0000947484 us-gaap:OtherInvestmentsMember us-gaap:FairValueMeasurementsRecurringMember acgl:FairValueOptionMember 2019-09-30
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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 September 30, 20192020
Or
TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934

Commission file number:  001-16209

 acgl-20200930_g1.jpg
ARCH CAPITAL GROUP LTD.
(Exact name of registrant as specified in its charter)
Bermuda98-0374481
(State or other jurisdiction of incorporation or organization)(I.R.S. Employer Identification No.)
Waterloo House, Ground Floor
100 Pitts Bay Road,PembrokeHM 08,Bermuda(441)278-9250
(Address of principal executive offices)(Registrant’s telephone number, including area code)

Securities registered pursuant to Section 12(b) of the Exchange Act:
Title of each classTrading Symbol (s)Name of each exchange on which registered
Common shares, $0.0011 par value per shareACGLNASDAQ Stock Market
Depositary shares, each representing a 1/100th1000th interest in a 5.25% Series E preferred share
ACGLPNASDAQ Stock Market
Depositary shares, each representing a 1/100th1000th interest in a 5.45% Series F preferred share
ACGLONASDAQ 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 November 1, 2019,October 30, 2020, there were 405,308,162406,026,570 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.
Item 3.
Item 4.
PART II
Item 1.
Item 1A.
72 
Item 1.2.
Item 1A.
Item 2.
Item 3.
Item 4.
Item 5.
Item 6.

ARCH CAPITAL 120192020 THIRD QUARTER FORM 10-Q


PART I.  FINANCIAL INFORMATION
Cautionary Note Regarding Forward-Looking Statements 
The Private Securities Litigation Reform Act of 1995 (“PSLRA”) provides a “safe harbor” for forward-looking statements. This report or any other written or oral statements made by or on behalf of us may include forward-looking statements, which reflect our current views with respect to future events and financial performance. All statements other than statements of historical fact included in or incorporated by reference in this report are forward-looking statements. Forward-looking statements, for purposes of the PSLRA or otherwise, can generally be identified by the use of forward-looking terminology such as “may,” “will,” “expect,” “intend,” “estimate,” “anticipate,” “believe” or “continue” and similar statements of a future or forward-looking nature or their negative or variations or similar terminology.
Forward-looking statements involve our current assessment of risks and uncertainties. Actual events and results may differ materially from those expressed or implied in these statements. Important factors that could cause actual events or results to differ materially from those indicated in such statements are discussed below and elsewhere in this report and in our periodic reports filed with the Securities and Exchange Commission (the “SEC”), and include:
our ability to successfully implement our business strategy during “soft” as well as “hard” markets;
acceptance of our business strategy, security and financial condition by rating agencies and regulators, as well as by brokers and our insureds and reinsureds;
our ability to consummate acquisitions and integrate the integration of any businessesbusiness 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)recession, including those resulting from COVID-19) and conditions specific to the reinsurance and insurance markets (including the length and magnitude of the current “soft” market) 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;
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, which for a relatively new insurance and reinsurance company, like our company, are even more difficult to make than those made in a mature company since relatively limited historical information has been reported to us through September 30, 2019;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;
severity and/or frequency of losses;
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;
acts of terrorism, political unrest and other hostilities or other unforecasted and unpredictable events;
the effect of contagious disease (including COVID-19) on our business;
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;

ARCH CAPITAL 220192020 THIRD QUARTER FORM 10-Q

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our investment performance, including legislative or regulatory developments that may adversely affect the fair value of our investments;
changes in general economic conditions, including new or continued sovereign debt concerns in Eurozone countries 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, 2018,2019, “ITEM 1A—Risk Factors” of this Form 10-Q 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 32020 THIRD QUARTER FORM 10-Q

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ARCH CAPITAL 32019 THIRD QUARTER FORM 10-Q



ITEM 1. CONSOLIDATED FINANCIAL STATEMENTS
Page No.
Page No.
September 30, 20192020 (unaudited) and December 31, 20182019
For the three and nine month periods ended September 30, 2020 and 2019 and 2018 (unaudited)
For the three and nine month periods ended September 30, 2020 and 2019 and 2018 (unaudited)
For the three and nine month periods ended September 30, 2020 and 2019 and 2018 (unaudited)
For the nine month periods ended September 30, 2020 and 2019 and 2018 (unaudited)
Notes to Consolidated Financial Statements (unaudited)


ARCH CAPITAL 420192020 THIRD QUARTER FORM 10-Q


Report of Independent Registered Public Accounting Firm


To theBoard of Directors and Shareholders of Arch Capital Group Ltd.


Results of Review of Interim Financial Statements

We have reviewed the accompanying consolidated balance sheet ofArch Capital Group Ltd. and its subsidiaries(the (the “Company”) as ofSeptember 30, 2019,2020, and the relatedconsolidatedstatements of income, comprehensive income, and changes in shareholders’ equity for the three-month and nine-month periods endedSeptember 30, 2020 and 2019, and2018, and the consolidated statements of cash flows for the nine-month periods ended September 30, 2020 and 2019, and 2018,including the related notes (collectively referred to as the “interim financialstatements”).Based on our reviews, we are not aware of any material modifications that should be made to the accompanying interim financial statementsfor 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 consolidatedbalance sheet of the Company as of December 31, 2018,2019, and the related consolidatedstatements of income, comprehensive income, changes in shareholders’ equity, and cash flowsfor the year then ended (not presented herein), and in our report dated February 28, 2019,2020, 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, 2018,2019, 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 arethe responsibility of the Company’s management.We are a public accounting firm registered with the Public Company Accounting Oversight Board (United States) (PCAOB)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
November 8, 2019

5, 2020
ARCH CAPITAL 520192020 THIRD QUARTER FORM 10-Q


ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED BALANCE SHEETS
ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED BALANCE SHEETS
(U.S. dollars in thousands, except share data)
 (Unaudited)  
 September 30,
2019
 December 31,
2018
Assets 
  
Investments: 
  
Fixed maturities available for sale, at fair value (amortized cost: $16,146,333 and $14,829,902)$16,470,523
 $14,699,010
Short-term investments available for sale, at fair value (amortized cost: $752,207 and $956,238)751,989
 955,880
Collateral received under securities lending, at fair value (amortized cost: $430,255 and $274,125)430,263
 274,133
Equity securities, at fair value550,485
 338,899
Investments accounted for using the fair value option3,838,243
 3,983,571
Investments accounted for using the equity method1,575,832
 1,493,791
Total investments23,617,335
 21,745,284
    
Cash880,099
 646,556
Accrued investment income116,196
 114,641
Securities pledged under securities lending, at fair value (amortized cost: $419,297 and $266,786)420,415
 268,395
Premiums receivable1,618,186
 1,299,150
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses3,168,195
 2,919,372
Contractholder receivables2,094,683
 2,079,111
Ceded unearned premiums1,168,258
 975,469
Deferred acquisition costs622,028
 569,574
Receivable for securities sold50,615
 36,246
Goodwill and intangible assets624,500
 634,920
Other assets1,192,093
 929,611
Total assets$35,572,603
 $32,218,329
    
Liabilities   
Reserve for losses and loss adjustment expenses$12,389,384
 $11,853,297
Unearned premiums4,243,372
 3,753,636
Reinsurance balances payable601,891
 393,107
Contractholder payables2,094,683
 2,079,111
Collateral held for insured obligations205,449
 236,630
Senior notes1,871,386
 1,733,528
Revolving credit agreement borrowings490,720
 455,682
Securities lending payable430,255
 274,125
Payable for securities purchased176,130
 90,034
Other liabilities1,007,524
 911,500
Total liabilities23,510,794
 21,780,650
    
Commitments and Contingencies


 


Redeemable noncontrolling interests48,789
 206,292
    
Shareholders' Equity   
Non-cumulative preferred shares780,000
 780,000
Common shares ($0.0011 par, shares issued: 574,173,205 and 570,737,283)638
 634
Additional paid-in capital1,864,468
 1,793,781
Retained earnings10,705,025
 9,426,299
Accumulated other comprehensive income (loss), net of deferred income tax211,714
 (178,720)
Common shares held in treasury, at cost (shares: 168,942,674 and 168,282,449)(2,403,749) (2,382,167)
Total shareholders' equity available to Arch11,158,096
 9,439,827
Non-redeemable noncontrolling interests854,924
 791,560
Total shareholders' equity12,013,020
 10,231,387
Total liabilities, noncontrolling interests and shareholders' equity$35,572,603
 $32,218,329

(U.S. dollars in thousands, except share dat
a)

(Unaudited)
September 30,
2020
December 31,
2019
Assets  
Investments:  
Fixed maturities available for sale, at fair value (amortized cost: $17,955,515 and $16,598,808; net of allowance for credit losses: $3,933 at September 30, 2020)$18,452,888 $16,894,526 
Short-term investments available for sale, at fair value (amortized cost: $2,038,244 and $957,283; net of allowance for credit losses: $0 at September 30, 2020)2,039,097 956,546 
Collateral received under securities lending, at fair value (amortized cost: $64,251 and $388,366)64,259 388,376 
Equity securities, at fair value1,502,015 838,925 
Investments accounted for using the fair value option3,749,575 3,663,477 
Investments accounted for using the equity method1,883,702 1,660,396 
Total investments27,691,536 24,402,246 
Cash976,398 726,230 
Accrued investment income106,940 117,937 
Securities pledged under securities lending, at fair value (amortized cost: $62,662 and $378,738)62,749 379,868 
Premiums receivable (net of allowance for credit losses: $37,100 and $21,003)2,225,311 1,778,717 
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $13,994 and $1,364)4,621,937 4,346,816 
Contractholder receivables (net of allowance for credit losses: $5,902 and $0)2,185,614 2,119,460 
Ceded unearned premiums1,450,200 1,234,683 
Deferred acquisition costs750,901 633,400 
Receivable for securities sold158,674 24,133 
Goodwill and intangible assets713,777 738,083 
Other assets1,771,998 1,383,788 
Total assets$42,716,035 $37,885,361 
Liabilities
Reserve for losses and loss adjustment expenses$15,900,526 $13,891,842 
Unearned premiums5,062,052 4,339,549 
Reinsurance balances payable873,067 667,072 
Contractholder payables2,191,515 2,119,460 
Collateral held for insured obligations221,957 206,698 
Senior notes2,860,811 1,871,626 
Revolving credit agreement borrowings210,687 484,287 
Securities lending payable64,251 388,366 
Payable for securities purchased382,236 87,579 
Other liabilities1,681,181 1,513,330 
Total liabilities29,448,283 25,569,809 
Commitments and Contingencies
Redeemable noncontrolling interests57,835 55,404 
Shareholders' Equity
Non-cumulative preferred shares780,000 780,000 
Common shares ($0.0011 par, shares issued: 578,024,671 and 574,617,195)642 638 
Additional paid-in capital1,950,782 1,889,683 
Retained earnings11,829,322 11,021,006 
Accumulated other comprehensive income (loss), net of deferred income tax386,357 212,091 
Common shares held in treasury, at cost (shares: 172,005,713 and 168,997,994)(2,495,106)(2,406,047)
Total shareholders' equity available to Arch12,451,997 11,497,371 
Non-redeemable noncontrolling interests757,920 762,777 
Total shareholders' equity13,209,917 12,260,148 
Total liabilities, noncontrolling interests and shareholders' equity$42,716,035 $37,885,361 
See Notes to Consolidated Financial Statements

ARCH CAPITAL620192020 THIRD QUARTER FORM 10-Q


ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF INCOME
(U.S. dollars in thousands, except share data)
 (Unaudited) (Unaudited)
 Three Months Ended Nine Months Ended
 September 30, September 30,
 2019 2018 2019 2018
Revenues 
  
  
  
Net premiums written$1,613,457
 $1,333,553
 $4,583,614
 $4,044,993
Change in unearned premiums(175,434) (42,675) (312,998) (182,453)
Net premiums earned1,438,023
 1,290,878
 4,270,616
 3,862,540
Net investment income161,488
 144,024
 473,475
 406,416
Net realized gains (losses)62,518
 (51,705) 324,889
 (239,314)
        
Other-than-temporary impairment losses(1,163) (492) (2,521) (1,124)
Less investment impairments recognized in other comprehensive income, before taxes
 
 
 
Net impairment losses recognized in earnings(1,163) (492) (2,521) (1,124)
        
Other underwriting income3,326
 5,823
 18,104
 15,046
Equity in net income of investment funds accounted for using the equity method17,130
 15,982
 96,533
 52,523
Other income1,338
 (726) 3,550
 2,461
Total revenues1,682,660
 1,403,784
 5,184,646
 4,098,548
        
Expenses       
Losses and loss adjustment expenses802,455
 699,420
 2,288,530
 2,062,433
Acquisition expenses211,120
 201,602
 619,057
 595,816
Other operating expenses196,512
 161,098
 596,589
 512,294
Corporate expenses17,061
 14,335
 53,274
 52,159
Amortization of intangible assets20,003
 26,315
 60,214
 79,523
Interest expense31,328
 29,730
 89,673
 90,710
Net foreign exchange (gains) losses(33,124) (10,838) (31,697) (44,823)
Total expenses1,245,355
 1,121,662
 3,675,640
 3,348,112
        
Income before income taxes437,305
 282,122
 1,509,006
 750,436
Income tax expense(38,116) (33,356) (128,474) (78,939)
Net income$399,189
 $248,766
 $1,380,532
 $671,497
Net (income) loss attributable to noncontrolling interests(6,736) (21,358) (70,597) (50,020)
Net income available to Arch392,453
 227,408
 1,309,935
 621,477
Preferred dividends(10,403) (10,402) (31,209) (31,242)
Loss on redemption of preferred shares
 
 
 (2,710)
Net income available to Arch common shareholders$382,050
 $217,006
 $1,278,726
 $587,525
        
Net income per common share and common share equivalent 
  
  
  
Basic$0.95
 $0.54
 $3.19
 $1.45
Diluted$0.92
 $0.53
 $3.11
 $1.42
        
Weighted average common shares and common share equivalents outstanding     
  
Basic402,564,121
 402,939,092
 401,419,153
 405,076,228
Diluted413,180,201
 411,721,214
 410,807,402
 413,993,192
CONSOLIDATED STATEMENTS OF INCOME

(U.S. dollars in thousands, except share data)

(Unaudited)(Unaudited)
Three Months EndedNine Months Ended
September 30,September 30,
 2020201920202019
Revenues    
Net premiums written$1,874,144 $1,613,457 $5,679,701 $4,583,614 
Change in unearned premiums(103,052)(175,434)(498,811)(312,998)
Net premiums earned1,771,092 1,438,023 5,180,890 4,270,616 
Net investment income128,512 161,488 405,150 473,475 
Net realized gains (losses)280,499 61,355 470,127 322,368 
Other underwriting income5,413 3,326 18,932 18,104 
Equity in net income (loss) of investment funds accounted for using the equity method126,735 17,130 57,407 96,533 
Other income (loss)919 1,338 6,327 3,550 
Total revenues2,313,170 1,682,660 6,138,833 5,184,646 
Expenses
Losses and loss adjustment expenses1,216,273 802,455 3,562,214 2,288,530 
Acquisition expenses247,942 211,120 750,014 619,057 
Other operating expenses215,686 196,512 659,479 596,589 
Corporate expenses17,937 17,061 56,653 53,274 
Amortization of intangible assets16,715 20,003 49,835 60,214 
Interest expense41,343 31,328 105,037 89,673 
Net foreign exchange (gains) losses44,885 (33,124)11,425 (31,697)
Total expenses1,800,781 1,245,355 5,194,657 3,675,640 
Income (loss) before income taxes512,389 437,305 944,176 1,509,006 
Income tax expense(23,707)(38,116)(77,779)(128,474)
Net income (loss)$488,682 $399,189 $866,397 $1,380,532 
Net (income) loss attributable to noncontrolling interests(69,643)(6,736)(4,420)(70,597)
Net income (loss) available to Arch419,039 392,453 861,977 1,309,935 
Preferred dividends(10,403)(10,403)(31,209)(31,209)
Net income (loss) available to Arch common shareholders$408,636 $382,050 $830,768 $1,278,726 
Net income per common share and common share equivalent    
Basic$1.01 $0.95 $2.06 $3.19 
Diluted$1.00 $0.92 $2.02 $3.11 
Weighted average common shares and common share equivalents outstanding  
Basic402,850,485 402,564,121 403,081,266 401,419,153 
Diluted409,194,657 413,180,201 410,314,897 410,807,402 



