losses)(17,892)117 (17,775)
Income (loss) before income taxes and income (loss) from operating affiliates697,799 47,568 745,367 
Income tax (expense) benefit(50,953)(226)(51,179)
Income (loss) from operating affiliates24,476 24,476 
Net income (loss)671,322 47,342 718,664 
Amounts attributable to redeemable noncontrolling interests(580)(981)(1,561)
Amounts attributable to nonredeemable noncontrolling interests(41,617)(41,617)
Net income (loss) available to Arch670,742 4,744 675,486 
Preferred dividends(11,666)(11,666)
Net income (loss) available to Arch common shareholders$659,076 $4,744 $663,820 
Underwriting Ratios
Loss ratio63.1 %62.9 %3.0 %52.6 %76.1 %54.7 %
Acquisition expense ratio15.8 %18.1 %9.0 %15.5 %18.8 %15.8 %
Other operating expense ratio15.4 %6.1 %14.5 %11.7 %10.1 %11.5 %
Combined ratio94.3 %87.1 %26.5 %79.8 %105.0 %82.0 %
Goodwill and intangible assets$270,262 $16,168 $370,405 $656,835 $10,318 $667,153 
(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.
(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

ARCH CAPITAL 142021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
Three Months Ended
June 30, 2020
 InsuranceReinsuranceMortgageSub-TotalOtherTotal
Gross premiums written (1)$1,030,362 $807,065 $369,144 $2,206,410 $157,927 $2,317,692 
Premiums ceded(358,101)(241,971)(44,044)(643,955)(52,071)(649,381)
Net premiums written672,261 565,094 325,100 1,562,455 105,856 1,668,311 
Change in unearned premiums15,648 (84,897)40,613 (28,636)25,679 (2,957)
Net premiums earned687,909 480,197 365,713 1,533,819 131,535 1,665,354 
Other underwriting income (loss)(651)6,450 5,799 868 6,667 
Losses and loss adjustment expenses(518,203)(383,433)(224,100)(1,125,736)(104,786)(1,230,522)
Acquisition expenses(107,671)(90,522)(34,052)(232,245)(22,544)(254,789)
Other operating expenses(118,757)(38,716)(37,574)(195,047)(14,202)(209,249)
Underwriting income (loss)$(56,722)$(33,125)$76,437 (13,410)(9,129)(22,539)
Net investment income101,031 30,454 131,485 
Net realized gains (losses)385,089 171,499 556,588 
Equity in net income (loss) of investment funds accounted for using the equity method(65,119)(65,119)
Other income (loss)33 33 
Corporate expenses (2)(16,943)(16,943)
Transaction costs and other (2)(977)(977)
Amortization of intangible assets(16,489)(16,489)
Interest expense(25,130)(6,009)(31,139)
Net foreign exchange gains (losses)(42,438)3,227 (39,211)
Income (loss) before income taxes and income (loss) from operating affiliates305,647 190,042 495,689 
Income tax (expense) benefit(26,529)402 (26,127)
Income (loss) from operating affiliates(3,173)(3,173)
Net income (loss)275,945 190,444 466,389 
Amounts attributable to redeemable noncontrolling interests(934)(1,036)(1,970)
Amounts attributable to nonredeemable noncontrolling interests(165,598)(165,598)
Net income (loss) available to Arch275,011 23,810 298,821 
Preferred dividends(10,403)(10,403)
Net income (loss) available to Arch common shareholders$264,608 $23,810 $288,418 
Underwriting Ratios     
Loss ratio75.3 %79.8 %61.3 %73.4 %79.7 %73.9 %
Acquisition expense ratio15.7 %18.9 %9.3 %15.1 %17.1 %15.3 %
Other operating expense ratio17.3 %8.1 %10.3 %12.7 %10.8 %12.6 %
Combined ratio108.3 %106.8 %80.9 %101.2 %107.6 %101.8 %
Goodwill and intangible assets$263,086 $2,516 $415,238 $680,840 $7,650 $688,490 

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

ARCH CAPITAL 152021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
Six Months Ended
June 30, 2021
 InsuranceReinsuranceMortgageSub-TotalOtherTotal
Gross premiums written (1)$2,784,753 $2,829,080 $782,757 $6,394,798 $457,465 $6,683,497 
Premiums ceded(826,359)(905,236)(111,716)(1,841,519)(102,763)(1,775,516)
Net premiums written1,958,394 1,923,844 671,041 4,553,279 354,702 4,907,981 
Change in unearned premiums(273,493)(541,920)(503)(815,916)(22,734)(838,650)
Net premiums earned1,684,901 1,381,924 670,538 3,737,363 331,968 4,069,331 
Other underwriting income (loss)(145)11,045 10,900 739 11,639 
Losses and loss adjustment expenses(1,081,627)(948,693)(73,569)(2,103,889)(259,042)(2,362,931)
Acquisition expenses(265,074)(251,610)(60,199)(576,883)(62,741)(639,624)
Other operating expenses(270,455)(105,209)(97,443)(473,107)(32,869)(505,976)
Underwriting income (loss)$67,745 $76,267 $450,372 $594,384 $(21,945)$572,439 
Net investment income168,159 42,310 210,469 
Net realized gains (losses)264,730 80,638 345,368 
Equity in net income (loss) of investment funds accounted for using the equity method193,872 193,872 
Other income (loss)5,111 5,111 
Corporate expenses (2)(40,643)(40,643)
Transaction costs and other (2)243 (935)(692)
Amortization of intangible assets(28,790)(898)(29,688)
Interest expense(65,636)(8,410)(74,046)
Net foreign exchange gains (losses)3,613 (1,325)2,288 
Income (loss) before income taxes and income (loss) from operating affiliates1,095,043 89,435 1,184,478 
Income tax (expense) benefit(89,805)(234)(90,039)
Income (loss) from operating affiliates99,933 99,933 
Net income (loss)1,105,171 89,201 1,194,372 
Amounts attributable to redeemable noncontrolling interests(463)(1,953)(2,416)
Amounts attributable to nonredeemable noncontrolling interests(78,314)(78,314)
Net income (loss) available to Arch1,104,708 8,934 1,113,642 
Preferred dividends(22,069)(22,069)
Net income (loss) available to Arch common shareholders$1,082,639 $8,934 $1,091,573 
Underwriting Ratios
Loss ratio64.2 %68.7 %11.0 %56.3 %78.0 %58.1 %
Acquisition expense ratio15.7 %18.2 %9.0 %15.4 %18.9 %15.7 %
Other operating expense ratio16.1 %7.6 %14.5 %12.7 %9.9 %12.4 %
Combined ratio96.0 %94.5 %34.5 %84.4 %106.8 %86.2 %
(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.
(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

ARCH CAPITAL 162021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
Six Months Ended
June 30, 2020
 InsuranceReinsuranceMortgageSub-TotalOtherTotal
Gross premiums written (1)$2,238,007 $1,929,584 $738,089 $4,904,947 $392,829 $5,150,522 
Premiums ceded(736,998)(567,310)(88,371)(1,391,946)(100,273)(1,344,965)
Net premiums written1,501,009 1,362,274 649,718 3,513,001 292,556 3,805,557 
Change in unearned premiums(97,181)(338,617)61,021 (374,777)(20,982)(395,759)
Net premiums earned1,403,828 1,023,657 710,739 3,138,224 271,574 3,409,798 
Other underwriting income (loss)1,469 11,049 12,518 1,001 13,519 
Losses and loss adjustment expenses(1,025,311)(813,502)(291,666)(2,130,479)(215,462)(2,345,941)
Acquisition expenses(215,008)(170,128)(72,588)(457,724)(44,348)(502,072)
Other operating expenses(248,406)(84,013)(83,470)(415,889)(27,904)(443,793)
Underwriting income (loss)$(84,897)$(42,517)$274,064 $146,650 $(15,139)$131,511 
Net investment income214,059 62,579 276,638 
Net realized gains (losses)312,980 (123,352)189,628 
Equity in net income (loss) of investment funds accounted for using the equity method(69,328)(69,328)
Other income (loss)65 65 
Corporate expenses (2)(35,144)(35,144)
Transaction costs and other (2)(3,572)(3,572)
Amortization of intangible assets(33,120)(33,120)
Interest expense(50,375)(13,319)(63,694)
Net foreign exchange gains (losses)20,869 12,591 33,460 
Income (loss) before income taxes and income (loss) from operating affiliates503,084 (76,640)426,444 
Income tax (expense) benefit(54,474)402 (54,072)
Income (loss) from operating affiliates5,343 5,343 
Net income (loss)453,953 (76,238)377,715 
Amounts attributable to redeemable noncontrolling interests(991)(2,132)(3,123)
Amounts attributable to nonredeemable noncontrolling interests68,346 68,346 
Net income (loss) available to Arch452,962 (10,024)442,938 
Preferred dividends(20,806)(20,806)
Net income (loss) available to Arch common shareholders$432,156 $(10,024)$422,132 
Underwriting Ratios
Loss ratio73.0 %79.5 %41.0 %67.9 %79.3 %68.8 %
Acquisition expense ratio15.3 %16.6 %10.2 %14.6 %16.3 %14.7 %
Other operating expense ratio17.7 %8.2 %11.7 %13.3 %10.3 %13.0 %
Combined ratio106.0 %104.3 %62.9 %95.8 %105.9 %96.5 %
(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.
(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

ARCH CAPITAL 172021 SECOND QUARTER FORM 10-Q

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 EndedSix Months Ended
June 30,June 30,
2021202020212020
Reserve for losses and loss adjustment expenses at beginning of period$16,443,952 $14,309,580 $16,513,929 $13,891,842 
Unpaid losses and loss adjustment expenses recoverable3,916,650 4,070,114 4,314,855 4,082,650 
Net reserve for losses and loss adjustment expenses at beginning of period12,527,302 10,239,466 12,199,074 9,809,192 
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year1,219,081 1,274,589 2,463,853 2,409,031 
Prior years(59,250)(44,067)(100,922)(63,090)
Total net incurred losses and loss adjustment expenses1,159,831 1,230,522 2,362,931 2,345,941 
Retroactive reinsurance transactions (1)(183,893)60,635 
Net foreign exchange (gains) losses135,847 51,157 88,970 (91,416)
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year(164,441)(128,174)(223,425)(169,434)
Prior years(607,911)(504,254)(1,193,029)(1,066,201)
Total net paid losses and loss adjustment expenses(772,352)(632,428)(1,416,454)(1,235,635)
Net reserve for losses and loss adjustment expenses at end of period13,050,628 10,888,717 13,050,628 10,888,717 
Unpaid losses and loss adjustment expenses recoverable4,146,020 4,156,157 4,146,020 4,156,157 
Reserve for losses and loss adjustment expenses at end of period$17,196,648 $15,044,874 $17,196,648 $15,044,874 
(1)     During the 2021 first quarter, the Company entered into a reinsurance to close and other related agreements with Premia Managing Agency Limited (“Premia”), in connection with the 2018 and prior years of account related to the acquisition of Barbican Group Holdings Limited (“Barbican”). During the 2020 first quarter, the Company entered into a reinsurance to close agreement of the 2017 and prior years of account previously covered by a third party arrangement.

Development on Prior Year Loss Reserves

2021 Second Quarter

During the 2021 second quarter, the Company recorded net favorable development on prior year loss reserves of $59.3 million, which consisted of $4.0 million from the insurance segment, $20.5 million from the reinsurance segment and $43.1 million from the mortgage segment, partially offset by $8.3 million of adverse development from the ‘other’ segment.
The insurance segment’s net favorable development of $4.0 million, or 0.5 loss ratio points, for the 2021 second quarter consisted of $28.5 million of net favorable development in short-tailed and long-tailed lines and $24.5 million of net adverse development in medium-tailed lines. Net favorable development in short-tailed lines reflected $10.7 million of favorable development in lenders products, primarily from the 2020 accident year (i.e., the year in which a loss occurred), $7.1 million of favorable development from property (excluding marine), primarily from the 2017, 2019
and 2020 accident years and $6.7 million of favorable development in travel and accident, primarily from the 2020 accident year. Net favorable development in long-tailed lines reflected $5.6 million of favorable development related to construction and national accounts, primarily from the 2016 to 2020 accident years. Net adverse development in medium-tailed lines included $20.1 million of adverse development in contract binding business, primarily from the 2014 to 2019 accident years.

The reinsurance segment’s net favorable development of $20.5 million, or 2.8 loss ratio points, for the 2021 second quarter consisted of $53.7 million of net favorable development in short-tailed and medium-tailed lines and $33.2 million of net adverse development in long-tailed lines. Net favorable development in short-tailed lines reflected $61.6 million of favorable development related to other specialty, primarily from the 2019 underwriting year (i.e., all premiums and losses attributable to contracts having an inception or renewal date within the given twelve-month period), which was partially offset by $17.1 million of net
ARCH CAPITAL 182021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
adverse development related to property catastrophe, primarily from the 2020 underwriting year. Net favorable development of $4.0 million in medium-tailed lines reflected favorable development in marine and aviation, across most underwriting years. Net adverse development in long-tailed lines reflected $34.2 million of adverse development in casualty, primarily from the 2018 underwriting year.

