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UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
WASHINGTON, D.C.  20549
 
FORM 10-Q
QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934
For the quarterly period ended June 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)
Bermuda 98-0374481
(State or other jurisdiction of incorporation or organization) (I.R.S. Employer Identification No.)
Waterloo House, Ground Floor
100 Pitts Bay Road, Pembroke HM 08, Bermuda (441) 278-9250
(Address of principal executive offices) (Registrant’s telephone number, including area code)

Securities registered pursuant to Section 12(b) of the Exchange Act:
Title of each class Trading Symbol (s) Name of each exchange on which registered
Common shares, $0.0011 par value per share ACGL NASDAQ  Stock Market
Depositary shares, each representing a 1/1000th interest in a 5.25% Series E preferred share
ACGLP
NASDAQ  Stock Market
Depositary shares, each representing a 1/1000th interest in a 5.45% Series F preferred share
ACGLO
NASDAQ  Stock Market
Depositary shares, each representing a 1/1000th interest in a 4.55% Series G preferred share
ACGLN
NASDAQ Stock Market
Indicate by check mark whether the registrant (1) has filed all reports required to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during the preceding 12 months (or for such shorter period that the registrant was required to file such reports), and (2) has been subject to such filing requirements for the past 90 days.  Yes      No
Indicate by check mark whether the registrant has submitted electronically every Interactive Data File required to be submitted pursuant to Rule 405 of Regulation S-T (§232.405 of this chapter) during the preceding 12 months (or for such shorter period that the registrant was required to submit such files). Yes      No
Indicate by check mark whether the registrant is a large accelerated filer, an accelerated filer, a non-accelerated filer, a smaller reporting company, or an emerging growth company. See the definitions of “large accelerated filer,” “accelerated filer,” “smaller reporting company,” and “emerging growth company” in Rule 12b-2 of the Exchange Act.
Large Accelerated Filer Accelerated Filer Non-accelerated Filer Smaller reporting company Emerging growth company
If an emerging growth company, indicate by check mark if the Registrant has elected not to use the extended transition period for complying with any new or revised financial accounting standards provided pursuant to Section 13(a) of the Exchange Act.
Indicate by check mark whether the Registrant is a shell company (as defined in Rule 12b-2 of the Exchange Act). Yes    No

As of July 30, 2021, there were 396,039,032 common shares, $0.0011 par value per share, of the registrant outstanding.


Table of Contents
ARCH CAPITAL GROUP LTD.
 
INDEX TO FORM 10-Q
 
    Page No.
PART I    
 
 2
Item 1.  
 4
Item 2.  
43
Item 3.  
69
Item 4.  
70
     
PART II    
 
70
Item 1.  
70
Item 1A.  
70 
Item 2.  
71
Item 3.
71
Item 4.
71
Item 5.  
71
Item 6.  
72
73
ARCH CAPITAL
 1
2021 SECOND QUARTER FORM 10-Q

Table of Contents
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
 2
2021 SECOND QUARTER FORM 10-Q

Table of Contents
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
 3
2021 SECOND QUARTER FORM 10-Q

Table of Contents
ITEM 1. CONSOLIDATED FINANCIAL STATEMENTS
  Page No.
   
5
   
 
June 30, 2021 (unaudited) and December 31, 2020
6
   
For the three and six month periods ended June 30, 2021 and 2020 (unaudited)
7
 
For the three and six month periods ended June 30, 2021 and 2020 (unaudited)
8
   
 
For the three and six month periods ended June 30, 2021 and 2020 (unaudited)
9
   
 
For the six month periods ended June 30, 2021 and 2020 (unaudited)
10
   
Notes to Consolidated Financial Statements (unaudited)
11
11
12
13
18
20
22
30
36
37
37
41
42
42
42
42

ARCH CAPITAL
 4
2021 SECOND QUARTER FORM 10-Q

Table of Contents
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
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2021 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 value 1,693,552  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 method 2,539,124  2,047,889 
Total investments 29,298,681  28,761,358 
Cash 1,234,059  906,448 
Accrued investment income 96,546  103,299 
Securities pledged under securities lending, at fair value (amortized cost: $167,871 and $294,493)
168,548  294,912 
Investment in operating affiliates 731,810  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 premiums 1,541,093  1,234,075 
Deferred acquisition costs 1,013,657  790,708 
Receivable for securities sold 309,234  92,743 
Goodwill and intangible assets 667,153  692,863 
Other assets 2,357,064  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 premiums 6,011,369  4,838,965 
Reinsurance balances payable 1,079,106  683,263 
Contractholder payables 1,887,418  1,995,562 
Collateral held for insured obligations 235,618  215,581 
Senior notes 2,861,728  2,861,113 
Revolving credit agreement borrowings 155,687  155,687 
Securities lending payable 172,109  301,089 
Payable for securities purchased 586,881  218,779 
Other liabilities 1,332,843  1,510,888 
Total liabilities 31,519,407  29,294,856 
Commitments and Contingencies
Redeemable noncontrolling interests 57,533  58,548 
Shareholders' Equity
Non-cumulative preferred shares 1,280,000  780,000 
Common shares ($0.0011 par, shares issued: 582,654,893 and 579,000,841)
647  643 
Additional paid-in capital 2,028,919  1,977,794 
Retained earnings 13,454,036  12,362,463 
Accumulated other comprehensive income (loss), net of deferred income tax 230,048  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 Arch 13,986,072  13,105,886 
Non-redeemable noncontrolling interests 918,874  823,007 
Total shareholders' equity 14,904,946  13,928,893 
Total liabilities, noncontrolling interests and shareholders' equity $ 46,481,886  $ 43,282,297 
See Notes to Consolidated Financial Statements

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Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF INCOME
(U.S. dollars in thousands, except share data)
(Unaudited) (Unaudited)
Three Months Ended Six Months Ended
June 30, June 30,
  2021 2020 2021 2020
Revenues        
Net premiums earned $ 2,120,909  $ 1,665,354  4,069,331  3,409,798 
Net investment income 111,613  131,485  210,469  276,638 
Net realized gains (losses) 202,907  556,588  345,368  189,628 
Other underwriting income 5,529  6,667  11,639  13,519 
Equity in net income (loss) of investment funds accounted for using the equity method 122,186  (65,119) 193,872  (69,328)
Other income (loss) 6,852  33  5,111  65 
Total revenues 2,569,996  2,295,008  4,835,790  3,820,320 
Expenses
Losses and loss adjustment expenses 1,159,831  1,230,522  2,362,931  2,345,941 
Acquisition expenses 335,143  254,789  639,624  502,072 
Other operating expenses 244,943  209,249  505,976  443,793 
Corporate expenses 15,951  17,920  41,335  38,716 
Amortization of intangible assets 15,286  16,489  29,688  33,120 
Interest expense 35,700  31,139  74,046  63,694 
Net foreign exchange (gains) losses 17,775  39,211  (2,288) (33,460)
Total expenses 1,824,629  1,799,319  3,651,312  3,393,876 
Income (loss) before income taxes and income (loss) from operating affiliates 745,367  495,689  1,184,478  426,444 
Income tax expense (51,179) (26,127) (90,039) (54,072)
Income (loss) from operating affiliates 24,476  (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 Arch 675,486  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    
Basic 397,743,402  402,503,687  399,267,183  403,197,924 
Diluted 406,485,994  408,119,681  407,687,680  411,005,591 



See Notes to Consolidated Financial Statements

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Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME
(U.S. dollars in thousands)
(Unaudited) (Unaudited)
Three Months Ended Six Months Ended
June 30, June 30,
  2021 2020 2021 2020
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 period 78,571  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 adjustments 6,205  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

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Table of Contents

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF CHANGES IN SHAREHOLDERS’ EQUITY
(U.S. dollars in thousands)
(Unaudited) (Unaudited)
Three Months Ended Six Months Ended
June 30, June 30,
  2021 2020 2021 2020
Non-cumulative preferred shares    
Balance at beginning of period $ 780,000  $ 780,000  $ 780,000  $ 780,000 
Preferred shares issued 500,000  —  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 period 645  642  643  638 
Common shares issued, net — 
Balance at end of period 647  642  647  642 
Additional paid-in capital    
Balance at beginning of period 2,014,741  1,921,487  1,977,794  1,889,683 
Amortization of share-based compensation 16,490  13,160  57,063  41,210 
Issue costs on preferred shares (14,179) —  (14,179) — 
Other changes 11,867  867  8,241  4,621 
Balance at end of period 2,028,919  1,935,514  2,028,919  1,935,514 
Retained earnings    
Balance at beginning of period 12,790,216  11,132,268  12,362,463  11,021,006 
Cumulative effect of an accounting change (1) —  —  —  (22,452)
Balance at beginning of period, as adjusted 12,790,216  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 period 13,454,036  11,420,686  13,454,036  11,420,686 
Accumulated other comprehensive income (loss), net of deferred income tax
Balance at beginning of period 205,827  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 period 246,711  113,149  501,295  258,486 
Unrealized holding gains (losses) during period, net of reclassification adjustment 18,024  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 period 264,702  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 adjustments 6,205  22,251  (22,379) (22,438)
Foreign currency translation adjustments attributable to noncontrolling interests 25  (45) 125  (166)
Balance at end of period (34,654) (68,999) (34,654) (68,999)
Balance at end of period 230,048  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 Arch 13,986,072  11,991,825  13,986,072  11,991,825 
Non-redeemable noncontrolling interests 918,874  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

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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF CASH FLOWS
(U.S. dollars in thousands)
(Unaudited)
Six Months Ended
June 30,
  2021 2020
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 assets 29,688  33,120 
Share-based compensation 57,564  41,912 
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable 948,505  1,158,446 
Unearned premiums, net of ceded unearned premiums 838,650  395,759 
Premiums receivable (781,391) (463,638)
Deferred acquisition costs (214,893) (92,437)
Reinsurance balances payable 331,461  132,161 
Other items, net (231,307) (192,066)
Net cash provided by (used for) operating activities 1,612,572  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 investments 23,130,388  24,833,030 
Proceeds from sales of equity securities 542,290  580,346 
Proceeds from sales, redemptions and maturities of other investments 772,549  472,188 
Proceeds from redemptions and maturities of fixed maturity investments 805,836  369,240 
Net settlements of derivative instruments 17,286  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, net 485,821  — 
Purchases of common shares under share repurchase program (485,315) (75,486)
Proceeds from common shares issued, net 185  (9,661)
Proceeds from borrowings —  1,004,918 
Repayments of borrowings —  (165,000)
Change in cash collateral related to securities lending 826  (54,596)
Third party investment in non-redeemable noncontrolling interests 15,971  (2,867)
Dividends paid to redeemable noncontrolling interests (1,907) (2,540)
Other 27,639  (2,625)
Preferred dividends paid (20,805) (20,806)
Net cash provided by (used for) financing activities 22,415  671,337 
Effects of exchange rate changes on foreign currency cash and restricted cash (13,390) (21,742)
Increase (decrease) in cash and restricted cash 527,919  160,985 
Cash and restricted cash, beginning of year 1,290,544  903,698 
Cash and restricted cash, end of period $ 1,818,463  $ 1,064,683 

See Notes to Consolidated Financial Statements

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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
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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 Ended Six Months Ended
June 30, June 30,
  2021 2020 2021 2020
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 Arch 675,486  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 — basic 397,743,402  402,503,687  399,267,183  403,197,924 
Effect of dilutive common share equivalents:
Nonvested restricted shares 1,990,729  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 — diluted 406,485,994  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.
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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
4.    Segment Information
The Company classifies its businesses into three underwriting segments — insurance, reinsurance and mortgage — and two other operating segments — ‘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.
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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
  Insurance Reinsurance Mortgage Sub-Total Other Total
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 written 963,555  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 earned 865,427  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 income 89,430  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 method 122,186  —  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 affiliates 697,799  47,568  745,367 
Income tax (expense) benefit (50,953) (226) (51,179)
Income (loss) from operating affiliates 24,476  —  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 Arch 670,742  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 ratio 63.1  % 62.9  % 3.0  % 52.6  % 76.1  % 54.7  %
Acquisition expense ratio 15.8  % 18.1  % 9.0  % 15.5  % 18.8  % 15.8  %
Other operating expense ratio 15.4  % 6.1  % 14.5  % 11.7  % 10.1  % 11.5  %
Combined ratio 94.3  % 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.’

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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
Three Months Ended
June 30, 2020
  Insurance Reinsurance Mortgage Sub-Total Other Total
Gross premiums written (1) $ 1,030,362  $ 807,065  $ 369,144  $ 2,206,410  $ 157,927  $ 2,317,692 
Premiums ceded (358,101) (241,971) (44,044) (643,955) (52,071) (649,381)
Net premiums written 672,261  565,094  325,100  1,562,455  105,856  1,668,311 
Change in unearned premiums 15,648  (84,897) 40,613  (28,636) 25,679  (2,957)
Net premiums earned 687,909  480,197  365,713  1,533,819  131,535  1,665,354 
Other underwriting income (loss) —  (651) 6,450  5,799  868  6,667 
Losses and loss adjustment expenses (518,203) (383,433) (224,100) (1,125,736) (104,786) (1,230,522)
Acquisition expenses (107,671) (90,522) (34,052) (232,245) (22,544) (254,789)
Other operating expenses (118,757) (38,716) (37,574) (195,047) (14,202) (209,249)
Underwriting income (loss) $ (56,722) $ (33,125) $ 76,437  (13,410) (9,129) (22,539)
Net investment income 101,031  30,454  131,485 
Net realized gains (losses) 385,089  171,499  556,588 
Equity in net income (loss) of investment funds accounted for using the equity method (65,119) —  (65,119)
Other income (loss) 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 affiliates 305,647  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 Arch 275,011  23,810  298,821 
Preferred dividends (10,403) —  (10,403)
Net income (loss) available to Arch common shareholders $ 264,608  $ 23,810  $ 288,418 
Underwriting Ratios          
Loss ratio 75.3  % 79.8  % 61.3  % 73.4  % 79.7  % 73.9  %
Acquisition expense ratio 15.7  % 18.9  % 9.3  % 15.1  % 17.1  % 15.3  %
Other operating expense ratio 17.3  % 8.1  % 10.3  % 12.7  % 10.8  % 12.6  %
Combined ratio 108.3  % 106.8  % 80.9  % 101.2  % 107.6  % 101.8  %
Goodwill and intangible assets $ 263,086  $ 2,516  $ 415,238  $ 680,840  $ 7,650  $ 688,490 

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

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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
Six Months Ended
June 30, 2021
  Insurance Reinsurance Mortgage Sub-Total Other Total
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 written 1,958,394  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 earned 1,684,901  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 income 168,159  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 method 193,872  —  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 affiliates 1,095,043  89,435  1,184,478 
Income tax (expense) benefit (89,805) (234) (90,039)
Income (loss) from operating affiliates 99,933  —  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 Arch 1,104,708  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 ratio 64.2  % 68.7  % 11.0  % 56.3  % 78.0  % 58.1  %
Acquisition expense ratio 15.7  % 18.2  % 9.0  % 15.4  % 18.9  % 15.7  %
Other operating expense ratio 16.1  % 7.6  % 14.5  % 12.7  % 9.9  % 12.4  %
Combined ratio 96.0  % 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.’

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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
Six Months Ended
June 30, 2020
  Insurance Reinsurance Mortgage Sub-Total Other Total
Gross premiums written (1) $ 2,238,007  $ 1,929,584  $ 738,089  $ 4,904,947  $ 392,829  $ 5,150,522 
Premiums ceded (736,998) (567,310) (88,371) (1,391,946) (100,273) (1,344,965)
Net premiums written 1,501,009  1,362,274  649,718  3,513,001  292,556  3,805,557 
Change in unearned premiums (97,181) (338,617) 61,021  (374,777) (20,982) (395,759)
Net premiums earned 1,403,828  1,023,657  710,739  3,138,224  271,574  3,409,798 
Other underwriting income (loss) —  1,469  11,049  12,518  1,001  13,519 
Losses and loss adjustment expenses (1,025,311) (813,502) (291,666) (2,130,479) (215,462) (2,345,941)
Acquisition expenses (215,008) (170,128) (72,588) (457,724) (44,348) (502,072)
Other operating expenses (248,406) (84,013) (83,470) (415,889) (27,904) (443,793)
Underwriting income (loss) $ (84,897) $ (42,517) $ 274,064  $ 146,650  $ (15,139) $ 131,511 
Net investment income 214,059  62,579  276,638 
Net realized gains (losses) 312,980  (123,352) 189,628 
Equity in net income (loss) of investment funds accounted for using the equity method (69,328) —  (69,328)
Other income (loss) 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 affiliates 503,084  (76,640) 426,444 
Income tax (expense) benefit (54,474) 402  (54,072)
Income (loss) from operating affiliates 5,343  —  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 interests —  68,346  68,346 
Net income (loss) available to Arch 452,962  (10,024) 442,938 
Preferred dividends (20,806) —  (20,806)
Net income (loss) available to Arch common shareholders $ 432,156  $ (10,024) $ 422,132 
Underwriting Ratios
Loss ratio 73.0  % 79.5  % 41.0  % 67.9  % 79.3  % 68.8  %
Acquisition expense ratio 15.3  % 16.6  % 10.2  % 14.6  % 16.3  % 14.7  %
Other operating expense ratio 17.7  % 8.2  % 11.7  % 13.3  % 10.3  % 13.0  %
Combined ratio 106.0  % 104.3  % 62.9  % 95.8  % 105.9  % 96.5  %
(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.
(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
5.    Reserve for Losses and Loss Adjustment Expenses
The following table represents an analysis of losses and loss adjustment expenses and a reconciliation of the beginning and ending reserve for losses and loss adjustment expenses:
Three Months Ended Six Months Ended
June 30, June 30,
2021 2020 2021 2020
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 recoverable
3,916,650  4,070,114  4,314,855  4,082,650 
Net reserve for losses and loss adjustment expenses at beginning of period
12,527,302  10,239,466  12,199,074  9,809,192 
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year
1,219,081  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 expenses
1,159,831  1,230,522  2,362,931  2,345,941 
Retroactive reinsurance transactions (1)
—  —  (183,893) 60,635 
Net foreign exchange (gains) losses
135,847  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 period
13,050,628  10,888,717  13,050,628  10,888,717 
Unpaid losses and loss adjustment expenses recoverable
4,146,020  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
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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
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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 Allowance Allowance 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)”.

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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 Allowance Allowance 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 losses 157 
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 losses 221 
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
2021 2020
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 better 66.0  % 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’ equity 2.4  % 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 Allowance Allowance 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 period 2,179,124  $ 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)”.
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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 securities 389,041  4,480  (3,479) (269) 388,309 
Municipal bonds 415,483  23,153  (1,660) (6) 393,996 
Commercial mortgage backed securities 266,733  4,017  (611) (3) 263,330 
U.S. government and government agencies 5,091,183  14,814  (14,013) —  5,090,382 
Non-U.S. government securities 2,449,782  108,823  (18,441) (128) 2,359,528 
Asset backed securities 2,487,845  16,460  (4,056) (486) 2,475,927 
Total 18,229,835  388,808  (77,011) (2,124) 17,920,162 
Short-term investments 2,248,613  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 securities 630,001  8,939  (5,028) (278) 626,368 
Municipal bonds 494,522  27,291  (3,835) (11) 471,077 
Commercial mortgage backed securities 389,900  8,722  (2,954) (122) 384,254 
U.S. government and government agencies 5,557,077  22,612  (12,611) —  5,547,076 
Non-U.S. government securities 2,433,733  153,891  (8,060) —  2,287,902 
Asset backed securities 1,634,804  19,225  (10,715) (1,090) 1,627,384 
Total 18,996,608  654,927  (77,591) (2,397) 18,421,669 
Short-term investments 1,924,922  2,693  (2,063) —  1,924,292 
Total $ 20,921,530  $ 657,620  $ (79,654) $ (2,397) $ 20,345,961 
(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.
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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
The following table summarizes, for all available for sale securities in an unrealized loss position, the fair value and gross unrealized loss by length of time the security has been in a continual unrealized loss position:
  Less than 12 Months 12 Months or More Total
Estimated
Fair
Value
Gross
Unrealized
Losses
Estimated
Fair
Value
Gross
Unrealized
Losses
Estimated
Fair
Value
Gross
Unrealized
Losses
June 30, 2021
Fixed maturities (1):
Corporate bonds $ 2,264,801  $ (32,733) $ 22,895  $ (2,018) $ 2,287,696  $ (34,751)
Mortgage backed securities 196,765  (2,893) 13,632  (586) 210,397  (3,479)
Municipal bonds 24,711  (1,612) 2,859  (48) 27,570  (1,660)
Commercial mortgage backed securities 20,039  (180) 7,961  (431) 28,000  (611)
U.S. government and government agencies 2,920,944  (14,013) —  —  2,920,944  (14,013)
Non-U.S. government securities 1,282,422  (17,562) 16,885  (879) 1,299,307  (18,441)
Asset backed securities 781,596  (2,364) 93,923  (1,692) 875,519  (4,056)
Total 7,491,278  (71,357) 158,155  (5,654) 7,649,433  (77,011)
Short-term investments 531,130  (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 securities 284,619  (4,788) 3,637  (240) 288,256  (5,028)
Municipal bonds 67,937  (3,835) —  —  67,937  (3,835)
Commercial mortgage backed securities 126,624  (2,916) 2,655  (38) 129,279  (2,954)
U.S. government and government agencies 1,285,907  (12,611) —  —  1,285,907  (12,611)
Non-U.S. government securities 543,844  (7,658) 2,441  (402) 546,285  (8,060)
Asset backed securities 634,470  (9,110) 57,737  (1,605) 692,207  (10,715)
Total 3,690,843  (74,004) 70,404  (3,587) 3,761,247  (77,591)
Short-term investments 97,920  (2,063) —  —  97,920  (2,063)
Total $ 3,788,763  $ (76,067) $ 70,404  $ (3,587) $ 3,859,167  $ (79,654)
(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.