See Notes to Consolidated Financial Statements

ARCH CAPITAL720192020 THIRD QUARTER FORM 10-Q


ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME
(U.S. dollars in thousands)
 (Unaudited) (Unaudited)
 Three Months Ended Nine Months Ended
 September 30, September 30,
 2019 2018 2019 2018
Comprehensive Income     
  
Net income$399,189
 $248,766
 $1,380,532
 $671,497
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 period59,290
 (53,308) 507,650
 (305,256)
Reclassification of net realized (gains) losses, net of income taxes, included in net income (loss)(38,743) 23,203
 (104,309) 122,307
Foreign currency translation adjustments(16,424) 2,063
 (6,641) (9,250)
Comprehensive income403,312
 220,724
 1,777,232
 479,298
Net (income) loss attributable to noncontrolling interests(6,736) (21,358) (70,597) (50,020)
Other comprehensive (income) loss attributable to noncontrolling interests764
 1,158
 (6,266) 2,908
Comprehensive income available to Arch$397,340
 $200,524
 $1,700,369
 $432,186
CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME

(U.S. dollars in thousands)

(Unaudited)(Unaudited)
Three Months EndedNine Months Ended
September 30,September 30,
 2020201920202019
Comprehensive Income  
Net income (loss)$488,682 $399,189 $866,397 $1,380,532 
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 period110,782 59,290 546,291 507,650 
Reclassification of net realized (gains) losses, included in net income (loss)(79,803)(38,743)(368,423)(104,309)
Foreign currency translation adjustments16,709 (16,424)(5,729)(6,641)
Comprehensive income (loss)536,370 403,312 1,038,536 1,777,232 
Net (income) loss attributable to noncontrolling interests(69,643)(6,736)(4,420)(70,597)
Other comprehensive (income) loss attributable to noncontrolling interests(10,820)764 2,127 (6,266)
Comprehensive income (loss) available to Arch$455,907 $397,340 $1,036,243 $1,700,369 



See Notes to Consolidated Financial Statements

ARCH CAPITAL820192020 THIRD QUARTER FORM 10-Q


ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF CHANGES IN SHAREHOLDERS’ EQUITY
(U.S. dollars in thousands)
 (Unaudited) (Unaudited)
 Three Months Ended Nine Months Ended
 September 30, September 30,
 2019 2018 2019 2018
Non-cumulative preferred shares     
  
Balance at beginning of period$780,000
 $780,000
 $780,000
 $872,555
Preferred shares redeemed
 
 
 (92,555)
Balance at end of period780,000
 780,000
 780,000
 780,000
        
Convertible non-voting common equivalent preferred shares       
Balance at beginning of period
 
 
 489,627
Preferred shares converted to common shares
 
 
 (489,627)
Balance at end of period
 
 
 
        
Common shares       
Balance at beginning of period638
 633
 634
 611
Common shares issued, net
 
 4
 22
Balance at end of period638
 633
 638
 633
        
Additional paid-in capital     
  
Balance at beginning of period1,847,949
 1,760,606
 1,793,781
 1,230,617
Preferred shares converted to common shares
 
 
 489,608
Other changes16,519

14,893

70,687

55,274
Balance at end of period1,864,468
 1,775,499
 1,864,468
 1,775,499
        
Retained earnings     
  
Balance at beginning of period10,322,975
 9,083,202
 9,426,299
 8,562,889
Cumulative effect of an accounting change
 
 
 149,794
Balance at beginning of period, as adjusted10,322,975
 9,083,202
 9,426,299
 8,712,683
Net income399,189
 248,766
 1,380,532
 671,497
Net (income) loss attributable to noncontrolling interests(6,736) (21,358) (70,597) (50,020)
Preferred share dividends(10,403) (10,402) (31,209) (31,242)
Loss on redemption of preferred shares
 
 
 (2,710)
Balance at end of period10,705,025
 9,300,208
 10,705,025
 9,300,208
        
Accumulated other comprehensive income (loss), net of deferred income tax       
Balance at beginning of period206,827
 (194,157) (178,720) 118,044
Unrealized appreciation (decline) in value of available-for-sale investments, net of deferred income tax:       
Balance at beginning of period261,627
 (143,353) (114,178) 157,400
Cumulative effect of an accounting change
 
 
 (149,794)
Balance at beginning of period, as adjusted261,627
 (143,353) (114,178) 7,606
Unrealized holding gains (losses) during period, net of reclassification adjustment20,547
 (30,105) 403,341
 (182,949)
Unrealized holding gains (losses) during period attributable to noncontrolling interests1,019
 1,238
 (5,970) 3,123
Balance at end of period283,193
 (172,220) 283,193
 (172,220)
Foreign currency translation adjustments, net of deferred income tax:       
Balance at beginning of period(54,800) (50,804) (64,542) (39,356)
Foreign currency translation adjustments(16,424) 2,063
 (6,641) (9,250)
Foreign currency translation adjustments attributable to noncontrolling interests(255) (80) (296) (215)
Balance at end of period(71,479) (48,821) (71,479) (48,821)
Balance at end of period211,714
 (221,041) 211,714
 (221,041)
        
Common shares held in treasury, at cost       
Balance at beginning of period(2,401,037) (2,266,529) (2,382,167) (2,077,741)
Shares repurchased for treasury(2,712) (13,622) (21,582) (202,410)
Balance at end of period(2,403,749) (2,280,151) (2,403,749) (2,280,151)
        
Total shareholders’ equity available to Arch11,158,096
 9,355,148
 11,158,096
 9,355,148
Non-redeemable noncontrolling interests854,924
 876,754
 854,924
 876,754
Total shareholders’ equity$12,013,020
 $10,231,902
 $12,013,020
 $10,231,902
CONSOLIDATED STATEMENTS OF CHANGES IN SHAREHOLDERS’ EQUITY
(U.S. dollars in thousands)
(Unaudited)(Unaudited)
Three Months EndedNine Months Ended
September 30,September 30,
 2020201920202019
Non-cumulative preferred shares  
Balance at beginning and end of period$780,000 $780,000 $780,000 $780,000 
Common shares
Balance at beginning of period642 638 638 634 
Common shares issued, net
Balance at end of period642 638 642 638 
Additional paid-in capital  
Balance at beginning of period1,935,514 1,847,949 1,889,683 1,793,781 
Amortization of share-based compensation14,662 12,775 55,872 52,290 
Other changes606 3,744 5,227 18,397 
Balance at end of period1,950,782 1,864,468 1,950,782 1,864,468 
Retained earnings  
Balance at beginning of period11,420,686 10,322,975 11,021,006 9,426,299 
Cumulative effect of an accounting change (1)(22,452)
Balance at beginning of period, as adjusted11,420,686 10,322,975 10,998,554 9,426,299 
Net income (loss)488,682 399,189 866,397 1,380,532 
Net (income) loss attributable to noncontrolling interests(69,643)(6,736)(4,420)(70,597)
Preferred share dividends(10,403)(10,403)(31,209)(31,209)
Balance at end of period11,829,322 10,705,025 11,829,322 10,705,025 
Accumulated other comprehensive income (loss), net of deferred income tax
Balance at beginning of period349,488 206,827 212,091 (178,720)
Unrealized appreciation (decline) in value of available-for-sale investments, net of deferred income tax:
Balance at beginning of period418,487 261,627 258,486 (114,178)
Unrealized holding gains (losses) during period, net of reclassification adjustment30,979 20,547 177,868 403,341 
Unrealized holding gains (losses) during period attributable to noncontrolling interests(11,179)1,019 1,933 (5,970)
Balance at end of period438,287 283,193 438,287 283,193 
Foreign currency translation adjustments, net of deferred income tax:
Balance at beginning of period(68,999)(54,800)(46,395)(64,542)
Foreign currency translation adjustments16,709 (16,424)(5,729)(6,641)
Foreign currency translation adjustments attributable to noncontrolling interests360 (255)194 (296)
Balance at end of period(51,930)(71,479)(51,930)(71,479)
Balance at end of period386,357 211,714 386,357 211,714 
Common shares held in treasury, at cost
Balance at beginning of period(2,494,505)(2,401,037)(2,406,047)(2,382,167)
Shares repurchased for treasury(601)(2,712)(89,059)(21,582)
Balance at end of period(2,495,106)(2,403,749)(2,495,106)(2,403,749)
Total shareholders’ equity available to Arch12,451,997 11,158,096 12,451,997 11,158,096 
Non-redeemable noncontrolling interests757,920 854,924 757,920 854,924 
Total shareholders’ equity$13,209,917 $12,013,020 $13,209,917 $12,013,020 

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

See Notes to Consolidated Financial Statements

ARCH CAPITAL920192020 THIRD QUARTER FORM 10-Q


ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF CASH FLOWS
(U.S. dollars in thousands)
 (Unaudited)
 Nine Months Ended
 September 30,
 2019 2018
Operating Activities 
  
Net income$1,380,532
 $671,497
Adjustments to reconcile net income to net cash provided by operating activities:   
Net realized (gains) losses(329,053) 224,757
Net impairment losses recognized in earnings2,521
 1,124
Equity in net income or loss of investment funds accounted for using the equity method and other income or loss(38,912) 6,357
Amortization of intangible assets60,214
 79,523
Share-based compensation54,432
 45,806
Changes in:   
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable377,074
 68,245
Unearned premiums, net of ceded unearned premiums312,998
 182,453
Premiums receivable(328,765) (203,247)
Deferred acquisition costs(38,606) (36,074)
Reinsurance balances payable214,902
 83,696
Other items, net(124,198) (3,150)
Net cash provided by (used for) operating activities1,543,139
 1,120,987
Investing Activities 
  
Purchases of fixed maturity investments(24,010,623) (24,837,917)
Purchases of equity securities(524,051) (819,342)
Purchases of other investments(1,014,925) (1,543,332)
Proceeds from sales of fixed maturity investments22,707,854
 23,310,203
Proceeds from sales of equity securities371,130
 866,919
Proceeds from sales, redemptions and maturities of other investments827,517
 1,178,035
Proceeds from redemptions and maturities of fixed maturity investments394,719
 724,021
Net settlements of derivative instruments92,423
 765
Net sales of short-term investments129,078
 554,315
Change in cash collateral related to securities lending6,990
 137,073
Purchases of fixed assets(27,635) (19,050)
Other(202,953) 58,227
Net cash provided by (used for) investing activities(1,250,476) (390,083)
Financing Activities 
  
Redemption of preferred shares
 (92,555)
Purchases of common shares under share repurchase program(2,871) (184,529)
Proceeds from common shares issued, net518
 (12,029)
Proceeds from borrowings200,083
 167,259
Repayments of borrowings(27,538) (427,000)
Change in cash collateral related to securities lending(6,990) (137,073)
Change in third party investment in redeemable noncontrolling interests(161,874) 
Dividends paid to redeemable noncontrolling interests(11,408) (13,491)
Other(5,207) (6,084)
Preferred dividends paid(31,209) (31,242)
Net cash provided by (used for) financing activities(46,496) (736,744)
    
Effects of exchange rate changes on foreign currency cash and restricted cash(8,335) (11,625)
    
Increase (decrease) in cash and restricted cash237,832
 (17,465)
Cash and restricted cash, beginning of year724,643
 727,284
Cash and restricted cash, end of period$962,475
 $709,819


ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF CASH FLOWS
(U.S. dollars in thousands)
(Unaudited)
Nine Months Ended
September 30,
 20202019
Operating Activities  
Net income (loss)$866,397 $1,380,532 
Adjustments to reconcile net income (loss) to net cash provided by operating activities:
Net realized (gains) losses(477,683)(326,532)
Equity in net income or loss of investment funds accounted for using the equity method and other income or loss30,306 (38,912)
Amortization of intangible assets49,835 60,214 
Share-based compensation56,433 54,432 
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable1,668,069 377,074 
Unearned premiums, net of ceded unearned premiums498,811 312,998 
Premiums receivable(461,766)(328,765)
Deferred acquisition costs(107,238)(38,606)
Reinsurance balances payable205,620 214,902 
Other items, net2,666 (124,198)
Net cash provided by (used for) operating activities2,331,450 1,543,139 
Investing Activities  
Purchases of fixed maturity investments(34,050,883)(24,010,623)
Purchases of equity securities(1,355,848)(524,051)
Purchases of other investments(841,886)(1,014,925)
Proceeds from sales of fixed maturity investments32,544,867 22,707,854 
Proceeds from sales of equity securities731,793 371,130 
Proceeds from sales, redemptions and maturities of other investments791,807 827,517 
Proceeds from redemptions and maturities of fixed maturity investments645,292 394,719 
Net settlements of derivative instruments163,290 92,423 
Net (purchases) sales of short-term investments(1,159,351)129,078 
Change in cash collateral related to securities lending81,210 6,990 
Purchases of fixed assets(26,717)(27,635)
Other(131,992)(202,953)
Net cash provided by (used for) investing activities(2,608,418)(1,250,476)
Financing Activities  
Purchases of common shares under share repurchase program(75,486)(2,871)
Proceeds from common shares issued, net(9,656)518 
Proceeds from borrowings1,018,793 200,083 
Repayments of borrowings(304,000)(27,538)
Change in cash collateral related to securities lending(81,210)(6,990)
Third party investment in non-redeemable noncontrolling interests(2,867)
Change in third party investment in redeemable noncontrolling interests(161,874)
Dividends paid to redeemable noncontrolling interests(3,541)(11,408)
Other55,266 (5,207)
Preferred dividends paid(31,209)(31,209)
Net cash provided by (used for) financing activities566,090 (46,496)
Effects of exchange rate changes on foreign currency cash and restricted cash(5,847)(8,335)
Increase (decrease) in cash and restricted cash283,275 237,832 
Cash and restricted cash, beginning of year903,698 724,643 
Cash and restricted cash, end of period$1,186,973 $962,475 