The mortgage segment’s net favorable development was $43.1 million, or 12.9 loss ratio points, for the 2021 second quarter, with the largest contributor being reserve releases associated with the various vintage credit risk transfer contracts that were called by the GSEs. The net favorable development also included reserve releases in our international portfolio and subrogation recoveries on second lien and student loan business.
2020 Second Quarter
During the 2020 second quarter, the Company recorded net favorable development on prior year loss reserves of $44.1 million, which consisted of $2.5 million from the insurance segment, $40.2 million from the reinsurance segment, $0.2 million from the mortgage segment and $1.1 million from the ‘other’ segment.
The insurance segment’s net favorable development of $2.5 million, or 0.4 loss ratio points, for the 2020 second quarter consisted of $19.7 million of net favorable development in short-tailed and long-tailed lines and $17.1 million of net adverse development in medium-tailed lines. Net favorable development of $11.5 million in short-tailed lines reflected $7.5 million of favorable development from property (excluding marine), primarily from the 2016 to 2019 accident years and $3.5 million of favorable development on travel and accident, primarily from the 2019 accident year. Net favorable development of $8.1 million in long-tailed lines reflected $2.4 million of favorable development in executive assurance, primarily from the 2013 accident year, and $4.9 million of favorable development related to other business, including alternative markets and excess workers’ compensation, across most accident years. Net adverse development in medium-tailed lines included $6.3 million of adverse development in professional liability, primarily from the 2009, 2016 and 2019 accident years, $6.1 million of adverse development in contract binding, across all accident years, and $4.0 million of adverse development on program business, primarily from the 2014 and 2017 accident years.
The reinsurance segment’s net favorable development of $40.2 million, or 8.4 loss ratio points, for the 2020 second quarter consisted of $46.2 million of net favorable development from short-tailed lines and net adverse development of $6.0 million from and medium-tailed and long-tailed lines. Net favorable development in short-tailed lines reflected $27.5 million of favorable development from
other specialty, across most underwriting years, and $18.3 million of favorable development related to property catastrophe and property other than property catastrophe business, primarily from the 2016 to 2019 underwriting years. Adverse development of $5.8 million in long-tailed lines reflected an increase in reserves from casualty, primarily from the 2012 to 2015 underwriting years.
The mortgage segment’s net favorable development was $0.2 million, or 0.1 loss ratio points, for the 2020 second quarter.
Six Months Ended June 30, 2021
During the six months ended June 30, 2021, the Company recorded net favorable development on prior year loss reserves of $100.9 million, which consisted of $8.1 million favorable from the insurance segment, $47.3 million from the reinsurance segment and $54.0 million from the mortgage segment, partially offset by $8.4 million of adverse development from the ‘other’ segment.
The insurance segment’s net favorable development of $8.1 million, or 0.5 loss ratio points, for the 2021 period consisted of $53.5 million of net favorable development in short-tailed and long-tailed lines, partially offset by $45.4 million of net adverse development in medium-tailed lines. Net favorable development of $49.4 million in short-tailed lines reflected $21.6 million of favorable development from property (excluding marine), primarily from the 2018 to 2020 accident years, $18.6 million of favorable development in lenders products, primarily from the 2020 accident year and $9.3 million of favorable development in travel and accident, primarily from the 2020 accident year. Net favorable development of in long-tailed lines included favorable development primarily related to construction and national accounts, primarily in the 2016 to 2019 accident years. Net adverse development in medium-tailed lines reflected $20.1 million of adverse development in contract binding business, primarily in the 2014 to 2019 accident years, $12.6 million of adverse development on programs business, primarily from the 2016 to 2020 accident years, and $11.2 million of adverse development in professional liability business, primarily from the 2019 and 2020 accident years.
The reinsurance segment’s net favorable development of $47.3 million, or 3.4 loss ratio points, for the 2021 period consisted of $72.1 million of net favorable development from short-tailed and medium-tailed lines, partially offset by $24.8 million of net adverse development from long-tailed lines. Net favorable development of $67.2 million in short-tailed lines reflected $78.2 million of favorable development from other specialty lines, primarily from the 2019 underwriting year and $28.8 million of favorable development from property other than property catastrophe business, partially offset by adverse development of $39.6 million from property catastrophe, primarily from the
ARCH CAPITAL 192021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
2020 underwriting year. Adverse development in long-tailed lines reflected an increase in reserves from casualty, primarily from the 2018 underwriting year.
The mortgage segment’s net favorable development was $54.0 million, or 8.1 loss ratio points, for the 2021 period, primarily driven by favorable development in the credit risk transfer and international portfolios. Subrogation recoveries on second lien and student loan business also contributed.
Six Months Ended June 30, 2020
During the six months ended June 30, 2020, the Company recorded net favorable development on prior year loss reserves of $63.1 million, which consisted of $3.6 million from the insurance segment, $51.8 million from the reinsurance segment, $6.3 million from the mortgage segment and $1.3 million from the ‘other’ segment.
The insurance segment’s net favorable development of $3.6 million, or 0.3 loss ratio points, for the 2020 period consisted of $28.7 million of net favorable development in short-tailed and long-tailed lines, partially offset by $25.1 million of net adverse development in medium-tailed lines. Net favorable development of $15.4 million in short-tailed lines reflected $9.6 million of favorable development from property (excluding marine), primarily from the 2015 to 2018 accident years and $3.1 million of favorable development in lenders products, primarily from the 2017 to 2019 accident years. Net favorable development of $13.3 million in long-tailed lines included $7.6 million of favorable development related to other business, including alternative markets and excess workers’ compensation, primarily in the 2016 and 2017 accident years. Net adverse development in medium-tailed lines reflected $19.3 million of adverse development in contract binding business, primarily in the 2016 to 2019 accident years, and $6.3 million of adverse development in program business, primarily from the 2017 and 2018 accident years.
The reinsurance segment’s net favorable development of $51.8 million, or 5.1 loss ratio points, for the 2020 period consisted of $67.4 million of net favorable development from short-tailed and medium-tailed lines, offset by $15.6 million of net adverse development from long-tailed lines. Net favorable development of $65.7 million in short-tailed lines reflected $39.3 million from other specialty lines and $21.3 million from property catastrophe, primarily from the 2015 to 2019 underwriting years. Adverse development in long-tailed lines reflected an increase in reserves from casualty, primarily from the 2012 to 2015 underwriting years.
The mortgage segment’s net favorable development was $6.3 million, or 0.9 loss ratio points, for the 2020 period. The 2020 development was primarily driven by subrogation recoveries on second lien business and student loan business.
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 AllowanceAllowance for Expected Credit Losses
Three Months Ended June 30, 2021
Balance at beginning of period$2,618,175 $36,111 
Change for provision of expected credit losses (1)(132)
Balance at end of period$2,866,578 $35,979 
Three Months Ended June 30, 2020
Balance at beginning of period$2,155,204 $27,990 
Change for provision of expected credit losses (1)8,064 
Balance at end of period$2,203,753 $36,054 
Six Months Ended June 30, 2021
Balance at beginning of period$2,064,586 $37,781 
Change for provision of expected credit losses (1)(1,802)
Balance at end of period$2,866,578 $35,979 
Six Months Ended June 30, 2020
Balance at beginning of period$1,778,717 $21,003 
Cumulative effect of accounting change (2)6,539 
Change for provision of expected credit losses (1)8,512 
Balance at end of period$2,203,753 $36,054 
(1)Amounts deemed uncollectible are written-off in operating expenses. For the 2021 second quarter and 2020 second quarter, amounts written off were $1.1 million and $1.8 million, respectively. For the six months ended June 30, 2021 and 2020 period, amounts written off were were $1.2 million and $2.3 million, respectively.
(2)Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

ARCH CAPITAL 202021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
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 AllowanceAllowance for Expected Credit Losses
Three Months Ended June 30, 2021
Balance at beginning of period$4,041,076 $10,872 
Change for provision of expected credit losses157 
Balance at end of period$4,314,515 $11,029 
Three Months Ended June 30, 2020
Balance at beginning of period$4,303,135 $13,700 
Change for provision of expected credit losses(105)
Balance at end of period$4,363,507 $13,595 
Six Months Ended June 30, 2021
Balance at beginning of period$4,500,802 $11,636 
Change for provision of expected credit losses(607)
Balance at end of period$4,314,515 $11,029 
Six Months Ended June 30, 2020
Balance at beginning of period$4,346,816 $1,364 
Cumulative effect of accounting change (1)12,010 
Change for provision of expected credit losses221 
Balance at end of period$4,363,507 $13,595 
(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.
The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums):
June 30,December 31
20212020
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses$4,314,515$4,500,802
% due from carriers with A.M. Best rating of “A-” or better66.0 %63.9 %
% due from all other carriers with no A.M. Best rating (1)34.0 %36.1 %
Largest balance due from any one carrier as % of total shareholders’ equity2.4 %1.8 %
(1)    At June 30, 2021 and December 31, 2020 over 91% and 94% of such amount were collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other, respectively.
Contractholder Receivables
The following table provides a roll forward of the allowance for expected credit losses of the Company’s contractholder receivables:
Contract-holder Receivables, Net of AllowanceAllowance for Expected Credit Losses
Three Months Ended June 30, 2021
Balance at beginning of period$1,919,655 $5,853 
Change for provision of expected credit losses(1,382)
Balance at end of period$1,882,948 $4,471 
Three Months Ended June 30, 2020
Balance at beginning of period$2,140,724 $9,038 
Change for provision of expected credit losses(2,748)
Balance at end of period2,179,124 $6,290 
Six Months Ended June 30, 2021
Balance at beginning of period$1,986,924 $8,638 
Change for provision of expected credit losses(4,167)
Balance at end of period$1,882,948 $4,471 
Six Months Ended June 30, 2020
Balance at beginning of period$2,119,460 $
Cumulative effect of accounting change (1)6,663 
Change for provision of expected credit losses(373)
Balance at end of period$2,179,124 $6,290 
(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.
ARCH CAPITAL 212021 SECOND QUARTER FORM 10-Q

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

At June 30, 2021, total investable assets of $30.2 billion included $27.3 billion held by the Company and $2.9 billion attributable to Watford.
Available For Sale Investments
The following table summarizes the fair value and cost or amortized cost of the Company’s securities classified as available for sale:
Estimated
Fair
Value
Gross
Unrealized
Gains
Gross
Unrealized
Losses
Allowance for Expected Credit Losses (2)Cost or
Amortized
Cost
June 30, 2021
Fixed maturities (1):
Corporate bonds$7,129,768 $217,061 $(34,751)$(1,232)$6,948,690 
Mortgage backed securities389,041 4,480 (3,479)(269)388,309 
Municipal bonds415,483 23,153 (1,660)(6)393,996 
Commercial mortgage backed securities266,733 4,017 (611)(3)263,330 
U.S. government and government agencies5,091,183 14,814 (14,013)5,090,382 
Non-U.S. government securities2,449,782 108,823 (18,441)(128)2,359,528 
Asset backed securities2,487,845 16,460 (4,056)(486)2,475,927 
Total18,229,835 388,808 (77,011)(2,124)17,920,162 
Short-term investments2,248,613 1,404 (1,406)2,248,615 
Total$20,478,448 $390,212 $(78,417)$(2,124)$20,168,777 
December 31, 2020
Fixed maturities (1):
Corporate bonds$7,856,571 $414,247 $(34,388)$(896)$7,477,608 
Mortgage backed securities630,001 8,939 (5,028)(278)626,368 
Municipal bonds494,522 27,291 (3,835)(11)471,077 
Commercial mortgage backed securities389,900 8,722 (2,954)(122)384,254 
U.S. government and government agencies5,557,077 22,612 (12,611)5,547,076 
Non-U.S. government securities2,433,733 153,891 (8,060)2,287,902 
Asset backed securities1,634,804 19,225 (10,715)(1,090)1,627,384 
Total18,996,608 654,927 (77,591)(2,397)18,421,669 
Short-term investments1,924,922 2,693 (2,063)1,924,292 
Total$20,921,530 $657,620 $(79,654)$(2,397)$20,345,961 
(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”
(2)    Effective January 1, 2020, the Company adopted ASU 2016-13 and as a result any credit impairment losses on the Company’s available-for-sale investments are recorded as an allowance, subject to reversal.
ARCH CAPITAL 222021 SECOND QUARTER FORM 10-Q

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 Months12 Months or MoreTotal
Estimated
Fair
Value
Gross
Unrealized
Losses
Estimated
Fair
Value
Gross
Unrealized
Losses
Estimated
Fair
Value
Gross
Unrealized
Losses
June 30, 2021
Fixed maturities (1):
Corporate bonds$2,264,801 $(32,733)$22,895 $(2,018)$2,287,696 $(34,751)
Mortgage backed securities196,765 (2,893)13,632 (586)210,397 (3,479)
Municipal bonds24,711 (1,612)2,859 (48)27,570 (1,660)
Commercial mortgage backed securities20,039 (180)7,961 (431)28,000 (611)
U.S. government and government agencies2,920,944 (14,013)2,920,944 (14,013)
Non-U.S. government securities1,282,422 (17,562)16,885 (879)1,299,307 (18,441)
Asset backed securities781,596 (2,364)93,923 (1,692)875,519 (4,056)
Total7,491,278 (71,357)158,155 (5,654)7,649,433 (77,011)
Short-term investments531,130 (1,406)531,130 (1,406)
Total$8,022,408 $(72,763)$158,155 $(5,654)$8,180,563 $(78,417)
December 31, 2020
Fixed maturities (1):
Corporate bonds$747,442 $(33,086)$3,934 $(1,302)$751,376 $(34,388)
Mortgage backed securities284,619 (4,788)3,637 (240)288,256 (5,028)
Municipal bonds67,937 (3,835)67,937 (3,835)
Commercial mortgage backed securities126,624 (2,916)2,655 (38)129,279 (2,954)
U.S. government and government agencies1,285,907 (12,611)1,285,907 (12,611)
Non-U.S. government securities543,844 (7,658)2,441 (402)546,285 (8,060)
Asset backed securities634,470 (9,110)57,737 (1,605)692,207 (10,715)
Total3,690,843 (74,004)70,404 (3,587)3,761,247 (77,591)
Short-term investments97,920 (2,063)97,920 (2,063)
Total$3,788,763 $(76,067)$70,404 $(3,587)$3,859,167 $(79,654)
(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

At June 30, 2021, on a lot level basis, approximately 3,240 security lots out of a total of approximately 10,890 security lots were in an unrealized loss position and the largest single unrealized loss from a single lot in the Company’s fixed maturity portfolio was $2.4 million. At December 31, 2020, on a lot level basis, approximately 2,320 security lots out of a total of approximately 11,180 security lots were in an unrealized loss position and the largest single unrealized loss from a single lot in the Company’s fixed maturity portfolio was $0.9 million.