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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
The contractual maturities of the Company’s fixed maturities are shown in the following table. Expected maturities, which are management’s best estimates, will differ from contractual maturities because borrowers may have the right to call or prepay obligations with or without call or prepayment penalties.
June 30, 2021 December 31, 2020
Maturity Estimated
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 years 10,114,276  9,942,182  10,629,959  10,340,819 
Due after five years through 10 years 4,148,538  4,055,318  4,881,564  4,654,754 
Due after 10 years 371,337  355,241  482,180  448,139 
  15,086,216  14,792,596  16,341,903  15,783,663 
Mortgage backed securities 389,041  388,309  630,001  626,368 
Commercial mortgage backed securities 266,733  263,330  389,900  384,254 
Asset backed securities 2,487,845  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 nil, and the fair value of security collateral received was $301.1 million.
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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 Continuous Less than 30 Days 30-90 Days 90 Days or More Total
June 30, 2021
U.S. government and government agencies $ 15,745  $ 137,713  $ —  $ —  $ 153,458 
Corporate bonds 5,800  —  —  —  5,800 
Equity securities 12,851  —  —  —  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 bonds 3,021  —  —  —  3,021 
Equity securities 16,461  —  —  —  16,461 
Total $ 161,799  $ —  $ 139,290  $ —  $ 301,089 
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 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 investments 2,370,472  2,331,885 
Short-term investments 610,114  557,008 
Equity securities 94,931  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 
Lending 638,786  572,636 
Credit related funds 73,171  90,780 
Energy 84,891  65,813 
Investment grade fixed income 110,375  138,646 
Infrastructure 32,109  165,516 
Private equity 70,878  48,750 
Real estate 27,248  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 
Equities 403,003  343,058 
Real estate 323,566  258,518 
Lending 295,228  179,629 
Private equity 305,662  235,289 
Infrastructure 210,174  175,882 
Energy 118,212  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
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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,
  2021 2020
Three Months Ended
Fixed maturities $ 88,625  $ 105,391 
Term loans 16,879  20,512 
Equity securities 8,584  6,219 
Short-term investments 1,138  3,383 
Other (1) 19,950  16,460 
Gross investment income 135,176  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 loans 31,607  43,682 
Equity securities 14,234  12,226 
Short-term investments 1,745  8,279 
Other (1) 34,305  35,866 
Gross investment income 261,142  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.
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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,
  2021 2020
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 maturities 10,912  68,181 
Other investments 60,884  178,570 
Equity securities 5,492  6,664 
Short-term investments (104) 3,368 
Equity securities, at fair value:
Net realized gains (losses) on sales during the period 33,570  (18,250)
Net unrealized gains (losses) on equity securities still held at reporting date 65,847  145,686 
Allowance for credit losses:
Investments related 896  3,225 
Underwriting related 1,381  (5,834)
Derivative instruments (1) (51,109) (836)
Other 10,224  (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 maturities 27,465  (59,485)
Other investments 107,739  (129,230)
Equity securities 7,557  1,755 
Short-term investments 632  (5,313)
Equity securities, at fair value:
Net realized gains (losses) on sales during the period 71,419  (18,789)
Net unrealized gains (losses) on equity securities still held at reporting date 85,555  (29,880)
Allowance for credit losses:
Investments related (752) (6,095)
Underwriting related 6,649  (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.

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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 Investments Total
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 losses 52  —  —  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 losses 695  44  290  (29) 1,000 
Additions (reductions) for previously recognized expected credit losses (1,304) (25) (2,903) —  (4,232)
Reductions due to disposals (319) (14) (504) —  (837)
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 losses 234  —  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 losses 2,841  67  7,441  —  10,349 
Additions (reductions) for previously recognized expected credit losses (1,306) (25) (2,924) —  (4,255)
Reductions due to disposals (326) (14) (519) —  (859)
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)”.

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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 agreements 3,441,929  3,083,324 
Deposits with U.S. regulatory authorities 814,084  827,552 
Deposits with non-U.S. regulatory authorities 428,132  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 

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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
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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
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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.

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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 securities 389,041  —  389,041  — 
Municipal bonds 415,483  —  415,483  — 
Commercial mortgage backed securities 266,733  —  266,733  — 
U.S. government and government agencies 5,091,183  5,062,571  28,612  — 
Non-U.S. government securities 2,449,782  —  2,449,782  — 
Asset backed securities 2,487,845  —  2,484,421  3,424 
Total 18,229,835  5,062,571  13,163,827  3,437 
Short-term investments 2,248,613  1,996,304  252,309  — 
Equity securities, at fair value 1,706,044  1,631,937  24,971  49,136 
Derivative instruments (4) 98,488  —  98,488  — 
Residential mortgage loans 44,925  —  44,925  — 
Fair value option:
Corporate bonds 790,186  —  789,188  998 
Non-U.S. government bonds 22,552  —  22,552  — 
Mortgage backed securities 2,707  —  2,707  — 
Commercial mortgage backed securities 841  —  841  — 
Asset backed securities 179,423  —  179,423  — 
U.S. government and government agencies 271  163  108  — 
Short-term investments 610,114  482,815  127,299  — 
Equity securities 94,930  21,252  —  73,678 
Other investments 1,219,294  23,610  1,121,784  73,900 
Other investments measured at net asset value (2) 1,151,178 
Total 4,071,496  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.
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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 securities 630,001  —  630,001  — 
Municipal bonds 494,522  —  494,522  — 
Commercial mortgage backed securities 389,900  —  389,900  — 
U.S. government and government agencies 5,557,077  5,463,356  93,721  — 
Non-U.S. government securities 2,433,733  —  2,433,733  — 
Asset backed securities 1,634,804  —  1,631,378  3,426 
Total 18,996,608  5,463,356  13,529,813  3,439 
Short-term investments 1,924,922  1,920,565  4,357  — 
Equity securities, at fair value 1,460,959  1,401,653  17,291  42,015 
Derivative instruments (4) 177,383  —  177,383  — 
Fair value option:
Corporate bonds 651,294  —  650,309  985 
Non-U.S. government bonds 35,263  —  35,263  — 
Mortgage backed securities 3,282  —  3,282  — 
Commercial mortgage backed securities 1,090  —  1,090  — 
Asset backed securities 152,151  —  152,151  — 
U.S. government and government agencies 274  164  110  — 
Short-term investments 557,008  420,131  136,877  — 
Equity securities 92,549  23,373  188  68,988 
Other investments 1,134,229  51,149  1,015,977  67,103 
Other investments measured at net asset value (2) 1,197,656 
Total 3,824,796  494,817  1,995,247  137,076 
Total assets measured at fair value $ 26,384,668  $ 9,280,391  $ 15,724,091  $ 182,530 
Liabilities measured at fair value:
Contingent consideration liabilities $ (461) $ —  $ —  $ (461)
Securities sold but not yet purchased (3) (21,679) —  (21,679) — 
Derivative instruments (4) (108,705) —  (108,705) — 
Total liabilities measured at fair value $ (130,845) $ —  $ (130,384) $ (461)

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

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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:
Assets Liabilities
s Available For Sale Fair Value Option Fair 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
Purchases —  —  —  5,638  —  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
Purchases —  —  33  —  —  — 
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 income 57  —  —  —  —  —  — 
Purchases, issuances, sales and settlements
Purchases —  —  —  13,003  —  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
Purchases —  —  66  24  —  3,464  — 
Issuances —  —  —  —  —  —  — 
Sales —  —  —  (24,358) —  (15,450) — 
Settlements (1,402) (1,462) —  —  —  —  6,820 
Transfers in and/or out of Level 3 —  —  —  2,984  —  —  — 
Balance at end of period $ 3,450  $ 857  $ 998  $ 46,453  $ 61,447  $ 51,981  $ (1,250)
(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.
(2)    Gains or losses were included in net realized gains (losses).
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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 Derivatives Liability Derivatives Notional
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:
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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
Derivatives not designated as June 30,
hedging instruments: 2021 2020
Three Months Ended
Net realized gains (losses):
Futures contracts $ (54,759) $ (1,607)
Foreign currency forward contracts 1,295  3,523 
TBAs —  264 
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)
TBAs —  1,009 
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.

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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,
2021 2020
Assets
Investments accounted for using the fair value option (1) $ 1,984,919  $ 1,790,385 
Fixed maturities available for sale, at fair value 663,902  655,249 
Equity securities, at fair value 97,623  52,410 
Cash 349,202  211,451 
Accrued investment income 14,549  14,679 
Premiums receivable 305,026  224,377 
Reinsurance recoverable on unpaid and paid losses and LAE 520,531  286,590 
Ceded unearned premiums 123,272  122,339 
Deferred acquisition costs 65,532  53,705 
Receivable for securities sold 102,287  37,423 
Goodwill and intangible assets 10,318  7,650 
Other assets 112,794  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 premiums 468,948  407,714 
Reinsurance balances payable 132,929  63,269 
Revolving credit agreement borrowings 155,687  155,687 
Senior notes 172,825  172,689 
Payable for securities purchased 199,342  25,881 
Other liabilities 227,396  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,
  2021 2020
Three Months Ended
Balance, beginning of period $ 876,864  $ 492,785 
Additional paid in capital attributable to noncontrolling interests 383  595 
Amounts attributable to noncontrolling interests 41,617  165,598 
Other comprehensive income (loss) attributable to noncontrolling interests 10  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 interests 22,113  472 
Repurchases attributable to non-redeemable noncontrolling interests (1) —  (2,867)
Amounts attributable to noncontrolling interests 78,314  (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.
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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,
  2021 2020
Three Months Ended
Balance, beginning of period $ 57,670  $ 55,376 
Accretion of preference share issuance costs 23  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 costs 46  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,
  2021 2020
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 

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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, 2021
December 31, 2020
Maximum Exposure to Loss Maximum Exposure to Loss
Bellemeade Entities (Issue Date) Total VIE Assets On-Balance Sheet (Asset) Liability Off-Balance Sheet Total Total VIE Assets On-Balance Sheet (Asset) Liability Off-Balance Sheet Total
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.
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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 Income Three Months Ended Six Months Ended
Details About Line Item That Includes June 30, June 30,
AOCI Components Reclassification 2021 2020 2021 2020
Unrealized appreciation on available-for-sale investments
Net realized gains (losses) $ 64,914  $ 182,329  $ 66,918  $ 328,561 
Provision for credit losses 896  3,225  (751) (6,095)
Other-than-temporary impairment losses —  —  —  (533)
Total before tax 65,810  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 Amount Tax 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 income 65,810  5,263  60,547 
Foreign currency translation adjustments 6,392  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 income 185,554  18,163  167,391 
Foreign currency translation adjustments 22,595  344  22,251 
Other comprehensive income (loss) $ 392,617  $ 44,961  $ 347,656 
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 income 66,167  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 income 321,933  33,313  288,620 
Foreign currency translation adjustments (22,829) (391) (22,438)
Other comprehensive income (loss) $ 147,363  $ 22,912  $ 124,451 
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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 nil 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.
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Table of Contents
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.

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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 Quarter 1.58  % 1.80  %
2020 Second Quarter 3.72  % 6.06  %
Six Months Ended June 30, 2021 1.39  % 1.28  %
Six Months Ended June 30, 2020 2.82  % 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.
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The benchmark return index included weightings to the following indices:
%
ICE BoAML 1-5 Year A - AAA U.S. Corporate Index
13.00  %
ICE BoAML 5-10 Year A - AAA U.S. Corporate Index
11.00 
ICE BoAML 1-5 Year U.S. Treasury Index 11.00 
MSCI ACWI Net Total Return USD Index 9.30 
ICE BoAML 1-10 Year BBB U.S. Corporate Index 5.00 
JPM CLOIE Investment Grade 5.00 
S&P/LSTA Leveraged Loan Total Return Index 4.965 
ICE BoAML U.S. Mortgage Backed Securities Index 4.00 
ICE BoAML AAA US Fixed Rate CMBS 4.00 
ICE BoAML 1-5 Year U.K. Gilt Index 4.00 
ICE BoAML German Government 1-10 Year Index 3.50 
ICE BoAML 0-3 Year U.S. Treasury Index 3.25 
ICE BoAML 5-10 Year U.S. Treasury Index 3.00 
ICE BoAML 1-10 Year U.S. Municipal Securities Index 3.00 
Bloomberg Barclays ABS Aaa Index 3.00 
ICE BoAML 1-5 Year Australia Government Index 2.75 
ICE BoAML U.S. High Yield Constrained Index 2.50 
ICE BoAML 1-5 Year Canada Government Index 2.00 
ICE BofA CCC and Lower US High Yield Constrained Index 1.38 
Bloomberg Barclays Global High Yield Index 1.38 
S&P DJ Global ex-US Select Real Estate Securities Net Index 0.825 
FTSE Nareit All Mortgage Capped Index Total Return USD 0.825 
Bloomberg Barclays CMBS: Erisa Eligible Unhedged USD 0.825 
ICE BoAML 15+ Year Canada Government Index 0.50 
Total
100.00  %
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
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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.
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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 Ended Six Months Ended
June 30, June 30,
2021 2020 2021 2020
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) losses 17,888  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,
  2021 2020
Change
Gross premiums written $ 1,368,867  $ 1,030,362  32.9 
Premiums ceded (405,312) (358,101)
Net premiums written 963,555  672,261  43.3 
Change in unearned premiums (98,128) 15,648 
Net premiums earned 865,427  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 ratio 63.1  % 75.3  % (12.2)
Acquisition expense ratio 15.8  % 15.7  % 0.1 
Other operating expense ratio 15.4  % 17.3  % (1.9)
Combined ratio 94.3  % 108.3  % (14.0)

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  Six Months Ended June 30,
  2021 2020 % Change
Gross premiums written $ 2,784,753  $ 2,238,007  24.4 
Premiums ceded (826,359) (736,998)
Net premiums written 1,958,394  1,501,009  30.5 
Change in unearned premiums (273,493) (97,181)
Net premiums earned 1,684,901  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 ratio 64.2  % 73.0  % (8.8)
Acquisition expense ratio 15.7  % 15.3  % 0.4 
Other operating expense ratio 16.1  % 17.7  % (1.6)
Combined ratio 96.0  % 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,
  2021 2020
  Amount % Amount %
Property, energy, marine and aviation $ 207,762  21.6  $ 159,801  23.8 
Professional lines 254,961  26.5  157,899  23.5 
Programs 149,373  15.5  104,930  15.6 
Construction and national accounts 77,579  8.1  57,144  8.5 
Excess and surplus casualty 74,346  7.7  64,703  9.6 
Travel, accident and health 71,071  7.4  27,997  4.2 
Lenders products 40,386  4.2  23,690  3.5 
Other 88,077  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.
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  Six Months Ended June 30,
  2021 2020
  Amount % Amount %
Property, energy, marine and aviation $ 378,260  19.3  $ 287,386  19.1 
Professional Lines 493,207  25.2  327,017  21.8 
Programs 307,774  15.7  217,462  14.5 
Construction and national accounts 212,371  10.8  173,143  11.5 
Excess and surplus casualty 159,939  8.2  130,122  8.7 
Travel, accident and health 163,377  8.3  154,043  10.3 
Lenders products 75,246  3.8  56,982  3.8 
Other 168,220  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,
  2021 2020
  Amount % Amount %
Property, energy, marine and aviation $ 167,716  19.4  $ 120,781  17.6 
Professional lines 214,098  24.7  154,812  22.5 
Programs 118,974  13.7  108,464  15.8 
Construction and national accounts 95,849  11.1  91,605  13.3 
Excess and surplus casualty 72,899  8.4  60,966  8.9 
Travel, accident and health 62,610  7.2  52,117  7.6 
Lenders products 46,396  5.4  23,111  3.4 
Other 86,885  10.0  76,053  11.1 
Total $ 865,427  100.0  $ 687,909  100.0 
  Six Months Ended June 30,
  2021 2020
  Amount % Amount %
Property, energy, marine and aviation $ 324,975  19.3  $ 231,964  16.5 
Professional Lines 413,769  24.6  306,512  21.8 
Programs 231,814  13.8  217,342  15.5 
Construction and national accounts 198,520  11.8  191,305  13.6 
Excess and surplus casualty 148,266  8.8  126,063  9.0 
Travel, accident and health 112,276  6.7  129,492  9.2 
Lenders products 86,477  5.1  48,454  3.5 
Other 168,804  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 Ended Six Months Ended
June 30, June 30,
  2021 2020 2021 2020
Current year 63.6  % 75.7  % 64.7  % 73.3  %
Prior period reserve development (0.5) % (0.4) % (0.5) % (0.3) %
Loss ratio 63.1  % 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.
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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,
  2021 2020
Change
Gross premiums written $ 1,358,020  $ 807,065  68.3 
Premiums ceded (433,288) (241,971)
Net premiums written 924,732  565,094  63.6 
Change in unearned premiums (187,708) (84,897)
Net premiums earned 737,024  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 ratio 62.9  % 79.8  % (16.9)
Acquisition expense ratio 18.1  % 18.9  % (0.8)
Other operating expense ratio 6.1  % 8.1  % (2.0)
Combined ratio 87.1  % 106.8  % (19.7)
  Six Months Ended June 30,
  2021 2020 % Change
Gross premiums written $ 2,829,080  $ 1,929,584  46.6 
Premiums ceded (905,236) (567,310)
Net premiums written 1,923,844  1,362,274  41.2 
Change in unearned premiums (541,920) (338,617)
Net premiums earned 1,381,924  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 ratio 68.7  % 79.5  % (10.8)
Acquisition expense ratio 18.2  % 16.6  % 1.6 
Other operating expense ratio 7.6  % 8.2  % (0.6)
Combined ratio 94.5  % 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
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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,
  2021 2020
  Amount % Amount %
Property excluding property catastrophe $ 249,101  26.9  $ 163,639  29.0 
Property catastrophe 87,642  9.5  117,676  20.8 
Other specialty 296,325  32.0  117,375  20.8 
Casualty 225,890  24.4  105,049  18.6 
Marine and aviation 50,248  5.4  32,372  5.7 
Other 15,526  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,
  2021 2020
  Amount % Amount %
Property excluding property catastrophe $ 541,934  28.2  $ 322,563  23.7 
Property catastrophe 204,849  10.6  206,768  15.2 
Other Specialty 580,656  30.2  402,327  29.5 
Casualty 444,146  23.1  295,929  21.7 
Marine and aviation 111,886  5.8  82,157  6.0 
Other 40,373  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,
  2021 2020
  Amount % Amount %
Property excluding property catastrophe $ 202,780  27.5  $ 124,019  25.8 
Property catastrophe 76,167  10.3  55,226  11.5 
Other specialty 211,817  28.7  123,006  25.6 
Casualty 183,846  24.9  132,756  27.6 
Marine and aviation 42,773  5.8  24,960  5.2 
Other 19,641  2.7  20,230  4.2 
Total $ 737,024  100.0  $ 480,197  100.0 
  Six Months Ended June 30,
  2021 2020
  Amount % Amount %
Property excluding property catastrophe $ 390,562  28.3  $ 236,671  23.1 
Property catastrophe 164,178  11.9  108,226  10.6 
Other Specialty 375,715  27.2  326,391  31.9 
Casualty 332,877  24.1  267,827  26.2 
Marine and aviation 82,881  6.0  49,818  4.9 
Other 35,711  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.