See Notes to Consolidated Financial Statements

ARCH CAPITAL1020192020 THIRD QUARTER FORM 10-Q

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

1.    Basis of Presentation and Recent Accounting Pronouncements

General
Arch Capital Group Ltd. (“Arch Capital”) is a Bermuda public limited liability company which provides insurance, reinsurance and mortgage insurance on a worldwide basis through its wholly-owned subsidiaries. As used herein, the “Company” means Arch Capital and its subsidiaries. The Company’s consolidated financial statements include 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.
On January 1, 2019, the Company’s U.K. insurance operations entered into a transaction with The Ardonagh Group to acquire renewal rights for a U.K. commercial lines book of business, consisting of commercial property, casualty, motor, professional liability, personal accident and travel business.
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, 20182019 (“20182019 Form 10-K”), including the Company’s audited consolidated financial statements and related notes.
The Company has reclassified the presentation of certain prior year information to conform to the current presentation. Such reclassifications had no effect on the Company’s net income, comprehensive income, shareholders’ equity or cash flows. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.
Recent Accounting Pronouncements
Recently Issued Accounting Standards Adopted
The Company adopted ASU 2016-02, “Leases2018-13, “Fair Value Measurement (Topic 842)”, which provides a new comprehensive model820): Disclosure Framework - Changes to the Disclosure Requirements for lease accounting. Topic 842 requires a lessee to recognize a liability to make lease payments (the lease liability) and a right-of-use asset representing its right to useFair Value Measurement.” The ASU modifies the underlying asset for the lease term. The Company adopted the modified retrospective approach of this standard, that resulted in the recognition of a right-of-use asset of  $147.9 milliondisclosure requirements on fair value measurement as part of other assets and a lease liabilitythe disclosure framework project with the objective to improve the effectiveness of $163.6 million as part of other liabilitiesdisclosures in the consolidated balance sheet as of January 1, 2019. The Company de-recognized the liability for deferred rent that was required under the previous guidance.
In addition, the Company adopted ASU 2018-11, “Leases: Targeted Improvements (Topic 842),” which provides an additional (optional) transition method to adopt the new lease standard. The Company adopted the alternative transition method and elected to utilize a cumulative-effect adjustmentnotes to the opening balancefinancial statements. The amendments in this update allow for removal of (1) the amount and reasons for transfer between Level 1 and Level 2 of the retained earnings for the year of adoption. As such, the Company’s reporting for the comparative periods prior to the adoption continue to be presented in the financial statements in accordance with previous lease accounting guidance. The Company also adopted the practical expedients as a package which allows the Company to not reassess (1) whether any expired or existing contracts are or contain leasesfair value hierarchy; (2) the lease classificationpolicy for any expired or existing leasestransfers between levels; and (3) initial direct coststhe valuation processes for any existing leases and (4) to account for the lease and non lease components as a single lease component. In addition to electing the practical expedients as a package, the Company elected to include hindsight to determine the lease term of existing leases, and made an accounting policy election to not apply the recognition requirements to short-term leases (lease term of less than twelve months). The cumulative effect adjustment to the opening balance of retained earnings was 0.Level 3 fair value measurements. The adoption of the updatedthis guidance did not have a material effect on the Company’s results of operations or liquidity.consolidated financial statements.
The Company adopted ASU 2018-07 “Improvements to Nonemployee Share-Based Payment Accounting,2018-15, “Intangibles - Goodwill and Other - Internal Use Software (Subtopic 350-40).which was issuedThis ASU aligns the requirements for capitalizing certain implementation costs incurred in June 2018 to simplify the accounting for share-based payments granted to nonemployees for goods and services. Under this ASU, most of the guidance on such payments to nonemployees would be aligneda cloud computing arrangement that is a service contract with the requirements for share-based payments grantedcapitalizing implementation costs incurred to employees.develop or obtain internal-use software. The guidance provides flexibility in adoption, allowing for either retrospective adjustment or prospective adjustment for all implementation costs incurred after the date of adoption. The Company adopted this guidance prospectively. The adoption of this guidance did not have a material effect on the Company’s consolidated financial statements.
In March 2020, the SEC amended Rule 3-10 of Regulation S-X regarding financial disclosure requirements for registered debt offerings involving subsidiaries as either issuers or guarantors and affiliates whose securities are pledged as collateral. This new guidance narrows the circumstances that require separate financial statements of subsidiary issuers and guarantors and streamlines the alternative disclosures required in lieu of those statements. The amendment is effective on January 4, 2021 with early adoption permitted. The Company elected to apply the amended requirements for the quarter ended March 31, 2020, and is no longer providing condensed consolidating financial information that resulted from the registered debt obligations of its subsidiaries, Arch Capital Group (U.S.) Inc. and Arch Capital Finance LLC., that were disclosed in Note 26 of the financial statements in the Company’s 2019 Form 10-K.
The Company adopted ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326).” The ASU is effectiveapplies a new credit loss model (current expected credit losses) for reporting periods beginning after December 15,determining credit related impairments for financial instruments measured at amortized cost, including reinsurance recoverable, contractholder receivables, and premiums receivable, and

ARCH CAPITAL 1120192020 THIRD QUARTER FORM 10-Q

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

2018. This guidancerequires an entity to estimate its lifetime “expected credit loss” and record an allowance that, when deducted from the adoptionamortized cost basis of this provision did not have a material effectthe financial asset, presents the net amount expected to be collected on the Company's financial asset. The estimate of expected credit losses should consider historical information, current information, as well as reasonable and supportable forecasts, including estimates of prepayments.
The ASU also amends the previous other-than-temporary impairment model for available-for-sale debt securities by requiring the recognition of impairments relating to credit losses through an allowance account and limits the amount of credit loss to the difference between a security’s amortized cost basis and its fair value. In addition, the length of time a security has been in an unrealized loss position resultswill no longer impact the determination of operations or cash flows.

whether a credit loss exists.
The Company adopted the ASU 2018-02 “Income Statement-Reporting Comprehensive Income (Topic 220) - Reclassificationfor the quarter ending March 31, 2020 by recognizing an after-tax cumulative effect adjustment of Certain Tax Effects from Accumulated Other Comprehensive Income,” which was issued in February 2018$22.5 million to allow the reclassificationopening balance of retained earnings as of January 1, 2020. The cumulative effect adjustment decreased retained earnings and increased the allowance for credit losses.
Significant Accounting Policies
The following accounting policies have been updated to reflect the Company's adoption of the stranded tax effectsnew accounting guidance on credit losses.
Investments
The Company conducts a periodic review to identify and evaluate credit based impairments related to the Company’s available for sale investments. The Company derives estimated credit losses by comparing expected future cash flows to be collected to the amortized cost of the security. Estimates of expected future cash flows consider among other things, macroeconomic conditions as well as the financial condition, near-term and long-term prospects for the issuer, and the likelihood of the recoverability of principal and interest. Effective January 1, 2020, credit losses are recognized through an allowance account subject to reversal, rather than a reduction in accumulatedamortized cost. Declines in value attributable to factors other than credit are reported in other comprehensive income (“AOCI”) resulting fromwhile the Tax Cuts and Jobs Act of 2017 (“Tax Cuts Act”)allowance for credit loss is charged to net realized gains (losses). Current guidance requires
For available for sale investments that the effect of a changeCompany intends to sell or for which it is more likely than not that the Company would be required to sell before an anticipated recovery in tax laws or rates on deferred tax balances to be reported in income from continuing operations invalue, the accounting period that includes the period of enactment, even if the related income tax effects were originally charged or credited directly to AOCI. Thefull amount of the reclassification would include the effectimpairment is included in net realized gains (losses). The new cost basis of the changeinvestment is the previous amortized cost basis reduced by the impairment recognized in net realized gains (losses). The new cost basis is not adjusted for any subsequent recoveries in fair value.
The Company reports accrued investment income separately from investment balances and has elected not to measure an allowance for credit losses for accrued investment income. Any uncollectible accrued interest income is written off in the U.S. federal corporate income tax rateperiod it is deemed uncollectible.
Reinsurance Recoverables
In the normal course of business, the Company’s subsidiaries cede a portion of their premium and losses through pro rata and excess of loss reinsurance agreements on a treaty or facultative basis. Reinsurance recoverables are recorded as assets, predicated on the gross deferred taxreinsurers’ ability to meet their obligations under the reinsurance agreements. In certain instances, the Company obtains collateral, including letters of credit and trust accounts to further reduce the credit exposure on its reinsurance recoverables. The Company reports its reinsurance recoverables net of an allowance for expected credit loss. The allowance is based upon the Company’s ongoing review of amounts outstanding, the financial condition of its reinsurers, amounts and related valuation allowances, if any, atform of collateral obtained and other relevant factors. A ratings based probability-of-default and loss-given-default methodology is used to estimate the dateallowance for expected credit loss. Any allowance for credit losses is charged to net realized gains (losses) in the period the recoverable is recorded and revised in subsequent periods to reflect changes in the Company’s estimate of expected credit losses.
Contractholder Receivables
Certain insurance policies written by the Company’s U.S. insurance operations feature large deductibles, primarily in its construction and national accounts line of business. Under such contracts, the Company is obligated to pay the claimant for the full amount of the enactmentclaim. The Company is subsequently reimbursed by the policy holder for the deductible amount. These amounts are included on a gross basis in the consolidated balance sheet as contractholder payables and contractholder receivables. In the event that the Company is unable to collect from the policyholder, the Company would be liable for such defaulted amounts. Collateral, primarily in the form of letters of credit, cash and trusts, is obtained from the policyholder to mitigate the Company’s credit risk.
Contractholder receivables are reported net of an allowance for expected credit losses. The allowance is based upon the Company’s ongoing review of amounts outstanding, changes in policyholder credit standing, amounts and form of collateral obtained, and other relevant factors. A ratings based probability-of-default and loss-given-default methodology is used to estimate the allowance for expected credit losses. Any allowance for credit losses is charged to net realized gains (losses) in the period the receivable is
ARCH CAPITAL 122020 THIRD QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
recorded and revised in subsequent periods to reflect changes in the Company’s estimate of expected credit losses.
Premiums Receivable
Premiums receivable include amounts receivable from agents, brokers and insured that are both currently due and amounts not yet due on insurance, reinsurance and mortgage insurance policies. Premiums receivable balances are reported net of an allowance for expected credit losses. The Company monitors credit risk associated with premiums receivable through its ongoing review of amounts outstanding, aging of the Tax Cuts Actreceivable, historical loss data, and counterparty financial strength measures. The allowance also includes estimated uncollectible amounts related to itemsdispute risk. In certain instances, credit risk may be reduced by the Company’s right to offset loss obligations or unearned premiums against premiums receivable. Any allowance for credit losses is charged to net realized gains (losses) in AOCI.the period the receivable is recorded and revised in subsequent periods to reflect changes in the Company’s estimate of expected credit losses.
Recently Issued Accounting Standards Not Yet Adopted
In December 2019, the FASB issued ASU 2019-12, “Simplifying the Accounting for Income Taxes.” This ASU eliminates certain exceptions for recognizing deferred taxes for investments, performing intraperiod tax allocation and calculating income taxes in interim periods. The updated guidanceASU also clarifies the accounting for transactions that result in a step-up in the tax basis of goodwill. The ASU is effective for reporting periodsfiscal years beginning after December 15, 2018 and is to be applied retrospectively to each period in which the effect of the Tax Cuts Act related to items remaining in AOCI are recognized or at the beginning of the period of adoption. The adoption of this ASU did not have a material effect on the Company’s results of operations, financial position or liquidity.

The Company adopted ASU 2017-08 “Receivables - Nonrefundable Fees and Other Costs (Subtopic 310-20), Premium Amortization on Purchased Callable Debt Securities,” which was issued in March, 2017. This ASU shortens the amortization period for certain callable debt securities held at a premium and requires the premium to be amortized to the earliest call date. However, the new guidance does not require an accounting change for securities held at a discount whose discount continues to be amortized to maturity. The standard is effective for financial statements issued for fiscal years,2020 and interim periods within those fiscal years beginning after December 15, 2018, with early adoption permitted. The adoptionCompany is currently evaluating the impact of the new guidance requires a modified retrospective approach with a cumulative-effect adjustmenton its consolidated financial statements and does not expect this guidance to retained earnings. The adoption of this ASU did not have a material effect on the Company’s consolidated financial statements.

In March 2020, the FASB issued ASU 2020-04, “Facilitation of the Effects of Reference Rate Reform on Financial Reporting.” This ASU provides optional expedients and exceptions for applying GAAP to investments, derivatives, or other transactions that reference the London Interbank Offered Rate (LIBOR) or another reference rate expected to be discontinued because of reference rate reform. Along with the optional expedients, the amendments include a general principle that permits an entity to consider contract modifications due to reference reform to be an event that does not require contract re-measurement at the modification date or reassessment of a previous accounting determination. This standard may be elected over time through December 31, 2022 as reference rate reform activities occur. The Company is currently evaluating the impact of the new guidance on its consolidated financial statements and does
Recently Issued Accounting Standards Not Yet Adopted
not expect this guidance to 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(q)3(r), “Significant Accounting Policies—Recent Accounting Pronouncements,” of the notes to consolidated financial statements in the Company’s 20182019 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 386.3388.9 million common shares for an aggregate purchase price of $3.97$4.04 billion. For the nine months ended September 30, 2019,2020, Arch Capital repurchased 2.6 million shares under the share repurchase program with an aggregate purchase price of $75.5 million. Arch Capital repurchased 0.1 million shares under the share repurchase program with an aggregate purchase price of $2.9 million. Arch Capital repurchased 6.9 million shares under the share repurchase program with an aggregate purchase price of $184.5 million during the nine months ended September 30, 2018.2019. At September 30, 2019, $160.92020, $924.5 million of share repurchases were available under the program, which may be effected from time to time in open market or privately negotiated transactions.transactions through December 31, 2021. The timing and amount of the repurchase transactions under this program will depend on a variety of factors, including market conditions and corporate and regulatory considerations. (see note 16).
Conversion Depending upon results of Convertible Non-Voting Common Equivalent Preferred Shares
In March 2018,operations, market conditions and the development of the economy, as well as other factors, generally Arch Capital completedwill consider share repurchases on an underwritten public secondary offering of 17.0 million common shares (split adjusted) by American International Group, Inc. (“AIG”) following transfer of 0.6 million Series D convertible non-voting common equivalent preferred shares (“Series D Preferred Shares”). Proceedsopportunistic basis from time to time. During the sale of common shares pursuant to the public offering were received by AIG. At September 30, 2019, no Series D Preferred Shares were outstanding.
Series C Preferred Shares
On January 2, 2018,2020 third quarter, Arch Capital redeemed all outstanding 6.75% Series C non-cumulative preferred shares. The preferredhas not repurchased any shares were redeemed at a redemption price equal to $25 perunder our share plus all declared and unpaid dividends to (but excluding) the redemption date. In accordance with GAAP, following the redemption, original issuance costs related to such shares were removed from additional paid-in capital and recorded as a “loss on redemption of preferred shares.” Such adjustment had no impact on total shareholders’ equity or cash flows.repurchase program.


ARCH CAPITAL 121320192020 THIRD QUARTER FORM 10-Q

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

3.    Earnings Per Common Share

The following table sets forth the computation of basic and diluted earnings per common share:
Three Months EndedNine Months Ended
September 30,September 30,
 2020201920202019
Numerator:
Net income (loss)$488,682 $399,189 $866,397 $1,380,532 
Amounts attributable to noncontrolling interests(69,643)(6,736)(4,420)(70,597)
Net income (loss) available to Arch419,039 392,453 861,977 1,309,935 
Preferred dividends(10,403)(10,403)(31,209)(31,209)
Net income (loss) available to Arch common shareholders$408,636 $382,050 $830,768 $1,278,726 
Denominator:
Weighted average common shares and common share equivalents outstanding — basic402,850,485 402,564,121 403,081,266 401,419,153 
Effect of dilutive common share equivalents:
Nonvested restricted shares1,580,791 1,895,972 1,690,447 1,637,015 
Stock options (1)4,763,381 8,720,108 5,543,184 7,751,234 
Weighted average common shares and common share equivalents outstanding — diluted409,194,657 413,180,201 410,314,897 410,807,402 
Earnings per common share:
Basic$1.01 $0.95 $2.06 $3.19 
Diluted$1.00 $0.92 $2.02 $3.11 
 Three Months Ended
Nine Months Ended
 September 30, September 30,
 2019 2018 2019 2018
Numerator:       
Net income$399,189
 $248,766
 $1,380,532
 $671,497
Amounts attributable to noncontrolling interests(6,736) (21,358) (70,597) (50,020)
Net income available to Arch392,453
 227,408
 1,309,935
 621,477
Preferred dividends(10,403) (10,402) (31,209) (31,242)
Loss on redemption of preferred shares
 
 
 (2,710)
Net income available to Arch common shareholders$382,050
 $217,006
 $1,278,726
 $587,525
        
Denominator:       
Weighted average common shares outstanding402,564,121
 402,939,092
 401,419,153
 400,649,105
Series D preferred shares (1)
 
 
 4,427,123
Weighted average common shares and common share equivalents outstanding — basic402,564,121
 402,939,092
 401,419,153
 405,076,228
Effect of dilutive common share equivalents:       
Nonvested restricted shares1,895,972
 1,619,286
 1,637,015
 1,568,044
Stock options (2)8,720,108
 7,162,836
 7,751,234
 7,348,920
Weighted average common shares and common share equivalents outstanding — diluted413,180,201
 411,721,214
 410,807,402
 413,993,192
        
Earnings per common share:       
Basic$0.95
 $0.54
 $3.19
 $1.45
Diluted$0.92
 $0.53
 $3.11
 $1.42
(1)
Such shares are convertible non-voting common equivalent preferred shares issued in connection with the UGC acquisition. See note 2.
(2)Certain stock options were not included in the computation of diluted earnings per share where the exercise price of the stock options exceeded the average market price and would have been anti-dilutive or where, when applying the treasury stock method to in-the-money options, the sum of the proceeds, including unrecognized compensation, exceeded the average market price and would have been anti-dilutive. For the 2019 third quarter and 2018 third quarter, the number of stock options excluded were 37,394 and 4,396,352,(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 2020 third quarter and 2019 third quarter, the number of stock options excluded were 4,713,241 and 37,394, respectively. For the nine months ended September 30, 2020 and 2019 period, the number of stock options excluded were 2,361,413 and 2,198,115, respectively. For the nine months ended September 30, 2019 and 2018 period, the number of stock options excluded were 2,198,115 and 5,481,584, respectively.