ARCH CAPITAL 232021 SECOND QUARTER FORM 10-Q

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.
June 30, 2021December 31, 2020
MaturityEstimated
Fair
Value
Amortized
Cost
Estimated
Fair
Value
Amortized
Cost
Due in one year or less$452,065 $439,855 $348,200 $339,951 
Due after one year through five years10,114,276 9,942,182 10,629,959 10,340,819 
Due after five years through 10 years4,148,538 4,055,318 4,881,564 4,654,754 
Due after 10 years371,337 355,241 482,180 448,139 
 15,086,216 14,792,596 16,341,903 15,783,663 
Mortgage backed securities389,041 388,309 630,001 626,368 
Commercial mortgage backed securities266,733 263,330 389,900 384,254 
Asset backed securities2,487,845 2,475,927 1,634,804 1,627,384 
Total (1)$18,229,835 $17,920,162 $18,996,608 $18,421,669 
(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

Securities Lending Agreements
The Company enters into securities lending agreements with financial institutions to enhance investment income whereby it loans certain of its securities to third parties, primarily major brokerage firms, for short periods of time through a lending agent. The Company maintains legal control over the securities it lends (shown as ‘Securities pledged under securities lending, at fair value’ on the Company’s balance sheet), retains the earnings and cash flows associated with the loaned securities and receives a fee from the borrower for the temporary use of the securities. An indemnification agreement with the lending agent protects the Company in the event a borrower becomes insolvent or fails to return any of the securities on loan from the Company.
The Company receives collateral (shown as ‘Collateral received under securities lending, at fair value’ on the Company’s balance sheet) in the form of cash or U.S. government and government agency securities. At June 30, 2021, the fair value of the cash collateral received on securities lending was $0.8 million and the fair value of security collateral received was $171.3 million. At December 31, 2020, the fair value of the cash collateral received on securities lending was NaN, and the fair value of security collateral received was $301.1 million.
ARCH CAPITAL 242021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
The carrying value of collateral held under the Company’s securities lending transactions by significant investment category and remaining contractual maturity of the underlying agreements is as follows:
Remaining Contractual Maturity of the Agreements
Overnight and ContinuousLess than 30 Days30-90 Days90 Days or MoreTotal
June 30, 2021
U.S. government and government agencies$15,745 $137,713 $$$153,458 
Corporate bonds5,800 5,800 
Equity securities12,851 12,851 
Total$34,396 $137,713 $$$172,109 
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9
$
Amounts related to securities lending not included in offsetting disclosure in note 9
$172,109 
December 31, 2020
U.S. government and government agencies$142,317 $$139,290 $$281,607 
Corporate bonds3,021 3,021 
Equity securities16,461 16,461 
Total$161,799 $$139,290 $$301,089 
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9
$
Amounts related to securities lending not included in offsetting disclosure in note 9
$301,089 
Equity Securities, at Fair Value
At June 30, 2021, the Company held $1.7 billion of equity securities, at fair value, compared to $1.4 billion at December 31, 2020. Such holdings include publicly traded common stocks primarily in the consumer cyclical and non-cyclical, technology, communication and financial sectors and exchange-traded funds in fixed income, equity and other sectors.
Other Investments
The following table summarizes the Company’s other investments and other investable assets:
June 30,
2021
December 31,
2020
Fixed maturities$995,980 $843,354 
Other investments2,370,472 2,331,885 
Short-term investments610,114 557,008 
Equity securities94,931 92,549 
Investments accounted for using the fair value option$4,071,497 $3,824,796 
Other investable assets (1)500,000 500,000 
Total other investments$4,571,497 $4,324,796 
(1) Participation interests in a receivable of a reverse repurchase agreement.
The following table summarizes the Company’s other investments, as detailed in the previous table, by strategy:
June 30,
2021
December 31,
2020
Term loan investments$1,333,014 $1,231,731 
Lending638,786 572,636 
Credit related funds73,171 90,780 
Energy84,891 65,813 
Investment grade fixed income110,375 138,646 
Infrastructure32,109 165,516 
Private equity70,878 48,750 
Real estate27,248 18,013 
Total$2,370,472 $2,331,885 
Investments Accounted For Using the Equity Method
The following table summarizes the Company’s investments accounted for using the equity method, by strategy:
June 30,
2021
December 31,
2020
Credit related funds$883,279 $740,060 
Equities403,003 343,058 
Real estate323,566 258,518 
Lending295,228 179,629 
Private equity305,662 235,289 
Infrastructure210,174 175,882 
Energy118,212 115,453 
Total$2,539,124 $2,047,889 
Certain of the Company’s other investments are in investment funds for which the Company has the option to redeem at agreed upon values as described in each investment fund’s subscription agreement. Depending on the
ARCH CAPITAL 252021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
terms of the various subscription agreements, investments in investment funds may be redeemed daily, monthly, quarterly or on other terms. Two common redemption restrictions which may impact the Company’s ability to redeem these investment funds are gates and lockups. A gate is a suspension of redemptions which may be implemented by the general partner or investment manager of the fund in order to defer, in whole or in part, the redemption request in the event the aggregate amount of redemption requests exceeds a predetermined percentage of the investment fund’s net assets which may otherwise hinder the general partner or investment manager’s ability to liquidate holdings in an orderly fashion in order to generate the cash necessary to fund extraordinarily large redemption payouts. A lockup period is the initial amount of time an investor is contractually required to hold the security before having the ability to redeem. If the investment funds are eligible to be redeemed, the time to redeem such fund can take weeks or months following the notification.
Limited Partnership Interests
In the normal course of its activities, the Company invests in limited partnerships as part of its overall investment strategy. Such amounts are included in ‘investments accounted for using the equity method’ and ‘investments accounted for using the fair value option.’ The Company has determined that it is not required to consolidate these investments because it is not the primary beneficiary of the funds. The Company’s maximum exposure to loss with respect to these investments is limited to the investment carrying amounts reported in the Company’s consolidated balance sheet and any unfunded commitment.
The following table summarizes investments in limited partnership interests where the Company has a variable interest by balance sheet line item:
June 30,
2021
December 31,
2020
Investments accounted for using the equity method (1)2,539,124 2,047,889 
Investments accounted for using the fair value option (2)182,260 184,720 
Total$2,721,384 $2,232,609 
(1)    Aggregate unfunded commitments were $2.0 billion at June 30, 2021, compared to $1.8 billion at December 31, 2020.
(2)    Aggregate unfunded commitments were $26.3 million at June 30, 2021, compared to $35.6 million at December 31, 2020.
Net Investment Income
The components of net investment income were derived from the following sources:
June 30,
 20212020
Three Months Ended
Fixed maturities$88,625 $105,391 
Term loans16,879 20,512 
Equity securities8,584 6,219 
Short-term investments1,138 3,383 
Other (1)19,950 16,460 
Gross investment income135,176 151,965 
Investment expenses(23,563)(20,480)
Net investment income$111,613 $131,485 
Six Months Ended
Fixed maturities$179,251 $220,238 
Term loans31,607 43,682 
Equity securities14,234 12,226 
Short-term investments1,745 8,279 
Other (1)34,305 35,866 
Gross investment income261,142 320,291 
Investment expenses(50,673)(43,653)
Net investment income$210,469 $276,638 
(1)    Includes income distributions from investment funds and other items.
ARCH CAPITAL 262021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
Net Realized Gains (Losses)
Net realized gains (losses), which include changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings were as follows:
June 30,
 20212020
Three Months Ended
Available for sale securities:  
Gross gains on investment sales$115,541 $232,153 
Gross losses on investment sales(50,627)(49,824)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities10,912 68,181 
Other investments60,884 178,570 
Equity securities5,492 6,664 
Short-term investments(104)3,368 
Equity securities, at fair value:
Net realized gains (losses) on sales during the period33,570 (18,250)
Net unrealized gains (losses) on equity securities still held at reporting date65,847 145,686 
Allowance for credit losses:
Investments related896 3,225 
Underwriting related1,381 (5,834)
Derivative instruments (1)(51,109)(836)
Other10,224 (6,515)
Net realized gains (losses)$202,907 $556,588 
Six Months Ended
Available for sale securities:
Gross gains on investment sales$180,543 $410,353 
Gross losses on investment sales(113,625)(81,792)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities27,465 (59,485)
Other investments107,739 (129,230)
Equity securities7,557 1,755 
Short-term investments632 (5,313)
Equity securities, at fair value:
Net realized gains (losses) on sales during the period71,419 (18,789)
Net unrealized gains (losses) on equity securities still held at reporting date85,555 (29,880)
Allowance for credit losses:
Investments related(752)(6,095)
Underwriting related6,649 (9,104)
Net impairments losses(533)
Derivative instruments (1)(14,993)126,353 
Other(12,821)(8,612)
Net realized gains (losses)$345,368 $189,628 
(1)    See note 9 for information on the Company’s derivative instruments.

Equity in Net Income (Loss) of Investment Funds Accounted for Using the Equity Method
The Company recorded $122.2 million of equity in net income related to investment funds accounted for using the equity method in the 2021 second quarter, compared to loss of $65.1 million for the 2020 second quarter, and an income of $193.9 million for the six months ended June 30, 2021, compared to a loss of $69.3 million for six months ended June 30, 2020. In applying the equity method, investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the market value of the underlying securities in the funds). Such investments are generally recorded on a one 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 and Premia Holdings Ltd. (“Premia”) and are generally recorded on a three month 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. At June 30, 2021 the Company’s carrying value in Coface was $601.9 million.

Income from operating affiliates for the 2021 second quarter was $24.5 million, compared to a loss of $3.2 million, for the 2020 second quarter, and income of $99.9 million for the six months ended June 30, 2021, compared to $5.3 million for the six months ended June 30, 2020. The income from operating affiliates for the 2021 period, primarily related to the Company’s recent acquisition of a 29.5% stake in Coface.

ARCH CAPITAL 272021 SECOND QUARTER FORM 10-Q

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

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
Short Term InvestmentsTotal
Three Months Ended June 30, 2021
Balance at beginning of period$1,207 $$2,621 $$3,830 
Additions for current-period provision for expected credit losses52 59 
Additions (reductions) for previously recognized expected credit losses(383)(412)(791)
Reductions due to disposals(117)(857)(974)
Balance at end of period$759 $$1,359 $$2,124 
Three Months Ended June 30, 2020
Balance at beginning of period$2,654 $23 $7,232 $29 $9,938 
Additions for current-period provision for expected credit losses695 44 290 (29)1,000 
Additions (reductions) for previously recognized expected credit losses(1,304)(25)(2,903)(4,232)
Reductions due to disposals(319)(14)(504)(837)
Balance at end of period$1,726 $28 $4,115 $$5,869 
Six Months Ended June 30, 2021
Balance at beginning of period$1,490 $11 $896 $$2,397 
Additions for current-period provision for expected credit losses234 2,428 2,662 
Additions (reductions) for previously recognized expected credit losses(765)(5)(952)(1,722)
Reductions due to disposals(200)(1,013)(1,213)
Balance at end of period$759 $$1,359 $$2,124 
Six Months Ended June 30, 2020
Balance at beginning of period$$$$$
Cumulative effect of accounting change (2)517 117 634 
Additions for current-period provision for expected credit losses2,841 67 7,441 10,349 
Additions (reductions) for previously recognized expected credit losses(1,306)(25)(2,924)(4,255)
Reductions due to disposals(326)(14)(519)(859)
Balance at end of period$1,726 $28 $4,115 $$5,869 
(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.
(2)    Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

ARCH CAPITAL 282021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
Restricted Assets
The Company is required to maintain assets on deposit, which primarily consist of fixed maturities, with various regulatory authorities to support its underwriting operations. The Company’s subsidiaries maintain assets in trust accounts as collateral for transactions with affiliated companies and also have investments in segregated portfolios primarily to provide collateral or guarantees for letters of credit to third parties. See note 18, “Commitments and Contingencies,” of the notes to consolidated financial statements in the Company’s 2020 Form 10-K.
The following table details the value of the Company’s restricted assets:
June 30,
2021
December 31,
2020
Assets used for collateral or guarantees:  
Affiliated transactions$5,041,190 $4,643,334 
Third party agreements3,441,929 3,083,324 
Deposits with U.S. regulatory authorities814,084 827,552 
Deposits with non-U.S. regulatory authorities428,132 179,099 
Total restricted assets$9,725,335 $8,733,309 
In addition, Watford maintains secured credit facilities to provide borrowing capacity for investment purposes and a total return swap agreement and maintains assets pledged as collateral for such purposes. The Company does not guarantee or provide credit support for Watford, and the Company’s financial exposure to Watford is limited to its investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from reinsurance transactions. As of June 30, 2021 and December 31, 2020, Watford held $1.1 billion and $954.6 million, respectively, in pledged assets to collateralize the credit facility mentioned above.
Reconciliation of Cash and Restricted Cash
The following table details reconciliation of cash and restricted cash within the Consolidated Balance Sheets:
June 30,
2021
December 31,
2020
Cash$1,234,059 $906,448 
Restricted cash (included in ‘other assets’)$584,404 $384,096 
Cash and restricted cash$1,818,463 $1,290,544 