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Losses and Loss Adjustment Expenses.
The table below shows the components of the reinsurance segment’s loss ratio:
Three Months Ended Six Months Ended
June 30, June 30,
  2021 2020 2021 2020
Current year 65.7  % 88.2  % 72.1  % 84.6  %
Prior period reserve development (2.8) % (8.4) % (3.4) % (5.1) %
Loss ratio 62.9  % 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,
  2021 2020 % Change
Gross premiums written $ 391,511  $ 369,144  6.1 
Premiums ceded (55,665) (44,044)
Net premiums written 335,846  325,100  3.3 
Change in unearned premiums (1,625) 40,613 
Net premiums earned 334,221  365,713  (8.6)
Other underwriting income 4,148  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 ratio 3.0  % 61.3  % (58.3)
Acquisition expense ratio 9.0  % 9.3  % (0.3)
Other operating expense ratio 14.5  % 10.3  % 4.2 
Combined ratio 26.5  % 80.9  % (54.4)
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  Six Months Ended June 30,
  2021 2020 % Change
Gross premiums written $ 782,757  $ 738,089  6.1 
Premiums ceded (111,716) (88,371)
Net premiums written 671,041  649,718  3.3 
Change in unearned premiums (503) 61,021 
Net premiums earned 670,538  710,739  (5.7)
Other underwriting income 11,045  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 ratio 11.0  % 41.0  % (30.0)
Acquisition expense ratio 9.0  % 10.2  % (1.2)
Other operating expense ratio 14.5  % 11.7  % 2.8 
Combined ratio 34.5  % 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,
  2021 2020
  Amount % Amount %
Underwriting location:
United States $ 234,645  69.9  $ 261,124  80.3 
Other 101,201  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,
  2021 2020
  Amount % Amount %
Underwriting location:
United States $ 482,174  71.9  $ 525,232  80.8 
Other 188,867  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,
2021 2020
Amount % Amount %
Total new insurance written (NIW) (1) $ 28,372  $ 24,551 
Credit quality (FICO):
>=740 $ 19,240  67.8  $ 15,851  64.6 
680-739 8,113  28.6  7,781  31.7 
620-679 1,019  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 below 4,277  15.1  5,060  20.6 
Total $ 28,372  100.0  $ 24,551  100.0 
Monthly vs. single:
Monthly $ 26,725  94.2  $ 23,391  95.3 
Single 1,647  5.8  1,160  4.7 
Total $ 28,372  100.0  $ 24,551  100.0 
Purchase vs. refinance:
Purchase $ 25,010  88.2  $ 14,956  60.9 
Refinance 3,362  11.8  9,595  39.1 
Total $ 28,372  100.0  $ 24,551  100.0 
(1)Represents the original principal balance of all loans that received coverage during the period.

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(U.S. Dollars in millions) Six Months Ended June 30,
2021 2020
Amount % Amount %
Total new insurance written (NIW) (1) $ 55,391  $ 41,329 
Credit quality (FICO):
>=740 $ 37,058  66.9  $ 25,920  62.7 
680-739 16,531  29.8  13,568  32.8 
620-679 1,802  3.3  1,841  4.5 
Total $ 55,391  100.0  $ 41,329  100.0 
Loan-to-value (LTV):
95.01% and above $ 3,092  5.6  $ 3,616  8.7 
90.01% to 95.00% 26,224  47.3  16,602  40.2 
85.01% to 90.00% 16,987  30.7  13,469  32.6 
85.01% and below 9,088  16.4  7,642  18.5 
Total $ 55,391  100.0  $ 41,329  100.0 
Monthly vs. single:
Monthly $ 51,714  93.4  $ 39,083  94.6 
Single 3,677  6.6  2,246  5.4 
Total $ 55,391  100.0  $ 41,329  100.0 
Purchase vs. refinance:
Purchase $ 45,515  82.2  $ 27,255  65.9 
Refinance 9,876  17.8  14,074  34.1 
Total $ 55,391  100.0  $ 41,329  100.0 
(1)Represents the original principal balance of all loans that received coverage during the period.
Net Premiums Earned.
The following tables set forth our mortgage segment’s net premiums earned by underwriting location:
  Three Months Ended June 30,
  2021 2020
  Amount % Amount %
Underwriting location:
United States $ 248,388  74.3  $ 304,652  83.3 
Other 85,833  25.7  61,061  16.7 
Total $ 334,221  100.0  $ 365,713  100.0 
2021 Second Quarter versus 2020 Period. Net premiums earned for the 2021 second quarter were 8.6% lower than in the 2020 second quarter, and reflected a lower level of single premium policy terminations and a decrease in U.S. primary mortgage insurance in force on monthly premium policies.
  Six Months Ended June 30,
  2021 2020
  Amount % Amount %
Underwriting location:
United States $ 510,938  76.2  $ 593,814  83.5 
Other 159,600  23.8  116,925  16.5 
Total $ 670,538  100.0  $ 710,739  100.0 
Six Months Ended June 30, 2021 versus 2020 Period. Net premiums earned for the six months ended June 30, 2021 were 5.7% lower than in the 2020 period, primarily reflecting a lower level of single premiums earned, partially offset by an increase in earnings from Australian single premium policy terminations.
Other Underwriting Income.
Other underwriting income, which is primarily related to GSE credit risk-sharing transactions was $4.1 million for the 2021 second quarter, compared to $6.5 million for the 2020 second quarter.
Losses and Loss Adjustment Expenses.
The table below shows the components of the mortgage segment’s loss ratio:
Three Months Ended Six Months Ended
June 30, June 30,
  2021 2020 2021 2020
Current year 15.9  % 61.4  % 19.1  % 41.9  %
Prior period reserve development (12.9) % (0.1) % (8.1) % (0.9) %
Loss ratio 3.0  % 61.3  % 11.0  % 41.0  %
Current Year Loss Ratio.
2021 Second Quarter versus 2020 Period. The mortgage segment’s current year loss ratio was 45.5 points lower in the 2021 second quarter than in the 2020 second quarter. The mortgage segment’s current year loss ratio was 22.8 points lower for the six months ended June 30, 2021 than for the 2020 period. The lower current year loss ratios for the 2021 period reflect decrease in loss assumptions related to COVID-19 pandemic.
For the 2020 periods, the increase in incurred losses was primarily due to, the financial stress related to the COVID-19 pandemic. Segregating estimated losses due to COVID-19 from the overall mortgage segment estimated losses would require the number of delinquencies specifically attributable to COVID-19. As this analysis cannot be performed accurately, the Company is not reporting COVID-19 provisions separately from its overall loss provisions.
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Prior Period Reserve Development.
The mortgage segment’s net favorable development was $43.1 million, or 12.9 points, for the 2021 second quarter, compared to $0.2 million, or 0.1 points, for the 2020 second quarter, and $54.0 million, or 8.1 points, for the six months ended June 30, 2021, compared to $6.3 million, or 0.9 points, for the 2020 period. See note 5, “Reserve for Losses and Loss Adjustment Expenses,” to our consolidated financial statements for information about the mortgage segment’s prior year reserve development.
Underwriting Expenses.
2021 Second Quarter versus 2020 Period. The underwriting expense ratio for the mortgage segment was 23.5% in the 2021 second quarter, compared to 19.6% in the 2020 second quarter, with the increase primarily reflecting higher operating expenses and, to a lesser extent, a decline in net premiums earned on U.S. primary mortgage insurance business.
Six Months Ended June 30, 2021 versus 2020 period. The underwriting expense ratio for the mortgage segment was 23.5% for the six months ended June 30, 2021, compared to 21.9% for the 2020 period, with the increase primarily reflecting higher operating expenses and, to a lesser extent, a decline in net premiums earned on U.S. primary mortgage insurance business.
Corporate (Non-Underwriting) Segment
The corporate (non-underwriting) segment results include net investment income, other income (loss), corporate expenses, transaction costs and other, amortization of intangible assets, interest expense, items related to our 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. See note 1, “Basis of Presentation and Recent Accounting Pronouncements,” to our consolidated financial statements for information about the change in presentation of income or loss from operating affiliates.
Net Investment Income.
The components of net investment income were derived from the following sources:
Three Months Ended Six Months Ended
June 30, June 30,
  2021 2020 2021 2020
Fixed maturities $ 77,709  $ 91,491  $ 156,726  $ 193,254 
Equity securities 8,282  6,023  13,932  11,653 
Short-term investments 972  897  1,616  4,282 
Other (1) 21,026  17,825  36,585  38,304 
Gross investment income 107,989  116,236  208,859  247,493 
Investment expenses (2) (18,559) (15,205) (40,700) (33,434)
Net investment income $ 89,430  $ 101,031  $ 168,159  214,059 
(1)    Amounts include dividends and other distributions on investment funds, term loan investments, funds held balances, cash balances and other items.
(2)    Investment expenses were approximately 0.30% of average invested assets for the 2021 second quarter, compared to 0.28% for the 2020 second quarter, and 0.32% for the six months ended June 30, 2021, compared to 0.32% for the 2020 period.
The lower level of net investment income for the 2021 second quarter primarily related to lower yields available in the financial market. The pre-tax investment income yield, calculated based on amortized cost and on an annualized basis, was 1.47% for the 2021 second quarter, compared to 1.92% for the 2020 second quarter, and 1.40% for the six months ended June 30, 2021, compared to 2.08% for the 2020 period.
Corporate Expenses.
Corporate expenses were $17.2 million for the 2021 second quarter, compared to $16.9 million for the 2020 second quarter, and $40.6 million for the six months ended June 30, 2021, compared to $35.1 million for the 2020 period. The increase in corporate expenses was primarily due to higher incentive compensation costs.
Transaction Costs and Other.
Transaction costs and other were a benefit of $1.4 million for the 2021 second quarter, compared to an expense of $1.0 million for the 2020 second quarter, and a benefit of $0.2 million for the six months ended June 30, 2021, compared to an expense of $3.6 million for the 2020 period. Amounts in the 2021 and 2020 periods are primarily related to acquisitions activity for the respective period.
Amortization of Intangible Assets.
Amortization of intangible assets for the 2021 second quarter was $14.4 million, compared to $16.5 million for the 2020
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second quarter, and $28.8 million for the six months ended June 30, 2021, compared to $33.1 million for the 2020 period. Amounts in 2021 and 2020 primarily related to amortization of finite-lived intangible assets. See the consolidated financial statements contained in our 2020 Form 10-K for disclosures on our amortization pattern.
Interest Expense.
Interest expense was $31.4 million for the 2021 second quarter, compared to the $25.1 million for the 2020 second quarter, and $65.6 million for the six months ended June 30, 2021, compared to $50.4 million for the 2020 period.The higher level of interest expense mainly resulted from the issuance of $1.0 billion of 3.635% senior notes on June 30, 2020.
Net Realized Gains or Losses.
We recorded net realized gains of $163.4 million for the 2021 second quarter, compared to net realized gains of $385.1 million for the 2020 second quarter, and net realized gains of $264.7 million for the six months ended June 30, 2021, compared to net realized gains of $313.0 million for the 2020 period. Currently, our portfolio is actively managed to maximize total return within certain guidelines. The effect of financial market movements on the investment portfolio will directly impact net realized gains and losses as the portfolio is adjusted and rebalanced. Net realized gains or losses from the sale of fixed maturities primarily results from our decisions to reduce credit exposure, to change duration targets, to rebalance our portfolios or due to relative value determinations.
Net realized gains or losses also include realized and unrealized contract gains and losses on our derivative instruments, changes in the fair value of assets accounted for using the fair value option and in the fair value of equities, along with changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings. See note 7, “Investment Information—Net Realized Gains (Losses),” to our consolidated financial statements for additional information. See note 7, “Investment Information—Allowance for Credit Losses,” to our consolidated financial statements for additional information.
Equity in Net Income (Loss) of Investment Funds Accounted for Using the Equity Method.
We 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 a loss of $65.1 million for the 2020 second quarter, and $193.9 million of income for the six months ended June 30, 2021, compared to a loss of $69.3 million for the 2020 period. Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds. Investment
funds accounted for using the equity method totaled $2.5 billion at June 30, 2021, compared to $2.0 billion at December 31, 2020. See note 7, “Investment Information—Investments Accounted For Using the Equity Method,” to our consolidated financial statements for additional information.
Net Foreign Exchange Gains or Losses.
Net foreign exchange losses for the 2021 second quarter were $17.9 million, compared to net foreign exchange losses for the 2020 second quarter of $42.4 million. Net foreign exchange gains for the six months ended June 30, 2021 were $3.6 million, compared to net foreign exchange gains for the 2020 period of $20.9 million. Amounts in both periods were primarily unrealized and resulted from the effects of revaluing our net insurance liabilities required to be settled in foreign currencies at each balance sheet date.
Income Tax Expense.
Our income tax provision on income (loss) before income taxes, including income (loss) from operating affiliates, resulted in an expense of 7.1% for the 2021 second quarter, compared to 8.8% for the 2020 second quarter, and 7.5% for the six months ended June 30, 2021, compared to 10.7% for the 2020 period. Such amounts exclude the results of the ‘other’ segment. Our 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.
Income (loss) from operating affiliates.
We recorded $24.5 million of net income from our operating affiliates in the 2021 second quarter, compared to a loss of $3.2 million for the 2020 second quarter, and $99.9 million of income for the six months ended June 30, 2021, compared to $5.3 million for the 2020 period. Results for the 2021 period, primarily reflected our acquisition of 29.5% of the common equity in Coface, which included a one-time gain of $74.5 million. 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.
Other Segment 
Through June 30, 2021, the ‘other’ segment included the results of 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. See note 11, “Variable Interest Entities and Noncontrolling Interests,” note 4, “Segment Information,” and Note 16,
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Subsequent Event, to our consolidated financial statements for additional information on Watford.
CRITICAL ACCOUNTING POLICIES,
ESTIMATES AND RECENT ACCOUNTING PRONOUNCEMENTS
Critical accounting policies, estimates and recent accounting pronouncements are discussed in Management’s Discussion and Analysis of Financial Condition and Results of Operations contained in our 2020 Form 10-K, updated where applicable in the notes accompanying our consolidated financial statements, including note 1, “Basis of Presentation and Recent Accounting Pronouncements.”
FINANCIAL CONDITION
Investable Assets 
At June 30, 2021, total investable assets held by Arch were $27.3 billion, excluding the $2.9 billion included in the ‘other’ segment (i.e., attributable to Watford).
Investable Assets Held by Arch 
The following table summarizes the fair value of the investable assets held by Arch:
Investable assets (1): Estimated
Fair Value
% of
Total
June 30, 2021
Fixed maturities (2) $ 18,022,113  66.0 
Short-term investments (2) 2,380,016  8.7 
Cash 884,857  3.2 
Equity securities (2) 1,633,579  6.0 
Other investments (2) 1,512,317  5.5 
Other investable assets (3) 500,000  1.8 
Investments accounted for using the equity method 2,539,124  9.3 
Securities transactions entered into but not settled at the balance sheet date (180,592) (0.7)
Total investable assets held by Arch $ 27,291,414  100.0 
Average effective duration (in years) 2.31 
Average S&P/Moody’s credit ratings (4) AA/Aa2
Embedded book yield (5) 1.45  %
December 31, 2020
Fixed maturities (2) $ 18,771,296  69.9 
Short-term investments (2) 2,063,240  7.7 
Cash 694,997  2.6 
Equity securities (2) 1,436,104  5.3 
Other investments (2) 1,480,347  5.5 
Other investable assets (3) 500,000  1.9 
Investments accounted for using the equity method 2,047,889  7.6 
Securities transactions entered into but not settled at the balance sheet date (137,578) (0.5)
Total investable assets held by Arch $ 26,856,295  100.0 
Average effective duration (in years) 3.01 
Average S&P/Moody’s credit ratings (4) AA/Aa2
Embedded book yield (5) 1.56  %
(1)In securities lending transactions, we receive collateral in excess of the fair value of the securities pledged. For purposes of this table, we have excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value.
(2)Includes investments carried as available for sale, at fair value and at fair value under the fair value option.
(3)Represents participation interests in a receivable of a reverse repurchase agreement.
(4)Average credit ratings on our investment portfolio on securities with ratings by Standard & Poor’s Rating Services (“S&P”) and Moody’s Investors Service (“Moody’s”).
(5)Before investment expenses.
At June 30, 2021, approximately $18.5 billion, or 67.9%, of total investable assets held by Arch were internally managed, compared to $19.2 billion, or 71.4%, at December 31, 2020.
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The following table summarizes our fixed maturities and fixed maturities pledged under securities lending agreements (“Fixed Maturities”) by type:
Estimated
Fair Value
% of
Total
June 30, 2021  
Corporate bonds $ 7,375,350  40.9 
Residential mortgage backed securities 374,565  2.1 
Municipal bonds 413,709  2.3 
Commercial mortgage backed securities 267,574  1.5 
U.S. government and government agencies 4,855,595  26.9 
Non-U.S. government securities 2,308,403  12.8 
Asset backed securities 2,426,917  13.5 
Total $ 18,022,113  100.0 
December 31, 2020  
Corporate bonds $ 8,039,745  42.8 
Residential mortgage backed securities 616,619  3.3 
Municipal bonds 492,734  2.6 
Commercial mortgage backed securities 390,990  2.1 
U.S. government and government agencies 5,354,863  28.5 
Non-U.S. government securities 2,310,157  12.3 
Asset backed securities 1,566,188  8.3 
Total $ 18,771,296  100.0 
The following table provides the credit quality distribution of our Fixed Maturities. For individual fixed maturities, S&P ratings are used. In the absence of an S&P rating, ratings from Moody’s are used, followed by ratings from Fitch Ratings.
Estimated Fair Value % of
Total
June 30, 2021
U.S. government and gov’t agencies (1) $ 5,221,296  29.0 
AAA 3,432,285  19.0 
AA 2,004,442  11.1 
A 3,268,661  18.1 
BBB 2,896,453  16.1 
BB 544,730  3.0 
B 330,639  1.8 
Lower than B 48,230  0.3 
Not rated 275,377  1.5 
Total $ 18,022,113  100.0 
December 31, 2020
U.S. government and gov’t agencies (1) $ 5,963,758  31.8 
AAA 3,117,046  16.6 
AA 2,063,738  11.0 
A 3,760,280  20.0 
BBB 2,699,201  14.4 
BB 574,189  3.1 
B 268,095  1.4 
Lower than B 54,795  0.3 
Not rated 270,194  1.4 
Total $ 18,771,296  100.0 
(1)Includes U.S. government-sponsored agency residential mortgage-backed securities and agency commercial mortgage-backed securities.
The following table provides information on the severity of the unrealized loss position as a percentage of amortized cost for all Fixed Maturities which were in an unrealized loss position:
Severity of gross unrealized losses: Estimated Fair Value Gross
Unrealized
Losses
% of
Total Gross
Unrealized
Losses
June 30, 2021
0-10% $ 7,387,667  $ (68,781) 92.0 
10-20% 28,039  (4,166) 5.6 
20-30% 1,999  (553) 0.7 
Greater than 30% 1,326  (1,239) 1.7 
Total $ 7,419,031  $ (74,739) 100.0 
December 31, 2020
0-10% $ 3,583,981  $ (55,542) 79.4 
10-20% 95,495  (12,183) 17.4 
20-30% 1,061  (406) 0.6 
Greater than 30% 1,249  (1,785) 2.6 
Total $ 3,681,786  $ (69,916) 100.0 
The following table summarizes our top ten exposures to fixed income corporate issuers by fair value at June 30, 2021, excluding guaranteed amounts and covered bonds:
  Estimated Fair Value Credit
Rating (1)
Bank of America Corporation $ 373,742  A-/A2
JPMorgan Chase & Co. 372,381  A-/A2
Citigroup Inc. 288,574  BBB+/A3
Morgan Stanley 253,549  BBB+/A1
Wells Fargo & Company 247,222  BBB+/A2
The Goldman Sachs Group, Inc. 185,647  BBB+/A2
Nestlé S.A. 129,191  AA-/Aa3
Amazon.com, Inc. 118,047  AA/A1
Nippon Telegraph and Telephone Corporation 95,958  A/A1
AT&T Inc. 92,795  BBB/Baa2
Total $ 2,157,106 
(1)Average credit ratings as assigned by S&P and Moody’s, respectively.
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The following table provides information on our structured securities, which includes residential mortgage-backed securities (“RMBS”), commercial mortgage-backed securities (“CMBS”) and asset-backed securities (“ABS”):
Agencies Investment Grade Below Investment Grade Total
Jun 30, 2021
RMBS $ 336,784  $ 14,716  $ 23,065  $ 374,565 
CMBS 28,917  213,655  25,002  267,574 
ABS —  2,206,453  220,464  2,426,917 
Total $ 365,701  $ 2,434,824  $ 268,531  $ 3,069,056 
Dec 31, 2020
RMBS $ 584,499  $ 4,102  $ 28,018  $ 616,619 
CMBS 24,396  342,491  24,103  390,990 
ABS —  1,403,137  163,051  1,566,188 
Total $ 608,895  $ 1,749,730  $ 215,172  $ 2,573,797 
The following table summarizes our equity securities, which include investments in exchange traded funds:
June 30,
2021
December 31,
2020
Equities (1) $ 864,688  $ 676,437 
Exchange traded funds
Fixed income (2) 304,723  341,139 
Equity and other (3) 464,168  418,528 
Total $ 1,633,579  $ 1,436,104 
(1)Primarily in consumer non-cyclical, consumer cyclical, technology, communications and financial stocks at June 30, 2021.
(2)Primarily in corporate, MBS and municipal strategies at June 30, 2021.
(3)Primarily in utilities, large cap stocks and foreign equities at June 30, 2021.