ARCH CAPITAL 131420192020 THIRD QUARTER FORM 10-Q

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

4.    Segment Information

The Company classifies its businesses into 3 underwriting segments — insurance, reinsurance and mortgage — and 2 other operating segments — ‘other’ and corporate (non-underwriting). The Company determined its reportable segments using the management approach described in accounting guidance regarding disclosures about segments of an enterprise and related information. The accounting policies of the segments are the same as those used for the preparation of the Company’s consolidated financial statements. Intersegment business is allocated to the segment accountable for the underwriting results.
The Company’s insurance, reinsurance and mortgage segments each have managers who are responsible for the overall profitability of their respective segments and who are directly accountable to the Company’s chief operating decision makers, the President and Chief Executive Officer of Arch Capital, and the Chief Financial 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.
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 includedrecognized in earnings,earnings), equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses and income taxes. Such amounts exclude the results of the ‘other’ segment.
The ‘other’ segment includes the results of Watford (see note 11). For the ‘other’ segment, performance is measured based on net income or loss.

ARCH CAPITAL 141520192020 THIRD QUARTER FORM 10-Q

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

The following tables summarize the Company’s underwriting income or loss by segment, together with a reconciliation of underwriting income or loss to net income available to Arch common shareholders:
Three Months Ended
September 30, 2020
 InsuranceReinsuranceMortgageSub-TotalOtherTotal
Gross premiums written (1)$1,206,328 $1,004,590 $346,248 $2,556,914 $197,480 $2,681,032 
Premiums ceded(382,167)(400,388)(47,783)(830,086)(50,164)(806,888)
Net premiums written824,161 604,202 298,465 1,726,828 147,316 1,874,144 
Change in unearned premiums(105,007)(49,704)52,944 (101,767)(1,285)(103,052)
Net premiums earned719,154 554,498 351,409 1,625,061 146,031 1,771,092 
Other underwriting income (loss)(31)298 4,600 4,867 546 5,413 
Losses and loss adjustment expenses(525,321)(422,084)(153,055)(1,100,460)(115,813)(1,216,273)
Acquisition expenses(102,420)(85,388)(35,716)(223,524)(24,418)(247,942)
Other operating expenses(122,541)(41,818)(36,708)(201,067)(14,619)(215,686)
Underwriting income (loss)$(31,159)$5,506 $130,530 104,877 (8,273)96,604 
Net investment income99,857 28,655 128,512 
Net realized gains (losses)210,984 69,515 280,499 
Equity in net income (loss) of investment funds accounted for using the equity method126,735 126,735 
Other income (loss)919 919 
Corporate expenses (2)(16,263)(16,263)
Transaction costs and other (2)(1,674)(1,674)
Amortization of intangible assets(16,715)(16,715)
Interest expense(36,224)(5,119)(41,343)
Net foreign exchange gains (losses)(38,681)(6,204)(44,885)
Income (loss) before income taxes433,815 78,574 512,389 
Income tax (expense) benefit(23,638)(69)(23,707)
Net income (loss)410,177 78,505 488,682 
Amounts attributable to redeemable noncontrolling interests(882)(993)(1,875)
Amounts attributable to nonredeemable noncontrolling interests(67,768)(67,768)
Net income (loss) available to Arch409,295 9,744 419,039 
Preferred dividends(10,403)(10,403)
Net income (loss) available to Arch common shareholders$398,892 $9,744 $408,636 
Underwriting Ratios
Loss ratio73.0 %76.1 %43.6 %67.7 %79.3 %68.7 %
Acquisition expense ratio14.2 %15.4 %10.2 %13.8 %16.7 %14.0 %
Other operating expense ratio17.0 %7.5 %10.4 %12.4 %10.0 %12.2 %
Combined ratio104.2 %99.0 %64.2 %93.9 %106.0 %94.9 %
Goodwill and intangible assets$282,146 $20,319 $403,662 $706,127 $7,650 $713,777 
 Three Months Ended
 September 30, 2019
 Insurance Reinsurance Mortgage Sub-Total Other Total
            
Gross premiums written (1)$1,005,874
 $662,572
 $375,092
 $2,043,292
 $249,960
 $2,181,121
Premiums ceded(302,034) (226,096) (57,703) (585,587) (94,208) (567,664)
Net premiums written703,840
 436,476
 317,389
 1,457,705
 155,752
 1,613,457
Change in unearned premiums(98,504) (72,621) 25,611
 (145,514) (29,920) (175,434)
Net premiums earned605,336
 363,855
 343,000
 1,312,191
 125,832
 1,438,023
Other underwriting income (loss)
 (1,208) 3,955
 2,747
 579
 3,326
Losses and loss adjustment expenses(422,782) (270,379) (13,080) (706,241) (96,214) (802,455)
Acquisition expenses(91,259) (62,393) (34,396) (188,048) (23,072) (211,120)
Other operating expenses(115,408) (32,533) (37,003) (184,944) (11,568) (196,512)
Underwriting income (loss)$(24,113) $(2,658) $262,476
 235,705
 (4,443) 231,262
            
Net investment income      126,874
 34,614
 161,488
Net realized gains (losses)      81,177
 (18,659) 62,518
Net impairment losses recognized in earnings      (1,163) 
 (1,163)
Equity in net income (loss) of investment funds accounted for using the equity method      17,130
 
 17,130
Other income (loss)      1,338
 
 1,338
Corporate expenses (2)      (15,066) 
 (15,066)
Transaction costs and other (2)      (1,995) 
 (1,995)
Amortization of intangible assets      (20,003) 
 (20,003)
Interest expense      (23,237) (8,091) (31,328)
Net foreign exchange gains (losses)      29,794
 3,330
 33,124
Income before income taxes      430,554
 6,751
 437,305
Income tax expense      (38,116) 
 (38,116)
Net income      392,438
 6,751
 399,189
Dividends attributable to redeemable noncontrolling interests      
 (6,600) (6,600)
Amounts attributable to nonredeemable noncontrolling interests      
 (136) (136)
Net income available to Arch      392,438
 15
 392,453
Preferred dividends      (10,403) 
 (10,403)
Net income available to Arch common shareholders      $382,035
 $15
 $382,050
            
Underwriting Ratios 
  
  
    
  
Loss ratio69.8% 74.3% 3.8% 53.8% 76.5% 55.8%
Acquisition expense ratio15.1% 17.1% 10.0% 14.3% 18.3% 14.7%
Other operating expense ratio19.1% 8.9% 10.8% 14.1% 9.2% 13.7%
Combined ratio104.0% 100.3% 24.6% 82.2% 104.0% 84.2%
            
Goodwill and intangible assets$158,990
 $
 $457,860
 $616,850
 $7,650
 $624,500
(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.’

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


ARCH CAPITAL 151620192020 THIRD QUARTER FORM 10-Q

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

Three Months Ended
September 30, 2019
 InsuranceReinsuranceMortgageSub-TotalOtherTotal
Gross premiums written (1)$1,005,874 $662,572 $375,092 $2,043,292 $249,960 $2,181,121 
Premiums ceded(302,034)(226,096)(57,703)(585,587)(94,208)(567,664)
Net premiums written703,840 436,476 317,389 1,457,705 155,752 1,613,457 
Change in unearned premiums(98,504)(72,621)25,611 (145,514)(29,920)(175,434)
Net premiums earned605,336 363,855 343,000 1,312,191 125,832 1,438,023 
Other underwriting income (loss)(1,208)3,955 2,747 579 3,326 
Losses and loss adjustment expenses(422,782)(270,379)(13,080)(706,241)(96,214)(802,455)
Acquisition expenses(91,259)(62,393)(34,396)(188,048)(23,072)(211,120)
Other operating expenses(115,408)(32,533)(37,003)(184,944)(11,568)(196,512)
Underwriting income (loss)$(24,113)$(2,658)$262,476 235,705 (4,443)231,262 
Net investment income126,874 34,614 161,488 
Net realized gains (losses)80,014 (18,659)61,355 
Equity in net income (loss) of investment funds accounted for using the equity method17,130 17,130 
Other income (loss)1,338 1,338 
Corporate expenses (2)(15,066)(15,066)
Transaction costs and other (2)(1,995)(1,995)
Amortization of intangible assets(20,003)(20,003)
Interest expense(23,237)(8,091)(31,328)
Net foreign exchange gains (losses)29,794 3,330 33,124 
Income (loss) before income taxes430,554 6,751 437,305 
Income tax (expense) benefit(38,116)(38,116)
Net income (loss)392,438 6,751 399,189 
Amounts attributable to redeemable noncontrolling interests(6,600)(6,600)
Amounts attributable to nonredeemable noncontrolling interests(136)(136)
Net income (loss) available to Arch392,438 15 392,453 
Preferred dividends(10,403)(10,403)
Net income (loss) available to Arch common shareholders$382,035 $15 $382,050 
Underwriting Ratios     
Loss ratio69.8 %74.3 %3.8 %53.8 %76.5 %55.8 %
Acquisition expense ratio15.1 %17.1 %10.0 %14.3 %18.3 %14.7 %
Other operating expense ratio19.1 %8.9 %10.8 %14.1 %9.2 %13.7 %
Combined ratio104.0 %100.3 %24.6 %82.2 %104.0 %84.2 %
Goodwill and intangible assets$158,990 $$457,860 $616,850 $7,650 $624,500 

 Three Months Ended
 September 30, 2018
 Insurance Reinsurance Mortgage Sub-Total Other Total
            
Gross premiums written (1)$836,820
 $435,396
 $350,559
 $1,622,532
 $185,033
 $1,731,328
Premiums ceded(259,968) (123,705) (57,226) (440,656) (33,356) (397,775)
Net premiums written576,852
 311,691
 293,333
 1,181,876
 151,677
 1,333,553
Change in unearned premiums(15,794) (18,418) 7,591
 (26,621) (16,054) (42,675)
Net premiums earned561,058
 293,273
 300,924
 1,155,255
 135,623
 1,290,878
Other underwriting income (loss)
 1,387
 3,733
 5,120
 703
 5,823
Losses and loss adjustment expenses(409,435) (183,413) (9,615) (602,463) (96,957) (699,420)
Acquisition expenses(88,255) (50,367) (33,361) (171,983) (29,619) (201,602)
Other operating expenses(90,081) (29,936) (31,122) (151,139) (9,959) (161,098)
Underwriting income (loss)$(26,713) $30,944
 $230,559
 234,790
 (209) 234,581
            
Net investment income      114,328
 29,696
 144,024
Net realized gains (losses)      (47,010) (4,695) (51,705)
Net impairment losses recognized in earnings      (492) 
 (492)
Equity in net income (loss) of investment funds accounted for using the equity method      15,982
 
 15,982
Other income (loss)      (726) 
 (726)
Corporate expenses (2)      (13,244) 
 (13,244)
Transaction costs and other (2)      (1,091) 
 (1,091)
Amortization of intangible assets      (26,315) 
 (26,315)
Interest expense      (24,666) (5,064) (29,730)
Net foreign exchange gains (losses)      7,130
 3,708
 10,838
Income before income taxes      258,686
 23,436
 282,122
Income tax expense      (33,356) 
 (33,356)
Net income      225,330
 23,436
 248,766
Dividends attributable to redeemable noncontrolling interests      
 (4,599) (4,599)
Amounts attributable to nonredeemable noncontrolling interests      
 (16,759) (16,759)
Net income available to Arch      225,330
 2,078
 227,408
Preferred dividends      (10,402) 
 (10,402)
Net income available to Arch common shareholders      $214,928
 $2,078
 $217,006
            
Underwriting Ratios 
  
  
    
  
Loss ratio73.0% 62.5% 3.2% 52.1% 71.5% 54.2%
Acquisition expense ratio15.7% 17.2% 11.1% 14.9% 21.8% 15.6%
Other operating expense ratio16.1% 10.2% 10.3% 13.1% 7.3% 12.5%
Combined ratio104.8% 89.9% 24.6% 80.1% 100.6% 82.3%
            
Goodwill and intangible assets$20,141
 $
 $538,871
 $559,012
 $7,650
 $566,662
(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.

(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)(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’




ARCH CAPITAL 161720192020 THIRD QUARTER FORM 10-Q

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

Nine Months Ended
September 30, 2020
 InsuranceReinsuranceMortgageSub-TotalOtherTotal
Gross premiums written (1)$3,444,335 $2,934,174 $1,084,337 $7,461,860 $590,309 $7,831,554 
Premiums ceded(1,119,165)(967,698)(136,154)(2,222,031)(150,437)(2,151,853)
Net premiums written2,325,170 1,966,476 948,183 5,239,829 439,872 5,679,701 
Change in unearned premiums(202,188)(388,321)113,965 (476,544)(22,267)(498,811)
Net premiums earned2,122,982 1,578,155 1,062,148 4,763,285 417,605 5,180,890 
Other underwriting income (loss)(31)1,767 15,649 17,385 1,547 18,932 
Losses and loss adjustment expenses(1,550,632)(1,235,586)(444,721)(3,230,939)(331,275)(3,562,214)
Acquisition expenses(317,428)(255,516)(108,304)(681,248)(68,766)(750,014)
Other operating expenses(370,947)(125,831)(120,178)(616,956)(42,523)(659,479)
Underwriting income (loss)$(116,056)$(37,011)$404,594 251,527 (23,412)228,115 
Net investment income313,916 91,234 405,150 
Net realized gains (losses)523,964 (53,837)470,127 
Equity in net income (loss) of investment funds accounted for using the equity method57,407 57,407 
Other income (loss)6,327 6,327 
Corporate expenses (2)(51,407)(51,407)
Transaction costs and other (2)(5,246)(5,246)
Amortization of intangible assets(49,835)(49,835)
Interest expense(86,599)(18,438)(105,037)
Net foreign exchange gains (losses)(17,812)6,387 (11,425)
Income (loss) before income taxes942,242 1,934 944,176 
Income tax (expense) benefit(78,112)333 (77,779)
Net income (loss)864,130 2,267 866,397 
Dividends attributable to redeemable noncontrolling interests(1,873)(3,125)(4,998)
Amounts attributable to nonredeemable noncontrolling interests578 578 
Net income (loss) available to Arch862,257 (280)861,977 
Preferred dividends(31,209)(31,209)
Net income (loss) available to Arch common shareholders$831,048 $(280)$830,768 
Underwriting Ratios     
Loss ratio73.0 %78.3 %41.9 %67.8 %79.3 %68.8 %
Acquisition expense ratio15.0 %16.2 %10.2 %14.3 %16.5 %14.5 %
Other operating expense ratio17.5 %8.0 %11.3 %13.0 %10.2 %12.7 %
Combined ratio105.5 %102.5 %63.4 %95.1 %106.0 %96.0 %
(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.
 Nine Months Ended
 September 30, 2019
 Insurance Reinsurance Mortgage Sub-Total Other Total
            