ARCH CAPITAL 292021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
8.    Fair Value
Accounting guidance regarding fair value measurements addresses how companies should measure fair value when they are required to use a fair value measure for recognition or disclosure purposes under GAAP and provides a common definition of fair value to be used throughout GAAP. It defines fair value as the price that would be received to sell an asset or paid to transfer a liability in an orderly fashion between market participants at the measurement date. In addition, it establishes a three-level valuation hierarchy for the disclosure of fair value measurements. The valuation hierarchy is based upon the transparency of inputs to the valuation of an asset or liability as of the measurement date. The level in the hierarchy within which a given fair value measurement falls is determined based on the lowest level input that is significant to the measurement (Level 1 being the highest priority and Level 3 being the lowest priority).
The levels in the hierarchy are defined as follows:
Level 1:
Inputs to the valuation methodology are observable inputs that reflect quoted prices (unadjusted) for identical assets or liabilities in active markets
Level 2:Inputs to the valuation methodology include quoted prices for similar assets and liabilities in active markets, and inputs that are observable for the asset or liability, either directly or indirectly, for substantially the full term of the financial instrument
Level 3:Inputs to the valuation methodology are unobservable and significant to the fair value measurement
Following is a description of the valuation methodologies used for securities measured at fair value, as well as the general classification of such securities pursuant to the valuation hierarchy. The Company reviews its securities measured at fair value and discusses the proper classification of such investments with investment advisers and others.
The Company determines the existence of an active market based on its judgment as to whether transactions for the financial instrument occur in such market with sufficient frequency and volume to provide reliable pricing information. The independent pricing sources obtain market quotations and actual transaction prices for securities that have quoted prices in active markets. The Company uses quoted values and other data provided by nationally recognized independent pricing sources as inputs into its process for determining fair values of its fixed maturity investments. To validate the techniques or models used by pricing sources, the Company's review process includes, but
is not limited to: (i) quantitative analysis (e.g., comparing the quarterly return for each managed portfolio to its target benchmark, with significant differences identified and investigated); (ii) a review of the average number of prices obtained in the pricing process and the range of resulting fair values; (iii) initial and ongoing evaluation of methodologies used by outside parties to calculate fair value; (iv) a comparison of the fair value estimates to the Company’s knowledge of the current market; (v) a comparison of the pricing services' fair values to other pricing services' fair values for the same investments; and (vi) periodic back-testing, which includes randomly selecting purchased or sold securities and comparing the executed prices to the fair value estimates from the pricing service. A price source hierarchy was maintained in order to determine which price source would be used (i.e., a price obtained from a pricing service with more seniority in the hierarchy will be used over a less senior one in all cases). The hierarchy prioritizes pricing services based on availability and reliability and assigns the highest priority to index providers. Based on the above review, the Company will challenge any prices for a security or portfolio which are considered not to be representative of fair value. The Company did not adjust any of the prices obtained from the independent pricing sources at June 30, 2021.
In certain circumstances, when fair values are unavailable from these independent pricing sources, quotes are obtained directly from broker-dealers who are active in the corresponding markets. Such quotes are subject to the validation procedures noted above. Where quotes are unavailable, fair value is determined by the Investment Manager using quantitative and qualitative assessments such as internally modeled values. Of the $26.5 billion of financial assets and liabilities measured at fair value at June 30, 2021, approximately $187.6 million, or 0.7%, were priced using non-binding broker-dealer quotes or modeled valuations. Of the $26.5 billion of financial assets and liabilities measured at fair value at December 31, 2020, approximately $150.1 million, or 0.6%, were priced using non-binding broker-dealer quotes or modeled valuations.
Fixed maturities
The Company uses the market approach valuation technique to estimate the fair value of its fixed maturity securities, when possible. The market approach includes obtaining prices from independent pricing services, such as index providers and pricing vendors, as well as to a lesser extent quotes from broker-dealers. The independent pricing sources obtain market quotations and actual transaction prices for securities that have quoted prices in active markets. Each source has its own proprietary method for determining the fair value of securities that are not actively traded. In general, these methods involve the use of “matrix pricing” in which the independent pricing source uses observable market inputs
ARCH CAPITAL 302021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
including, but not limited to, investment yields, credit risks and spreads, benchmarking of like securities, broker-dealer quotes, reported trades and sector groupings to determine a reasonable fair value.
The following describes the significant inputs generally used to determine the fair value of the Company’s fixed maturity securities by asset class:
U.S. government and government agencies — valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The Company determined that all U.S. Treasuries would be classified as Level 1 securities due to observed levels of trading activity, the high number of strongly correlated pricing quotes received on U.S. Treasuries and other factors. The fair values of U.S. government agency securities are generally determined using the spread above the risk-free yield curve. As the yields for the risk-free yield curve and the spreads for these securities are observable market inputs, the fair values of U.S. government agency securities are classified within Level 2.
Corporate bonds — valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined using the spread above the risk-free yield curve. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. As the significant inputs used in the pricing process for corporate bonds are observable market inputs, the fair value of these securities are classified within Level 2. A small number of securities are included in Level 3 due to a low level of transparency on the inputs used in the pricing process.
Mortgage-backed securities — valuations provided by independent pricing services, substantially all through pricing vendors and index providers with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models (including Option Adjusted Spread) which use spreads to determine the expected average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. The pricing services also review prepayment speeds and other indicators, when applicable. As the significant inputs used in the pricing process for mortgage-backed securities are observable market inputs, the fair value of these securities are classified within Level 2. A small number of securities are included in Level 3 due to a low level of transparency on the inputs used in the pricing process.
Municipal bonds — valuations provided by independent pricing services, with all prices provided
through index providers and pricing vendors. The fair values of these securities are generally determined using spreads obtained from broker-dealers who trade in the relevant security market, trade prices and the new issue market. As the significant inputs used in the pricing process for municipal bonds are observable market inputs, the fair value of these securities are classified within Level 2.
Commercial mortgage-backed securities — valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models which use spreads to determine the appropriate average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. The pricing services also review prepayment speeds and other indicators, when applicable. As the significant inputs used in the pricing process for commercial mortgage-backed securities are observable market inputs, the fair value of these securities are classified within Level 2.
Non-U.S. government securities — valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The fair values of these securities are generally based on international indices or valuation models which include daily observed yield curves, cross-currency basis index spreads and country credit spreads. As the significant inputs used in the pricing process for non-U.S. government securities are observable market inputs, the fair value of these securities are classified within Level 2.
Asset-backed securities — valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models (including Option Adjusted Spread) which use spreads to determine the appropriate average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. The pricing services also review prepayment speeds and other indicators, when applicable. As the significant inputs used in the pricing process for asset-backed securities are observable market inputs, the fair value of these securities are classified within Level 2. A small number of securities are included in Level 3 due to a low level of transparency on the inputs used in the pricing process.
Equity securities
The Company determined that exchange-traded equity securities would be included in Level 1 as their fair values are based on quoted market prices in active markets. Certain
ARCH CAPITAL 312021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
equity securities are included in Level 2 of the valuation hierarchy as the significant inputs used in the pricing process for such securities are observable market inputs. Other equity securities are included in Level 3 due to the lack of an available independent price source for such securities. As the significant inputs used to price these securities are unobservable, the fair value of such securities are classified as Level 3.
Other investments
The Company’s other investments include term loan investments for which fair values are estimated by using quoted prices of term loan investments with similar characteristics, pricing models or matrix pricing. Such investments are generally classified within Level 2. The fair values for certain of the Company’s other investments are determined using net asset values as advised by external fund managers. The net asset value is based on the fund manager’s valuation of the underlying holdings in accordance with the fund’s governing documents. In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. A small number of securities are included in Level 3 due to the lack of an available independent price source for such securities.
Derivative instruments
The Company’s futures contracts, foreign currency forward contracts, interest rate swaps and other derivatives trade in the over-the-counter derivative market. The Company uses the market approach valuation technique to estimate the fair value for these derivatives based on significant observable market inputs from third party pricing vendors, non-binding broker-dealer quotes and/or recent trading activity. As the significant inputs used in the pricing process for these derivative instruments are observable market inputs, the fair value of these securities are classified within Level 2.

Short-term investments
The Company determined that certain of its short-term investments held in highly liquid money market-type funds, Treasury bills and commercial paper would be included in Level 1 as their fair values are based on quoted market prices in active markets. The fair values of other short-term investments are generally determined using the spread above the risk-free yield curve and are classified within Level 2.
Residential mortgage loans
The Company’s residential mortgage loans (included in ‘other assets’ in the consolidated balance sheets) include amounts related to the Company’s whole mortgage loan purchase and sell program. Fair values of residential mortgage loans are generally determined based on market prices. As significant inputs used in pricing process for these residential mortgage loans are observable market inputs, the fair value of these securities are classified within Level 2.
Contingent consideration liabilities
Contingent consideration liabilities (included in ‘other liabilities’ in the consolidated balance sheets) include amounts related to various Company’s acquisitions. Such amounts are remeasured at fair value at each balance sheet date with changes in fair value recognized in ‘net realized gains (losses).’ To determine the fair value of contingent consideration liabilities, the Company estimates future payments using an income approach based on modeled inputs which include a weighted average cost of capital. The Company determined that contingent consideration liabilities would be included within Level 3.

ARCH CAPITAL 322021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
The following table presents the Company’s financial assets and liabilities measured at fair value by level at June 30, 2021:
  Estimated Fair Value Measurements Using:
 Estimated
Fair
Value
Quoted Prices in
Active Markets
for Identical
Assets
(Level 1)
Significant
Other
Observable
Inputs
(Level 2)
Significant
Unobservable
Inputs
(Level 3)
Assets measured at fair value (1):    
Available for sale securities:    
Fixed maturities:    
Corporate bonds$7,129,768 $$7,129,755 $13 
Mortgage backed securities389,041 389,041 
Municipal bonds415,483 415,483 
Commercial mortgage backed securities266,733 266,733 
U.S. government and government agencies5,091,183 5,062,571 28,612 
Non-U.S. government securities2,449,782 2,449,782 
Asset backed securities2,487,845 2,484,421 3,424 
Total18,229,835 5,062,571 13,163,827 3,437 
Short-term investments2,248,613 1,996,304 252,309 
Equity securities, at fair value1,706,044 1,631,937 24,971 49,136 
Derivative instruments (4)98,488 98,488 
Residential mortgage loans44,925 44,925 
Fair value option:
Corporate bonds790,186 789,188 998 
Non-U.S. government bonds22,552 22,552 
Mortgage backed securities2,707 2,707 
Commercial mortgage backed securities841 841 
Asset backed securities179,423 179,423 
U.S. government and government agencies271 163 108 
Short-term investments610,114 482,815 127,299 
Equity securities94,930 21,252 73,678 
Other investments1,219,294 23,610 1,121,784 73,900 
Other investments measured at net asset value (2)1,151,178 
Total4,071,496 527,840 2,243,902 148,576 
Total assets measured at fair value$26,399,401 $9,218,652 $15,828,422 $201,149 
Liabilities measured at fair value:    
Contingent consideration liabilities$(466)$$$(466)
Securities sold but not yet purchased (3)(28,068)(28,068)
Derivative instruments (4)(67,304)(67,304)
Total liabilities measured at fair value$(95,838)$$(95,372)$(466)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See note 7, “—Securities Lending Agreements.”
(2)    In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.
(3)    Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets.
(4)    See note 9.
ARCH CAPITAL 332021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2020:
  Estimated Fair Value Measurements Using:
 Estimated
Fair
Value
Quoted Prices in
Active Markets
for Identical
Assets
(Level 1)
Significant
Other
Observable
Inputs
(Level 2)
Significant
Unobservable
Inputs
(Level 3)
Assets measured at fair value (1):
Available for sale securities:
Fixed maturities:
Corporate bonds$7,856,571 $$7,856,558 $13 
Mortgage backed securities630,001 630,001 
Municipal bonds494,522 494,522 
Commercial mortgage backed securities389,900 389,900 
U.S. government and government agencies5,557,077 5,463,356 93,721 
Non-U.S. government securities2,433,733 2,433,733 
Asset backed securities1,634,804 1,631,378 3,426 
Total18,996,608 5,463,356 13,529,813 3,439 
Short-term investments1,924,922 1,920,565 4,357 
Equity securities, at fair value1,460,959 1,401,653 17,291 42,015 
Derivative instruments (4)177,383 177,383 
Fair value option:
Corporate bonds651,294 650,309 985 
Non-U.S. government bonds35,263 35,263 
Mortgage backed securities3,282 3,282 
Commercial mortgage backed securities1,090 1,090 
Asset backed securities152,151 152,151 
U.S. government and government agencies274 164 110 
Short-term investments557,008 420,131 136,877 
Equity securities92,549 23,373 188 68,988 
Other investments1,134,229 51,149 1,015,977 67,103 
Other investments measured at net asset value (2)1,197,656 
Total3,824,796 494,817 1,995,247 137,076 
Total assets measured at fair value$26,384,668 $9,280,391 $15,724,091 $182,530 
Liabilities measured at fair value:
Contingent consideration liabilities$(461)$$$(461)
Securities sold but not yet purchased (3)(21,679)(21,679)
Derivative instruments (4)(108,705)(108,705)
Total liabilities measured at fair value$(130,845)$$(130,384)$(461)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See note 7, “—Securities Lending Agreements.”
(2)    In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.
(3)    Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets.
(4)    See note 9.

ARCH CAPITAL 342021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
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:
AssetsLiabilities
sAvailable For SaleFair Value OptionFair Value
 Structured Securities (1)Corporate
Bonds
Corporate
Bonds
Other
Investments
Equity
Securities
Equity
Securities
Contingent Consideration Liabilities
Three Months Ended June 30, 2021  
Balance at beginning of period$3,472 $13 $989 $67,930 $71,176 $43,112 $(465)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)12 633 2,502 922 
Included in other comprehensive income(57)
Purchases, issuances, sales and settlements
Purchases5,638 5,102 
Issuances
Sales(301)
Settlements(3)(1)
Transfers in and/or out of Level 3
Balance at end of period$3,424 $13 $998 $73,900 $73,678 $49,136 $(466)
Three Months Ended June 30, 2020  
Balance at beginning of period$3,846 $1,980 $965 $54,620 $60,015 $55,632 $(7,967)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)(64)(987)1,432 11,799 (18)
Included in other comprehensive income(287)(1,123)
Purchases, issuances, sales and settlements
Purchases33 
Issuances
Sales(7,183)(15,450)
Settlements(45)6,735 
Transfers in and/or out of Level 3
Balance at end of period$3,450 $857 $998 $46,453 $61,447 $51,981 $(1,250)
Six Months Ended June 30, 2021  
Balance at beginning of year$3,426 $13 $985 $67,103 $68,988 $42,015 $(461)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)(56)13 881 4,690 1,826 
Included in other comprehensive income57 
Purchases, issuances, sales and settlements
Purchases13,003 5,295 
Issuances
Sales(7,087)
Settlements(3)(5)
Transfers in and/or out of Level 3
Balance at end of period$3,424 $13 $998 $73,900 $73,678 $49,136 $(466)
Six Months Ended June 30, 2020  
Balance at beginning of year$5,216 $8,851 $932 $68,817 $58,094 $55,889 $(7,998)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)(55)(1,014)3,353 8,078 (72)
Included in other comprehensive income(309)(6,539)
Purchases, issuances, sales and settlements
Purchases66 24 3,464 
Issuances
Sales(24,358)(15,450)
Settlements(1,402)(1,462)6,820 
Transfers in and/or out of Level 32,984 
Balance at end of period$3,450 $857 $998 $46,453 $61,447 $51,981 $(1,250)
(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.
(2)    Gains or losses were included in net realized gains (losses).
ARCH CAPITAL 352021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
Financial Instruments Disclosed, But Not Carried, At Fair Value
The Company uses various financial instruments in the normal course of its business. The carrying values of cash, accrued investment income, receivable for securities sold, certain other assets, payable for securities purchased and certain other liabilities approximated their fair values at June 30, 2021, due to their respective short maturities. As these financial instruments are not actively traded, their respective fair values are classified within Level 2.
At June 30, 2021, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.9 billion and had a fair value of $3.5 billion. At December 31, 2020, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.9 billion and had a fair value of $3.7 billion. 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 values of the senior notes are classified within Level 2.
9.    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 DerivativesLiability DerivativesNotional
Value (1)
June 30, 2021
Futures contracts (2)$36,277 $(21,515)$2,907,342 
Foreign currency forward contracts (2)8,242 (20,729)1,573,973 
Other (2)53,969 (25,060)4,838,552 
Total$98,488 $(67,304)
December 31, 2020
Futures contracts (2)$11,046 $(4,496)$3,099,796 
Foreign currency forward contracts (2)52,716 (6,202)1,656,729 
Other (2)113,621 (98,007)5,763,919 
Total$177,383 $(108,705)
(1)    Represents the absolute notional value of all outstanding contracts, consisting of long and short positions.
(2)    The fair value of asset derivatives are included in ‘other assets’ and the fair value of liability derivatives are included in ‘other liabilities.’