The following table summarizes our other investments and other investable assets:
June 30,
2021
December 31,
2020
Lending $ 638,786  $ 572,636 
Term loan investments 474,859  380,193 
Energy 84,891  65,813 
Credit related funds 73,171  90,780 
Investment grade fixed income 110,375  138,646 
Infrastructure 32,109  165,516 
Private equity 70,878  48,750 
Real estate 27,248  18,013 
Total fair value option $ 1,512,317  $ 1,480,347 
Other investable assets $ 500,000  $ 500,000 
Total other investments $ 2,012,317  $ 1,980,347 
For details on our investments accounted for using the equity method, see note 7, “Investment Information—Investments Accounted For Using the Equity Method,” to our consolidated financial statements.
Our investment strategy allows for the use of derivative instruments. We utilize various derivative instruments such as futures contracts to enhance investment performance, replicate investment positions or manage market exposures and duration risk that would be allowed under our investment guidelines if implemented in other ways. See note 9, “Derivative Instruments,” to our consolidated financial statements for additional disclosures related to derivatives.
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. See note 8, “Fair Value,” to our consolidated financial statements for a summary of our financial assets and liabilities measured at fair value, segregated by level in the fair value hierarchy.
Investable Assets in the ‘Other’ Segment
Investable assets in the ‘other’ segment are managed by Watford. The board of directors of Watford establishes its investment policies and guidelines. A significant amount of Watford’s investments are accounted for using the fair value option with changes in the carrying value of such investments recorded in net realized gains or losses.
The following table summarizes investable assets in the ‘other’ segment:
June 30,
2021
December 31,
2020
Investments accounted for using the fair value option:
Other investments $ 858,155  $ 851,538 
Fixed maturities 578,280  455,163 
Short-term investments 478,711  418,690 
Equity securities 69,773  64,994 
Total 1,984,919  1,790,385 
Fixed maturities available for sale, at fair value 625,422  613,503 
Equity securities, at fair value 97,623  52,410 
Cash 349,202  211,451 
Securities sold but not yet purchased (28,068) (21,679)
Securities transactions entered into but not settled at the balance sheet date (97,055) 11,542 
Total investable assets included in ‘other’ segment $ 2,932,043  $ 2,657,612 

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2021 SECOND QUARTER FORM 10-Q

Reinsurance
The effects of reinsurance on written and earned premiums and losses and loss adjustment expenses (“LAE”) with unaffiliated reinsurers were as follows:
Three Months Ended Six Months Ended
June 30, June 30,
2021 2020 2021 2020
Premiums written:
Direct $ 1,909,893  $ 1,485,627  $ 3,802,138  $ 3,174,425 
Assumed 1,376,398  832,065  2,881,359  1,976,097 
Ceded (886,767) (649,381) (1,775,516) (1,344,965)
Net $ 2,399,524  $ 1,668,311  $ 4,907,981  $ 3,805,557 
Premiums earned:
Direct $ 1,795,899  $ 1,559,222  $ 3,508,824  $ 3,105,047 
Assumed 1,091,968  746,188  2,039,582  1,507,262 
Ceded (766,958) (640,056) (1,479,075) (1,202,511)
Net $ 2,120,909  $ 1,665,354  $ 4,069,331  $ 3,409,798 
Losses and LAE:
Direct $ 1,046,579  $ 1,162,958  $ 2,032,512  $ 2,148,041 
Assumed 554,256  508,108  1,221,567  1,053,977 
Ceded (441,004) (440,544) (891,148) (856,077)
Net $ 1,159,831  $ 1,230,522  $ 2,362,931  $ 2,345,941 
See note 6, “Allowance for Expected Credit Losses,” to our consolidated financial statements for information about our reinsurance recoverables and related allowance for credit losses.
Bellemeade Re
We have entered into various aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda (the “Bellemeade Agreements”). For the respective coverage periods, we will retain the first layer of the respective aggregate losses and the special purpose reinsurance companies will provide second layer coverage up to the outstanding coverage amount. We will then retain losses in excess of the outstanding coverage limit. The aggregate excess of loss reinsurance coverage generally decreases over a ten-year period as the underlying covered mortgages amortize, unless provisional call options embedded within certain of the Bellemeade Agreements are executed or if pre-defined delinquency triggering events occur.
The following table summarizes the respective coverages and retentions at June 30, 2021:
June 30, 2021
Initial Coverage at Issuance Current Coverage Remaining Retention, Net
Bellemeade 2017-1 Ltd. (1) $ 368,114  $ 145,573  $ 125,297 
Bellemeade 2018-1 Ltd. (2) 374,460  250,095  123,173 
Bellemeade 2018-3 Ltd. (3) 506,110  302,563  126,127 
Bellemeade 2019-1 Ltd. (4) 341,790  219,256  102,017 
Bellemeade 2019-2 Ltd. (5) 621,022  398,316  156,718 
Bellemeade 2019-3 Ltd. (6) 700,920  528,084  176,565 
Bellemeade 2019-4 Ltd. (7) 577,267  468,737  113,415 
Bellemeade 2020-1 Ltd. (8) 528,540  18,843  747,799 
Bellemeade 2020-2 Ltd. (9) 449,167  328,375  232,481 
Bellemeade 2020-3 Ltd. (10) 451,816  451,816  163,905 
Bellemeade 2020-4 Ltd. (11) 337,013  281,750  138,183 
Bellemeade 2021-1 Ltd. (12) 643,577  643,577  166,199 
Bellemeade 2021-2 Ltd. (13) 616,017  616,017  152,734 
Total $ 6,515,813  $ 4,653,002  $ 2,524,613 
(1)    Issued in October 2017, covering in-force policies issued between January 1, 2017 and June 30, 2017.
(2)    Issued in April 2018, covering in-force policies issued between July 1, 2017 and December 31, 2017.
(3)    Issued in October 2018, covering in-force policies issued between January 1, 2018 and June 30, 2018.
(4)    Issued in March 2019, covering in-force policies primarily issued between 2005-2008 under United Guaranty Residential Insurance Company (“UGRIC”); as well as policies issued through 2015 under both UGRIC and Arch Mortgage Insurance Company.
(5)    Issued in April 2019, covering in-force policies issued between July 1, 2018 and December 31, 2018.
(6)    Issued in July 2019, covering in-force policies issued in 2016.
(7)    Issued in October 2019, covering in-force policies issued between January 1, 2019 and June 30, 2019.
(8)     Issued in June 2020, covering in-force policies issued between July 1, 2019 and December 31, 2019. $450 million was directly funded by Bellemeade 2020-1 Ltd. with an additional $79 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.
(9)    Issued in September 2020, covering in-force policies issued between January 1, 2020 and May 31, 2020. $423 million was directly funded by Bellemeade 2020-2 Ltd. with an additional $26 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.
(10)    Issued in November 2020, covering in-force policies issued between June 1, 2020 and August 31, 2020. $418 million was directly funded by Bellemeade 2020-3 Ltd. with an additional $34 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.
(11) Issued in December 2020, covering in-force policies issued between July 1, 2019 and December 31, 2019. $321 million was directly funded by Bellemeade 2020-4 Ltd. with an additional $16 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.
(12) Issued in March 2021, covering in-force policies issued between September 1, 2020 and November 30, 2020. $580 million was directly funded by Bellemeade Re 2021-1 Ltd. with an additional $64 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.
(13) Issued in June 2021, covering in-force policies issued between December 1, 2020 and March 31, 2021. $523 million was directly funded by Bellemeade Re 2021-2 Ltd. via insurance-linked notes, with an additional $93 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.
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2021 SECOND QUARTER FORM 10-Q

Reserve for Losses and Loss Adjustment Expenses 
We establish reserve for losses and loss adjustment expenses (“Loss Reserves”) which represent estimates involving actuarial and statistical projections, at a given point in time, of our expectations of the ultimate settlement and administration costs of losses incurred. Estimating Loss Reserves is inherently difficult. We utilize actuarial models as well as available historical insurance industry loss ratio experience and loss development patterns to assist in the establishment of Loss Reserves. Actual losses and loss adjustment expenses paid will deviate, perhaps substantially, from the reserve estimates reflected in our financial statements.
At June 30, 2021 and December 31, 2020, our Loss Reserves, net of unpaid losses and loss adjustment expenses recoverable, by type and by operating segment were as follows:
June 30,
2021
December 31,
2020
Insurance segment:    
Case reserves $ 2,100,109  $ 2,051,640 
IBNR reserves 4,117,169  3,889,823 
Total net reserves 6,217,278  5,941,463 
Reinsurance segment:
Case reserves 1,523,486  1,560,523 
Additional case reserves 432,516  280,472 
IBNR reserves 2,435,575  2,253,953 
Total net reserves 4,391,577  4,094,948 
Mortgage segment:
Case reserves 704,314  631,921 
IBNR reserves 266,690  271,702 
Total net reserves 971,004  903,623 
Other segment:
Case reserves 682,341  566,587 
Additional case reserves 47,774  32,321 
IBNR reserves 740,654  660,132 
Total net reserves 1,470,769  1,259,040 
Total:    
Case reserves 5,010,250  4,810,671 
Additional case reserves 480,290  312,793 
IBNR reserves 7,560,088  7,075,610 
Total net reserves $ 13,050,628  $ 12,199,074 
At June 30, 2021 and December 31, 2020, the insurance segment’s Loss Reserves by major line of business, net of unpaid losses and loss adjustment expenses recoverable, were as follows:
June 30,
2021
December 31,
2020
Insurance segment:
Professional lines (1) $ 1,516,878  $ 1,482,820 
Construction and national accounts 1,470,201  1,395,067 
Excess and surplus casualty (2) 859,662  816,495 
Programs 748,015  699,354 
Property, energy, marine and aviation 500,880  517,692 
Travel, accident and health 96,345  98,910 
Lenders products 64,560  48,946 
Other (3) 960,737  882,179 
Total net reserves $ 6,217,278  $ 5,941,463 
(1)Includes professional liability, executive assurance and healthcare business.
(2)Includes casualty and contract binding business.
(3)Includes alternative markets, excess workers’ compensation and surety business.
At June 30, 2021 and December 31, 2020, the reinsurance segment’s Loss Reserves by major line of business, net of unpaid losses and loss adjustment expenses recoverable, were as follows:
June 30,
2021
December 31,
2020
Reinsurance segment:
Casualty (1) $ 2,024,591  $ 1,995,849 
Other specialty (2) 955,770  917,178 
Property excluding property catastrophe 668,339  594,033 
Marine and aviation 215,345  204,205 
Property catastrophe 410,034  268,858 
Other (3) 117,498  114,825 
Total net reserves $ 4,391,577  $ 4,094,948 
(1)Includes executive assurance, professional liability, workers’ compensation, excess motor, healthcare and other.
(2)Includes non-excess motor, surety, accident and health, workers’ compensation catastrophe, agriculture, trade credit and other.
(3)Includes life, casualty clash and other.
At June 30, 2021 and December 31, 2020, the mortgage segment’s Loss Reserves by major line of business, net of unpaid losses and loss adjustment expenses recoverable, were as follows:
June 30,
2021
December 31,
2020
U.S. primary mortgage insurance (1) $ 713,135  $ 649,748 
Other 257,869  253,875 
Total net reserves $ 971,004  $ 903,623 
(1)    At June 30, 2021, 28.0% represents policy years 2011 and prior and the remainder from later policy years. At December 31, 2020, 28.3% of total net reserves represent policy years 2011 and prior and the remainder from later policy years.

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2021 SECOND QUARTER FORM 10-Q

Mortgage Operations Supplemental Information
The mortgage segment’s insurance in force (“IIF”) and risk in force (“RIF”) were as follows at June 30, 2021 and December 31, 2020:
(U.S. Dollars in millions) June 30, 2021 December 31, 2020
Amount % Amount %
Insurance In Force (IIF) (1):
U.S. primary mortgage insurance $ 277,887  65.8  $ 280,579  66.2 
Mortgage reinsurance 32,666  7.7  31,220  7.4 
Other (2) 111,884  26.5  111,740  26.4 
Total $ 422,437  100.0  $ 423,539  100.0 
Risk In Force (RIF) (3):
U.S. primary mortgage insurance $ 69,587  90.3  $ 70,522  90.5 
Mortgage reinsurance 2,245  2.9  2,226  2.9 
Other (2) 5,188  6.7  5,146  6.6 
Total $ 77,020  100.0  $ 77,894  100.0 
(1)Represents the aggregate dollar amount of each insured mortgage loan’s current principal balance.
(2)Includes GSE credit risk-sharing transactions and international insurance business.
(3)Represents the aggregate dollar amount of each insured mortgage loan’s current principal balance multiplied by the insurance coverage percentage specified in the policy for insurance policies issued and after contract limits and/or loss ratio caps for credit risk-sharing or reinsurance transactions.
The IIF and RIF for our U.S. primary mortgage insurance business by policy year were as follows at June 30, 2021:
(U.S. Dollars in millions) IIF RIF Delinquency
Amount % Amount % Rate (1)
Policy year:
2011 and prior $ 12,591  4.5  $ 2,839  4.1  9.75  %
2012 2,261  0.8  587  0.8  3.00  %
2013 5,635  2.0  1,563  2.2  2.95  %
2014 6,288  2.3  1,729  2.5  3.52  %
2015 11,208  4.0  3,017  4.3  3.19  %
2016 18,500  6.7  4,958  7.1  4.11  %
2017 17,577  6.3  4,574  6.6  4.87  %
2018 19,044  6.9  4,827  6.9  6.25  %
2019 34,944  12.6  8,727  12.5  4.02  %
2020 95,419  34.3  23,316  33.5  0.88  %
2021 54,420  19.6  13,450  19.3  0.10  %
Total $ 277,887  100.0  $ 69,587  100.0  3.11  %
(1)Represents the ending percentage of loans in default.
The IIF and RIF for our U.S. primary mortgage insurance business by policy year were as follows at December 31, 2020:
(U.S. Dollars in millions) IIF RIF Delinquency
Amount % Amount % Rate (1)
Policy year:
2011 and prior $ 14,588  5.2  $ 3,327  4.7  11.36  %
2012 3,651  1.3  992  1.4  2.98  %
2013 7,546  2.7  2,107  3.0  3.30  %
2014 8,261  2.9  2,273  3.2  4.06  %
2015 15,032  5.4  4,048  5.7  3.72  %
2016 24,958  8.9  6,648  9.4  4.77  %
2017 24,748  8.8  6,413  9.1  5.52  %
2018 27,304  9.7  6,918  9.8  6.76  %
2019 48,304  17.2  12,001  17.0  4.61  %
2020 106,187  37.8  25,795  36.6  0.76  %
Total $ 280,579  100.0  $ 70,522  100.0  4.19  %
(1)Represents the ending percentage of loans in default.
The following tables provide supplemental disclosures on risk in force for our U.S. primary mortgage insurance business at June 30, 2021 and December 31, 2020:
(U.S. Dollars in millions) June 30, 2021 December 31, 2020
Amount % Amount %
Credit quality (FICO):
>=740 $ 41,156  59.1  $ 40,774  57.8 
680-739 23,663  34.0  24,498  34.7 
620-679 4,401  6.3  4,837  6.9 
<620 367  0.5  413  0.6 
Total $ 69,587  100.0  $ 70,522  100.0 
Weighted average FICO score 745  743 
Loan-to-value (LTV):
95.01% and above $ 7,975  11.5  $ 8,643  12.3 
90.01% to 95.00% 37,619  54.1  37,877  53.7 
85.01% to 90.00% 19,784  28.4  20,013  28.4 
85.00% and below 4,209  6.0  3,989  5.7 
Total $ 69,587  100.0  $ 70,522  100.0 
Weighted average LTV 92.8  % 92.8  %
Total RIF, net of external reinsurance $ 55,557  $ 56,658 
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2021 SECOND QUARTER FORM 10-Q

(U.S. Dollars in millions) June 30, 2021 December 31, 2020
Amount % Amount %
Total RIF by State:
Texas $ 5,560  8.0  $ 5,636  8.0 
California 5,324  7.7  5,261  7.5 
Florida 3,367  4.8  3,632  5.2 
Minnesota 2,973  4.3  2,520  3.6 
North Carolina 2,924  4.2  2,622  3.7 
Georgia 2,886  4.1  2,959  4.2 
Illinois 2,832  4.1  2,762  3.9 
Massachusetts 2,459  3.5  2,464  3.5 
Virginia 2,372  3.4  2,526  3.6 
Ohio 2,229  3.2  2,264  3.2 
Other 36,661  52.7  37,876  53.7 
Total $ 69,587  100.0  $ 70,522  100.0 
The following table provides supplemental disclosures for our U.S. primary mortgage insurance business related to insured loans and loss metrics:
(U.S. Dollars in thousands, except policy, loan and claim count) Six Months Ended
June 30,
2021 2020
Roll-forward of insured loans in default:
Beginning delinquent number of loans 52,234  20,163 
New notices
18,415  67,793 
Cures
(32,924) (22,205)
Paid claims
(406) (1,084)
Ending delinquent number of loans (1) 37,319  64,667 
Ending number of policies in force (1) 1,199,918  1,259,328 
Delinquency rate (1) 3.11  % 5.14  %
Losses:
Number of claims paid 406  1,084 
Total paid claims $ 15,297  $ 46,139 
Average per claim $ 37.7  $ 42.6 
Severity (2) 81.0  % 94.3  %
Average case reserve per default (in thousands) $ 19.5  $ 6.9 
(1)Includes first lien primary and pool policies.
(2)Represents total paid claims divided by RIF of loans for which claims were paid.
The risk to capital ratio, which represents total current (non-delinquent) risk in force, net of reinsurance, divided by total statutory capital, for Arch MI U.S. was approximately 8.5 to 1 at June 30, 2021, compared to 9.3 to 1 at December 31, 2020.
Shareholders’ Equity and Book Value per Share
The following table presents the calculation of book value per share:
(U.S. dollars in thousands, except 
share data)
June 30,
2021
December 31,
2020
Total shareholders’ equity available to Arch $ 13,986,072  $ 13,105,886 
Less preferred shareholders’ equity 1,280,000  780,000 
Common shareholders’ equity available to Arch $ 12,706,072  $ 12,325,886 
Common shares and common share equivalents outstanding, net of treasury shares (1) 396,771,251  406,720,642 
Book value per share $ 32.02  $ 30.31 
(1)Excludes the effects of 17,717,327 and 17,839,333 stock options and 759,926 and 1,153,784 restricted stock units outstanding at June 30, 2021 and December 31, 2020, respectively.