Gross premiums written (1)$2,867,753
 $1,890,974
 $1,095,607
 $5,853,574
 $598,627
 $6,196,809
Premiums ceded(914,751) (627,120) (149,358) (1,690,469) (178,118) (1,613,195)
Net premiums written1,953,002
 1,263,854
 946,249
 4,163,105
 420,509
 4,583,614
Change in unearned premiums(201,719) (186,450) 72,436
 (315,733) 2,735
 (312,998)
Net premiums earned1,751,283
 1,077,404
 1,018,685
 3,847,372
 423,244
 4,270,616
Other underwriting income (loss)
 4,393
 11,867
 16,260
 1,844
 18,104
Losses and loss adjustment expenses(1,168,677) (751,147) (50,226) (1,970,050) (318,480) (2,288,530)
Acquisition expenses(265,177) (173,504) (98,722) (537,403) (81,654) (619,057)
Other operating expenses(338,327) (102,197) (116,697) (557,221) (39,368) (596,589)
Underwriting income (loss)$(20,898) $54,949
 $764,907
 798,958
 (14,414) 784,544
            
Net investment income      371,161
 102,314
 473,475
Net realized gains (losses)      318,722
 6,167
 324,889
Net impairment losses recognized in earnings      (2,521) 
 (2,521)
Equity in net income (loss) of investment funds accounted for using the equity method      96,533
 
 96,533
Other income (loss)      3,550
 
 3,550
Corporate expenses (2)      (47,911) 
 (47,911)
Transaction costs and other (2)      (5,363) 
 (5,363)
Amortization of intangible assets      (60,214) 
 (60,214)
Interest expense      (70,094) (19,579) (89,673)
Net foreign exchange gains (losses)      28,779
 2,918
 31,697
Income before income taxes      1,431,600
 77,406
 1,509,006
Income tax expense      (128,454) (20) (128,474)
Net income      1,303,146
 77,386
 1,380,532
Dividends attributable to redeemable noncontrolling interests ��    
 (15,778) (15,778)
Amounts attributable to nonredeemable noncontrolling interests      
 (54,819) (54,819)
Net income available to Arch      1,303,146
 6,789
 1,309,935
Preferred dividends      (31,209) 
 (31,209)
Net income available to Arch common shareholders      $1,271,937
 $6,789
 $1,278,726
            
Underwriting Ratios 
  
  
    
  
Loss ratio66.7% 69.7% 4.9% 51.2% 75.2% 53.6%
Acquisition expense ratio15.1% 16.1% 9.7% 14.0% 19.3% 14.5%
Other operating expense ratio19.3% 9.5% 11.5% 14.5% 9.3% 14.0%
Combined ratio101.1% 95.3% 26.1% 79.7% 103.8% 82.1%
(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)(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’


ARCH CAPITAL 171820192020 THIRD QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
Nine Months Ended
September 30, 2019
 InsuranceReinsuranceMortgageSub-TotalOtherTotal
Gross premiums written (1)$2,867,753 $1,890,974 $1,095,607 $5,853,574 $598,627 $6,196,809 
Premiums ceded(914,751)(627,120)(149,358)(1,690,469)(178,118)(1,613,195)
Net premiums written1,953,002 1,263,854 946,249 4,163,105 420,509 4,583,614 
Change in unearned premiums(201,719)(186,450)72,436 (315,733)2,735 (312,998)
Net premiums earned1,751,283 1,077,404 1,018,685 3,847,372 423,244 4,270,616 
Other underwriting income (loss)4,393 11,867 16,260 1,844 18,104 
Losses and loss adjustment expenses(1,168,677)(751,147)(50,226)(1,970,050)(318,480)(2,288,530)
Acquisition expenses(265,177)(173,504)(98,722)(537,403)(81,654)(619,057)
Other operating expenses(338,327)(102,197)(116,697)(557,221)(39,368)(596,589)
Underwriting income (loss)$(20,898)$54,949 $764,907 798,958 (14,414)784,544 
Net investment income371,161 102,314 473,475 
Net realized gains (losses)316,201 6,167 322,368 
Equity in net income (loss) of investment funds accounted for using the equity method96,533 96,533 
Other income (loss)3,550 3,550 
Corporate expenses (2)(47,911)(47,911)
Transaction costs and other (2)(5,363)(5,363)
Amortization of intangible assets(60,214)(60,214)
Interest expense(70,094)(19,579)(89,673)
Net foreign exchange gains (losses)28,779 2,918 31,697 
Income (loss) before income taxes1,431,600 77,406 1,509,006 
Income tax (expense) benefit(128,454)(20)(128,474)
Net income (loss)1,303,146 77,386 1,380,532 
Dividends attributable to redeemable noncontrolling interests(15,778)(15,778)
Amounts attributable to nonredeemable noncontrolling interests(54,819)(54,819)
Net income (loss) available to Arch1,303,146 6,789 1,309,935 
Preferred dividends(31,209)(31,209)
Net income (loss) available to Arch common shareholders$1,271,937 $6,789 $1,278,726 
Underwriting Ratios     
Loss ratio66.7 %69.7 %4.9 %51.2 %75.2 %53.6 %
Acquisition expense ratio15.1 %16.1 %9.7 %14.0 %19.3 %14.5 %
Other operating expense ratio19.3 %9.5 %11.5 %14.5 %9.3 %14.0 %
Combined ratio101.1 %95.3 %26.1 %79.7 %103.8 %82.1 %

(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.’



 Nine Months Ended
 September 30, 2018
 Insurance Reinsurance Mortgage Sub-Total Other Total
            
Gross premiums written (1)$2,429,570
 $1,503,206
 $1,002,727
 $4,935,339
 $574,078
 $5,266,086
Premiums ceded(752,413) (455,682) (154,230) (1,362,161) (102,263) (1,221,093)
Net premiums written1,677,157
 1,047,524
 848,497
 3,573,178
 471,815
 4,044,993
Change in unearned premiums(30,913) (134,761) 23,147
 (142,527) (39,926) (182,453)
Net premiums earned1,646,244
 912,763
 871,644
 3,430,651
 431,889
 3,862,540
Other underwriting income (loss)
 2,490
 10,464
 12,954
 2,092
 15,046
Losses and loss adjustment expenses(1,120,630) (555,044) (74,672) (1,750,346) (312,087) (2,062,433)
Acquisition expenses(264,094) (148,828) (87,665) (500,587) (95,229) (595,816)
Other operating expenses(274,735) (101,185) (108,622) (484,542) (27,752) (512,294)
Underwriting income (loss)$(13,215) $110,196
 $611,149
 708,130
 (1,087) 707,043
            
Net investment income      322,332
 84,084
 406,416
Net realized gains (losses)      (218,414) (20,900) (239,314)
Net impairment losses recognized in earnings      (1,124) 
 (1,124)
Equity in net income (loss) of investment funds accounted for using the equity method      52,523
 
 52,523
Other income (loss)      2,461
 
 2,461
Corporate expenses (2)      (43,330) 
 (43,330)
Transaction costs and other (2)      (8,829) 
 (8,829)
Amortization of intangible assets      (79,523) 
 (79,523)
Interest expense      (76,631) (14,079) (90,710)
Net foreign exchange gains (losses)      38,302
 6,521
 44,823
Income before income taxes      695,897
 54,539
 750,436
Income tax expense      (78,912) (27) (78,939)
Net income      616,985
 54,512
 671,497
Dividends attributable to redeemable noncontrolling interests      
 (13,769) (13,769)
Amounts attributable to nonredeemable noncontrolling interests      
 (36,251) (36,251)
Net income available to Arch      616,985
 4,492
 621,477
Preferred dividends      (31,242) 
 (31,242)
Loss on redemption of preferred shares      (2,710) 
 (2,710)
Net income available to Arch common shareholders      $583,033
 $4,492
 $587,525
            
Underwriting Ratios 
  
  
    
  
Loss ratio68.1% 60.8% 8.6% 51.0% 72.3% 53.4%
Acquisition expense ratio16.0% 16.3% 10.1% 14.6% 22.0% 15.4%
Other operating expense ratio16.7% 11.1% 12.5% 14.1% 6.4% 13.3%
Combined ratio100.8% 88.2% 31.2% 79.7% 100.7% 82.1%

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




ARCH CAPITAL 181920192020 THIRD QUARTER FORM 10-Q

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

5.    Reserve for Losses and Loss Adjustment Expenses

The following table represents an analysis of losses and loss adjustment expenses and a reconciliation of the beginning and ending reserve for losses and loss adjustment expenses:
Three Months EndedNine Months Ended
September 30,September 30,
2020201920202019
Reserve for losses and loss adjustment expenses at beginning of period$15,044,874 $12,230,316 $13,891,842 $11,853,297 
Unpaid losses and loss adjustment expenses recoverable4,156,157 3,024,797 4,082,650 2,814,291 
Net reserve for losses and loss adjustment expenses at beginning of period10,888,717 9,205,519 9,809,192 9,039,006 
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year1,264,315 855,352 3,673,346 2,419,044 
Prior years(48,042)(52,897)(111,132)(130,514)
Total net incurred losses and loss adjustment expenses1,216,273 802,455 3,562,214 2,288,530 
Retroactive reinsurance transactions (1)60,635 (225,500)
Net foreign exchange (gains) losses114,122 (73,200)22,706 (74,981)
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year(189,961)(175,611)(359,395)(301,099)
Prior years(512,263)(399,948)(1,578,464)(1,366,741)
Total net paid losses and loss adjustment expenses(702,224)(575,559)(1,937,859)(1,667,840)
Net reserve for losses and loss adjustment expenses at end of period11,516,888 9,359,215 11,516,888 9,359,215 
Unpaid losses and loss adjustment expenses recoverable4,383,638 3,030,169 4,383,638 3,030,169 
Reserve for losses and loss adjustment expenses at end of period$15,900,526 $12,389,384 $15,900,526 $12,389,384 
 Three Months Ended Nine Months Ended
 September 30, September 30,
 2019 2018 2019 2018
Reserve for losses and loss adjustment expenses at beginning of period$12,230,316
 $11,424,337
 $11,853,297
 $11,383,792
Unpaid losses and loss adjustment expenses recoverable3,024,797
 2,651,749
 2,814,291
 2,464,910
Net reserve for losses and loss adjustment expenses at beginning of period9,205,519
 8,772,588
 9,039,006
 8,918,882
        
Net incurred losses and loss adjustment expenses relating to losses occurring in:       
Current year855,352
 779,043
 2,419,044
 2,257,670
Prior years(52,897) (79,623) (130,514) (195,237)
Total net incurred losses and loss adjustment expenses802,455
 699,420
 2,288,530
 2,062,433
        
Retroactive reinsurance transactions (1)
 
 (225,500) (420,404)
        
Net foreign exchange (gains) losses(73,200) (33,783) (74,981) (110,061)
        
Net paid losses and loss adjustment expenses relating to losses occurring in:       
Current year(175,611) (149,999) (301,099) (245,021)
Prior years(399,948) (396,695) (1,366,741) (1,314,298)
Total net paid losses and loss adjustment expenses(575,559) (546,694) (1,667,840) (1,559,319)
        
Net reserve for losses and loss adjustment expenses at end of period9,359,215
 8,891,531
 9,359,215
 8,891,531
Unpaid losses and loss adjustment expenses recoverable3,030,169
 2,662,790
 3,030,169
 2,662,790
Reserve for losses and loss adjustment expenses at end of period$12,389,384
 $11,554,321
 $12,389,384
 $11,554,321
(1)     During 2020 first quarter, a subsidiary of the Company entered into a reinsurance to close agreement of the 2017 and prior years of account previously covered by a third party arrangement, while in the 2019 first quarter, a subsidiary of the Company entered into a retroactive reinsurance transaction with third party reinsurer to reinsure run-off liabilities associated with certain U.S. insurance exposures.

(1)During the 2019 first quarter and 2018 second quarter, a subsidiary of the Company entered into two separate retroactive reinsurance transactions with third party reinsurers to reinsure run-off liabilities associated with certain U.S. insurance exposures.
Development on Prior Year Loss Reserves

2020 Third Quarter

During the 2020 third quarter, the Company recorded net favorable development on prior year loss reserves of $48.0 million, which consisted of $2.3 million from the insurance segment, $42.0 million from the reinsurance segment, $4.5 million from the mortgage segment, partially offset by $0.7 million unfavorable from the ‘other’ segment.
The insurance segment’s net favorable development of $2.3 million, or 0.3 loss ratio points, for the 2020 third quarter consisted of $12.9 million of net favorable development in short-tailed and long-tailed lines and $10.6 million of net adverse development in medium-tailed lines. Net favorable development of $11.8 million in short-tailed lines reflected $8.0 million of favorable development from property (excluding marine), primarily from the 2015 to 2018 accident years (i.e., the year in which a loss occurred) and $3.4 million of favorable development in travel and accident, primarily from the 2019 accident year. Net favorable development of $1.1 million in long-tailed lines reflected $8.7 million of
favorable development in construction and national accounts, primarily from the 2018 accident year, and $4.2 million of favorable development related to other business, including alternative markets and excess workers’ compensation, primarily from the 2013 to 2017 accident years, partially offset by $11.7 million of adverse development in executive assurance and casualty, primarily from the 2015 and 2019 accident year. Net adverse development in medium-tailed lines included $7.1 million of adverse development in program business, primarily from 2015 to 2018 accident years and $3.7 million of adverse development in contract binding, across all accident years.

The reinsurance segment’s net favorable development of $42.0 million, or 7.6 loss ratio points, for the 2020 third quarter consisted of $45.6 million of net favorable development in short-tailed and medium-tailed lines and net adverse development of $3.6 million from long-tailed lines. Net favorable development in short-tailed lines reflected $27.6 million of favorable development related to property catastrophe and property other than property catastrophe business, primarily from the 2016 to 2019 underwriting years
ARCH CAPITAL 202020 THIRD QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
(i.e., all premiums and losses attributable to contracts having an inception or renewal date within the given twelve-month period), and $7.8 million of favorable development from other specialty, primarily from the 2016 to 2019 underwriting years. Net favorable development of $9.4 million in medium-tailed lines reflected favorable development in marine and aviation across most underwriting years. Adverse development of $3.6 million in long-tailed lines reflected an increase in reserves from casualty, primarily from the 2012 to 2019 underwriting years.