The Company did not hold any derivatives which were designated as hedging instruments at June 30, 2021 or December 31, 2020.
The Company’s derivative instruments can be traded under master netting agreements, which establish terms that apply to all derivative transactions with a counterparty. In the event of a bankruptcy or other stipulated event of default, such agreements provide that the non-defaulting party may elect to terminate all outstanding derivative transactions, in which case all individual derivative positions (loss or gain) with a counterparty are closed out and netted and replaced with a single amount, usually referred to as the termination amount, which is expressed in a single currency. The resulting single net amount, where positive, is payable to the party “in-the-money” regardless of whether or not it is the defaulting party, unless the parties have agreed that only the non-defaulting party is entitled to receive a termination payment where the net amount is positive and is in its favor. Contractual close-out netting reduces derivatives credit exposure from gross to net exposure.
At June 30, 2021, asset derivatives and liability derivatives of $89.9 million and $66.7 million, respectively, were subject to a master netting agreement, compared to $138.8 million and $93.0 million, respectively, at December 31, 2020. The remaining derivatives included in the preceding table were not subject to a master netting agreement.
Realized and unrealized contract gains and losses on the Company’s derivative instruments are reflected in ‘net realized gains (losses)’ in the consolidated statements of income, as summarized in the following table:
ARCH CAPITAL 362021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
Derivatives not designated asJune 30,
hedging instruments:20212020
Three Months Ended
Net realized gains (losses):
Futures contracts$(54,759)$(1,607)
Foreign currency forward contracts1,295 3,523 
TBAs264 
Other (1)2,355 (3,016)
Total$(51,109)$(836)
Six Months Ended
Net realized gains (losses):
Futures contracts$(7,321)$94,337 
Foreign currency forward contracts(20,776)(7,347)
TBAs1,009 
Other (1)13,104 38,354 
Total$(14,993)$126,353 
(1)    Includes realized gains and losses on swaps, options and other derivatives contracts.
10.    Commitments and Contingencies
Investment Commitments
The Company’s investment commitments, which are primarily related to agreements entered into by the Company to invest in funds and separately managed accounts when called upon, were approximately $2.4 billion at June 30, 2021, compared to $2.1 billion at December 31, 2020.
Interest Paid
Interest paid on the Company’s senior notes and other borrowings were $74.7 million for the six months ended June 30, 2021, compared to $57.4 million for the 2020 period.
11.    Variable Interest Entities and Noncontrolling Interests
Watford
In March 2014, the Company invested $100.0 million and acquired 2,500,000 common shares, approximately 11% of Watford’s outstanding common equity. As of June 30, 2021, the Company owned approximately 10.2% of Watford’s outstanding common equity. The Company also owns $35.0 million in aggregate principal amount of Watford Holdings Ltd’s 6.5% senior notes, due July 2, 2029 and approximately 6.6% of Watford’s preference shares.
Watford is considered a VIE and the Company concluded that it is the primary beneficiary of Watford, through June 30, 2021. As such, the results of Watford are included in the
Company’s consolidated financial statements as of and for the periods ended June 30, 2021.
The Company does not guarantee or provide credit support for Watford, and the Company’s financial exposure to Watford is limited to its investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from reinsurance transactions.
In the 2020 fourth quarter, Arch Capital, Watford Holdings Ltd. and Greysbridge Ltd., a wholly-owned subsidiary of Arch Capital, entered into an Agreement and Plan of Merger (as amended, the “Merger Agreement”) pursuant to which, among other things, Arch Capital agreed to acquire all of the common shares of Watford Holdings Ltd. not owned by Arch for a cash purchase price of $35.00 per common share. Arch Capital assigned its rights under the Merger Agreement to Greysbridge Holdings Ltd., a wholly-owned subsidiary of Arch Capital (“Greysbridge”). The merger and the related Greysbridge equity financing closed on July 1, 2021. Effective July 1, 2021, Watford is wholly owned by Greysbridge and Greysbridge is owned 40% by Arch Re Bermuda, 30% by certain investment funds managed by Kelso & Company and 30% by certain investment funds managed by Warburg Pincus LLC. See note 16.

ARCH CAPITAL 372021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
The following table provides the carrying amount and balance sheet caption in which the assets and liabilities of Watford are reported:

June 30,December 31,
20212020
Assets
Investments accounted for using the fair value option (1)$1,984,919 $1,790,385 
Fixed maturities available for sale, at fair value663,902 655,249 
Equity securities, at fair value97,623 52,410 
Cash349,202 211,451 
Accrued investment income14,549 14,679 
Premiums receivable305,026 224,377 
Reinsurance recoverable on unpaid and paid losses and LAE520,531 286,590 
Ceded unearned premiums123,272 122,339 
Deferred acquisition costs65,532 53,705 
Receivable for securities sold102,287 37,423 
Goodwill and intangible assets10,318 7,650 
Other assets112,794 75,801 
Total assets of consolidated VIE$4,349,955 $3,532,059 
Liabilities
Reserve for losses and loss adjustment expenses$1,916,742 $1,519,583 
Unearned premiums468,948 407,714 
Reinsurance balances payable132,929 63,269 
Revolving credit agreement borrowings155,687 155,687 
Senior notes172,825 172,689 
Payable for securities purchased199,342 25,881 
Other liabilities227,396 193,494 
Total liabilities of consolidated VIE$3,273,869 $2,538,317 
Redeemable noncontrolling interests$52,444 $52,398 
(1)    Included in “other investments” on the Company’s balance sheet.
For the six months ended June 30, 2021, Watford generated $47.0 million of cash provided by operating activities, $96.3 million of cash provided by investing activities and $2.0 million of cash used for financing activities, compared to $87.3 million of cash provided by operating activities, $78.0 million of cash provided by investing activities and $153.8 million of cash used for financing activities for the six months ended June 30, 2020.
Non-redeemable noncontrolling interests
The Company accounts for the portion of Watford’s common equity attributable to third party investors in the shareholders’ equity section of its consolidated balance sheets. The noncontrolling ownership in Watford’s common shares was approximately 90% at June 30, 2021. The portion of Watford’s income or loss attributable to third party investors is recorded in the consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests.’
The following table sets forth activity in the non-redeemable noncontrolling interests:
June 30,
 20212020
Three Months Ended
Balance, beginning of period$876,864 $492,785 
Additional paid in capital attributable to noncontrolling interests383 595 
Amounts attributable to noncontrolling interests41,617 165,598 
Other comprehensive income (loss) attributable to noncontrolling interests10 20,111 
Balance, end of period$918,874 $679,089 
Six Months Ended
Balance, beginning of year$823,007 $762,777 
Additional paid in capital attributable to noncontrolling interests22,113 472 
Repurchases attributable to non-redeemable noncontrolling interests (1)(2,867)
Amounts attributable to noncontrolling interests78,314 (68,346)
Other comprehensive income (loss) attributable to noncontrolling interests(4,560)(12,947)
Balance, end of period$918,874 $679,089 
(1) During 2020, Watford’s board of directors authorized the investment in Watford’s common shares through a share repurchase program.

Redeemable noncontrolling interests
The Company accounts for redeemable noncontrolling interests in the mezzanine section of its consolidated balance sheets in accordance with applicable accounting guidance. Such redeemable noncontrolling interests primarily relate to the Watford Preference Shares issued in late March 2014 with a par value of $0.01 per share and a liquidation preference of $25.00 per share. The Watford Preference Shares were issued at a discounted amount of $24.50 per share. Preferred dividends, including the accretion of the discount and issuance costs, are included in ‘net (income) loss attributable to noncontrolling interests’ in the Company’s consolidated statements of income.
ARCH CAPITAL 382021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
The following table sets forth activity in the redeemable non-controlling interests:
June 30,
 20212020
Three Months Ended
Balance, beginning of period$57,670 $55,376 
Accretion of preference share issuance costs23 23 
Other(160)587 
Balance, end of period$57,533 $55,986 
Six Months Ended
Balance, beginning of year$58,548 $55,404 
Accretion of preference share issuance costs46 46 
Other(1,061)536 
Balance, end of period$57,533 $55,986 
The portion of income or loss attributable to third party investors, recorded in the Company’s consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests,’ are summarized in the table below:
June 30,
 20212020
Three Months Ended
Amounts attributable to non-redeemable noncontrolling interests$(41,617)$(165,598)
Amounts attributable to redeemable noncontrolling interests(1,561)(1,970)
Net (income) loss attributable to noncontrolling interests$(43,178)$(167,568)
Six Months Ended
Amounts attributable to non-redeemable noncontrolling interests$(78,314)$68,346 
Amounts attributable to redeemable noncontrolling interests(2,416)(3,123)
Net (income) loss attributable to noncontrolling interests$(80,730)$65,223 

ARCH CAPITAL 392021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
Bellemeade Re
The Company has entered into various aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda (the “Bellemeade Agreements”). At the time the Bellemeade Agreements were entered into, the applicability of the accounting guidance that addresses VIEs was evaluated. As a result of the evaluation of the Bellemeade Agreements, the Company concluded that these entities are VIEs. However, given that the ceding insurers do not have the unilateral power to direct those activities that are significant to their economic performance, the Company does not consolidate such entities in its consolidated financial statements.
The following table presents the total assets of the Bellemeade entities, as well as the Company’s maximum exposure to loss associated with these VIEs, calculated as the maximum historical observable spread between the benchmark index for each respective transaction and short term invested trust asset yields. The benchmark index for agreements effective prior to 2021 is based on one-month LIBOR, while the 2021 agreements benchmark index is based on the Secured Overnight Financing Rate (“SOFR”). SOFR is a measure of the cost of borrowing cash overnight, collateralized by U.S. Treasury securities, and is based on directly observable U.S. Treasury-backed repurchase transactions.
June 30, 2021December 31, 2020
Maximum Exposure to LossMaximum Exposure to Loss
Bellemeade Entities (Issue Date)Total VIE AssetsOn-Balance Sheet (Asset) LiabilityOff-Balance SheetTotalTotal VIE AssetsOn-Balance Sheet (Asset) LiabilityOff-Balance SheetTotal
Bellemeade 2017-1 Ltd. (Oct-17)$145,573 $(283)$779 $496 $145,573 $(245)$844 $599 
Bellemeade 2018-1 Ltd. (Apr-18)250,095 (909)1,984 1,075 250,095 (903)2,245 1,342 
Bellemeade 2018-2 Ltd. (Aug-18)108,395 (138)280 142 
Bellemeade 2018-3 Ltd. (Oct-18)302,563 (1,622)3,706 2,084 302,563 (1,320)3,262 1,942 
Bellemeade 2019-1 Ltd. (Mar-19)219,256 (1,237)8,204 6,967 219,256 (1,361)8,461 7,100 
Bellemeade 2019-2 Ltd. (Apr-19)398,316 (1,042)6,723 5,681 398,316 (730)5,201 4,471 
Bellemeade 2019-3 Ltd. (Jul-19)528,084 (969)4,527 3,558 528,084 (861)5,079 4,218 
Bellemeade 2019-4 Ltd. (Oct-19)468,737 (1,051)7,128 6,077 468,737 (890)6,676 5,786 
Bellemeade 2020-1 Ltd. (Jun-20) (1)18,843 275,068 (178)1,012 834 
Bellemeade 2020-2 Ltd. (Sep-20) (2)325,712 (442)4,299 3,857 423,420 (556)6,839 6,283 
Bellemeade 2020-3 Ltd. (Nov-20) (3)418,158 (618)8,250 7,632 418,158 (631)9,605 8,974 
Bellemeade 2020-4 Ltd. (Dec-20) (4)268,405 (150)3,891 3,741 321,393 (156)6,816 6,660 
Bellemeade 2021-1 Ltd. (Mar-21) (5)579,717 (83)4,387 4,304 
Bellemeade 2021-2 Ltd. (Jun-21) (6)522,807 630 5,207 5,837 — 
Total$4,446,266 $(7,776)$59,085 $51,309 $3,859,058 $(7,969)$56,320 $48,351 

(1)  An additional $79 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.
(2)  An additional $26 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.
(3)  An additional $34 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.
(4)  An additional $16 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.
(5)  An additional $64 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.
(6)  An additional $93 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.
ARCH CAPITAL 402021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
12.    Other Comprehensive Income (Loss)
The following tables present details about amounts reclassified from accumulated other comprehensive income and the tax effects allocated to each component of other comprehensive income (loss):
Amounts Reclassified from AOCI
Consolidated Statement of IncomeThree Months EndedSix Months Ended
Details AboutLine Item That IncludesJune 30,June 30,
AOCI ComponentsReclassification2021202020212020
Unrealized appreciation on available-for-sale investments
Net realized gains (losses)$64,914 $182,329 $66,918 $328,561 
Provision for credit losses896 3,225 (751)(6,095)
Other-than-temporary impairment losses(533)
Total before tax65,810 185,554 66,167 321,933 
Income tax (expense) benefit(5,263)(18,163)(8,317)(33,313)
Net of tax$60,547 $167,391 $57,850 $288,620 
Before Tax AmountTax Expense (Benefit)Net of Tax Amount
Three Months Ended June 30, 2021
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period$91,057 $12,486 $78,571 
Less reclassification of net realized gains (losses) included in net income65,810 5,263 60,547 
Foreign currency translation adjustments6,392 187 6,205 
Other comprehensive income (loss)$31,639 $7,410 $24,229 
Three Months Ended June 30, 2020
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period$555,576 $62,780 $492,796 
Less reclassification of net realized gains (losses) included in net income185,554 18,163 167,391 
Foreign currency translation adjustments22,595 344 22,251 
Other comprehensive income (loss)$392,617 $44,961 $347,656 
Six Months Ended June 30, 2021
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period$(203,303)$(20,124)$(183,179)
Less reclassification of net realized gains (losses) included in net income66,167 8,317 57,850 
Foreign currency translation adjustments(22,023)356 (22,379)
Other comprehensive income (loss)$(291,493)$(28,085)$(263,408)
Six Months Ended June 30, 2020
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period$492,125 $56,616 $435,509 
Less reclassification of net realized gains (losses) included in net income321,933 33,313 288,620 
Foreign currency translation adjustments(22,829)(391)(22,438)
Other comprehensive income (loss)$147,363 $22,912 $124,451 
ARCH CAPITAL 412021 SECOND QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
13.    Income Taxes
The Company’s income tax provision on income before income taxes, including income (loss) from operating affiliates, resulted in an effective tax rate of 7.0% for the six months ended June 30, 2021, compared to 12.5% for the six months ended June 30, 2020.
The Company’s effective tax rate, which is based upon the expected annual effective tax rate, may fluctuate from period to period based on the relative mix of income or loss reported by jurisdiction and the varying tax rates in each jurisdiction.
The Company had a net deferred tax asset of $93.0 million at June 30, 2021, compared to a net deferred tax asset of $15.7 million at December 31, 2020. The change is primarily a result of mortgage contingency reserves activity and market value fluctuations in the investment portfolio. In addition, the Company paid $141.1 million and $10.4 million of income taxes for the six months ended June 30, 2021 and 2020, respectively.
14.    Legal Proceedings
The Company, in common with the insurance industry in general, is subject to litigation and arbitration in the normal course of its business. As of June 30, 2021, the Company was not a party to any litigation or arbitration which is expected by management to have a material adverse effect on the Company’s results of operations and financial condition and liquidity.