LIQUIDITY
This section does not include information specific to Watford. We do not guarantee or provide credit support for Watford, and 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 reinsurance transactions with Watford.
Liquidity is a measure of our ability to access sufficient cash flows to meet the short-term and long-term cash requirements of our business operations.

Arch Capital is a holding company whose assets primarily consist of the shares in its subsidiaries. Generally, Arch Capital depends on its available cash resources, liquid investments and dividends or other distributions from its subsidiaries to make payments, including the payment of debt service obligations and operating expenses it may incur and any dividends or liquidation amounts with respect to our preferred and common shares.
For the six months ended June 30, 2021, Arch Capital received dividends of $563.7 million from Arch Re Bermuda, our Bermuda-based reinsurer and insurer, which can pay approximately $3.2 billion to Arch Capital during the remainder of 2021 without providing an affidavit to the Bermuda Monetary Authority (“BMA”).
In June 2021, Arch Capital completed a $500.0 million underwritten public offering of 20.0 million depositary shares, each of which represents a 1/1,000th interest in a share of its 4.550% Non-Cumulative Preferred Shares. See note 2, Share Transactions.
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2021 SECOND QUARTER FORM 10-Q

We expect that our liquidity needs, including our anticipated (re)insurance obligations and operating and capital expenditure needs, for the next twelve months, will be met by funds generated from underwriting activities and investment income, as well as by our balance of cash, short-term investments, proceeds on the sale or maturity of our investments, and our credit facilities.
Cash Flows
The following table summarizes our cash flows from operating, investing and financing activities, excluding amounts related to the ‘other’ segment (i.e., Watford). See note 11, “Variable Interest Entities and Noncontrolling Interests,” for cash flows related to Watford.
Six Months Ended
June 30,
  2021 2020
Total cash provided by (used for):    
Operating activities $ 1,565,718  $ 1,234,383 
Investing activities (1,174,033) (1,888,221)
Financing activities 8,352  824,990 
Effects of exchange rate changes on foreign currency cash (9,868) (15,384)
Increase (decrease) in cash and restricted cash $ 390,169  $ 155,768 

Cash provided by operating activities for the six months ended June 30, 2021 reflected a higher level of premiums collected than in the 2020 period.
Cash used for investing activities for the six months ended June 30, 2021 was lower than in the 2020 period. Activity for the six months ended June 30, 2021 reflected our $546.3 million purchase of a 29.5% interest in Coface, while the 2020 period reflected a higher level of securities purchased, and the investing of proceeds from our issuance of the senior notes.
Cash used for financing activities for the six months ended June 30, 2021 was lower than cash used in the 2020 period, reflecting $485.8 million inflow from issuance of preferred shares and $485.3 million of repurchases under our share repurchase program. Activity for the 2020 period primarily reflected the issuance of $1.0 billion of our senior notes and $75.5 million of repurchases under our share repurchase program.
CAPITAL RESOURCES
This section does not include information specific to Watford. We do not guarantee or provide credit support for Watford, and 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 reinsurance transactions with Watford.
The following table provides an analysis of our capital structure:
(U.S. dollars in thousands, except 
share data)
Jun 30,
2021
Dec 31,
2020
Senior notes $ 2,723,903  $ 2,723,423 
Shareholders’ equity available to Arch:
Series E non-cumulative preferred shares $ 450,000  $ 450,000 
Series F non-cumulative preferred shares 330,000  330,000 
Series G non-cumulative preferred shares 500,000  — 
Common shareholders’ equity 12,706,072  12,325,886 
Total $ 13,986,072  $ 13,105,886 
Total capital available to Arch $ 16,709,975  $ 15,829,309 
Debt to total capital (%) 16.3  17.2 
Preferred to total capital (%) 7.7  4.9 
Debt and preferred to total capital (%) 24.0  22.1 
Arch MI U.S. is required to maintain compliance with the GSEs requirements, known as the Private Mortgage Insurer Eligibility Requirements or “PMIERs.” The financial requirements require an eligible mortgage insurer’s available assets, which generally include only the most liquid assets of an insurer, to meet or exceed “minimum required assets” as of each quarter end. Minimum required assets are calculated from PMIERs tables with several risk dimensions (including origination year, original loan-to-value and original credit score of performing loans, and the delinquency status of non-performing loans) and are subject to a minimum amount. Arch MI U.S. satisfied the PMIERs’ financial requirements as of June 30, 2021 with an estimated PMIER sufficiency ratio of 196%, compared to 173% at December 31, 2020.
Arch Capital, through its subsidiaries, provides financial support to certain of its insurance subsidiaries and affiliates, through certain reinsurance arrangements beneficial to the ratings of such subsidiaries. Historically, our insurance, reinsurance and mortgage insurance subsidiaries have entered into separate reinsurance arrangements with Arch Re Bermuda covering individual lines of business. The reinsurance agreements between our U.S.-based property casualty insurance and reinsurance subsidiaries and Arch Re Bermuda were canceled on a cutoff basis as of January 1,
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2021 SECOND QUARTER FORM 10-Q

2018. In 2019, certain reinsurance agreements between our insurance subsidiaries and Arch Re Bermuda were reinstated.
GUARANTOR INFORMATION
The below table provides a description of our senior notes payable at June 30, 2021, excluding amounts attributable to the ‘other’ segment (i.e., Watford):
Interest
Principal
Carrying
Issuer/Due
(Fixed)
Amount
Amount
Arch Capital:
May 1, 2034
7.350  % $ 300,000  $ 297,426 
June 30, 2050
3.635  % 1,000,000 988,609
Arch-U.S.:
Nov. 1, 2043 (1)
5.144  % 500,000 495,003
Arch Finance:
Dec. 15, 2026 (1)
4.011  % 500,000 497,420
Dec. 15, 2046 (1)
5.031  % 450,000 445,445
Total
$ 2,750,000  $ 2,723,903 
(1)Fully and unconditionally guaranteed by Arch Capital.
Our senior notes were issued by Arch Capital, Arch Capital Group (U.S.) Inc. (“Arch-U.S.”) and Arch Capital Finance
LLC (“Arch Finance”). Arch-U.S. is a wholly-owned subsidiary of Arch Capital and Arch Finance is a wholly-owned finance subsidiary of Arch-U.S. Our 2034 senior notes and 2050 senior notes issued by Arch Capital are unsecured and unsubordinated obligations of Arch Capital and ranked equally with all of its existing and future unsecured and unsubordinated indebtedness. The 2043 senior notes issued by Arch-U.S. are unsecured and unsubordinated obligations of Arch-U.S. and Arch Capital and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch-U.S. and Arch Capital. The 2026 senior notes and 2046 senior notes issued by Arch Finance are unsecured and unsubordinated obligations of Arch Finance and Arch Capital and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch Finance and Arch Capital.
Arch-U.S. and Arch Finance depend on their available cash resources, liquid investments and dividends or other distributions from their subsidiaries or affiliates to make payments, including the payment of debt service obligations and operating expenses they may incur.

The following tables present condensed financial information for Arch Capital (parent guarantor) and Arch-U.S. (subsidiary issuer):
June 30, 2021 December 31, 2020
Arch Capital Arch-U.S. Arch Capital Arch-U.S.
Assets
Total investments $ 508  $ 373,784  $ 172  $ 396,547 
Cash 15,239  27,434  18,932  11,368 
Investment in operating affiliates 7,294  —  7,731  — 
Due from subsidiaries and affiliates —  225,006  —  201,515 
Other assets 15,244  27,568  10,659  34,405 
Total assets $ 38,285  $ 653,792  $ 37,494  $ 643,835 
Liabilities
Senior notes 1,286,035  495,003  1,285,867  494,944 
Due to subsidiaries and affiliates —  551,760  —  586,805 
Other liabilities 20,172  42,582  23,270  41,876 
Total liabilities $ 1,306,207  $ 1,089,345  $ 1,309,137  $ 1,123,625 
Non-cumulative preferred shares $ 1,280,000  —  $ 780,000  — 
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Six Months Ended Year Ended
June 30, 2021 December 31, 2020
Arch Capital Arch-U.S. Arch Capital Arch-U.S.
Revenues
Net investment income $ 796  $ 5,007  $ 53  $ 18,084 
Net realized gains (losses) —  70,522  (2,110) 26,096 
Equity in net income (loss) of investments accounted for using the equity method —  10,678  —  2,507 
Total revenues 796  86,207  (2,057) 46,687 
Expenses
Corporate expenses 37,021  3,007  65,566  7,227 
Interest expense 29,369  23,567  40,445  47,566 
Net foreign exchange (gains) losses —  — 
Total expenses 66,396  26,574  106,014  54,793 
Income (loss) before income taxes and income (loss) from operating affiliates (65,600) 59,633  (108,071) (8,106)
Income tax (expense) benefit —  (14,731) —  2,689 
Income (loss) from operating affiliates (317) —  (437) — 
Net income available to Arch (65,917) 44,902  (108,508) (5,417)
Preferred dividends (22,069) —  (41,612) — 
Net income available to Arch common shareholders $ (87,986) $ 44,902  $ (150,120) $ (5,417)

SHARE REPURCHASE PROGRAM
The board of directors of Arch Capital has authorized the investment in Arch Capital’s common shares through a share repurchase program. 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. Since the inception of the share repurchase program through June 30, 2021, Arch Capital has repurchased 402.3 million common shares for an aggregate purchase price of $4.54 billion. At June 30, 2021, approximately $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.
CATASTROPHIC EVENTS AND SEVERE ECONOMIC EVENTS
We have large aggregate exposures to natural and man-made catastrophic events, pandemic events like COVID-19 and severe economic events. Natural catastrophes can be caused by various events, including hurricanes, floods, windstorms, earthquakes, hailstorms, tornadoes, explosions, severe winter weather, fires, droughts and other natural disasters. Man-made catastrophic events may include acts of war, acts of
terrorism and political instability. Catastrophes can also cause losses in non-property business such as mortgage insurance, workers’ compensation or general liability. In addition to the nature of property business, we believe that economic and geographic trends affecting insured property, including inflation, property value appreciation and geographic concentration, tend to generally increase the size of losses from catastrophic events over time.
Our models employ both proprietary and vendor-based systems and include cross-line correlations for property, marine, offshore energy, aviation, workers compensation and personal accident. We seek to limit the probable maximum pre-tax loss to a specific level for severe catastrophic events. Currently, we seek to limit our 1-in-250 year return period net probable maximum loss from a severe catastrophic event in any geographic zone to approximately 25% of tangible shareholders’ equity available to Arch (total shareholders’ equity available to Arch less goodwill and intangible assets). We reserve the right to change this threshold at any time.
Based on in-force exposure estimated as of July 1, 2021, our modeled peak zone catastrophe exposure was a windstorm affecting the Northeastern U.S., with a net probable maximum pre-tax loss of $676 million, followed by windstorms affecting the Florida Tri-County and the Gulf of Mexico regions with net probable maximum pre-tax losses of $669 and $662 million, respectively. Our exposures to other perils, such as U.S. earthquake and international events, were less than the exposures arising from U.S. windstorms and
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hurricanes. As of July 1, 2021, our modeled peak zone earthquake exposure (San Francisco earthquake) represented approximately 75% of our peak zone catastrophe exposure, and our modeled peak zone international exposure (UK windstorm) was substantially less than both our peak zone windstorm and earthquake exposures.
Effective July 1, 2021, our insurance operations had in effect a reinsurance program which provided coverage for certain property-catastrophe related losses equal to $279 million in excess of various retentions per occurrence.
We also have significant exposure to losses due to mortgage defaults resulting from severe economic events in the future. For our U.S. mortgage insurance business, we have developed a proprietary risk model (“Realistic Disaster Scenario” or “RDS”) that simulates the maximum loss resulting from a severe economic downturn impacting the housing market. The RDS models the collective impact of adverse conditions for key economic indicators, the most significant of which is a decline in home prices. The RDS model projects paths of future home prices, unemployment rates, income levels and interest rates and assumes correlation across states and geographic regions. The resulting future performance of our in-force portfolio is then estimated under the economic stress scenario, reflecting loan and borrower information.
Currently, we seek to limit our modeled RDS loss from a severe economic event to approximately 25% of tangible shareholders’ equity available to Arch. We reserve the right to change this threshold at any time. Based on in-force exposure estimated as of July 1, 2021, our modeled RDS loss was approximately 6% of tangible shareholders’ equity available to Arch.
Net probable maximum loss estimates are net of expected reinsurance recoveries, before income tax and before excess reinsurance reinstatement premiums. RDS loss estimates are net of expected reinsurance recoveries and before income tax. Catastrophe loss estimates are reflective of the zone indicated and not the entire portfolio. Since hurricanes and windstorms can affect more than one zone and make multiple landfalls, our catastrophe loss estimates include clash estimates from other zones. Our catastrophe loss estimates and RDS loss estimates do not represent our maximum exposures and it is highly likely that our actual incurred losses would vary materially from the modeled estimates. There can be no assurances that we will not suffer pre-tax losses greater than 25% of our tangible shareholders’ equity from one or more catastrophic events or severe economic events due to several factors. These factors include the inherent uncertainties in estimating the frequency and severity of such events and the margin of error in making such determinations resulting from potential inaccuracies and inadequacies in the data provided by clients and brokers, the modeling techniques and the
application of such techniques or as a result of a decision to change the percentage of shareholders' equity exposed to a single catastrophic event or severe economic event. In addition, actual losses may increase if our reinsurers fail to meet their obligations to us or the reinsurance protections purchased by us are exhausted or are otherwise unavailable. See “Risk Factors—Risks Relating to Our Industry” and “Management’s Discussion and Analysis of Financial Condition and Results of Operations—Catastrophic Events and Severe Economic Events” in our 2020 Form 10-K.
OFF-BALANCE SHEET ARRANGEMENTS
Off-balance sheet arrangements are discussed in Management’s Discussion and Analysis of Financial Condition and Results of Operations contained in our 2020 Form 10-K.
MARKET SENSITIVE INSTRUMENTS AND RISK MANAGEMENT
In accordance with the SEC’s Financial Reporting Release No. 48, we performed a sensitivity analysis to determine the effects that market risk exposures could have on the future earnings, fair values or cash flows of our financial instruments as of June 30, 2021. Market risk represents the risk of changes in the fair value of a financial instrument and is comprised of several components, including liquidity, basis and price risks. We have not included Watford in the following analyses as we do not guarantee or provide credit support for Watford, and 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 reinsurance transactions.
An analysis of material changes in market risk exposures at June 30, 2021 that affect the quantitative and qualitative disclosures presented in our 2020 Form 10-K (see section captioned “Management’s Discussion and Analysis of Financial Condition and Results of Operations—Market Sensitive Instruments and Risk Management”) were as follows: 
Investment Market Risk
Fixed Income Securities. We invest in interest rate sensitive securities, primarily debt securities. We consider the effect of interest rate movements on the fair value of our fixed maturities, fixed maturities pledged under securities lending agreements, short-term investments and certain of our other investments, equity securities and investment funds accounted for using the equity method which invest in fixed income securities (collectively, “Fixed Income Securities”) and the corresponding change in unrealized appreciation. As interest rates rise, the fair value of our Fixed Income
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Securities falls, and the converse is also true. Based on historical observations, there is a low probability that all interest rate yield curves would shift in the same direction at the same time. Furthermore, at times interest rate movements in certain credit sectors exhibit a much lower correlation to changes in U.S. Treasury yields. Accordingly, the actual effect of interest rate movements may differ materially from the amounts set forth in the following tables.
The following table summarizes the effect that an immediate, parallel shift in the interest rate yield curve would have had on our Fixed Income Securities:
(U.S. dollars in 
billions)
Interest Rate Shift in Basis Points
-100 -50 +50 +100
Jun 30, 2021          
Total fair value $ 25.83  $ 25.45  $ 25.08  $ 24.70  $ 24.33 
Change from base 3.0  % 1.5  % (1.5) % (3.0) %
Change in unrealized value $ 0.75  $ 0.38  $ (0.38) $ (0.75)
Dec 31, 2020
Total fair value $ 25.82  $ 25.44  $ 25.07  $ 24.69  $ 24.31 
Change from base 3.0  % 1.5  % (1.5) % (3.0) %
Change in unrealized value $ 0.75  $ 0.38  $ (0.38) $ (0.75)
In addition, we consider the effect of credit spread movements on the market value of our Fixed Income Securities and the corresponding change in unrealized value. As credit spreads widen, the fair value of our Fixed Income Securities falls, and the converse is also true. In periods where the spreads on our Fixed Income Securities are much higher than their historical average due to short-term market dislocations, a parallel shift in credit spread levels would result in a much more pronounced change in unrealized value.
The following table summarizes the effect that an immediate, parallel shift in credit spreads in a static interest rate environment would have had on our Fixed Income Securities:
(U.S. dollars in 
billions)
Credit Spread Shift in Percentage Points
-100 -50 +50 +100
Jun 30, 2021
Total fair value $ 25.55  $ 25.33  $ 25.08  $ 24.83  $ 24.60 
Change from base 1.9  % 1.0  % (1.0) % (1.9) %
Change in unrealized value $ 0.48  $ 0.25  $ (0.25) $ (0.48)
Dec 31, 2020
Total fair value $ 25.54  $ 25.32  $ 25.07  $ 24.82  $ 24.59 
Change from base 1.9  % 1.0  % (1.0) % (1.9) %
Change in unrealized value $ 0.48  $ 0.25  $ (0.25) $ (0.48)
Another method that attempts to measure portfolio risk is Value-at-Risk (“VaR”). VaR measures the worst expected
loss under normal market conditions over a specific time interval at a given confidence level. The 1-year 95th percentile parametric VaR reported herein estimates that 95% of the time, the portfolio loss in a one-year horizon would be less than or equal to the calculated number, stated as a percentage of the measured portfolio’s initial value. The VaR is a variance-covariance based estimate, based on linear sensitivities of a portfolio to a broad set of systematic market risk factors and idiosyncratic risk factors mapped to the portfolio exposures. The relationships between the risk factors are estimated using historical data, and the most recent data points are generally given more weight. As of June 30, 2021, our portfolio’s VaR was estimated to be 6.1% compared to an estimated 4.3% at December 31, 2020. In periods where the volatility of the risk factors mapped to our portfolio’s exposures is higher due to market conditions, the resulting VaR is higher than in other periods.
Equity Securities. At June 30, 2021 and December 31, 2020, the fair value of our investments in equity securities (excluding securities included in Fixed Income Securities above) totaled $1.3 billion and $1.1 billion, respectively. These investments are exposed to price risk, which is the potential loss arising from decreases in fair value. An immediate hypothetical 10% decline in the value of each position would reduce the fair value of such investments by approximately $132.9 million and $109.5 million at June 30, 2021 and December 31, 2020, respectively, and would have decreased book value per share by approximately $0.33 and $0.27, respectively. An immediate hypothetical 10% increase in the value of each position would increase the fair value of such investments by approximately $132.9 million and $109.5 million at June 30, 2021 and December 31, 2020, respectively, and would have increased book value per share by approximately $0.33 and $0.27, respectively.
Investment-Related Derivatives. At June 30, 2021, the notional value of all derivative instruments (excluding to-be-announced mortgage backed securities which are included in the fixed income securities analysis above and foreign currency forward contracts which are included in the foreign currency exchange risk analysis below) was $7.5 billion, compared to $8.6 billion at December 31, 2020. If the underlying exposure of each investment-related derivative held at June 30, 2021 depreciated by 100 basis points, it would have resulted in a reduction in net income of approximately $75.0 million, and a decrease in book value per share of approximately $0.19 per share, compared to $85.7 million and $0.21 per share, respectively, on investment-related derivatives held at December 31, 2020. If the underlying exposure of each investment-related derivative held at June 30, 2021 appreciated by 100 basis points, it would have resulted in an increase in net income of approximately $75.0 million, and an increase in book value per share of approximately $0.19 per share, compared to $85.7 million and $0.21 per share, respectively, on
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investment-related derivatives held at December 31, 2020. See note 9, “Derivative Instruments,” to our consolidated financial statements for additional disclosures concerning derivatives.
For further discussion on investment activity, please refer to “Financial Condition—Investable Assets.”
Foreign Currency Exchange Risk
Foreign currency rate risk is the potential change in value, income and cash flow arising from adverse changes in foreign currency exchange rates. Through our subsidiaries and branches located in various foreign countries, we conduct our insurance and reinsurance operations in a variety of local currencies other than the U.S. Dollar. We generally hold investments in foreign currencies which are intended to mitigate our exposure to foreign currency fluctuations in our net insurance liabilities. We may also utilize foreign currency forward contracts and currency options as part of our investment strategy. See note 9, “Derivative Instruments,” to our consolidated financial statements for additional information.
The following table provides a summary of our net foreign currency exchange exposures, as well as foreign currency derivatives in place to manage these exposures:
(U.S. dollars in thousands, except 
per share data)
June 30,
2021
December 31,
2020
Net assets (liabilities), denominated in foreign currencies, excluding shareholders’ equity and derivatives $ (11,717) $ (309,968)
Shareholders’ equity denominated in foreign currencies (1) 808,505  695,355 
Net foreign currency forward contracts outstanding (2) 456,727  1,108,161 
Net exposures denominated in foreign currencies $ 1,253,515  $ 1,493,548 
Pre-tax impact of a hypothetical 10% appreciation of the U.S. Dollar against foreign currencies:    
Shareholders’ equity $ (125,352) $ (149,355)
Book value per share $ (0.32) $ (0.37)
Pre-tax impact of a hypothetical 10% decline of the U.S. Dollar against foreign currencies:    
Shareholders’ equity $ 125,352  $ 149,355 
Book value per share $ 0.32  $ 0.37 
(1)    Represents capital contributions held in the foreign currencies of our operating units.
(2)    Represents the net notional value of outstanding foreign currency forward contracts.
Although we generally attempt to match the currency of our projected liabilities with investments in the same currencies, from time to time we may elect to over or underweight one or more currencies, which could increase our exposure to
foreign currency fluctuations and increase the volatility of our shareholders’ equity. Historical observations indicate a low probability that all foreign currency exchange rates would shift against the U.S. Dollar in the same direction and at the same time and, accordingly, the actual effect of foreign currency rate movements may differ materially from the amounts set forth above. For further discussion on foreign exchange activity, please refer to “Results of Operations.”
Effects of Inflation
We do not believe that inflation has had a material effect on our consolidated results of operations, except insofar as inflation may affect our reserve for losses and loss adjustment expenses and interest rates. The potential exists, after a catastrophe loss or pandemic events like COVID-19, for the development of inflationary pressures in a local economy. The anticipated effects of inflation on us are considered in our catastrophe loss models. The actual effects of inflation on our results cannot be accurately known until claims are ultimately settled.
OTHER FINANCIAL INFORMATION
The consolidated financial statements as of June 30, 2021 have been reviewed by PricewaterhouseCoopers LLP, the registrant's independent public accountants, whose report is included as an exhibit to this filing. The report of PricewaterhouseCoopers LLP states that they did not audit and they do not express an opinion on that unaudited financial information. Accordingly, the degree of reliance on their report on such information should be restricted in light of the limited nature of the review procedures applied. PricewaterhouseCoopers LLP is not subject to the liability provisions of Section 11 of the Securities Act of 1933 for their report on the unaudited financial information because that report is not a "report" or a "part" of the registration statement prepared or certified by PricewaterhouseCoopers LLP within the meaning of Sections 7 and 11 of the Securities Act of 1933.