The mortgage segment’s net favorable development was $4.5 million, or 1.3 loss ratio points, for the 2020 third quarter, primarily driven by subrogation recoveries on second lien business and student loan business.
2019 Third Quarter

During the 2019 third quarter, the Company recorded net favorable development on prior year loss reserves of $52.9 million, which consisted of $4.4 million of favorable development from the insurance segment, $15.3 million from the reinsurance segment, $33.0 million from the mortgage segment and $0.2 million from the ‘other’ segment.
The insurance segment’s net favorable development of $4.4 million, or 0.7 loss ratio points, for the 2019 third quarter consisted of $24.8 million of net favorable development in short-tailed lines and $20.4 million of net adverse development in medium-tailed and long-tailed lines. Net favorable development in short-tailed lines primarily resulted from lenders products and property (including special risk other than marine) reserves across all accident years (i.e.(i.e., the year in which a loss occurred). Net adverse development in medium-tailed and long-tailed lines included $6.3 million of adverse development in executive assurance reserves, primarily from the 2016 to 2018 accident years, $4.9 million of adverse development onin casualty reserves, primarily related to contract
binding business across most accident years, $4.2 million of adverse development onin program business, primarily from the 2018 accident year, and $3.8 million in healthcare reserves, primarily from the 2016 to 2018 accident years.
The reinsurance segment’s net favorable development of $15.3 million, or 4.2 loss ratio points, for the 2019 third quarter consisted of $35.2 million of net favorable development from short-tailed and medium-tailed lines and net adverse development of $19.9 million from long-tailed lines. Net favorable development in short-tailed and medium lines reflected $26.5 million of favorable development from property catastrophe and property other than property catastrophe reserves, primarily related to 2017 and 2018 catastrophic events, and favorable development onin marine and aviation and other reserves across most underwriting years (i.e.(i.e., all premiums and losses attributable to contracts having
an inception or renewal date within the given twelve-month period). Adverse development in long-tailed lines reflected an increase in reserves from casualty from various underwriting years.
The mortgage segment’s net favorable development was $33.0 million, or 9.6 loss ratio points, for the 2019 third quarter. The 2019 third quarter development was primarily driven by

ARCH CAPITAL 192019 THIRD QUARTER FORM 10-Q

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

continued favorable claim rates on first lien business and subrogation recoveries on second lien and student loan business.
2018 Third QuarterNine Months Ended September 30, 2020
During the 2018 third quarter,nine months ended September 30, 2020, the Company recorded net favorable development on prior year loss reserves of $79.6$111.1 million, which consisted of $5.9 million from the insurance segment, $34.3$93.8 million from the reinsurance segment, $38.6$10.8 million from the mortgage segment and $0.7$0.6 million from the ‘other’ segment.
The insurance segment’s net favorable development of $5.9 million, or 1.10.3 loss ratio points, for the 2018 third quarter2020 period consisted of $14.3$41.6 million of net favorable development in short-tailed and long-tailed lines, and $8.4partially offset by $35.7 million of net adverse development in medium-tailed and long-tailed lines. Net favorable development of $27.2 million in short-tailed lines primarily resultedreflected $17.5 million of favorable development from property (including special risk other than(excluding marine) reserves from the 2017 accident year (i.e., the year in which a loss occurred) while net adverse development in medium-tailed and long-tailed lines primarily resulted from $16.4 million of adverse development on contract binding business, primarily from the 2015 to 2018 accident years, $6.2 million of favorable development on travel and accident, primarily from 2019 accident year, and $3.5 million of favorable development in lenders products, primarily from the 2018 and 2019 accident years. Net favorable development of $14.4 million in long-tailed lines included $11.7 million of favorable development related to other business, including alternative markets and excess workers’ compensation, primarily from the 2013 to 2017 accident years. Such amounts were partially offset by $8.0Net adverse development in medium-tailed lines reflected $23.0 million of net favorableadverse development in other medium-tailed and short-tailed lines, including professional liability and suretycontract binding business, across mostall accident years, and $13.5 million of adverse development in program business, primarily from the 2016 to 2018 accident years.
The reinsurance segment’s net favorable development of $34.3$93.8 million, or 11.75.9 loss ratio points, for the 2018 third quarter2020 period consisted of $26.5$113.0 million of net favorable development from short-tailed and medium-tailed lines, and $7.8partially offset by $19.2 million of net adverse development from long-tailed and medium-tailed lines. FavorableNet favorable development of $101.8 million in short-tailed lines included $15.9reflected $52.1 million fromrelated to property catastrophe and property other than property catastrophe reserves, across mostbusiness, primarily from the 2016 to 2019 underwriting years, (i.e., all premiums and losses attributable to contracts having an inception or renewal date within the given twelve-month period), reflecting lower levels of reported and paid claims activity than previously anticipated which led to decreases in certain loss ratio selections during the period, and $10.3$47.1 million from other specialty lines, across most underwriting years. Adverse development in long-tailed lines of $19.2 million reflected an increase in reserves from casualty, primarily from the 20162012 to 2015 underwriting year. Favorable development in long-tailed and medium-tailed lines reflected reductions in casualty reservesyears.
ARCH CAPITAL 212020 THIRD QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
The mortgage segment’s net favorable development was $38.6$10.8 million, or 12.81.0 loss ratio points, for the 2018 third quarter. The 2018 third quarter development was2020 period, primarily driven by lower than expected claim rates on first lien business and subrogation recoveries on second lien business and student loan business.
Nine Months Ended September 30, 2019

During the nine months ended September 30, 2019, the Company recorded net favorable development on prior year
loss reserves of $130.5 million, which consisted of $11.4 million from the insurance segment, $26.3 million from the reinsurance segment, $92.5 million from the mortgage segment and $0.3 million from the ‘other’ segment.
The insurance segment’s net favorable development of $11.4 million, or 0.7 loss ratio points, for the 2019 period consisted of $42.6 million of net favorable development in short-tailed lines, partially offset by $31.2 million of net adverse development in medium-tailed and long-tailed lines. Net favorable development in short-tailed lines primarily resulted from lenders products and property (including special risk other than marine) reserves across all accident years, partially offset by net adverse development in travel business, primarily from the 2018 accident year. Net adverse development in medium-tailed and long-tailed lines reflected $27.4 million of adverse development in program business, primarily from the 2018 accident year, and $12.8 million of adverse development onin casualty business, primarily from contract binding business across most accident years. Such amounts were partially offset by $9.0 million of net favorable development in other medium-tailed and long-tailed lines, including professional liability, marine and surety business, across most accident years.
The reinsurance segment’s net favorable development of $26.3 million, or 2.4 loss ratio points, for the 2019 period consisted of $37.1 million of net favorable development from short-tailed and medium-tailed lines, offset by $10.8 million of net adverse development from long-tailed lines. Net favorable development in short-tailed lines reflected $22.6 million from other specialty lines and $9.5 million from property catastrophe reserves. Favorable development in medium-tailed lines reflected reductions in marine and aviation reserves of $10.4 million across most underwriting years.
The mortgage segment’s net favorable development was $92.5 million, or 9.1 loss ratio points, for the 2019 period. The 2019 development was primarily driven by continued lower than expected claim rates on first lien business and subrogation recoveries on second lien 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:
September 30, 2020
Premium Receivables, Net of AllowanceAllowance for Expected Credit Losses
Three Months Ended
Balance at beginning of period$2,203,753 $36,054 
Cumulative effect of accounting change (1)
Change for provision of expected credit losses (2)1,046 
Balance at end of period$2,225,311 $37,100 
Nine Months Ended
Balance at beginning of period$1,778,717 $21,003 
Cumulative effect of accounting change (1)6,539 
Change for provision of expected credit losses (2)9,558 
Balance at end of period$2,225,311 $37,100 
Nine Months Ended September 30, 2018(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)” See note 1.

During(2) Amounts deemed uncollectible are written-off in operating expenses. For the 2020 third quarter and nine months ended September 30, 2018, the Company recorded net favorable development on prior year loss reserves of $195.2 million, which consisted of $14.1 million from the insurance segment, $103.9 million from the reinsurance segment, $74.9 million from the mortgage segment2020, amounts written off totaled NaN and $2.3 million, from the ‘other’ segment.
The insurance segment’s net favorable development of $14.1 million, or 0.9 loss ratio points, for the 2018 period consisted of $37.0 million of net favorable development in short-tailed lines and $16.4 million of net favorable development in long-tailed lines, partially offset by $39.3 million of net adverse development in medium-tailed lines. Net favorable development in short-tailed lines primarily resulted fromrespectively.

ARCH CAPITAL 202220192020 THIRD QUARTER FORM 10-Q

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

property (including special risk other than marine) reserves from the 2010 and 2017 accident years. Net favorable development in long-tailed lines reflected net reductions in executive assurance reserves of $8.0 million, primarily from the 2008 accident year, and in healthcare reserves of $8.1 million, primarily from the 2003 accident year. Net adverse development in medium-tailed lines reflected $23.4 million of adverse development in program business, primarily driven by a few inactive programs that were non-renewed in prior periods and $42.1 million of adverse development on contract binding business, primarily from the 2014 to 2017 accident years. Such amounts were partially offset by $26.2 million of net favorable development in other medium-tailed lines, including professional liability and surety business, across most accident years.
The reinsurance segment’s net favorable development of $103.9 million, or 11.4 loss ratio points, for the 2018 period consisted of $77.6 million from short-tailed lines and $26.3 million from long-tailed and medium-tailed lines. Favorable development in short-tailed lines included $56.4 million from property catastrophe and property other than property catastrophe reserves, across most underwriting years, reflecting lower levels of reported and paid claims activity than previously anticipated which led to decreases in certain loss ratio selections during the period, and $10.7 million from other specialty reserves, across most underwriting years. Favorable development in long-tailed and medium-tailed lines reflected reductions in casualty reserves of $16.0 million based on varying levels of reported and paid claims activity, primarily from the 2002 to 2010 underwriting years, and favorable development in marine reserves of $10.8 million across most underwriting years.Reinsurance Recoverables
The mortgage segment’s net favorable developmentfollowing table provides a roll forward of the allowance for expected credit losses of the Company’s reinsurance recoverables:
September 30, 2020
Reinsurance Recoverables, Net of AllowanceAllowance for Expected Credit Losses
Three Months Ended
Balance at beginning of period$4,363,507 $13,595 
Cumulative effect of accounting change (1)
Change for provision of expected credit losses399 
Balance at end of period$4,621,937 $13,994 
Nine Months Ended
Balance at beginning of period$4,346,816 $1,364 
Cumulative effect of accounting change (1)12,010 
Change for provision of expected credit losses620 
Balance at end of period$4,621,937 $13,994 
(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)” See note 1.
At September 30, 2020 and December 31, 2019, approximately 63.2% and 61.2% of reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums) of $4.64 billion and $4.35 billion, respectively, were due from carriers which had an A.M. Best rating of “A-” or better while 36.6% and 38.8%, respectively, were from companies not rated. For items not rated, over 90% of such amount was $74.9 million,collateralized through reinsurance trusts or 8.6 loss ratio points,letters of credit at September 30, 2020 and December 31, 2019. The largest reinsurance recoverables from any one carrier were approximately 1.8% and 1.7%, of total shareholders’ equity available to Arch at September 30, 2020 and December 31, 2019, respectively.
Contractholder Receivables
The following table provides a roll forward of the allowance for expected credit losses of the 2018 period. The 2018 development was primarily driven by lower than expected claim rates on first lien business and subrogation recoveries on second lien business.Company’s contractholder receivables:
September 30, 2020
Contractholder Receivables, Net of AllowanceAllowance for Expected Credit Losses
Three Months Ended
Balance at beginning of period$2,179,124 $6,290 
Cumulative effect of accounting change (1)
Change for provision of expected credit losses(389)
Balance at end of period$2,185,614 $5,901 
Nine Months Ended
Balance at beginning of period$2,119,460 $
Cumulative effect of accounting change (1)6,663 
Change for provision of expected credit losses(762)
Balance at end of period$2,185,614 $5,901 
(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)” See note 1.


ARCH CAPITAL 212320192020 THIRD QUARTER FORM 10-Q

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

6.7.    Investment Information


At September 30, 2019,2020, total investable assets of $24.30$28.42 billion included $21.57$25.72 billion held by the Company and $2.73$2.69 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
September 30, 2020
Fixed maturities (1):
Corporate bonds$7,965,599 $390,839 $(40,448)$(1,742)$7,616,950 
Mortgage backed securities717,081 12,456 (3,373)(336)708,334 
Municipal bonds527,410 26,980 (877)(62)501,369 
Commercial mortgage backed securities374,360 8,523 (4,660)(256)370,753 
U.S. government and government agencies4,861,349 39,350 (4,396)4,826,395 
Non-U.S. government securities2,302,646 86,996 (18,294)2,233,944 
Asset backed securities1,767,192 30,026 (21,729)(1,537)1,760,432 
Total18,515,637 595,170 (93,777)(3,933)18,018,177 
Short-term investments2,039,097 1,807 (954)2,038,244 
Total$20,554,734 $596,977 $(94,731)$(3,933)$20,056,421 
December 31, 2019
Fixed maturities (1):
Corporate bonds$6,406,591 $191,889 $(12,793)$6,227,495 
Mortgage backed securities562,309 9,669 (931)553,571 
Municipal bonds881,926 24,628 (2,213)859,511 
Commercial mortgage backed securities733,108 14,951 (2,330)720,487 
U.S. government and government agencies4,916,592 36,600 (10,134)4,890,126 
Non-U.S. government securities2,078,757 48,549 (20,330)2,050,538 
Asset backed securities1,683,753 24,017 (4,724)1,664,460 
Total17,263,036 350,303 (53,455)16,966,188 
Short-term investments956,546 811 (1,548)957,283 
Total$18,219,582 $351,114 $(55,003)$17,923,471 
 
Estimated
Fair
Value
 
Gross
Unrealized
Gains
 
Gross
Unrealized
Losses
 
Cost or
Amortized
Cost
 
OTTI
Unrealized
Losses (2)
September 30, 2019         
Fixed maturities (1):         
Corporate bonds$6,269,993
 $198,742
 $(18,420) $6,089,671
 $
Mortgage backed securities544,033
 11,185
 (918) 533,766
 (6)
Municipal bonds653,346
 27,095
 (379) 626,630
 
Commercial mortgage backed securities754,306
 27,523
 (158) 726,941
 
U.S. government and government agencies5,127,290
 67,957
 (6,671) 5,066,004
 
Non-U.S. government securities1,873,856
 48,212
 (52,767) 1,878,411
 
Asset backed securities1,657,494
 29,838
 (5,931) 1,633,587
 
Total16,880,318
 410,552
 (85,244) 16,555,010
 (6)
Short-term investments751,989
 227
 (445) 752,207
 
Total$17,632,307
 $410,779
 $(85,689) $17,307,217
 $(6)
          
December 31, 2018         
Fixed maturities (1):         
Corporate bonds$5,537,548
 $14,476
 $(105,428) $5,628,500
 $(69)
Mortgage backed securities541,193
 3,991
 (3,216) 540,418
 (6)
Municipal bonds1,013,395
 5,380
 (11,891) 1,019,906
 
Commercial mortgage backed securities729,442
 2,650
 (10,751) 737,543
 
U.S. government and government agencies3,758,698
 27,189
 (8,474) 3,739,983
 
Non-U.S. government securities1,771,338
 14,477
 (50,948) 1,807,809
 
Asset backed securities1,600,896
 8,060
 (14,798) 1,607,634
 
Total14,952,510
 76,223
 (205,506) 15,081,793
 (75)
Short-term investments955,880
 36
 (394) 956,238
 
Total$15,908,390
 $76,259
 $(205,900) $16,038,031
 $(75)
(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.”
(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)Represents the total other-than-temporary impairments (“OTTI”) recognized in accumulated other comprehensive income (“AOCI”). It does not include the change in fair value subsequent to the impairment measurement date. At September 30, 2019 the net unrealized loss related to securities for which a non-credit OTTI was recognized in AOCI was $0.01 million, compared to net unrealized loss of $0.04 million at December 31, 2018.