15.    Transactions with Related Parties
In the 2021 first quarter, as part of the Company’s acquisition of Barbican, the Company entered into an agreement with Premia Managing Agency Limited for the reinsurance to close of Syndicate 1955’s 2018 underwriting year of account into Premia Syndicate 1884’s 2021 underwriting year of account. The reinsurance to close covers legacy business underwritten by Syndicate 1955 on the underwriting 2018 and prior years of account and under the agreement, approximately $380 million of net liabilities was transferred to Syndicate 1884, with an effective date of January 1, 2021. Barbican recorded reinsurance recoverable on unpaid and paid losses and funds held liability of NaN and $9.9 million, respectively, at June 30, 2021, compared to $199.8 million and $149.6 million, respectively, at December 31, 2020.
Certain directors and executive officers of the Company own common and preference shares of Watford. See note 11, “Variable Interest Entity and Noncontrolling Interests,” for information about Watford.
16.    Subsequent Event
In July 2021, the Company announced the completion of the previously disclosed acquisition of Watford by Greysbridge. Based on the governing documents of Greysbridge the Company has concluded that, while it will retain significant influence over Watford, Watford will no longer constitute a variable interest entity of which the Company is the primary beneficiary. Accordingly, effective July 1, 2021, Arch will no longer consolidate the results of Watford in its consolidated financial statements and footnotes. As a result of the closing of the transaction, we expect to report a net gain of approximately $65 million in the third quarter.
ARCH CAPITAL 422021 SECOND QUARTER FORM 10-Q

ITEM 2.     MANAGEMENT’S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS OF OPERATIONS
The following is a discussion and analysis of our financial condition and results of operations. This should be read in conjunction with our consolidated financial statements included in Item 1 of this report and also our Management’s Discussion and Analysis of Financial Condition and Results of Operations contained in our Annual Report on Form 10-K for the year ended December 31, 2020 (“2020 Form 10-K”). In addition, readers should review “Risk Factors” set forth in Item 1A of Part I of our 2020 Form 10-K and “ITEM 1A—Risk Factors” of this Form 10-Q. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.
Arch Capital Group Ltd. (“Arch Capital” and, together with its subsidiaries, “Arch”, “we” or “us”) is a publicly listed Bermuda exempted company with approximately $16.7 billion in capital at June 30, 2021 and, through operations in Bermuda, the United States, Europe, Canada, Australia and Hong Kong, writes insurance, reinsurance and mortgage insurance on a worldwide basis.
CURRENT OUTLOOK
Our three primary areas of focus for 2021 are to continue our growth in the sectors where rates allow for returns that are substantially more than our cost of capital, to optimize our mortgage insurance book as it transitions from forbearance to recovery on its way back to normalcy in the next few quarters, and to actively manage our investments and capital to enhance our returns over the long run.
From an operating perspective, the 2021 second quarter reflected the benefits of attractive pricing in almost all of our insurance markets. As a result, we currently expect the next several quarters to continue to show improved underwriting margins, partially due to the compounding of rate-on-rate increases and the rebalancing of our mix of business. Importantly, the market is showing discipline in maintaining its momentum. We believe that this time-tested strategy of protecting capital through soft markets and writing business aggressively in hard markets gives us the best chance to generate superior risk adjusted returns over time. As long as rate increases support returns above our required thresholds, we expect to continue to grow our writings.
Consequently, these rate improvements have enabled us to continue to expand writings in our property casualty segments. We are now in the sixth consecutive quarter of rate increases with a weighted increase of approximately 10% this quarter, comfortably in excess of loss cost trends. Premiums increased across most lines of business and geographic areas
as pricing improvements spread and, while rate increases have tapered off from previous highs in some lines, our insurance segment is seeing increases in lines that had been resistant to meaningful change.
In reinsurance, strong growth was observed across most of our lines of business, but especially in our casualty and other specialty lines where strong rates increases and growth in new accounts helped increase the top line. Consistent with our insurance segment, we expect the ongoing rate improvements to be reflected in our underwriting results over the next several quarters.
For our U.S. primary mortgage operations, reported delinquencies were 3.11% at June 30, 2021, roughly 40% lower than it was at the end of the 2020 second quarter. Delinquencies continue to be better than our expectations at the beginning of the COVID-19 pandemic but delinquency rates remain at elevated levels, reflecting the impact of the recession and forbearance programs under the CARES Act to borrowers experiencing a hardship. Forbearance allows for mortgage payments to be suspended for up to 360 days or longer along with a suspension of foreclosures and evictions. See “Results of Operations—Mortgage Segment” for further details on our mortgage operations.
In the second quarter, our U.S. primary mortgage operations insurance in force remained steady at approximately $278 billion and $422 billion for the total mortgage segment. The refinancing boom that began last year has slowed and we expect improving persistency through remainder of the year.
Outside of the U.S., we increased our writings in Australia as the housing market remains strong there. We like the long-term opportunity in Australia as demonstrated by our announcement in March to acquire Westpac's LMI business. The agreement allows us to free up capital even as we build our Australian presence and diversify our earning streams at attractive risk-adjusted returns.
We remain committed to providing solutions across many offerings as the marketplace evolves, including the mortgage credit risk transfer programs initiated by government sponsored enterprises, or “GSEs.” In addition, we enter into aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda and issue mortgage insurance linked notes, increasing our protection for mortgage tail risk. The Bellemeade structures provide approximately $4.7 billion of aggregate reinsurance coverage at June 30, 2021.

ARCH CAPITAL 432021 SECOND QUARTER FORM 10-Q

FINANCIAL MEASURES
Management uses the following three key financial indicators in evaluating our performance and measuring the overall growth in value generated for Arch Capital’s common shareholders:
Book Value per Share
Book value per share represents total common shareholders’ equity available to Arch divided by the number of common shares outstanding. Management uses growth in book value per share as a key measure of the value generated for our common shareholders each period and believes that book value per share is the key driver of Arch Capital’s share price over time. Book value per share is impacted by, among other factors, our underwriting results, investment returns and share repurchase activity, which has an accretive or dilutive impact on book value per share depending on the purchase price.
Book value per share was $32.02 at June 30, 2021, compared to $30.54 at March 31, 2021 and $27.62 at June 30, 2020. The 4.8% increase in book value per share for the 2021 second quarter and 15.9% increase in book value per share over the trailing twelve months reflected strong underwriting results and investment returns.
Operating Return on Average Common Equity
Operating return on average common equity (“Operating ROAE”) represents annualized after-tax operating income available to Arch common shareholders divided by the average of beginning and ending common shareholders’ equity available to Arch during the period. After-tax operating income available to Arch common shareholders, a non-GAAP financial measure as defined in Regulation G, represents net income available to Arch common shareholders, excluding net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings) equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses, transaction costs and other and income taxes. Management uses Operating ROAE as a key measure of the return generated to common shareholders. See “Comment on Non-GAAP Financial Measures.”
Our Operating ROAE was 13.0% for the 2021 second quarter, compared to 0.6% for the 2020 second quarter, and 10.3% for the six months ended June 30, 2021, compared to 3.8% for the 2020 period. The higher 2021 period results, reflected strong underwriting returns and a one-time gain of $74.5 million realized during the 2021 first quarter from our acquisition of 29.5% stake in Coface, while the 2020 period
reflected the impact of COVID-19 on the underwriting results.
Total Return on Investments
Total return on investments includes investment income, equity in net income or loss of investment funds accounted for using the equity method, net realized gains and losses (excluding changes in the allowance for credit losses on non-investment related financial assets) and the change in unrealized gains and losses generated by Arch’s investment portfolio. Total return is calculated on a pre-tax basis and before investment expenses, excludes amounts reflected in the ‘other’ segment, and reflects the effect of financial market conditions along with foreign currency fluctuations. In addition, total return incorporates the timing of investment returns during the periods. The following table summarizes our total return compared to the benchmark return against which we measured our portfolio during the periods. See “Comment on Non-GAAP Financial Measures.”
Arch
Portfolio
Benchmark
Return
Pre-tax total return (before investment expenses):
2021 Second Quarter1.58 %1.80 %
2020 Second Quarter3.72 %6.06 %
Six Months Ended June 30, 20211.39 %1.28 %
Six Months Ended June 30, 20202.82 %1.23 %

Total return for the 2021 second quarter reflected movements in interest rates and credit spreads on our fixed income portfolio. We continue to maintain a short duration on our portfolio of 2.31 years at June 30, 2021.
The benchmark return index is a customized combination of indices intended to approximate a target portfolio by asset mix and average credit quality while also matching the approximate estimated duration and currency mix of our insurance and reinsurance liabilities. Although the estimated duration and average credit quality of this index will move as the duration and rating of its constituent securities change, generally we do not adjust the composition of the benchmark return index except to incorporate changes to the mix of liability currencies and durations noted above. The benchmark return index should not be interpreted as expressing a preference for or aversion to any particular sector or sector weight. The index is intended solely to provide, unlike many master indices that change based on the size of their constituent indices, a relatively stable basket of investable indices. At June 30, 2021, the benchmark return index had an average credit quality of “Aa2” by Moody’s Investors Service (“Moody’s”), and an estimated duration of 3.13 years.
ARCH CAPITAL 442021 SECOND QUARTER FORM 10-Q

The benchmark return index included weightings to the following indices:
%
ICE BoAML 1-5 Year A - AAA U.S. Corporate Index13.00 %
ICE BoAML 5-10 Year A - AAA U.S. Corporate Index11.00 
ICE BoAML 1-5 Year U.S. Treasury Index11.00 
MSCI ACWI Net Total Return USD Index9.30 
ICE BoAML 1-10 Year BBB U.S. Corporate Index5.00 
JPM CLOIE Investment Grade5.00 
S&P/LSTA Leveraged Loan Total Return Index4.965 
ICE BoAML U.S. Mortgage Backed Securities Index4.00 
ICE BoAML AAA US Fixed Rate CMBS4.00 
ICE BoAML 1-5 Year U.K. Gilt Index4.00 
ICE BoAML German Government 1-10 Year Index3.50 
ICE BoAML 0-3 Year U.S. Treasury Index3.25 
ICE BoAML 5-10 Year U.S. Treasury Index3.00 
ICE BoAML 1-10 Year U.S. Municipal Securities Index3.00 
Bloomberg Barclays ABS Aaa Index3.00 
ICE BoAML 1-5 Year Australia Government Index2.75 
ICE BoAML U.S. High Yield Constrained Index2.50 
ICE BoAML 1-5 Year Canada Government Index2.00 
ICE BofA CCC and Lower US High Yield Constrained Index1.38 
Bloomberg Barclays Global High Yield Index1.38 
S&P DJ Global ex-US Select Real Estate Securities Net Index0.825 
FTSE Nareit All Mortgage Capped Index Total Return USD0.825 
Bloomberg Barclays CMBS: Erisa Eligible Unhedged USD0.825 
ICE BoAML 15+ Year Canada Government Index0.50 
Total100.00 %
COMMENT ON NON-GAAP FINANCIAL MEASURES
Throughout this filing, we present our operations in the way we believe will be the most meaningful and useful to investors, analysts, rating agencies and others who use our financial information in evaluating the performance of our company. This presentation includes the use of after-tax operating income available to Arch common shareholders, which is defined as net income available to Arch common shareholders, excluding net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings), equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses, transaction costs and other and income taxes, and the use of annualized operating return on average common equity. The presentation of after-tax operating income available to Arch common shareholders and annualized operating return on average common equity are non-GAAP financial measures as defined in Regulation G. The reconciliation of such measures to net income available to Arch common shareholders and annualized return on average common equity (the most directly comparable
GAAP financial measures) in accordance with Regulation G is included under “Results of Operations” below.
We believe that net realized gains or losses, equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses and transaction costs and other in any particular period are not indicative of the performance of, or trends in, our business. Although net realized gains or losses, equity in net income or loss of investment funds accounted for using the equity method and net foreign exchange gains or losses are an integral part of our operations, the decision to realize investment gains or losses, the recognition of the change in the carrying value of investments accounted for using the fair value option in net realized gains or losses, the recognition of net impairment losses, the recognition of equity in net income or loss of investment funds accounted for using the equity method and the recognition of foreign exchange gains or losses are independent of the insurance underwriting process and result, in large part, from general economic and financial market conditions. Furthermore, certain users of our financial information believe that, for many companies, the timing of the realization of investment gains or losses is largely opportunistic. In addition, changes in the allowance for credit losses and net impairment losses recognized in earnings on the Company’s investments represent other-than-temporary declines in expected recovery values on securities without actual realization. The use of the equity method on certain of our investments in certain funds that invest in fixed maturity securities is driven by the ownership structure of such funds (either limited partnerships or limited liability companies). In applying the equity method, these investments are initially recorded at cost and are subsequently adjusted based on our 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). This method of accounting is different from the way we account for our other fixed maturity securities and the timing of the recognition of equity in net income or loss of investment funds accounted for using the equity method may differ from gains or losses in the future upon sale or maturity of such investments. Transaction costs and other include advisory, financing, legal, severance, incentive compensation and other transaction costs related to acquisitions. We believe that transaction costs and other, due to their non-recurring nature, are not indicative of the performance of, or trends in, our business performance. Due to these reasons, we exclude net realized gains or losses, equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses and transaction costs and other from the calculation of after-tax operating income available to Arch common shareholders.
We believe that showing net income available to Arch common shareholders exclusive of the items referred to above reflects the underlying fundamentals of our business
ARCH CAPITAL 452021 SECOND QUARTER FORM 10-Q

since we evaluate the performance of and manage our business to produce an underwriting profit. In addition to presenting net income available to Arch common shareholders, we believe that this presentation enables investors and other users of our financial information to analyze our performance in a manner similar to how management analyzes performance. We also believe that this measure follows industry practice and, therefore, allows the users of financial information to compare our performance with our industry peer group. We believe that the equity analysts and certain rating agencies which follow us and the insurance industry as a whole generally exclude these items from their analyses for the same reasons.
Our segment information includes the presentation of consolidated underwriting income or loss and a subtotal of underwriting income or loss before the contribution from the ‘other’ segment. Such measures represent the pre-tax profitability of our underwriting operations and include net premiums earned plus other underwriting income, less losses and loss adjustment expenses, acquisition expenses and other operating expenses. Other operating expenses include those operating expenses that are incremental and/or directly attributable to our individual underwriting operations. Underwriting income or loss does not incorporate items included in our corporate (non-underwriting) segment. While these measures are presented in note 4, “Segment Information,” of the notes accompanying our consolidated financial statements, they are considered non-GAAP financial measures when presented elsewhere on a consolidated basis. The reconciliations of underwriting income or loss to income before income taxes (the most directly comparable GAAP financial measure) on a consolidated basis and a subtotal before the contribution from the ‘other’ segment, in accordance with Regulation G, is shown in note 4, “Segment Information” to our consolidated financial statements.