ITEM 3. QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK
Reference is made to the information appearing above under the subheading “Market Sensitive Instruments and Risk Management” under the caption “Management’s Discussion and Analysis of Financial Condition and Results of Operations,” which information is hereby incorporated by reference. 
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ITEM 4. CONTROLS AND PROCEDURES
Evaluation of Disclosure Controls and Procedures
In connection with the filing of this Form 10-Q, our management, including the Chief Executive Officer and Chief Financial Officer, conducted an evaluation of the effectiveness of disclosure controls and procedures pursuant to applicable Exchange Act Rules as of the end of the period covered by this report. Based on that evaluation, the Chief Executive Officer and Chief Financial Officer concluded that the disclosure controls and procedures were effective as of the end of and during the period covered by this report with respect to information being recorded, processed, summarized and reported within time periods specified in the SEC’s rules and forms and with respect to timely communication to them and other members of management responsible for preparing periodic reports of all material information required to be disclosed in this report as it relates to Arch Capital and its consolidated subsidiaries.
We continue to enhance our operating procedures and internal controls to effectively support our business and our regulatory and reporting requirements. Our management does not expect that our disclosure controls or our internal controls will prevent all errors and all fraud. A control system, no matter how well conceived and operated, can provide only reasonable, not absolute, assurance that the objectives of the control system are met. Further, the design of a control system must reflect the fact that there are resource constraints, and the benefits of controls must be considered relative to their costs. As a result of the inherent limitations in all control systems, no evaluation of controls can provide absolute assurance that all control issues and instances of fraud, if any, within the company have been detected. These inherent limitations include the realities that judgments in decision-making can be faulty, and that breakdowns can occur because of simple error or mistake. Additionally, controls can be circumvented by the individual acts of some persons or by collusion of two or more people. The design of any system of controls also is based in part upon certain assumptions about the likelihood of future events, and there can be no assurance that any design will succeed in achieving its stated goals under all potential future conditions; over time, controls may become inadequate because of changes in conditions, or the degree of compliance with the policies or procedures may deteriorate. As a result of the inherent limitations in a cost-effective control system, misstatement due to error or fraud may occur and not be detected. Accordingly, our disclosure controls and procedures are designed to provide reasonable, not absolute, assurance that the disclosure controls and procedures are met.
Changes in Internal Controls Over Financial Reporting
There have been no changes in internal control over financial reporting that occurred during the quarter ended June 30, 2021 that have materially affected, or are reasonably likely to materially affect, internal control over financial reporting. We have not experienced any material impact to our internal controls over financial reporting despite the fact that most of our employees are working remotely due to the COVID-19. We are continually monitoring and assessing COVID-19 situation on our internal controls to minimize the impact on their design and operating effectiveness.
PART II.  OTHER INFORMATION
ITEM 1. LEGAL PROCEEDINGS
We, in common with the insurance industry in general, are subject to litigation and arbitration in the normal course of our business. As of June 30, 2021, we were not a party to any litigation or arbitration which is expected by management to have a material adverse effect on our results of operations and financial condition and liquidity.
ITEM 1A. RISK FACTORS
There were no material changes from the risk factors previously disclosed in our Annual Report on Form 10-K for the year ended December 31, 2020.
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ITEM 2. UNREGISTERED SALES OF EQUITY SECURITIES AND USE OF PROCEEDS
The following table summarizes our purchases of common shares for the 2021 second quarter:
Issuer Purchases of Equity Securities
Period Total Number of Shares
Purchased (1)
Average Price Paid per Share Total Number of Shares Purchased as Part of
Publicly Announced
Plans or Programs
Approximate Dollar
Value of Shares that
 May Yet be Purchased
Under the Plan or
Programs (2)
4/1/2021-4/30/2021 25,531  $ 39.91  —  $ 737,262 
5/1/2021-5/31/2021 2,739,667  39.99  2,604,338  $ 633,077 
6/1/2021-6/30/2021 5,205,413  38.81  5,201,117  $ 431,213 
Total 7,970,611  $ 39.22  7,805,455 
(1)Represents repurchases by Arch Capital of shares, from time to time, from employees in order to facilitate the payment of withholding taxes on restricted shares granted and the exercise of stock appreciation rights. We purchased these shares at their fair value, as determined by reference to the closing price of our common shares on the day the restricted shares vested or the stock appreciation rights were exercised.
(2)Remaining amount available at June 30, 2021 under Arch Capital’s share repurchase authorization, under which repurchases may be effected from time to time in open market or privately negotiated transactions through December 31, 2021.
ITEM 3. DEFAULTS UPON SENIOR SECURITIES
None.
ITEM 4. MINE SAFETY DISCLOSURES
Not applicable.
ITEM 5. OTHER INFORMATION
In accordance with Section 10a(i)(2) of the Securities Exchange Act of 1934, as amended, we are responsible for disclosing non-audit services to be provided by our independent auditor, PricewaterhouseCoopers LLP, which are approved by the Audit Committee of our board of directors. During the 2021 second quarter, the Audit Committee approved engagements of PricewaterhouseCoopers LLP for permitted non-audit services, which consisted of tax consulting services, tax compliance services and other accounting consulting services.
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ITEM 6. EXHIBITS
Incorporated by Reference
Exhibit Number Exhibit Description Form Original Number Date Filed Filed Herewith
1.01 8-K 1.01 6/3/2021
4.1 8-K 4.1 6/11/2021
4.2 8-K 4.2 6/11/2021
4.3 8-K 4.3 6/11/2021
4.4 8-K 4.4 6/11/2021
10.1 X
15 X
31.1 X
31.2 X
32.1 X
32.2 X
101.INS XBRL Instance Document
101.SCH XBRL Taxonomy Extension Schema Document
101.CAL XBRL Taxonomy Extension Calculation Linkbase Document
101.DEF XBRL Taxonomy Extension Definition Linkbase Document
101.LAB XBRL Taxonomy Extension Label Linkbase Document
101.PRE XBRL Taxonomy Extension Presentation Linkbase Document
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SIGNATURES
Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned thereunto duly authorized.
    ARCH CAPITAL GROUP LTD.
    (REGISTRANT)
     
    /s/ Marc Grandisson
Date: August 5, 2021   Marc Grandisson
    Chief Executive Officer (Principal Executive Officer)
     
    /s/ François Morin
Date: August 5, 2021   François Morin
    Executive Vice President, Chief Financial Officer (Principal Financial and Accounting Officer) and Treasurer
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Exhibit 10.1


EMPLOYMENT AGREEMENT

EMPLOYMENT AGREEMENT (“Agreement”), dated May 7, 2021, between Arch Capital Group Ltd., a Bermuda corporation (the “Company”), and Christine Todd (the “Executive”).

The parties hereto agree as follows:

ARTICLE 1

DEFINITIONS

SECTION 1.01. Definitions. For purposes of this Agreement, the following terms have the meanings set forth below:

Accounting Firm” has the meaning set forth in Section 12.10.

“Affiliate” means any Person, directly or indirectly, through one or more intermediaries,
Controlling, Controlled by, or under common Control with the Company. For purposes hereof, (a) “Control” means the ownership, directly or indirectly, of (i) in the case of a corporation, Voting Securities (as defined below) representing 50% or more of the total voting power or value of all the then outstanding Voting Securities of such corporation or (ii) in the case of a partnership, limited liability company, association or other business entity (“Business Entity”), 50% or more of the partnership or other similar ownership interest of such Business Entity; and (b) “Voting Security” means any security of a corporation which carries the right to vote generally in the election of directors. For purposes of the definition of “Control,” (x) a Person will be deemed to have a 50% or more ownership interest in a Business Entity if such Person is allocated 50% or more of Business Entity gains or losses or controls the managing director or member or general partner of such Business Entity; and (y) “Controlling” and “Controlled” have meanings correlative thereto.
Base Salary” has the meaning set forth in Section 4.01.

Bonus Amount” means the greater of (i) the Executive’s target annual bonus for the year during which Notice of Termination is given, or (ii) the average of the Executive’s actual annual bonus for the three years immediately preceding the year during which Notice of Termination is given (or such lesser number of years in which the Executive was employed by the Company or its Affiliate).

Cause” means (a) theft or embezzlement by the Executive with respect to the Company or its Affiliates; (b) malfeasance or gross negligence in the performance of the Executive’s duties; (c) the Executive’s conviction of any felony or any crime involving moral turpitude; (d)




willful or prolonged absence from work by the Executive (other than by reason of disability due to physical or mental illness) or failure, neglect or refusal by the Executive to perform her duties and responsibilities without the same being corrected within ten (10) days after being given written notice thereof; (e) continued and habitual use of alcohol by the Executive to an extent which materially impairs the Executive’s performance of her duties; (f) the Executive’s use of illegal drugs; or (g) the material breach by the Executive of any provision of this Agreement.
Code” means the U.S. Internal Revenue Code of 1986, as amended.

Confidential Information” means information that is not generally known to the public and that was or is used, developed or obtained by the Company or its Affiliates in connection with their business. It shall not include information (a) required to be disclosed by court or administrative order or called for in a subpoena or discovery request regular on its face, (b) lawfully obtainable from other sources or which is in the public domain through no fault of the Executive; or (c) the disclosure of which is consented to in writing by the Company.

Date of Termination” has the meaning set forth in Section 5.01.

Employment Period” has the meaning set forth in Section 2.01.

    “Good Reason” means, without the Executive’s written consent and subject to the timely notice requirement and the Company’s opportunity to cure set forth in Section 5.05 below, (a) the material diminution of any material duties or responsibilities of the Executive; (b) a material reduction in the Executive’s Base Salary; or (c) any material breach by the Company of the provisions contained in this Agreement.

Intellectual Property” has the meaning set forth in Section 7.01.

Notice of Termination” has the meaning set forth in Section 5.05.

Noncompetition Period has the meaning set forth in Section 9.01.
Nonsolicitation Period” has the meaning set forth in Section 9.02.

Person” means an individual, a partnership, a corporation, a limited liability company, an association, a joint stock company, an estate, a trust, a joint venture, an unincorporated organization or a governmental entity or any department, agency or political subdivision thereof.

Permanent Disability” means those circumstances where the Executive is a disabled person as defined in the Bermuda Human Rights Act 1981 (“HRA 1981”) and is unable to continue to perform the usual customary duties to the required standard (subject to Schedule 1 of the HRA 1981). Any questions as to the existence of a Permanent Disability shall be determined by a qualified, independent physician selected by the Company and approved by
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the Executive (which approval shall not be unreasonably withheld). The determination of any such physician shall be final and conclusive for all purposes of this Agreement.

Reimbursable Expenses” has the meaning set forth in Section 4.04.

“Start Date” has the meaning set forth in Section 2.01.

ARTICLE 2

EMPLOYMENT

SECTION 2.01. Employment. The Company shall employ the Executive, and the Executive shall accept employment with the Company, for the period beginning on June 7, 2021 (the “Start Date”) and ending on the Date of Termination as provided in Section 5.01 (the “Employment Period”). This Agreement is conditional on the Executive being given approval by the Bermuda Department of Immigration to work and reside in Bermuda. If the Executive fails to satisfy the conditions set forth in this section, she shall forfeit all rights hereunder.

ARTICLE 3

POSITION AND DUTIES

SECTION 3.01. Position and Duties. During the Employment Period, the Executive shall serve as Chief Investment Officer of the Company and shall have such responsibilities, powers and duties as may from time to time be prescribed by the Chief Executive Officer of the Company; provided that such responsibilities, powers and duties are substantially consistent with those customarily assigned to individuals serving in such positions at comparable companies or as may be reasonably required by the conduct of the business of the Company. During the Employment Period the Executive shall devote substantially all of her working time and efforts to the business and affairs of the Company. The Executive shall not directly or indirectly render any services of a business, commercial or professional nature to any other person or for-profit organization not related to the business of the Company or its Affiliates, whether for compensation or otherwise, without prior written consent of the Company.

    SECTION 3.02. Work Permits. The Executive shall cooperate in all reasonable respects with the Company to obtain, maintain and renew a suitable (for the purposes of the Executive’s contemplated employment by the Company) work permit by the Bermuda government authorities and any other permits required by any Bermuda government authority. The Company shall be responsible for permit fees, and all other expenses, including legal expenses, in connection with obtaining and maintaining such work permit.

    SECTION 3.03. Work Location. While employed by the Company hereunder, the Executive shall perform her duties (when not traveling or engaged elsewhere in the performance of her duties) at the offices of the Company in Bermuda. The Executive shall travel
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to such places on the business of the Company in such manner and on such occasions as the Company may from time to time reasonably require.

SECTION 3.04. Relocation. Upon the termination of the Executive’s employment for any reason, other than for Cause, the Company shall reimburse the Executive for all reasonable expenses incurred by her for the cost of relocating all of her household items to Massachusetts and airfare for the Executive and her family to return to Massachusetts, in each case, subject to the Company’s requirements with respect to reporting and documentation of such expenses; provided, however, that any such expenses must be incurred by the Executive not later than the last day of the calendar year following the calendar year in which the Executive’s “separation from service” (within the meaning of Treas. Reg. Section 1.409A-1(h)) with the Company occurs, and any such reimbursement shall be made promptly upon presentation by the Executive to the Company of the required documentation and, in all events, no later than the last day of the second calendar year following the calendar year in which the Executive’s “separation from service” with the Company occurs.

ARTICLE 4

BASE SALARY AND BENEFITS

SECTION 4.01. Base Salary. During the Employment Period, the Executive’s base salary will be $575,000 per annum (the “Base Salary”). The Base Salary will be payable monthly on the 15th day of each month, two weeks in arrears and two weeks in advance. Annually during the Employment Period the Company shall review with the Executive her job performance and compensation, and if deemed appropriate by the Board of Directors of the Company, in its discretion, the Executive’s Base Salary may be increased. Normal hours of employment are 8:30 a.m. to 5:00 p.m., Monday to Friday. The Executive’s salary has been computed to reflect that her regular duties are likely, from time to time, to require more than the normal hours per week and the Executive shall not be entitled to receive any additional remuneration for work outside normal hours, and, for the avoidance of doubt, Section 9(1) of the Bermuda Employment Act 2000 shall not apply to the Executive’s employment.
SECTION 4.02. Bonuses. In addition to the Base Salary, the Executive shall be eligible to participate in an annual bonus plan on terms set forth from time to time by the Board of Directors of the Company. The Executive’s target annual bonus will be 125% of her Base Salary.

SECTION 4.03. Benefits. In addition to the Base Salary, and any bonuses payable to the Executive pursuant to this Agreement, the Executive shall be entitled to the following benefits during the Employment Period:

(a)    such medical, life insurance and disability insurance coverage as is, or may during the Employment Period, be provided generally for other senior executive officers of the Company as set forth from time to time in the applicable plan documents;
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(b)    in addition to the usual public holidays and eight (8) paid days off for sick leave, a maximum of five (5) weeks of paid vacation annually during the term of the Employment Period (Section 11 of the Bermuda Employment Act 2000 shall otherwise not apply to the Executive’s employment hereunder);
(c)    benefits under any plan or arrangement available generally for the senior executive officers of the Company, subject to and consistent with the terms and conditions and overall administration of such plans as set forth from time to time in the applicable plan documents;
(d)payment by the Company of the reasonable cost of preparation of annual tax returns and associated tax planning on a basis no less favorable than such arrangements provided on the date hereof to similarly situated senior executives residing in Bermuda, and the cost paid by the Company under this Section 4.03(d) for one calendar year shall be paid by the Company promptly upon presentation by the Executive to the Company of the required documentation and, in all events, not later than the end of the following calendar year; and
(e)fringe benefits customarily provided from time to time during the Employment Period to similarly situated senior executives residing in Bermuda.
SECTION 4.04. Expenses. The Company shall reimburse the Executive for all reasonable expenses incurred by her in the course of performing her duties under this Agreement which are consistent with the Company’s policies in effect from time to time with respect to travel, entertainment and other business expenses (“Reimbursable Expenses”), subject to the Company’s requirements with respect to reporting and documentation of expenses.
SECTION 4.05. Share-Based Awards. The Executive shall be eligible to participate in the Company’s Long Term Incentive and Share Award Plans (and any similar plan adopted by the Company) under which share-based awards may be granted, as determined by the Board of Directors of the Company in its discretion.

SECTION 4.06. Sign-On Awards. Subject to approval by the Board of Directors of the Company, on the Start Date (the “Grant Date”) you will receive a sign-on bonus consisting of the share-based awards determined in accordance with the following clauses (a) and (b) on the Grant Date: (a) a number of restricted common shares (“Common Shares”) of the Company (“Restricted Shares”) which, together with (b) non-qualified stock options (“Stock Options”) with respect to the same number of Common Shares subject to the Restricted Shares, have an aggregate value (determined as set forth below) equal to $1,000,000. The Restricted Shares and Stock Options will vest in three equal annual installments on the first, second and third anniversaries of the Grant Date, provided that on each such date the Executive is still an employee of the Company as set forth in the award agreements.