(2)    Effective January 1, 2020, the Company adopted ASU 2016-13 and as a result any credit impairment losses on the Company’s available-for-sale investments are recorded as an allowance, subject to reversal. See note 1.
ARCH CAPITAL 222420192020 THIRD QUARTER FORM 10-Q

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

The following table summarizes, for all available for sale securities in an unrealized loss position, the fair value and gross unrealized loss by length of time the security has been in a continual unrealized loss position:
 Less than 12 Months12 Months or MoreTotal
Estimated
Fair
Value
Gross
Unrealized
Losses
Estimated
Fair
Value
Gross
Unrealized
Losses
Estimated
Fair
Value
Gross
Unrealized
Losses
September 30, 2020
Fixed maturities (1):
Corporate bonds$1,414,931 $(38,353)$4,169 $(2,095)$1,419,100 $(40,448)
Mortgage backed securities186,860 (3,262)690 (111)187,550 (3,373)
Municipal bonds36,469 (877)36,469 (877)
Commercial mortgage backed securities179,780 (4,601)2,850 (59)182,630 (4,660)
U.S. government and government agencies1,386,590 (4,396)1,386,590 (4,396)
Non-U.S. government securities921,890 (18,294)921,890 (18,294)
Asset backed securities636,373 (20,166)39,368 (1,563)675,741 (21,729)
Total4,762,893 (89,949)47,077 (3,828)4,809,970 (93,777)
Short-term investments81,964 (954)81,964 (954)
Total$4,844,857 $(90,903)$47,077 $(3,828)$4,891,934 $(94,731)
December 31, 2019
Fixed maturities (1):
Corporate bonds$675,131 $(12,350)$37,671 $(443)$712,802 $(12,793)
Mortgage backed securities102,887 (927)203 (4)103,090 (931)
Municipal bonds220,296 (2,213)220,296 (2,213)
Commercial mortgage backed securities147,290 (2,302)2,683 (28)149,973 (2,330)
U.S. government and government agencies1,373,127 (10,089)32,058 (45)1,405,185 (10,134)
Non-U.S. government securities1,224,243 (20,163)37,610 (167)1,261,853 (20,330)
Asset backed securities441,522 (3,334)48,313 (1,390)489,835 (4,724)
Total4,184,496 (51,378)158,538 (2,077)4,343,034 (53,455)
Short-term investments95,777 (1,548)95,777 (1,548)
Total$4,280,273 $(52,926)$158,538 $(2,077)$4,438,811 $(55,003)
 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
September 30, 2019           
Fixed maturities (1):           
Corporate bonds$538,471
 $(11,128) $113,987
 $(7,292) $652,458
 $(18,420)
Mortgage backed securities97,288
 (905) 200
 (13) 97,488
 (918)
Municipal bonds43,627
 (379) 
 
 43,627
 (379)
Commercial mortgage backed securities47,219
 (151) 1,872
 (7) 49,091
 (158)
U.S. government and government agencies1,592,232
 (6,531) 47,416
 (140) 1,639,648
 (6,671)
Non-U.S. government securities1,214,128
 (51,742) 47,576
 (1,025) 1,261,704
 (52,767)
Asset backed securities375,936
 (4,600) 48,743
 (1,331) 424,679
 (5,931)
Total3,908,901
 (75,436) 259,794
 (9,808) 4,168,695
 (85,244)
Short-term investments43,007
 (445) 
 
 43,007
 (445)
Total$3,951,908
 $(75,881) $259,794
 $(9,808) $4,211,702
 $(85,689)
            
December 31, 2018           
Fixed maturities (1):           
Corporate bonds$2,983,195
 $(68,910) $1,234,865
 $(36,518) $4,218,060
 $(105,428)
Mortgage backed securities84,296
 (695) 109,009
 (2,521) 193,305
 (3,216)
Municipal bonds233,081
 (2,074) 408,155
 (9,817) 641,236
 (11,891)
Commercial mortgage backed securities223,341
 (2,831) 193,956
 (7,920) 417,297
 (10,751)
U.S. government and government agencies635,049
 (1,354) 391,102
 (7,120) 1,026,151
 (8,474)
Non-U.S. government securities1,028,340
 (35,524) 389,671
 (15,424) 1,418,011
 (50,948)
Asset backed securities533,592
 (8,832) 368,095
 (5,966) 901,687
 (14,798)
Total5,720,894
 (120,220) 3,094,853
 (85,286) 8,815,747
 (205,506)
Short-term investments122,878
 (394) 
 
 122,878
 (394)
Total$5,843,772
 $(120,614) $3,094,853
 $(85,286) $8,938,625
 $(205,900)
(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.”
(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 September 30, 2019,2020, on a lot level basis, approximately 1,9803,270 security lots out of a total of approximately 9,26011,090 security lots were in an unrealized loss position and the largest single unrealized loss from a single lot in the Company’s fixed maturity portfolio was $3.0$0.9 million. At December 31, 2018,2019, on a lot level basis, approximately 5,8702,230 security lots out of a total of approximately 8,4509,590 security lots were in an unrealized loss position and the largest single unrealized loss from a single lot in the Company’s fixed maturity portfolio was $2.6$0.9 million.

ARCH CAPITAL 232520192020 THIRD QUARTER FORM 10-Q

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

The contractual maturities of the Company’s fixed maturities are shown in the following table. Expected maturities, which are management’s best estimates, will differ from contractual maturities because borrowers may have the right to call or prepay obligations with or without call or prepayment penalties.
September 30, 2020December 31, 2019
MaturityEstimated
Fair
Value
Amortized
Cost
Estimated
Fair
Value
Amortized
Cost
Due in one year or less$318,767 $312,569 $428,659 $423,617 
Due after one year through five years9,937,129 9,698,743 10,126,403 9,996,206 
Due after five years through 10 years4,849,248 4,641,483 3,317,535 3,219,567 
Due after 10 years551,860 525,863 411,269 388,280 
 15,657,004 15,178,658 14,283,866 14,027,670 
Mortgage backed securities717,081 708,334 562,309 553,571 
Commercial mortgage backed securities374,360 370,753 733,108 720,487 
Asset backed securities1,767,192 1,760,432 1,683,753 1,664,460 
Total (1)$18,515,637 $18,018,177 $17,263,036 $16,966,188 
  September 30, 2019 December 31, 2018
Maturity 
Estimated
Fair
Value
 
Amortized
Cost
 Estimated
Fair
Value
 
Amortized
Cost
Due in one year or less $545,056
 $538,903
 $276,682
 $279,135
Due after one year through five years 10,096,867
 9,971,896
 8,666,297
 8,738,944
Due after five years through 10 years 3,075,318
 2,952,478
 2,919,232
 2,951,582
Due after 10 years 207,244
 197,439
 218,768
 226,537
  13,924,485
 13,660,716
 12,080,979
 12,196,198
Mortgage backed securities 544,033
 533,766
 541,193
 540,418
Commercial mortgage backed securities 754,306
 726,941
 729,442
 737,543
Asset backed securities 1,657,494
 1,633,587
 1,600,896
 1,607,634
Total (1) $16,880,318
 $16,555,010
 $14,952,510
 $15,081,793

(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.
(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. Cash collateral primarily consists of short term investments. At September 30, 2020, the fair value of the cash collateral received on securities lending was NaN and the fair value of security collateral received was $64.3 million. At December 31, 2019, the fair value of the cash collateral received on securities lending was $12.0$81.2 million, and the fair value of security collateral received was $418.2$307.2 million. At December 31, 2018, the fair
The carrying value of the cash collateral received on securities lending was $19.0 million, andheld under the fair value of security collateral received was $255.1 million.
The Company’s securities lending transactions were accounted for as secured borrowings withby significant investment categoriescategory 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
September 30, 2019          
U.S. government and government agencies $257,979
 $
 $156,541
 $
 $414,520
Corporate bonds 4,820
 
 
 
 4,820
Equity securities 10,915
 
 
 
 10,915
Total $273,714
 $
 $156,541
 $
 $430,255
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 8 $
Amounts related to securities lending not included in offsetting disclosure in note 8 $430,255
           
December 31, 2018          
U.S. government and government agencies $219,276
 $
 $32,583
 $
 $251,859
Corporate bonds 7,129
 
 
 
 7,129
Equity securities 15,137
 
 
 
 15,137
Total $241,542
 $
 $32,583
 $
 $274,125
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 8
 $
Amounts related to securities lending not included in offsetting disclosure in note 8
 $274,125

Remaining Contractual Maturity of the Agreements
Overnight and ContinuousLess than 30 Days30-90 Days90 Days or MoreTotal
September 30, 2020
U.S. government and government agencies$64,251 $$$$64,251 
Corporate bonds
Equity securities
Total$64,251 $$$$64,251 
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9$
Amounts related to securities lending not included in offsetting disclosure in note 9$64,251 
December 31, 2019
U.S. government and government agencies$240,332 $$115,973 $$356,305 
Corporate bonds2,570 2,570 
Equity securities29,491 29,491 
Total$272,393 $$115,973 $$388,366 
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
$388,366 

ARCH CAPITAL 242620192020 THIRD QUARTER FORM 10-Q

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

Equity Securities, at Fair Value
At September 30, 2019,2020, the Company held $550.5 million$1.50 billion of equity securities, at fair value, compared to $338.9$838.9 million at December 31, 2018.2019. Such holdings include publicly traded common stocks primarily in the natural resources, energy, consumer staplescyclical and othernon-cyclical, technology, communication and financial sectors and exchange-traded funds.funds in fixed income, equity and other sectors.
Other Investments
The following table summarizes the Company’s other investments which are included in investments accounted for using the fair value option, by strategy:
 September 30,
2019
 December 31,
2018
Term loan investments (par value: $1,434,328 and $1,369,216)$1,330,886
 $1,282,287
Lending624,699
 524,112
Credit related funds165,444
 202,123
Energy113,791
 117,509
Investment grade fixed income83,649
 101,902
Infrastructure49,602
 45,371
Private equity54,609
 24,383
Real estate17,440
 14,252
Total$2,440,120
 $2,311,939

September 30,
2020
December 31,
2019
Term loan investments$1,202,526 $1,326,018 
Lending575,623 602,841 
Credit related funds98,121 123,020 
Energy65,330 97,402 
Investment grade fixed income114,784 151,594 
Infrastructure60,579 61,786 
Private equity34,983 49,376 
Real estate17,951 17,279 
Total$2,169,897 $2,429,316 
Investments Accounted For Using the Equity Method
The following table summarizes the Company’s investments accounted for using the equity method, by strategy:
 September 30,
2019
 December 31,
2018
Credit related funds$428,353
 $429,402
Equities284,465
 375,273
Real estate265,502
 232,647
Lending200,112
 125,041
Private equity141,343
 114,019
Infrastructure149,005
 113,748
Energy107,052
 103,661
Total$1,575,832
 $1,493,791

September 30,
2020
December 31,
2019
Credit related funds$687,178 $428,437 
Equities323,670 293,686 
Real estate246,998 246,851 
Lending141,305 202,690 
Private equity214,357 144,983 
Infrastructure156,029 235,033 
Energy114,165 108,716 
Total$1,883,702 $1,660,396 
Certain of the Company’s other investments are in investment funds for which the Company has the option to redeem at agreed upon values as described in each investment fund’s subscription agreement. Depending on the terms of the various subscription agreements, investments in investment funds may be redeemed daily, monthly, quarterly or on other terms. Two common redemption restrictions which may impact the Company’s ability to redeem these investment funds are gates and lockups. A gate is a suspension of redemptions which may be implemented by the general partner or investment manager of the fund in order to defer, in whole or in part, the redemption request in the event the aggregate amount of redemption requests exceeds a
predetermined percentage of the investment fund’s net assets which may otherwise hinder the general
partner or investment manager’s ability to liquidate holdings in an orderly fashion in order to generate the cash necessary to fund extraordinarily large redemption payouts. A lockup period is the initial amount of time an investor is contractually required to hold the security before having the ability to redeem. If the investment funds are eligible to be redeemed, the time to redeem such fund can take weeks or months following the notification.
Fair Value Option 
The following table summarizes the Company’s assets which are accounted for using the fair value option:
 September 30,
2019
 December 31,
2018
Fixed maturities$908,802
 $1,245,562
Other investments2,440,120
 2,311,939
Short-term investments390,980
 322,177
Equity securities98,341
 103,893
Investments accounted for using the fair value option$3,838,243
 $3,983,571

September 30,
2020
December 31,
2019
Fixed maturities$1,019,529 $754,452 
Other investments2,169,897 2,429,316 
Short-term investments468,704 377,014 
Equity securities91,445 102,695 
Investments accounted for using the fair value option$3,749,575 $3,663,477 
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 unfundedcommitment.
The following table summarizes investments in limited partnership interests where the Company has a variable interest by balance sheet line item:
September 30,
2020
December 31,
2019
Investments accounted for using the equity method (1)1,883,702 1,660,396 
Investments accounted for using the fair value option (2)180,409 188,283 
Total$2,064,111 $1,848,679 
(1)    Aggregate unfunded commitments were $1.59 billion at September 30, 2020, compared to $1.36 billion at December 31, 2019.
(2)    Aggregate unfunded commitments were $36.7 million at September 30, 2020, compared to $41.7 million at December 31, 2019.
 September 30,
2019
 December 31,
2018
Investments accounted for using the equity method (1)1,575,832
 1,493,791
Investments accounted for using the fair value option (2)189,186
 162,398
Total$1,765,018
 $1,656,189
(1)Aggregate unfunded commitments were $1.44 billion at September 30, 2019, compared to $1.22 billion at December 31, 2018.
(2)Aggregate unfunded commitments were $51.1 million at September 30, 2019, compared to $117.5 million at December 31, 2018.

ARCH CAPITAL 252720192020 THIRD QUARTER FORM 10-Q

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

Net Investment Income
The components of net investment income were derived from the following sources:
September 30,
 20202019
Three Months Ended
Fixed maturities$98,344 $126,889 
Term loans22,459 24,236 
Equity securities6,659 3,992 
Short-term investments1,332 3,834 
Other (1)22,060 22,704 
Gross investment income150,854 181,655 
Investment expenses(22,342)(20,167)
Net investment income$128,512 $161,488 
Nine Months Ended
Fixed maturities$318,582 $381,706 
Term loans66,141 73,582 
Equity securities18,885 11,348 
Short-term investments9,611 11,872 
Other (1)57,926 62,423 
Gross investment income471,145 540,931 
Investment expenses(65,995)(67,456)
Net investment income$405,150 $473,475 
(1)    Includes income distributions from investment funds and other items.
 September 30,
 2019 2018
Three Months Ended   
Fixed maturities$126,889
 $120,516
Term loans24,236
 21,903
Equity securities3,992
 3,165
Short-term investments3,834
 4,547
Other (1)22,704
 17,195
Gross investment income181,655
 167,326
Investment expenses(20,167) (23,302)
Net investment income$161,488
 $144,024
    
Nine Months Ended   
Fixed maturities$381,706
 $343,513
Term loans73,582
 62,430
Equity securities11,348
 10,510
Short-term investments11,872
 13,799
Other (1)62,423
 52,210
Gross investment income540,931
 482,462
Investment expenses(67,456) (76,046)
Net investment income$473,475
 $406,416
(1)Includes income distributions from investment funds and other items.
Net Realized Gains (Losses)
Net realized gains (losses) were as follows, excluding, which include changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings:earnings were as follows:
September 30,
 20202019
Three Months Ended
Available for sale securities:  
Gross gains on investment sales$104,733 $73,685 
Gross losses on investment sales(16,862)(30,561)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities34,115 (3,895)
Other investments61,622 (21,778)
Equity securities4,048 (1,231)
Short-term investments3,377 (1,941)
Equity securities, at fair value:
Net realized gains (losses) on sales during the period26,549 5,217 
Net unrealized gains (losses) on equity securities still held at reporting date33,562 (1,206)
Allowance for credit losses:
Investments related1,332 
Underwriting related351 
Net impairment losses(1,163)
Derivative instruments (1)20,369 42,893 
Other7,303 1,335 
Net realized gains (losses)$280,499 $61,355 
Nine Months Ended
Available for sale securities:
Gross gains on investment sales$515,086 $192,140 
Gross losses on investment sales(98,654)(77,498)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities(25,370)38,682 
Other investments(67,608)(37,363)
Equity securities5,803 9,449 
Short-term investments(1,936)(2,613)
Equity securities, at fair value:
Net realized gains (losses) on sales during the period7,760 9,503 
Net unrealized gains (losses) on equity securities still held at reporting date3,682 58,562 
Allowance for credit losses:
Investments related(4,763)
Underwriting related(8,753)
Net impairments losses(533)(2,521)
Derivative instruments (1)146,722 142,730 
Other(1,309)(8,703)
Net realized gains (losses)$470,127 $322,368 
 September 30,
 2019 2018
Three Months Ended   
Available for sale securities: 
  
Gross gains on investment sales$73,685
 $10,990
Gross losses on investment sales(30,561) (34,879)
Change in fair value of assets and liabilities accounted for using the fair value option:   
Fixed maturities(3,895) (6,604)
Other investments(21,778) (7,950)
Equity securities(1,231) 2,752
Short-term investments(1,941) (471)
Equity securities, at fair value:   
Net realized gains (losses) on sales during the period5,217
 (2,012)
Net unrealized gains (losses) on equity securities still held at reporting date(1,206) 10,798
Derivative instruments (1)42,893
 (17,556)
Other (2)1,335
 (6,773)
Net realized gains (losses)$62,518
 $(51,705)
    
Nine Months Ended   
Available for sale securities:   
Gross gains on investment sales$192,140
 $44,732
Gross losses on investment sales(77,498) (175,141)
Change in fair value of assets and liabilities accounted for using the fair value option:   
Fixed maturities38,682
 (47,082)
Other investments(37,363) (14,578)
Equity securities9,449
 10,650
Short-term investments(2,613) (758)
Equity securities, at fair value:   
Net realized gains (losses) on sales during the period9,503
 (13,298)
Net unrealized gains (losses) on equity securities still held at reporting date58,562
 (4,063)
Derivative instruments (1)142,730
 (23,665)
Other (2)(8,703) (16,111)
Net realized gains (losses)$324,889
 $(239,314)

(1)    See note 9 for information on the Company’s derivative instruments.