We measure segment performance for our three underwriting segments based on underwriting income or loss. We do not manage our assets by underwriting segment, with the exception of goodwill and intangibles and, accordingly, investment income and other non-underwriting related items are not allocated to each underwriting segment. For the ‘other’ segment, performance is measured based on net income or loss.

Along with consolidated underwriting income, we provide a subtotal of underwriting income or loss before the contribution from the ‘other’ segment. Through June 30, 2021, the ‘other’ segment included the results of Watford Holdings Ltd. Watford Holdings Ltd. is the parent of Watford Re Ltd., a multi-line Bermuda reinsurance company (together with Watford Holdings Ltd., “Watford”). Pursuant to GAAP, Watford was considered a variable interest entity and we
concluded that we are the primary beneficiary of Watford. As such, we consolidated the results of Watford in our consolidated financial statements through June 30, 2021, although we only owned approximately 10% of Watford’s common equity. Watford’s own management and board of directors are responsible for its results and profitability. In addition, we do not guarantee or provide credit support for Watford. Since Watford is an independent company, the assets of Watford can be used only to settle obligations of Watford and Watford is solely responsible for its own liabilities and commitments. Our financial exposure to Watford is limited to our investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from the reinsurance transactions. We believe that presenting certain information excluding the ‘other’ segment enables investors and other users of our financial information to analyze our performance in a manner similar to how our management analyzes performance. See note 11, “Variable Interest Entities and Noncontrolling Interests,” note 4, “Segment Information,” and Note 16, “Subsequent Event,” to our consolidated financial statements for additional information on Watford.

Our presentation of segment information includes the use of a current year loss ratio which excludes favorable or adverse development in prior year loss reserves. This ratio is a non-GAAP financial measure as defined in Regulation G. The reconciliation of such measure to the loss ratio (the most directly comparable GAAP financial measure) in accordance with Regulation G is shown on the individual segment pages. Management utilizes the current year loss ratio in its analysis of the underwriting performance of each of our underwriting segments.
Total return on investments includes investment income, equity in net income or loss of investment funds accounted for using the equity method, net realized gains and losses (excluding changes in the allowance for credit losses on non-investment related financial assets) and the change in unrealized gains and losses generated by Arch’s investment portfolio. Total return is calculated on a pre-tax basis and before investment expenses, excludes amounts reflected in the ‘other’ segment, and reflects the effect of financial market conditions along with foreign currency fluctuations. In addition, total return incorporates the timing of investment returns during the periods. There is no directly comparable GAAP financial measure for total return. Management uses total return on investments as a key measure of the return generated to Arch common shareholders, and compares the return generated by our investment portfolio against benchmark returns during the periods.
ARCH CAPITAL 462021 SECOND QUARTER FORM 10-Q

RESULTS OF OPERATIONS
The following table summarizes our consolidated financial data, including a reconciliation of net income or loss available to Arch common shareholders to after-tax operating income or loss available to Arch common shareholders. Each line item reflects the impact of our percentage ownership of Watford’s common equity during such period.
Three Months EndedSix Months Ended
June 30,June 30,
2021202020212020
Net income available to Arch common shareholders$663,820 $288,418 $1,091,573 $422,132 
Net realized (gains) losses(167,438)(406,645)(272,989)(297,281)
Equity in net (income) loss of investment funds accounted for using the equity method(122,186)65,119 (193,872)69,328 
Net foreign exchange (gains) losses17,888 42,032 (3,444)(22,459)
Transaction costs and other(1,421)977 (147)3,572 
Income tax expense (1)
16,553 26,713 25,864 31,078 
After-tax operating income available to Arch common shareholders$407,216 $16,614 $646,985 $206,370 
Beginning common shareholders’ equity$12,316,472 $10,587,244 $12,325,886 $10,717,371 
Ending common shareholders’ equity$12,706,072 $11,211,825 $12,706,072 $11,211,825 
Average common shareholders’ equity$12,511,272 $10,899,535 $12,515,979 $10,964,598 
Annualized return on average common equity %21.2 10.6 17.4 7.7 
Annualized operating return on average
common equity %
13.0 0.6 10.3 3.8 
(1) Income tax expense on net realized gains or losses, equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses and transaction costs and other reflects the relative mix reported by jurisdiction and the varying tax rates in each jurisdiction.
Segment Information
We classify our businesses into three underwriting segments — insurance, reinsurance and mortgage — and two other operating segments — corporate (non-underwriting) and ‘other.’ Our 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 our 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 our three underwriting segments based on underwriting income or loss. We do not manage our assets by underwriting segment, with the exception of goodwill and intangible assets, and, accordingly, investment income is not allocated to each underwriting segment.
We determined our 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 our consolidated financial statements. Intersegment business is allocated to the segment accountable for the underwriting results.
Insurance Segment
The following tables set forth our insurance segment’s underwriting results:
 Three Months Ended June 30,
 20212020
Change
Gross premiums written$1,368,867 $1,030,362 32.9 
Premiums ceded(405,312)(358,101)
Net premiums written963,555 672,261 43.3 
Change in unearned premiums(98,128)15,648 
Net premiums earned865,427 687,909 25.8 
Losses and loss adjustment expenses(545,880)(518,203) 
Acquisition expenses(136,852)(107,671) 
Other operating expenses(133,342)(118,757) 
Underwriting income (loss)$49,353 $(56,722)187.0 
Underwriting Ratios  % Point
Change
Loss ratio63.1 %75.3 %(12.2)
Acquisition expense ratio15.8 %15.7 %0.1 
Other operating expense ratio15.4 %17.3 %(1.9)
Combined ratio94.3 %108.3 %(14.0)

ARCH CAPITAL 472021 SECOND QUARTER FORM 10-Q

 Six Months Ended June 30,
 20212020% Change
Gross premiums written$2,784,753 $2,238,007 24.4 
Premiums ceded(826,359)(736,998)
Net premiums written1,958,394 1,501,009 30.5 
Change in unearned premiums(273,493)(97,181)
Net premiums earned1,684,901 1,403,828 20.0 
Losses and loss adjustment expenses(1,081,627)(1,025,311) 
Acquisition expenses(265,074)(215,008) 
Other operating expenses(270,455)(248,406) 
Underwriting income (loss)$67,745 $(84,897)179.8 
Underwriting Ratios  % Point
Change
Loss ratio64.2 %73.0 %(8.8)
Acquisition expense ratio15.7 %15.3 %0.4 
Other operating expense ratio16.1 %17.7 %(1.6)
Combined ratio96.0 %106.0 %(10.0)
The insurance segment consists of our insurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include:
Construction and national accounts: primary and excess casualty coverages to middle and large accounts in the construction industry and a wide range of products for middle and large national accounts, specializing in loss sensitive primary casualty insurance programs (including large deductible, self-insured retention and retrospectively rated programs).
Excess and surplus casualty: primary and excess casualty insurance coverages, including middle market energy business, and contract binding, which primarily provides casualty coverage through a network of appointed agents to small and medium risks.
Lenders products: collateral protection, debt cancellation and service contract reimbursement products to banks, credit unions, automotive dealerships and original equipment manufacturers and other specialty programs that pertain to automotive lending and leasing.
Professional lines: directors’ and officers’ liability, errors and omissions liability, employment practices liability, fiduciary liability, crime, professional indemnity and other financial related coverages for corporate, private equity, venture capital, real estate investment trust, limited partnership, financial institution and not-for-profit clients of all sizes and medical professional and general liability insurance coverages for the healthcare industry. The business is predominately written on a claims-made basis.
Programs: primarily package policies, underwriting workers’ compensation and umbrella liability business in support of desirable package programs, targeting program managers with unique expertise and niche products offering
general liability, commercial automobile, inland marine and property business with minimal catastrophe exposure.
Property, energy, marine and aviation: primary and excess general property insurance coverages, including catastrophe-exposed property coverage, for commercial clients. Coverages for marine include hull, war, specie and liability. Aviation and standalone terrorism are also offered.
Travel, accident and health: specialty travel and accident and related insurance products for individual, group travelers, travel agents and suppliers, as well as accident and health, which provides accident, disability and medical plan insurance coverages for employer groups, medical plan members, students and other participant groups.
Other: includes alternative market risks (including captive insurance programs), excess workers’ compensation and employer’s liability insurance coverages for qualified self-insured groups, associations and trusts, and contract and commercial surety coverages, including contract bonds (payment and performance bonds) primarily for medium and large contractors and commercial surety bonds for Fortune 1,000 companies and smaller transaction business programs.
Premiums Written.
The following tables set forth our insurance segment’s net premiums written by major line of business:
 Three Months Ended June 30,
 20212020
 Amount%Amount%
Property, energy, marine and aviation$207,762 21.6 $159,801 23.8 
Professional lines254,961 26.5 157,899 23.5 
Programs149,373 15.5 104,930 15.6 
Construction and national accounts77,579 8.1 57,144 8.5 
Excess and surplus casualty74,346 7.7 64,703 9.6 
Travel, accident and health71,071 7.4 27,997 4.2 
Lenders products40,386 4.2 23,690 3.5 
Other88,077 9.1 76,097 11.3 
Total$963,555 100.0 $672,261 100.0 
2021 Second Quarter versus 2020 Period. Gross premiums written by the insurance segment in the 2021 second quarter were 32.9% higher than in the 2020 second quarter, while net premiums written were 43.3% higher. The higher level of net premiums written reflected increases across most lines of business, due in part to rate increases, new business opportunities and growth in existing accounts.
ARCH CAPITAL 482021 SECOND QUARTER FORM 10-Q

 Six Months Ended June 30,
 20212020
 Amount%Amount%
Property, energy, marine and aviation$378,260 19.3 $287,386 19.1 
Professional Lines493,207 25.2 327,017 21.8 
Programs307,774 15.7 217,462 14.5 
Construction and national accounts212,371 10.8 173,143 11.5 
Excess and surplus casualty159,939 8.2 130,122 8.7 
Travel, accident and health163,377 8.3 154,043 10.3 
Lenders products75,246 3.8 56,982 3.8 
Other168,220 8.6 154,854 10.3 
Total$1,958,394 100.0 $1,501,009 100.0 
Six Months Ended June 30, 2021 versus 2020 period. Gross premiums written by the insurance segment for the six months ended June 30, 2021 were 24.4% higher than in the 2020 period, while net premiums written were 30.5% higher than in the 2020 period. The increase in net premiums written reflected growth across most lines of business, due in part to rate increases, new business opportunities and growth in existing accounts.
Net Premiums Earned.
The following tables set forth our insurance segment’s net premiums earned by major line of business:
 Three Months Ended June 30,
 20212020
 Amount%Amount%
Property, energy, marine and aviation$167,716 19.4 $120,781 17.6 
Professional lines214,098 24.7 154,812 22.5 
Programs118,974 13.7 108,464 15.8 
Construction and national accounts95,849 11.1 91,605 13.3 
Excess and surplus casualty72,899 8.4 60,966 8.9 
Travel, accident and health62,610 7.2 52,117 7.6 
Lenders products46,396 5.4 23,111 3.4 
Other86,885 10.0 76,053 11.1 
Total$865,427 100.0 $687,909 100.0 
 Six Months Ended June 30,
 20212020
 Amount%Amount%
Property, energy, marine and aviation$324,975 19.3 $231,964 16.5 
Professional Lines413,769 24.6 306,512 21.8 
Programs231,814 13.8 217,342 15.5 
Construction and national accounts198,520 11.8 191,305 13.6 
Excess and surplus casualty148,266 8.8 126,063 9.0 
Travel, accident and health112,276 6.7 129,492 9.2 
Lenders products86,477 5.1 48,454 3.5 
Other168,804 10.0 152,696 10.9 
Total$1,684,901 100.0 $1,403,828 100.0 
Net premiums written are primarily earned on a pro rata basis over the terms of the policies for all products, usually 12 months. Net premiums earned reflect changes in net premiums written over the previous five quarters. Net premiums earned in the 2021 second quarter were 25.8% higher than in the 2020 second quarter. Net premiums earned for the six months ended June 30, 2021 were 20.0% higher than in the 2020 period.
Losses and Loss Adjustment Expenses.
The table below shows the components of the insurance segment’s loss ratio:
Three Months EndedSix Months Ended
June 30,June 30,
 2021202020212020
Current year63.6 %75.7 %64.7 %73.3 %
Prior period reserve development(0.5)%(0.4)%(0.5)%(0.3)%
Loss ratio63.1 %75.3 %64.2 %73.0 %
Current Year Loss Ratio.
2021 Second Quarter versus 2020 Period. The insurance segment’s current year loss ratio in the 2021 second quarter was 12.1 points lower than in the 2020 second quarter. The 2021 second quarter loss ratio reflected 3.2 points of current year catastrophic activity, primarily from winter storms Uri and Viola, compared to 12.5 points of catastrophic activity for the 2020 second quarter, which included exposure to the COVID-19 global pandemic. The insurance segment’s current year loss ratio for the six months ended June 30, 2021 was 8.6 points lower than in the 2020 period and reflected 4.1 points of current year catastrophic activity, compared to 9.6 points in the 2020 period. The balance of the change in the 2021 loss ratios resulted, in part, from changes in mix of business and the level of large attritional losses.
ARCH CAPITAL 492021 SECOND QUARTER FORM 10-Q