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For these purposes, the value of Restricted Shares will be equal to the closing market price of the number of Common Shares subject to the Restricted Shares on the Grant Date, and the value of the Stock Options will be determined by the Company based on a Black-Scholes valuation consistent with the manner in which the Company reflects Stock Options in its consolidated financial statements. The Stock Options will have an exercise price per share equal to the closing market price of the Common Shares on the Grant Date. The other terms and conditions of the Restricted Shares and the Stock Options would be as set forth in the award agreements.

ARTICLE 5

TERM AND TERMINATION

SECTION 5.01. Term. The expected term of this Agreement is for at least three years from the Start Date. Notwithstanding the foregoing, the Employment Period shall in all events end on the Date of Termination, whenever occurring. For purposes of this Agreement, the “Date of Termination” shall mean the first to occur of the following: (a) the six (6) month anniversary of the Company providing Notice of Termination (as defined below) without Cause to the Executive; (b) immediately upon the Company providing Notice of Termination for Cause to the Executive; (c) the six (6) month anniversary of the Executive providing Notice of Termination specifying her resignation for Good Reason to the Company; (d) the six (6) month anniversary of the Executive providing Notice of Termination by the Executive without Good Reason to the Company; (e) the fifth (5th) day following the Company providing Notice of Termination to the Executive as a result of the Executive’s Permanent Disability; and (f) the date of Executive’s death. In the event that there are circumstances which would give rise to a termination by the Company for Cause, the Company may, in its sole and exclusive discretion, treat such termination as a termination without Cause. Upon termination of the Executive’s employment with the Company for any reason, the Executive shall resign from all positions and in all capacities with the Company and its Affiliates or from any other company or other Person with which the Executive is serving at the Company’s request.

SECTION 5.02. Resignation by the Executive Without Good Reason. If the Employment Period shall be terminated as a result of the Executive’s resignation or leaving of her employment, other than for Good Reason, the Executive shall continue to: (a) receive Base Salary and benefits set forth in Section 4.03 through the Date of Termination, except that any amount payable after the Executive’s “separation from service” (within the meaning of Treas. Reg. Section 1.409A-1(h)) with the Company will be subject to Section 12.09 below; (b) the Company will make a cash lump sum payment to the Executive equal to one half of the sum of (I) the Bonus Amount, and (II) a pro-rated portion of the Bonus Amount based on the number of days elapsed in the calendar year through the date Notice of Termination is given, which payment shall be made on the date that is sixty (60) days following the Date of Termination, and (c) receive reimbursement of all Reimbursable Expenses incurred by the Executive prior to the Date of Termination. The Executive’s entitlements under all other benefit plans and programs of the Company shall be as determined thereunder.
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SECTION 5.03. Termination for Good Reason or Without Cause. If the Employment Period shall be terminated by the Executive for Good Reason or by the Company without Cause, the Executive shall continue to: (a) receive Base Salary through the six (6) month anniversary of the Date of Termination, such amount to be paid in accordance with the regular payroll practices of the Company (except that any amount otherwise payable after the Date of Termination and prior to the sixtieth (60th) day following the Date of Termination shall instead be paid on such sixtieth (60th) day), and except that any amount payable after the Executive’s “separation from service” (within the meaning of Treas. Reg. Section 1.409A-1(h)) with the Company will be subject to Section 12.09 below; (b) receive an amount equal to the sum of (i) the Executive’s target annual bonus plus (ii) a pro-rated portion of the Executive’s target annual bonus based on the number of days elapsed in the calendar year through the date Notice of Termination is given, one half of which amount shall be paid in cash in a single lump sum on the date that is sixty (60) days following the Date of Termination and the remaining half of which shall be paid in accordance with the regular payroll practices of the Company (except that any amount otherwise payable after the Date of Termination and prior to the sixtieth (60th) day following the Date of Termination shall instead be paid on such sixtieth (60th) day); (c) receive benefits set forth in Section 4.03 above through the Date of Termination, except that any amount payable after the Executive’s “separation from service” (within the meaning of Treas. Reg. Section 1.409A-1(h)) with the Company will be subject to Section 12.09 below; (d) receive her medical insurance coverage benefits from the Company’s plan in effect from time to time (provided the Executive continues to pay the portion of the premiums for such coverage that are charged to similarly situated active employees) for a period equal to the lesser of (i) six (6) months after the Date of Termination, and (ii) until the Executive is provided by another employer with benefits substantially comparable to the benefits provided by such plan; and (e) receive reimbursement for all Reimbursable Expenses incurred by the Executive prior to the Date of Termination. The Executive’s entitlements under all other benefit plans and programs of the Company shall be as determined thereunder. Notwithstanding the foregoing, the Executive shall be entitled to the amounts described above (other than Base Salary and benefits as set forth in Section 4.03 through the Date of Termination) only if (i) the Executive has entered into an irrevocable (except to the extent required by law, and to the extent required by law to be revocable, has not revoked) general release of claims, which, subject to Section 5.07 below, is reasonably satisfactory to the Company (“Release”), on or before the date that is fifty (50) days following the Date of Termination (but not prior to the Date of Termination), and (ii) the Executive has complied with, and continues to comply with, the provisions of Sections 6.01, 7.01, 8.01, 9.01, 9.02 or 11.01 of this Agreement.

SECTION 5.04. Termination for Other Reasons. If the Employment Period shall be terminated by the Company with Cause, as a result of the Executive’s Permanent Disability or upon the Executive’s death, the Executive (or her beneficiaries or estate, in the case of death) shall continue to (a) receive Base Salary and benefits set forth in Section 4.03 above through the Date of Termination, except that any amount payable after the Executive’s “separation from service” (within the meaning of Treas. Reg. Section 1.409A-1(h)) with the Company will be subject to Section 12.09 below; and (b) in the case of termination due to the Executive’s
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Permanent Disability or death, receive her medical insurance coverage benefits from the Company’s plan in effect at the time of such termination for a period equal to the lesser of (i) twelve (12) months after the Date of Termination, and (ii) until the Executive is provided by another employer with benefits substantially comparable to the benefits provided by such plan; and (c) receive reimbursement for all Reimbursable Expenses incurred by the Executive prior to the Date of Termination. The Executive’s entitlements under all other benefit plans and programs of the Company shall be as determined thereunder.

    SECTION 5.05. Notice of Termination and Opportunity to Cure. Any termination by the Company for Permanent Disability or Cause or without Cause or by the Executive for Good Reason or without Good Reason shall be communicated by written Notice of Termination to the other party hereto. For purposes of this Agreement, a “Notice of Termination” shall mean a notice which shall indicate the date the termination is to take effect (consistent with the terms of this Agreement), the specific termination provision in this Agreement relied upon and, for a termination for Permanent Disability or for Cause or for a resignation for Good Reason, shall set forth in reasonable detail the facts and circumstances claimed to provide a basis for termination of employment under the provision indicated. It shall be a condition precedent to the Executive’s right to terminate employment for Good Reason that (i) the Executive shall first have given the Company written notice that an event or condition constituting Good Reason has occurred within ninety (90) days after such occurrence, and any failure to give such written notice within such period will result in a waiver by the Executive of her right to terminate for Good Reason as a result of such event or condition, and (ii) a period of thirty (30) days from and after the giving of such written notice shall have elapsed without the Company having effectively cured or remedied such occurrence during such 30-day period, unless such occurrence cannot be cured or remedied within thirty (30) days, in which case the period for remedy or cure shall be extended for a reasonable time (not to exceed an additional fifteen (15) days) provided that the Company has made and continues to make a diligent effort to effect such remedy or cure.

    SECTION 5.06. Garden Leave. Following any Notice of Termination, whether by the Company or the Executive and until the end of the Employment Period, the Company may direct, in its sole and exclusive discretion, that the Executive perform no duties and exercise no powers or authorities in connection with her employment, resign from any office with the Company and its Affiliates and not attend any premises of any of the Company and its Affiliates; provided, however, that, following any such direction, the Executive will continue to be required to comply with her other obligations under this Agreement and will continue to owe a duty of good faith and fidelity to the Company as an employee (“Garden Leave”). Notwithstanding the above, the Company may at its discretion require the Executive to perform duties at any time during the Garden Leave, which duties may be withdrawn at any time at the Company’s discretion, and, during the Garden Leave, the Executive shall: (a) remain an employee of the Company and be bound by the express and implied terms of this Agreement; (b) not, without the prior written consent of the Company, attend her place of work or any other premises of any of the Company and its Affiliates or access the information technology systems of the Company and its Affiliates; (c) not, without the prior written consent of the
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Company, contact or deal with (or attempt to contact or deal with) any officer, employee, consultant, client, customer, investor, supplier, agent, distributor, shareholder, adviser or other business contact of any of the Company and its Affiliates; (d) promptly disclose in writing to the Company any attempt at contact with the Executive made by any such person or entity with whom the Executive has been required to have no contact pursuant to this Section 5.06; (e) be ready and available to perform such duties as the Company may require, ensuring that the Company knows where and how she can be contacted and complying with any written requests to contact a specified employee of the Company at specified intervals; and (f) be deemed to take any accrued holiday during the Garden Leave period.
SECTION 5.07. Release. In consideration of the mutual promises herein and the payments detailed in this Article 5, the Executive, on behalf of herself and her heirs and assigns, in a form reasonably satisfactory to the Company, shall, with respect to any termination of employment under Section 5.03, execute a Release which irrevocably and unconditionally releases and forever discharges, individually and collectively, the Company and its Affiliates, and each of their respective officers, directors, employees, shareholders, representatives, parent companies, subsidiaries, predecessors, successors, assigns, attorneys and all persons acting by, through or in concert with them, of and from any and all charges, claims, complaints, demands, liabilities or causes of action, known or unknown, that the Executive may have at the effective date of the Release or has ever had against any such Person. Notwithstanding any other provision hereof, the Executive shall not be required by any general release to release claims that the Executive may have against the Company that arise after the effective date of the Release, any rights the Executive may have to enforce Section 5.03 of this Agreement, or any rights of the Executive to be indemnified under the organizational documents of the Company and its Affiliates or under applicable law or pursuant to the Company’s directors’ and officers’ liability insurance policies.
ARTICLE 6

CONFIDENTIAL INFORMATION

SECTION 6.01. Nondisclosure and Nonuse of Confidential Information. The Executive will not disclose or use at any time during or after the Employment Period any Confidential Information of which the Executive is or becomes aware, whether or not such Confidential Information is developed by her, except to the extent that such disclosure or use is directly related to and required by the Executive’s performance of duties assigned to the Executive pursuant to this Agreement. Under all circumstances and at all times, the Executive will take all appropriate steps to safeguard Confidential Information in her possession and to protect it against disclosure, misuse, espionage, loss and theft.

SECTION 6.02. Defend Trade Secrets Act. Pursuant to 18 U.S.C. § 1833(b), the Executive understands that the Executive will not be held criminally or civilly liable under any Federal or State trade secret law for the disclosure of a trade secret of the Company that (i) is made (x) in confidence to a Federal, State, or local government official, either directly or indirectly, or to
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the Executive’s attorney and (y) solely for the purpose of reporting or investigating a suspected violation of law; or (ii) is made in a complaint or other document that is filed under seal in a lawsuit or other proceeding. The Executive understands that if the Executive files a lawsuit for retaliation by the Company for reporting a suspected violation of law, the Executive may disclose the trade secret to the Executive’s attorney and use the trade secret information in the court proceeding if the Executive (I) files any document containing the trade secret under seal, and (II) does not disclose the trade secret, except pursuant to court order. Nothing in this Agreement is intended to conflict with 18 U.S.C. § 1833(b) or create liability for disclosures of trade secrets that are expressly allowed by such section. Further, nothing in this Agreement or any other agreement or arrangement with the Company or any of its Affiliates shall prohibit or restrict the Executive from making any disclosure of information or documents to any governmental agency or legislative body, any self-regulatory organization, the Legal Department of the Company, and/or pursuant to the whistleblower provisions of the Dodd-Frank Act or Sarbanes-Oxley Act.
ARTICLE 7

INTELLECTUAL PROPERTY

SECTION 7.01. Ownership of Intellectual Property. In the event that the Executive as part of her activities on behalf of the Company generates, authors or contributes to any invention, design, new development, device, product, method of process (whether or not patentable or reduced to practice or comprising Confidential Information), any copyrightable work (whether or not comprising Confidential Information) or any other form of Confidential Information relating directly or indirectly to the business of the Company as now or hereinafter conducted (collectively, “Intellectual Property”), the Executive acknowledges that such Intellectual Property is the sole and exclusive property of the Company and hereby assigns all right title and interest in and to such Intellectual Property to the Company as allowable under applicable law. Any copyrightable work prepared in whole or in part by the Executive during the Employment Period will be deemed “a work made for hire” under Section 201(b) of the United States Copyright Act of 1976, as amended, and the Company will own all of the rights comprised in the copyright therein. The Executive will promptly and fully disclose all Intellectual Property and will cooperate with the Company to protect the Company’s interests in and rights to such Intellectual Property (including providing reasonable assistance in securing patent protection and copyright registrations and executing all documents as reasonably requested by the Company, whether such requests occur prior to or after termination of Executive’s employment hereunder).

ARTICLE 8

DELIVERY OF MATERIALS UPON TERMINATION OF EMPLOYMENT

SECTION 8.01. Delivery of Materials upon Termination of Employment. As requested by the Company, from time to time and upon the termination of the Executive’s employment with
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the Company for any reason, the Executive will promptly deliver to the Company all property of the Company in the Executive’s possession or within her control, including, without limitation, all copies and embodiments, in whatever form or medium, of all Confidential Information or Intellectual Property in the Executive’s possession or within her control (including written records, notes, photographs, manuals, notebooks, documentation, program listings, flow charts, magnetic media, disks, diskettes, tapes and all other materials containing any Confidential Information or Intellectual Property), irrespective of the location or form of such property and, if requested by the Company, will provide the Company with written confirmation that all such property have been delivered to the Company.

ARTICLE 9

NONCOMPETITION AND NONSOLICITATION

SECTION 9.01. Noncompetition. The Executive acknowledges that during her employment with the Company, she will become familiar with trade secrets and other Confidential Information concerning the Company and its Affiliates and their respective predecessors, and that her services will be of special, unique and extraordinary value to the Company. In addition, the Executive hereby agrees that at any time during the Employment Period, and for a period ending one (1) year after the termination of the Executive's employment (the “Noncompetition Period”), she will not directly or indirectly own, manage, control, participate in, consult with, render services for or in any manner engage in any Restricted Business;
provided, however, that if the Executive’s termination of employment occurs as a result of the Executive’s resignation or leaving of her employment other than for Good Reason, except as provided in clause (Y) below, the Noncompetition Period shall continue beyond the Date of Termination only if (i) the Company pays the Executive, for each day during which the Noncompetition Period so continues (taking into account Section 9.04 below), an amount equal to 1/365th of the sum of (A) the Executive’s annual Base Salary, plus (B) the Executive’s Bonus Amount, and (C) a pro-rated portion of the Executive’s Bonus Amount based on the number of days elapsed in the calendar year through the date Notice of Termination is given, such amount to be paid in accordance with the regular payroll practices of the Company (except that any amount otherwise payable after the Date of Termination and prior to the sixtieth (60th) day following the Date of Termination shall instead be paid on such sixtieth (60th) day); and (ii) the Executive shall continue to receive her medical insurance coverage benefits from the Company’s plan in effect from time to time (provided the Executive continues to pay the portion of the premiums for such coverage that are charged to similarly situated active employees) for a period equal to the lesser of (x) the end of the Noncompetition Period, and (y) until the Executive is provided by another employer with benefits substantially comparable (with no pre-existing condition limitations) to the benefits provided by such plan; and provided further, however, that:
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(X) the Company may elect, in its sole discretion, by written notice to the Executive given not more than ten (10) business days after the date Notice of Termination is given by the Executive without Good Reason, to not continue the Noncompetition Period beyond the Date of Termination or to reduce the Noncompetition Period under such circumstances so that it ends on the date set forth in such written notice (which shall not be later than twelve (12) months after the Date of Termination), in which case the Company’s obligation to make payments and provide benefits under this Section 9.01 shall end at the end of the Noncompetition Period, and
(Y) the Company’s requirement to make payments under this Section 9.01 as a condition to continuation of the Noncompetition Period shall apply only if the Executive has entered into a general release of claims reasonably satisfactory to the Company on or before the date that is fifty (50) days following the Date of Termination (but not prior to the Date of Termination) and does not revoke such release prior to the end of any applicable revocation period (it being understood that such general release will not require the Executive to release her rights under this Section 9.01 and will not contain any employment restrictions or non-solicitation obligations other than those set forth in this Agreement) and the Executive has complied with, and continues to comply with, the provisions of Sections 6.01, 7.01, 8.01, 9.01, 9.02 or 10.01 hereof.
“Restricted Business” means any business that is materially competitive with the businesses that (I) are at the time in question being conducted by the Company or its Affiliates with which the Executive was involved to a material extent in the twelve (12) months prior to termination of the Executive’s employment, or (II) were, during the Executive’s employment, either being conducted by, or being actively developed by, the Company or its Affiliates with which the Executive was involved to a material extent in the twelve (12) months prior to termination of Executive’s employment, in either case within any geographical area in which the Company or its Affiliates engage or plan to engage in such businesses. It shall not be considered a violation of this Section 9.01 for the Executive to be a passive owner of not more than 2% of the outstanding stock of any class of a corporation which is publicly traded, so long as the Executive has no active participation in the business of such corporation.
SECTION 9.02. Nonsolicitation. The Executive acknowledges that during her employment with the Company, she will become familiar with trade secrets and other Confidential Information concerning the Company, its Affiliates and their respective predecessors, and that her services will be of special, unique and extraordinary value to the Company. The Executive hereby agrees that (a) during the Employment Period and for a period of one (1) year after the date of termination of employment (the “Nonsolicitation Period”) the Executive will not, directly or indirectly, induce or attempt to induce any Relevant Employee of the Company or its Affiliates to leave the employ of the Company or its Affiliates, or in any way interfere with the relationship between the Company or its Affiliates and any Relevant Employee thereof or
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otherwise employ or receive the services of any individual who was a Relevant Employee of the Company or its Affiliates at the Date of Termination or within the twelve-month period prior thereto, and (b) during the Nonsolicitation Period, the Executive will not induce or attempt to induce any Restricted Customer to cease doing business with the Company or its Affiliates. For purposes of this Agreement, a “Relevant Employee” shall mean a director, officer, underwriter or manager of the Company or its Affiliates, in each case with whom the Executive had material dealings at any time during the period of twelve (12) months prior to the Date of Termination. A “Restricted Customer” shall mean any firm, company or Person who was a customer, investor, supplier, client, insured, reinsured, reinsurer, broker, agent, licensee or other business relation of the Company or its Affiliates and with whom Executive had material dealings during the twelve (12) months prior to termination of the Executive’s employment.

SECTION 9.03. Enforcement. If, at the enforcement of Sections 9.01 or 9.02, a court holds that the duration or scope stated herein are unreasonable under circumstances then existing, the parties agree that the maximum duration and scope reasonable under such circumstances will be substituted for the stated duration or scope and that the court will be permitted to revise the restrictions contained in this Article 9 to cover the maximum duration and scope permitted by law.

SECTION 9.04. Coordination with Garden Leave. The lengths of the Noncompetition Period and the Nonsolicitation Period shall be reduced by any period that the Executive is required to remain away from the office during her notice period or not undertake her normal duties pursuant to Section 5.06 above.

SECTION 9.05. Notice of Covenants. If the Executive receives an offer to directly or indirectly own, manage, control, participate in, consult with, render services for or in any manner engage in any Restricted Business during the Employment Period or before the expiry of the Noncompetition Period or the Nonsolicitation Period, she shall provide the Person making the offer a copy of this Article 9 prior to acceptance of such offer.