Prior Period Reserve Development.
The insurance segment’s net favorable development was $4.0 million, or 0.5 points, for the 2021 second quarter, compared to $2.5 million, or 0.4 points, for the 2020 second quarter, and $8.1 million, or 0.5 points for the six months ended June 30, 2021, compared to $3.6 million, or 0.3 points, for the 2020 period. See note 5, “Reserve for Losses and Loss Adjustment Expenses,” to our consolidated financial statements for information about the insurance segment’s prior year reserve development.
Underwriting Expenses.
2021 Second Quarter versus 2020 Period. The insurance segment’s underwriting expense ratio was 31.2% in the 2021 second quarter, compared to 33.0% in the 2020 second quarter, with the decrease primarily due to growth in net premiums earned.
Six Months Ended June 30, 2021 versus 2020 Period. The insurance segment’s underwriting expense ratio was 31.8% six months ended June 30, 2021, compared to 33.0% for the 2020 period, with the decrease primarily due to growth in net premiums earned.
Reinsurance Segment 
The following tables set forth our reinsurance segment’s underwriting results:
 Three Months Ended June 30,
 20212020
Change
Gross premiums written$1,358,020 $807,065 68.3 
Premiums ceded(433,288)(241,971)
Net premiums written924,732 565,094 63.6 
Change in unearned premiums(187,708)(84,897)
Net premiums earned737,024 480,197 53.5 
Other underwriting income (loss)1,053 (651) 
Losses and loss adjustment expenses(463,823)(383,433) 
Acquisition expenses(133,585)(90,522) 
Other operating expenses(44,695)(38,716) 
Underwriting income (loss)$95,974 $(33,125)389.7 
Underwriting Ratios% Point
Change
Loss ratio62.9 %79.8 %(16.9)
Acquisition expense ratio18.1 %18.9 %(0.8)
Other operating expense ratio6.1 %8.1 %(2.0)
Combined ratio87.1 %106.8 %(19.7)
 Six Months Ended June 30,
 20212020% Change
Gross premiums written$2,829,080 $1,929,584 46.6 
Premiums ceded(905,236)(567,310)
Net premiums written1,923,844 1,362,274 41.2 
Change in unearned premiums(541,920)(338,617)
Net premiums earned1,381,924 1,023,657 35.0 
Other underwriting income(145)1,469  
Losses and loss adjustment expenses(948,693)(813,502) 
Acquisition expenses(251,610)(170,128) 
Other operating expenses(105,209)(84,013) 
Underwriting income (loss)$76,267 $(42,517)279.4 
Underwriting Ratios% Point
Change
Loss ratio68.7 %79.5 %(10.8)
Acquisition expense ratio18.2 %16.6 %1.6 
Other operating expense ratio7.6 %8.2 %(0.6)
Combined ratio94.5 %104.3 %(9.8)
The reinsurance segment consists of our reinsurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include:
Casualty: provides coverage to ceding company clients on third party liability and workers’ compensation exposures from ceding company clients, primarily on a treaty basis. Exposures include, among others, executive assurance, professional liability, workers’ compensation, excess and umbrella liability, excess motor and healthcare business.
Marine and aviation: provides coverage for energy, hull, cargo, specie, liability and transit, and aviation business, including airline and general aviation risks. Business written may also include space business, which includes coverages for satellite assembly, launch and operation for commercial space programs.
Other specialty: provides coverage to ceding company clients for proportional motor and other lines, including surety, accident and health, workers’ compensation catastrophe, agriculture, trade credit and political risk.
Property catastrophe: provides protection for most catastrophic losses that are covered in the underlying policies written by reinsureds, including hurricane, earthquake, flood, tornado, hail and fire, and coverage for other perils on a case-by-case basis. Property catastrophe reinsurance provides coverage on an excess of loss basis when aggregate losses and loss adjustment expense from a single occurrence or aggregation of losses from a covered peril exceed the retention specified in the contract.
Property excluding property catastrophe: provides coverage for both personal lines and commercial property exposures and principally covers buildings, structures, equipment and contents. The primary perils in this business
ARCH CAPITAL 502021 SECOND QUARTER FORM 10-Q

include fire, explosion, collapse, riot, vandalism, wind, tornado, flood and earthquake. Business is assumed on both a proportional and excess of loss treaty basis and on a facultative basis. In addition, facultative business is written which focuses on commercial property risks on an excess of loss basis.
Other: includes life reinsurance business on both a proportional and non-proportional basis, casualty clash business and, in limited instances, non-traditional business which is intended to provide insurers with risk management solutions that complement traditional reinsurance.
Premiums Written.
The following tables set forth our reinsurance segment’s net premiums written by major line of business:
 Three Months Ended June 30,
 20212020
 Amount%Amount%
Property excluding property catastrophe$249,101 26.9 $163,639 29.0 
Property catastrophe87,642 9.5 117,676 20.8 
Other specialty296,325 32.0 117,375 20.8 
Casualty225,890 24.4 105,049 18.6 
Marine and aviation50,248 5.4 32,372 5.7 
Other15,526 1.7 28,983 5.1 
Total$924,732 100.0 $565,094 100.0 
2021 Second Quarter versus 2020 Period. Gross premiums written by the reinsurance segment in the 2021 second quarter were 68.3% higher than in the 2020 second quarter, while net premiums written were 63.6% higher. The growth in net premiums written was observed in most lines of business, primarily related to new business opportunities in other specialty, casualty and property excluding property catastrophe lines and the benefit of rate increases.
 Six Months Ended June 30,
 20212020
 Amount%Amount%
Property excluding property catastrophe$541,934 28.2 $322,563 23.7 
Property catastrophe204,849 10.6 206,768 15.2 
Other Specialty580,656 30.2 402,327 29.5 
Casualty444,146 23.1 295,929 21.7 
Marine and aviation111,886 5.8 82,157 6.0 
Other40,373 2.1 52,530 3.9 
Total$1,923,844 100.0 $1,362,274 100.0 
Six Months Ended June 30, 2021 versus 2020 period. Gross premiums written by the reinsurance segment for the six months ended June 30, 2021 were 46.6% higher than in the 2020 period, while net premiums written were 41.2% higher than in the 2020 period. The increase in net premiums written reflected growth in property excluding property catastrophe,
other specialty and casualty primarily due to new business and rate increases.
Net Premiums Earned.
The following tables set forth our reinsurance segment’s net premiums earned by major line of business:
 Three Months Ended June 30,
 20212020
 Amount%Amount%
Property excluding property catastrophe$202,780 27.5 $124,019 25.8 
Property catastrophe76,167 10.3 55,226 11.5 
Other specialty211,817 28.7 123,006 25.6 
Casualty183,846 24.9 132,756 27.6 
Marine and aviation42,773 5.8 24,960 5.2 
Other19,641 2.7 20,230 4.2 
Total$737,024 100.0 $480,197 100.0 
 Six Months Ended June 30,
 20212020
 Amount%Amount%
Property excluding property catastrophe$390,562 28.3 $236,671 23.1 
Property catastrophe164,178 11.9 108,226 10.6 
Other Specialty375,715 27.2 326,391 31.9 
Casualty332,877 24.1 267,827 26.2 
Marine and aviation82,881 6.0 49,818 4.9 
Other35,711 2.6 34,724 3.4 
Total$1,381,924 100.0 $1,023,657 100.0 
Net 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. Net premiums earned by the reinsurance segment in the 2021 second quarter were 53.5% higher than in the 2020 second quarter, and reflect changes in net premiums written over the previous five quarters.
Other Underwriting Income (Loss).
Other underwriting income for the 2021 second quarter was $1.1 million, compared to a loss of $0.7 million for the 2020 second quarter, and a loss of $0.1 million for the six months ended June 30, 2021, compared to an income of $1.5 million for the 2020 period.

ARCH CAPITAL 512021 SECOND QUARTER FORM 10-Q

Losses and Loss Adjustment Expenses.
The table below shows the components of the reinsurance segment’s loss ratio:
Three Months EndedSix Months Ended
June 30,June 30,
 2021202020212020
Current year65.7 %88.2 %72.1 %84.6 %
Prior period reserve development(2.8)%(8.4)%(3.4)%(5.1)%
Loss ratio62.9 %79.8 %68.7 %79.5 %
Current Year Loss Ratio.
2021 Second Quarter versus 2020 Period. The reinsurance segment’s current year loss ratio in the 2021 second quarter was 22.5 points lower than in the 2020 second quarter. The 2021 second quarter loss ratio reflected 2.6 points of current year catastrophic activity, including winter storms Uri and Viola as well as other minor global events. The 2020 second quarter included 26.3 points of catastrophic activity, which included exposure to the COVID-19 pandemic.
Six Months Ended June 30, 2021 versus 2020 period.The reinsurance segment’s current year loss ratio for the six months ended June 30, 2021 was 12.5 points lower than in the 2020 period and reflected 12.9 points of current year catastrophic activity, compared to 19.1 points in the 2020 period. The 2020 period loss ratio included exposure to the COVID-19 pandemic.
Prior Period Reserve Development.
The reinsurance segment’s net favorable development was $20.5 million, or 2.8 points, for the 2021 second quarter, compared to $40.2 million, or 8.4 points, for the 2020 second quarter, and $47.3 million, or 3.4 points, for the six months ended June 30, 2021, compared to $51.8 million, or 5.1 points, for the 2020 period. See note 5, “Reserve for Losses and Loss Adjustment Expenses,” to our consolidated financial statements for information about the reinsurance segment’s prior year reserve development.
Underwriting Expenses.
2021 Second Quarter versus 2020 Period. The underwriting expense ratio for the reinsurance segment was 24.2% in the 2021 second quarter, compared to 27.0% in the 2020 second quarter. Approximately 2.1 points of the difference is due to a lower level of acquisition expenses related to favorable prior year loss reserve development this quarter than in the 2020 second quarter. The remainder of the decrease in the underwriting expense ratio was primarily related to growth in net premiums earned.
Six Months Ended June 30, 2021 versus 2020 period. The underwriting expense ratio for the reinsurance segment was 25.8% for the six months ended June 30, 2021, compared to 24.8% for the 2020 period. The comparison of the underwriting expense ratios also reflected changes in the mix and type of business and a higher level of net premiums earned for the 2021 period.
Mortgage Segment 
Our mortgage operations include U.S. and international mortgage insurance and reinsurance operations as well as participation in GSE credit risk-sharing transactions. Our mortgage group includes direct mortgage insurance in the U.S. primarily through Arch Mortgage Insurance Company, United Guaranty Residential Insurance Company and Arch Mortgage Guaranty Company (together, “Arch MI U.S.”); mortgage reinsurance by Arch Reinsurance Ltd. (“Arch Re Bermuda”) to mortgage insurers on both a proportional and non-proportional basis globally; direct mortgage insurance in Europe through Arch Insurance (EU) Designated Activity Company (“Arch Insurance EU”); in Hong Kong through Arch MI Asia Limited (“Arch MI Asia”); in Australia through Arch LMI Pty Ltd (“Arch LMI”) and participation in various GSE credit risk-sharing products primarily through Arch Re Bermuda.
The following tables set forth our mortgage segment’s underwriting results.
 Three Months Ended June 30,
 20212020% Change
Gross premiums written$391,511 $369,144 6.1 
Premiums ceded(55,665)(44,044)
Net premiums written335,846 325,100 3.3 
Change in unearned premiums(1,625)40,613 
Net premiums earned334,221 365,713 (8.6)
Other underwriting income4,148 6,450 
Losses and loss adjustment expenses(9,880)(224,100)
Acquisition expenses(30,117)(34,052)
Other operating expenses(48,312)(37,574)
Underwriting income$250,060 $76,437 227.1 
Underwriting Ratios% Point
Change
Loss ratio3.0 %61.3 %(58.3)
Acquisition expense ratio9.0 %9.3 %(0.3)
Other operating expense ratio14.5 %10.3 %4.2 
Combined ratio26.5 %80.9 %(54.4)
ARCH CAPITAL 522021 SECOND QUARTER FORM 10-Q

 Six Months Ended June 30,
 20212020% Change
Gross premiums written$782,757 $738,089 6.1 
Premiums ceded(111,716)(88,371)
Net premiums written671,041 649,718 3.3 
Change in unearned premiums(503)61,021 
Net premiums earned670,538 710,739 (5.7)
Other underwriting income11,045 11,049  
Losses and loss adjustment expenses(73,569)(291,666) 
Acquisition expenses(60,199)(72,588) 
Other operating expenses(97,443)(83,470) 
Underwriting income$450,372 $274,064 64.3 
Underwriting Ratios  % Point
Change
Loss ratio11.0 %41.0 %(30.0)
Acquisition expense ratio9.0 %10.2 %(1.2)
Other operating expense ratio14.5 %11.7 %2.8 
Combined ratio34.5 %62.9 %(28.4)
Premiums Written.
The following tables set forth our mortgage segment’s net premiums written by underwriting location (i.e., where the business is underwritten):
 Three Months Ended June 30,
 20212020
 Amount%Amount%
Underwriting location:
United States$234,645 69.9 $261,124 80.3 
Other101,201 30.1 63,976 19.7 
Total$335,846 100.0 $325,100 100.0 
2021 Second Quarter versus 2020 Period. Gross premiums written by the mortgage segment in the 2021 second quarter were 6.1% higher than in the 2020 second quarter, while net premiums written were 3.3% higher, primarily reflecting growth in Australian single premium mortgage insurance and the benefit of premiums received related to the exercise of early redemption options by GSEs for certain seasoned callable credit risk transfer contracts. This growth was partially offset by a lower level of U.S. primary mortgage insurance in force on monthly premium policies, which resulted from the continued high level of refinancing activity.
 Six Months Ended June 30,
 20212020
 Amount%Amount%
Underwriting location:
United States$482,174 71.9 $525,232 80.8 
Other188,867 28.1 124,486 19.2 
Total$671,041 100.0 $649,718 100.0 
Six Months Ended June 30, 2021 versus 2020 period. Gross premiums written by the mortgage segment for the six months ended June 30, 2021 were 6.1% higher than in the 2020 period, while net premiums written for the six months
ended June 30, 2021 were 3.3% higher than in the 2020 period, primarily reflecting growth in Australian single premium mortgage insurance and the benefit of premiums received related to the exercise of early redemption options by GSEs for certain seasoned callable credit risk transfer contracts. This growth was partially offset by a lower level of U.S. primary mortgage insurance in force on monthly premium policies, which resulted from the continued high level of refinancing activity.
The persistency rate, which represents the percentage of mortgage insurance in force at the beginning of a 12-month period that remains in force at the end of such period, was 54.8% for the Arch MI U.S. portfolio of mortgage insurance policies at June 30, 2021, reflecting the higher level of mortgage refinancing activity, compared to 58.7% at December 31, 2020.
The following tables provide details on the new insurance written (“NIW”) generated by Arch MI U.S. NIW represents the original principal balance of all loans that received coverage during the period.
(U.S. Dollars in millions)Three Months Ended June 30,
20212020
Amount%Amount%
Total new insurance written (NIW) (1)$28,372 $24,551 
Credit quality (FICO):
>=740$19,240 67.8 $15,851 64.6 
680-7398,113 28.6 7,781 31.7 
620-6791,019 3.6 919 3.7 
Total$28,372 100.0 $24,551 100.0 
Loan-to-value (LTV):
95.01% and above$1,484 5.2 $1,948 7.9 
90.01% to 95.00%13,936 49.1 9,403 38.3 
85.01% to 90.00%8,675 30.6 8,140 33.2 
85.00% and below4,277 15.1 5,060 20.6 
Total$28,372 100.0 $24,551 100.0 
Monthly vs. single:
Monthly$26,725