ARTICLE 10

EQUITABLE RELIEF

SECTION 10.01. Injunctive or Other Equitable Relief. The Executive acknowledges that (a) the covenants contained herein are reasonable, (b) the Executive’s services are unique, and (c) a breach or threatened breach by her of any of her covenants and agreements with the Company and its Affiliates contained in Sections 6.01, 7.01, 8.01, 9.01 or 9.02 could cause irreparable harm to the Company or its Affiliates for which they would have no adequate remedy at law. Accordingly, and in addition to any remedies which the Company and its Affiliates may have at law, in the event of an actual or threatened breach by the Executive of her covenants and agreements contained in Sections 6.01, 7.01, 8.01, 9.01 or 9.02, the Company and its Affiliates shall have the absolute right, without the need to post a bond or any other type of security, to commence a lawsuit or other proceeding in any court of competent
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jurisdiction (the “Selected Court”) seeking injunctive or other equitable relief (an “Injunction Proceeding”). In furtherance thereof, the Executive expressly and irrevocably agrees that the Selected Court may exercise personal jurisdiction over her in connection with any Injunction Proceeding and further agrees not to assert that any court other than the Selected Court is a more suitable forum for an Injunction Proceeding.

ARTICLE 11

EXECUTIVE REPRESENTATIONS

SECTION 11.01. Executive Representations. The Executive hereby represents and warrants to the Company that (a) the execution, delivery and performance of this Agreement by the Executive does not and will not conflict with, breach, violate or cause a default under any contract, agreement, instrument, order, judgment or decree to which the Executive is a party or by which she is bound, (b) the Executive is not a party to or bound by any employment agreement, noncompetition agreement or confidentiality agreement with any other Person that affects her right or ability to perform the duties contemplated by this Agreement, (c) the Executive did not, while working for any employer other than the Company: solicit her fellow employees to leave their employment and work with her at the Company; or solicit clients, or potential clients, of such employer, for the Company; or take any type of information that is proprietary information of such employer, and (d) upon the execution and delivery of this Agreement by the Company, this Agreement will be the valid and binding obligation of the Executive, enforceable in accordance with its terms.

SECTION 11.02. Company Representations. The Company hereby represents and
warrants to the Executive that (a) all acts required to be taken to authorize, deliver and perform this Agreement and the obligations of the Company provided for hereunder have been duly taken; and (b) upon the execution and delivery of this Agreement by the Company, this Agreement will be valid and binding obligation of the Company, enforceable in accordance with its terms.

ARTICLE 12

MISCELLANEOUS

SECTION 12.01. Remedies. The Company will have all rights and remedies set forth in this Agreement, all rights and remedies which the Company has been granted at any time under any other agreement or contract and all of the rights which the Company has under any law. The Company will be entitled to enforce such rights specifically, without posting a bond or other security, to recover damages by reason of any breach of any provision of this Agreement and to exercise all other rights granted by law. There are currently no disciplinary or grievance procedures in place, there is no collective agreement in place, and there is no probationary period.

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SECTION 12.02. Consent to Amendments. The provisions of this Agreement may be amended or waived only by a written agreement executed and delivered by the Company and the Executive. No other course of dealing between the parties to this Agreement or any delay in exercising any rights hereunder will operate as a waiver of any rights of any such parties.

SECTION 12.03. Successors and Assigns. All covenants and agreements contained in this Agreement by or on behalf of any of the parties hereto will bind and inure to the benefit of the respective successors and assigns of the parties hereto whether so expressed or not, provided that the Executive may not assign her rights or delegate her obligations under this Agreement without the written consent of the Company.

SECTION 12.04. Severability. Whenever possible, each provision of this Agreement will be interpreted in such manner as to be effective and valid under applicable law, but if any provision of this Agreement is held to be prohibited by or invalid under applicable law, such provision will be ineffective only to the extent of such prohibition or invalidity, without invalidating the remainder of this Agreement.

SECTION 12.05. Counterparts. This Agreement may be executed simultaneously in two counterparts, any one of which need not contain the signatures of more than one party, but all of which counterparts taken together will constitute one and the same agreement.

SECTION 12.06. Descriptive Headings. The descriptive headings of this Agreement are inserted for convenience only and do not constitute a part of this Agreement.

SECTION 12.07. Notices. All notices, demands or other communications to be given or delivered under or by reason of the provisions of this Agreement will be in writing and shall be delivered personally by hand, by electronic transmission (with a copy following by hand or by overnight courier), by registered or certified mail, postage prepaid, return receipt requested, or by overnight courier service (charges prepaid). Communications delivered personally by hand shall be deemed received on the date when delivered personally to the recipient; communications sent by electronic means shall be deemed received one (1) business day after the sending thereof; communications sent by registered or certified mail shall be deemed received four (4) business days after the sending thereof; and communications delivered by overnight courier shall be deemed received one (1) business day after the date when sent to the recipient. Such notices, demands and other communications will be sent to the Executive and to the Company at the addresses set forth below.

If to the Executive:    To the last address delivered to the Company by the Executive in the manner set forth herein.
    
    If to the Company:    Arch Capital Group Ltd.
        Waterloo House
    100 Pitts Bay Road
    Hamilton HM 12, Bermuda
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    Attention: Secretary
    Tel: (441) 278-9250
    Fax: (441) 278-9255
    
or to such other address or to the attention of such other person as the recipient party has specified by prior written notice to the sending party.

SECTION 12.08. Withholding. The Company may withhold from any amounts payable under this Agreement such federal, state, local or foreign taxes as shall be required to be withheld pursuant to any applicable law or regulation.

SECTION 12.09. 409A and 457A. This Section 12.09 shall apply to the Executive only if, and to the extent, she is subject to Section 409A or Section 457A of the Code. It is intended that this Agreement will comply with Sections 409A and 457A of the Code (and any regulations and guidelines issued thereunder), to the extent the Agreement is subject thereto, and the Agreement shall be interpreted on a basis consistent with such intent. If an amendment of the Agreement is necessary in order for it to comply with Section 409A or Section 457A, the parties hereto will negotiate in good faith to amend the Agreement in a manner that preserves the original intent of the parties to the extent reasonably possible. No action or failure to act, pursuant to this Section 12.09 shall subject the Company to any claim, liability, or expense, and the Company shall not have any obligation to indemnify or otherwise protect the Executive from the obligation to pay any taxes, interest or penalties pursuant to Section 409A or Section 457A of the Code.

Notwithstanding any provision to the contrary in this Agreement, if the Executive is deemed on the date of her “separation from service” (within the meaning of Treasury Regulation Section 1.409A-1(h)) to be a “specified employee” within the meaning of that term under Section 409A(a)(2)(B) of the Code, then with regard to any payment that is required to be delayed pursuant to Section 409A(a)(2)(B) of the Code (after taking into account the applicable provisions of Treasury Regulation Section 1.409A-1(b)(9)(iii)), the portion, if any, of such payment so required to be delayed shall not be made prior to the earlier of (i) the expiration of the six (6)-month period measured from the date of her “separation from service” or (ii) the date of her death (the “Delay Period”). Upon the expiration of the Delay Period, all payments and benefits delayed pursuant to this Section (whether they would have otherwise been payable in a single sum or in installments in the absence of such delay) shall be paid or reimbursed to the Executive in a lump sum, and any remaining payments due under this Agreement shall be paid in accordance with the normal payment dates specified for them herein. Whenever payments under this Agreement are to be made in installments, each such installment shall be deemed to be a separate payment for purposes of Section 409A of the Code. Notwithstanding any provision of this Agreement to the contrary, for purposes of any provision of this Agreement providing for the payment of any amounts or benefits upon or following a termination of employment that are considered deferred compensation under Section 409A, references to the Executive’s “termination of employment” (and corollary terms) with the Company shall be construed to refer to the Executive’s “separation from
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service” (within the meaning of Treas. Reg. Section 1.409A-1(h)) with the Company. In no case will compliance with this Section by the Company constitute a breach of the Company’s obligations under this Agreement.

With respect to any reimbursement or in-kind benefit arrangements of the Company and its subsidiaries provided for herein that constitute deferred compensation for purposes of Section 409A, except as otherwise permitted by Section 409A, the following conditions shall be applicable: (i) the amount eligible for reimbursement, or in-kind benefits provided, under any such arrangement in one calendar year may not affect the amount eligible for reimbursement, or in-kind benefits to be provided, under such arrangement in any other calendar year (except that the health and dental plans may impose a limit on the amount that may be reimbursed or paid), (ii) any reimbursement must be made on or before the last day of the calendar year following the calendar year in which the expense was incurred, and (iii) the right to reimbursement or in-kind benefits is not subject to liquidation or exchange for another benefit.

    SECTION 12.10. Section 4999 of the Code. Anything in this Agreement or the Company’s Incentive Compensation Plan to the contrary notwithstanding, in the event it shall be determined that any payment, award, benefit or distribution (including, without limitation, the acceleration of any payment, award, distribution or benefit), by the Company or any of its affiliates to or for the benefit of the Executive (whether pursuant to the terms of this Agreement or otherwise) (a “Payment”) would be subject to the excise tax imposed by Section 4999 of the Code or any corresponding provisions of state or local tax law (the “Excise Tax”), then such Payments shall either (a) be delivered in full, or (b) subject to, and in a manner consistent with the requirements of Section 409A of the Code, be reduced to the minimum extent necessary to ensure that no portion thereof will be subject to the Excise Tax, whichever of the foregoing amounts, taking into account the applicable federal, state or local income and employment taxes and the Excise Tax, results in receipt by the Executive, on an after-tax basis, of the greatest amount of payments and benefits, notwithstanding that all or some portion of such payments and benefits may be subject to the Excise Tax. In the event that any Payments are to be reduced pursuant to this Section 12.10, then the reduction shall be applied as follows: (i) first, on a pro rata basis to the Executive’s cash severance payments under Section 5.03 above, and (ii) second, on a pro rata basis to Executive’s equity incentive awards. All determinations required to be made under this Article 12 shall be made by a nationally recognized accounting or consulting firm (other than the regular outside accounting firm retained by the Company) selected by the Company and agreed to by the Executive, which agreement shall not be unreasonably withheld (the “Accounting Firm”), which Accounting Firm shall provide detailed supporting calculations both to the Company and the Executive within 15 business days after the receipt of notice from the Company that the Executive has received a Payment, or such earlier time as is requested by the Company. Any determination by the Accounting Firm meeting the requirements of this Section 12.10 shall be binding upon the Company and the Executive. The fees and disbursements of the Accounting Firm shall be paid by the Company. If required, the Company shall enter into an engagement letter with the Accounting Firm containing reasonable and customary terms and provisions.

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SECTION 12.11. No Third Party Beneficiary. This Agreement will not confer any rights or remedies upon any person other than the Company, the Executive and their respective heirs, executors, successors and assigns.

SECTION 12.12. Entire Agreement. This Agreement (including the documents referred to herein) constitutes the entire agreement among the parties and supersedes any prior understandings, agreements or representations by or among the parties, written or oral, that may have related in any way to the subject matter hereof. This Agreement shall serve as a written statement of employment for purposes of Section 6 of the Bermuda Employment Act 2000.

SECTION 12.13. Construction. The language used in this Agreement will be deemed to be the language chosen by the parties to express their mutual intent, and no rule of strict construction will be applied against any party. Any reference to any federal, state, local or foreign statute or law will be deemed also to refer to all rules and regulations promulgated thereunder, unless the context requires otherwise. The use of the word “including” in this Agreement means including without limitation and is intended by the parties to be by way of example rather than limitation.

SECTION 12.14. Survival. Sections 3.04, 5.03, 5.04, 6.01, 6.02, 7.01, 8.01 and Articles 9, 10, 11 and 12 will survive and continue in full force in accordance with their terms notwithstanding any termination of the Employment Period.

SECTION 12.15. GOVERNING LAW. ALL QUESTIONS CONCERNING THE CONSTRUCTION, VALIDITY AND INTERPRETATION OF THIS AGREEMENT WILL BE GOVERNED BY THE LAW OF BERMUDA, WITHOUT REGARD TO PRINCIPLES OF CONFLICT OF LAWS, SAVE THAT WHERE PROVISIONS OF FOREIGN LAW APPLY IN THIS AGREEMENT, THEY WILL BE INTERPRETED AND CONSTRUED IN ACCORDANCE WITH SUCH FOREIGN LAW.

    SECTION 12.16. Arbitration. Save for where the Company chooses to exercise its rights as described in Section 10.01, any dispute or difference arising out of or relating in any way whatsoever to this Agreement or the subject matter hereof shall be referred to and finally determined by arbitration (the “Arbitration”). The seat, or legal place, of the Arbitration shall be Bermuda. The Arbitration shall be conducted before a sole arbitrator appointed by agreement between the parties or, failing such agreement, by the Appointments’ Committee of the Chartered Institute of Arbitrators Bermuda Branch (the “Arbitrator”). Unless the parties agree otherwise, the Arbitration shall be conducted in accordance with the UNCITRAL rules in force at the time the Arbitration is commenced. The courts of Bermuda (as the supervisory courts of the Arbitration) shall have exclusive jurisdiction to hear and determine any application for relief in aid of the Arbitration (including any application for interim or conservatory measures prior to the appointment of the Arbitrator), except that either party may bring proceedings before any court or other judicial authority of competent jurisdiction for the purposes of enforcing any partial or final award rendered by the Arbitrator hereunder. Each party agrees that it shall maintain confidentiality in respect to the Arbitration (including any
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award or other decision rendered in such Arbitration), except as necessary in connection with a proceeding to enforce the Arbitrator's award or as otherwise required by law. The parties shall bear their respective costs (including attorney’s fees) and shall split the fee of the Arbitrator (50% paid by the Company and 50% by the Executive).

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IN WITNESS WHEREOF, the parties hereto have executed this Agreement on the date in the year first above written.

Arch Capital Group Ltd.
By: /s/ Marc Grandisson    
Name: Marc Grandisson    
Title: Chief Executive Officer    



/s/ Christine Todd    
                        Christine Todd

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Exhibit 15
    

August 5, 2021


Securities and Exchange Commission
100 F Street, N.E.
Washington, DC 20549

Commissioners:

We are aware that our report dated August 5, 2021, on our review of interim financial information of Arch Capital Group Ltd., which appears in this Quarterly Report on Form 10-Q, is incorporated by reference in the Registration Statements on Form S-3 (No. 333-250869) and in the Registration Statements on Form S-8 (Nos. 333-224783, 333-211193, 333-142835, 333-181308 and 333- 203993) of Arch Capital Group Ltd.

Very truly yours,

/s/ PricewaterhouseCoopers LLP


New York, NY



Exhibit 31.1

Certification
of Chief Executive Officer
Pursuant to Section 302 of the
Sarbanes-Oxley Act of 2002
I, Marc Grandisson, certify that:
1.    I have reviewed this quarterly report on Form 10-Q of Arch Capital Group Ltd.;
2.    Based on my knowledge, this report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by this report;
3.    Based on my knowledge, the financial statements, and other financial information included in this report, fairly present in all material respects the financial condition, results of operations and cash flows of the registrant as of, and for, the periods presented in the report;
4.    The registrant’s other certifying officer and I are responsible for establishing and maintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and internal control over financial reporting (as defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) for the registrant and have:
a.    Designed such disclosure controls and procedures, or caused such disclosure controls and procedures to be designed under our supervision, to ensure that material information relating to the registrant, including its consolidated subsidiaries, is made known to us by others within those entities, particularly during the period in which this report is being prepared;
b.    Designed such internal control over financial reporting, or caused such internal control over financial reporting to be designed under our supervision, to provide reasonable assurance regarding the reliability of financial reporting and the preparation of financial statements for external purposes in accordance with generally accepted accounting principles;
c.    Evaluated the effectiveness of the registrant’s disclosure controls and procedures and presented in this report our conclusions about the effectiveness of the disclosure controls and procedures, as of the end of the period covered by this report based on such evaluation; and
d.    Disclosed in this report any change in the registrant’s internal control over financial reporting that occurred during the registrant’s most recent fiscal quarter that has materially affected, or is reasonably likely to materially affect, the registrant’s internal control over financial reporting; and
5.    The registrant’s other certifying officer and I have disclosed, based on our most recent evaluation of internal control over financial reporting, to the registrant’s auditors and the audit committee of the registrant’s board of directors (or persons performing the equivalent functions):
a.    All significant deficiencies and material weaknesses in the design or operation of internal control over financial reporting which are reasonably likely to adversely affect the registrant’s ability to record, process, summarize and report financial information; and
b.    Any fraud, whether or not material, that involves management or other employees who have a significant role in the registrant’s internal control over financial reporting.
Date: August 5, 2021
By: /s/ Marc Grandisson
Name: Marc Grandisson
Title: Chief Executive Officer



Exhibit 31.2

Certification
of Chief Financial Officer
Pursuant to Section 302 of the
Sarbanes-Oxley Act of 2002
I, François Morin, certify that:
1.     I have reviewed this quarterly report on Form 10-Q of Arch Capital Group Ltd.;
2.     Based on my knowledge, this report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by this report;
3.     Based on my knowledge, the financial statements, and other financial information included in this report, fairly present in all material respects the financial condition, results of operations and cash flows of the registrant as of, and for, the periods presented in the report;
4.     The registrant’s other certifying officer and I are responsible for establishing and maintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and internal control over financial reporting (as defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) for the registrant and have:
a.     Designed such disclosure controls and procedures, or caused such disclosure controls and procedures to be designed under our supervision, to ensure that material information relating to the registrant, including its consolidated subsidiaries, is made known to us by others within those entities, particularly during the period in which this report is being prepared;
b.     Designed such internal control over financial reporting, or caused such internal control over financial reporting to be designed under our supervision, to provide reasonable assurance regarding the reliability of financial reporting and the preparation of financial statements for external purposes in accordance with generally accepted accounting principles;
c.     Evaluated the effectiveness of the registrant’s disclosure controls and procedures and presented in this report our conclusions about the effectiveness of the disclosure controls and procedures, as of the end of the period covered by this report based on such evaluation; and
d.     Disclosed in this report any change in the registrant’s internal control over financial reporting that occurred during the registrant’s most recent fiscal quarter that has materially affected, or is reasonably likely to materially affect, the registrant’s internal control over financial reporting; and
5.     The registrant’s other certifying officer and I have disclosed, based on our most recent evaluation of internal control over financial reporting, to the registrant’s auditors and the audit committee of the registrant’s board of directors (or persons performing the equivalent functions):
a.     All significant deficiencies and material weaknesses in the design or operation of internal control over financial reporting which are reasonably likely to adversely affect the registrant’s ability to record, process, summarize and report financial information; and
b.     Any fraud, whether or not material, that involves management or other employees who have a significant role in the registrant’s internal control over financial reporting.
Date: August 5, 2021
By: /s/ François Morin
Name: François Morin
Title: Executive Vice President, Chief Financial Officer and Treasurer

Exhibit 32.1
Certification Pursuant to Chapter 63, Title 18 United States Code §1350
As Adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002
    In connection with the Quarterly Report of Arch Capital Group Ltd. (the “Company”) on Form 10-Q for the period ending June 30, 2021 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), Marc Grandisson, as Chief Executive Officer of the Company, certifies pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:
(1)    the Report fully complies with the requirements of section 13(a) of the Securities Exchange Act of 1934; and
(2)    the information contained in such report fairly presents, in all material respects, the financial condition and results of operations of the Company.
Date: August 5, 2021
By: /s/ Marc Grandisson
Name: Marc Grandisson
Title: Chief Executive Officer
A signed original of this written statement required by Section 906 or other document authenticating, acknowledging or otherwise adopting the signature that appears in typed form within the electronic version of this written statement required by Section 906, has been provided to Arch Capital Group Ltd. and will be retained by Arch Capital Group Ltd. and furnished to the Securities and Exchange Commission or its staff upon request.

Exhibit 32.2

Certification Pursuant to Chapter 63, Title 18 United States Code §1350
As Adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002
    In connection with the Quarterly Report of Arch Capital Group Ltd. (the “Company”) on Form 10-Q for the period ending June 30, 2021 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), François Morin, as Executive Vice President, Chief Financial Officer and Treasurer of the Company, certifies pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:
(1)    the Report fully complies with the requirements of section 13(a) of the Securities Exchange Act of 1934; and
(2)    the information contained in such report fairly presents, in all material respects, the financial condition and results of operations of the Company.
Date: August 5, 2021
By: /s/ François Morin
Name: François Morin
Title: Executive Vice President, Chief Financial Officer and Treasurer
A signed original of this written statement required by Section 906 or other document authenticating, acknowledging or otherwise adopting the signature that appears in typed form within the electronic version of this written statement required by Section 906, has been provided to Arch Capital Group Ltd. and will be retained by Arch Capital Group Ltd. and furnished to the Securities and Exchange Commission or its staff upon request.