(1)ARCH CAPITAL
 28
See 2020 THIRD QUARTER FORM 10-Qnote 8 for information on the Company’s derivative instruments.
(2)Includes the re-measurement of contingent consideration liability amounts.


ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
Equity in Net Income (Loss) of Investment Funds Accounted for Using the Equity Method

The Company recorded $17.1$126.7 million of equity in net income related to investment funds accounted for using the equity method in the 20192020 third quarter, compared to $16.0income of $17.1 million for the 20182019 third quarter, and $96.5$57.4 million for the nine months ended September 30, 2019,2020, compared to $52.5
$96.5 million for the 2018 period.nine months ended September 30, 2019. 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

ARCH CAPITAL 262019 THIRD QUARTER FORM 10-Q

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

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.
Net Impairment Losses Recognized in Earnings
The Company performs quarterly reviews of its available for sale investments in order to determine whether declines in fair value below the amortized cost basis were considered other-than-temporary in accordance with applicable guidance.
The following table details the net impairment losses recognized in earnings by asset class:
 September 30,
 2019 2018
Three Months Ended   
Fixed maturities: 
  
Mortgage backed securities$(284) $(73)
Corporate bonds(666) (270)
Non-U.S. government securities
 (149)
Asset backed securities(213) 
Net impairment losses recognized in earnings$(1,163) $(492)
    
Nine Months Ended   
Fixed maturities:   
Mortgage backed securities$(839) $(196)
Corporate bonds(1,256) (631)
Non-U.S. government securities
 (149)
Asset backed securities(426) (148)
Net impairment losses recognized in earnings$(2,521) $(1,124)

Net impairment losses recognized in earnings in the 2019 periods were primarily related to foreign currency fluctuations and other impairments on corporate bonds and other securities.Allowance for Expected Credit Losses
The Company believes that the minimal amount of OTTI included in accumulated other comprehensive income at September 30, 2019 on the securities which were considered by the Company to be impaired was due to market and sector-related factors (i.e., not credit losses). At September 30, 2019, the Company did not intend to sell these securities, or any other securities which were in an unrealized loss position, and determined that it is more likely than not that the Company will not be required to sell such securities before recovery of their cost basis.
The following table provides a roll forward of the amount related toallowance for expected credit losses recognized in earningsof the Company’s securities classified as available for which a portion of an OTTI was recognized in accumulated other comprehensive income:sale:
September 30, 2020
Structured Securities (1)Municipal
Bonds
Corporate
Bonds
Short Term InvestmentsTotal
Three Months Ended
Balance at beginning of period$1,726 $28 $4,115 $$5,869 
Cumulative effect of accounting change
Additions for current-period provision for expected credit losses27 202 229 
Additions (reductions) for previously recognized expected credit losses403 33 (1,996)(1,560)
Reductions due to disposals(28)(577)(605)
Write-offs charged against the allowance
Balance at end of period$2,128 $61 $1,744 $$3,933 
Nine Months Ended
Balance at beginning of period$$$$$
Cumulative effect of accounting change517 117 634 
Additions for current-period provision for expected credit losses2,868 67 7,643 10,578 
Additions (reductions) for previously recognized expected credit losses(903)(4,920)(5,815)
Reductions due to disposals(354)(14)(1,096)(1,464)
Write-offs charged against the allowance
Balance at end of period$2,128 $61 $1,744 $$3,933 
 September 30,
 2019 2018
Three Months Ended   
Balance at start of period$346
 $698
Credit loss impairments recognized on securities not previously impaired
 
Credit loss impairments recognized on securities previously impaired
 
Reductions for increases in cash flows expected to be collected that are recognized over the remaining life of the security
 
Reductions for securities sold during the period
 (47)
Balance at end of period$346
 $651
    
Nine Months Ended   
Balance at start of year$637
 $767
Credit loss impairments recognized on securities not previously impaired
 
Credit loss impairments recognized on securities previously impaired
 
Reductions for increases in cash flows expected to be collected that are recognized over the remaining life of the security
 
Reductions for securities sold during the period(291) (116)
Balance at end of period$346
 $651
(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.


ARCH CAPITAL 292020 THIRD QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
Restricted Assets
The Company is required to maintain assets on deposit, which primarily consist of fixed maturities, with various regulatory authorities to support its underwriting operations. The Company’s subsidiaries maintain assets in trust accounts as collateral for transactions with affiliated companies and also have investments in segregated portfolios primarily to provide collateral or guarantees for letters of credit to third parties. See note 16,17, “Commitments and Contingencies,” of the notes to consolidated financial statements in the Company’s 20182019 Form 10-K.
The following table details the value of the Company’s restricted assets:
September 30,
2020
December 31,
2019
Assets used for collateral or guarantees:  
Affiliated transactions$4,829,252 $4,526,761 
Third party agreements2,636,097 2,278,248 
Deposits with U.S. regulatory authorities942,480 797,371 
Deposits with non-U.S. regulatory authorities179,726 119,238 
Total restricted assets$8,587,555 $7,721,618 
 September 30,
2019
 December 31,
2018
Assets used for collateral or guarantees: 
  
Affiliated transactions$4,629,369
 $4,623,483
Third party agreements2,605,587
 2,181,682
Deposits with U.S. regulatory authorities788,295
 689,114
Deposits with non-U.S. regulatory authorities71,800
 59,624
Total restricted assets$8,095,051
 $7,553,903



ARCH CAPITAL 272019 THIRD QUARTER FORM 10-Q

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

In addition, Watford maintains a secured credit facilityfacilities 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 September 30, 20192020 and December 31, 2018,2019, Watford held $1.06$1.19 billion and $1.30$1.0 billion, respectively, in pledged assets to collateralize the credit facility mentioned above.
Reconciliation of Cash and Restricted Cash
The following table details reconciliation of cash and restricted cash within the Consolidated Balance Sheets:
September 30,
2020
December 31,
2019
Cash$976,398 $726,230 
Restricted cash (included in ‘other assets’)$210,575 $177,468 
Cash and restricted cash$1,186,973 $903,698 
 September 30,
2019
 December 31,
2018
Cash$880,099
 $646,556
Restricted cash (included in ‘other assets’)$82,376
 $78,087
Cash and restricted cash$962,475
 $724,643


7.
ARCH CAPITAL 302020 THIRD QUARTER FORM 10-Q

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

Accounting guidance regarding fair value measurements addresses how companies should measure fair value when they are required to use a fair value measure for recognition or disclosure purposes under GAAP and provides a common definition of fair value to be used throughout GAAP. It defines fair value as the price that would be received to sell an asset or paid to transfer a liability in an orderly fashion between market participants at the measurement date. In addition, it establishes a three-level valuation hierarchy for the disclosure of fair value measurements. The valuation hierarchy is based upon the transparency of inputs to the valuation of an asset or liability as of the measurement date. The level in the hierarchy within which a given fair value measurement falls is determined based on the lowest level input that is significant to the measurement (Level 1 being the highest priority and Level 3 being the lowest priority).
The levels in the hierarchy are defined as follows:
Level 1:
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,
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
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 September 30, 2019.2020.
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 $22.21$26.04 billion of financial assets and liabilities measured at fair value at September 30, 2019,

ARCH CAPITAL 282019 THIRD QUARTER FORM 10-Q

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

2020, approximately $187.9$120.0 million, or 0.9%0.5%, were priced using non-binding broker-dealer quotes.quotes or modeled valuations. Of the $20.41$22.90 billion of financial assets and liabilities measured at fair value at December 31, 2018,2019, approximately $217.9$179.6 million, or 1.1%0.8%, were priced using non-binding broker-dealer quotes.quotes or modeled valuations.
Fixed maturities
The Company uses the market approach valuation technique to estimate the fair value of its fixed maturity securities, when possible. The market approach includes obtaining prices from independent pricing services, such as index providers and pricing vendors, as well as to a lesser extent quotes from broker-dealers. The independent pricing sources obtain market quotations and actual transaction prices for securities that have quoted prices in active markets. Each source has its own proprietary method for determining the fair value of securities that are not actively traded. In general, these methods involve the use of “matrix pricing” in which the independent pricing source uses observable market inputs
ARCH CAPITAL 312020 THIRD QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
including, but not limited to, investment yields, credit risks and spreads, benchmarking of like securities, broker-dealer quotes, reported trades and sector groupings to determine a reasonable fair value.
The following describes the significant inputs generally used to determine the fair value of the Company’s fixed maturity securities by asset class:
U.S. government and government agencies — valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The Company determined that all U.S. Treasuries would be classified as Level 1 securities due to observed levels of trading activity, the high number of strongly correlated pricing quotes received on U.S. Treasuries and other factors. The fair values of U.S. government agency securities are generally determined using the spread above the risk-free yield curve. As the yields for the risk-free yield curve and the spreads for these securities are observable market inputs, the fair values of U.S. government agency securities are classified within Level 2.
Corporate bonds — valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined using the spread above the risk-free yield curve. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. As the significant inputs used in the pricing process for corporate bonds are observable market inputs, the fair value of these securities are classified within Level 2. A small number of securities are included in Level 3 due to a low level of transparency on the inputs used in the pricing process. During the nine months ended September 30, 2019, the Company transferred $25.8 million of corporate bonds from Level 2 to Level 3 based on a review of the pricing of such securities, as described above.
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

ARCH CAPITAL 292019 THIRD QUARTER FORM 10-Q

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

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. During the nine months ended September 30, 2019, the Company transferred $5.5 millionA small number of asset-backed securities from Level 2 toare included in Level 3 baseddue to a low level of transparency on a review ofthe inputs used in the pricing process.
ARCH CAPITAL 322020 THIRD QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
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. OtherCertain equity securities are included in Level 2 of the valuation hierarchy. A small number ofhierarchy 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. During nine months ended September 30 2019, the Company transferred $107.4 million of equity securities from Level 2 to Level 3 based on a review of the pricing of such securities, as described above.

Other investments

The Company determined that exchange-traded investments in mutual funds would be included in Level 1 as their fair values are based on quoted market prices in active markets. Other investments also include term loan investments for which fair values are estimated by using quoted prices of term loan investments with similar characteristics, pricing models or matrix pricing. Such investments are generally classified within Level 2. 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. During the nine months ended September 30, 2019, the Company transferred $31.6 million of other investments from Level 2 to Level 3 based on a review of the pricing of such securities, as described above.

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

ARCH CAPITAL 303320192020 THIRD QUARTER FORM 10-Q

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

The following table presents the Company’s financial assets and liabilities measured at fair value by level at September 30, 2019:
2020:
  Estimated Fair Value Measurements Using:  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)
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): 
  
  
  
Assets measured at fair value (1):    
Available for sale securities: 
  
  
  
Available for sale securities:    
Fixed maturities: 
  
  
  
Fixed maturities:    
Corporate bonds$6,269,993
 $
 $6,261,248
 $8,745
Corporate bonds$7,965,599 $$7,965,586 $13 
Mortgage backed securities544,033
 
 543,761
 272
Mortgage backed securities717,081 716,873 208 
Municipal bonds653,346
 
 653,346
 
Municipal bonds527,410 527,410 
Commercial mortgage backed securities754,306
 
 754,306
 
Commercial mortgage backed securities374,360 374,360 
U.S. government and government agencies5,127,290
 5,005,512
 121,778
 
U.S. government and government agencies4,861,349 4,715,551 145,798 
Non-U.S. government securities1,873,856
 
 1,873,856
 
Non-U.S. government securities2,302,646 2,302,646 
Asset backed securities1,657,494
 
 1,652,045
 5,449
Asset backed securities1,767,192 1,763,845 3,347 
Total16,880,318
 5,005,512
 11,860,340
 14,466
Total18,515,637 4,715,551 13,796,518 3,568 
       
Short-term investments751,989
 720,518
 31,471
 
Short-term investments2,039,097 2,013,582 25,515 
       
Equity securities, at fair value561,105
 514,380
 11,402
 35,323
Equity securities, at fair value1,502,015 1,452,713 6,616 42,686 
       
Derivative instruments (4)51,647
 
 51,647
 
Derivative instruments (4)130,494 130,494 
       
Fair value option:       Fair value option:
Corporate bonds619,779
 
 597,000
 22,779
Corporate bonds780,237 779,273 964 
Non-U.S. government bonds61,755
 
 61,755
 
Non-U.S. government bonds44,963 44,963 
Mortgage backed securities15,512
 
 15,512
 
Mortgage backed securities13,026 13,026 
Municipal bonds1,140
 
 1,140
 
Municipal bonds
Commercial mortgage backed securitiesCommercial mortgage backed securities1,150 1,150 
Asset backed securities208,620
 
 208,620
 
Asset backed securities175,790 175,790 
U.S. government and government agencies1,996
 1,886
 110
 
U.S. government and government agencies4,363 4,252 111 
Short-term investments390,980
 376,033
 14,947
 
Short-term investments468,704 360,883 107,821 
Equity securities98,340
 41,333
 735
 56,272
Equity securities91,445 27,766 156 63,523 
Other investments1,411,420
 41,316
 1,284,661
 85,443
Other investments1,152,517 52,080 1,034,251 66,186 
Other investments measured at net asset value (2)1,028,700
      Other investments measured at net asset value (2)1,017,380 
Total3,838,242
 460,568
 2,184,480
 164,494
Total3,749,575 444,981 2,156,541 130,673 
       
Total assets measured at fair value$22,083,301
 $6,700,978
 $14,139,340
 $214,283
Total assets measured at fair value$25,936,818 $8,626,827 $16,115,684 $176,927 
       
Liabilities measured at fair value: 
  
  
  
Liabilities measured at fair value:    
Contingent consideration liabilities$(7,344) $
 $
 $(7,344)Contingent consideration liabilities$(630)$$$(630)
Securities sold but not yet purchased (3)(65,736) 
 (65,736) 
Securities sold but not yet purchased (3)(24,909)(24,909)
Derivative instruments (4)(53,740) 
 (53,740) 
Derivative instruments (4)(82,457)(82,457)
Total liabilities measured at fair value$(126,820) $
 $(119,476) $(7,344)Total liabilities measured at fair value$(107,996)$$(107,366)$(630)

(1)
(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 9note 6, “—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 8.

ARCH CAPITAL 313420192020 THIRD QUARTER FORM 10-Q

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

The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2018:2019:
  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$6,406,591 $$6,397,740 $8,851 
Mortgage backed securities562,309 562,055 254 
Municipal bonds881,926 881,926 
Commercial mortgage backed securities733,108 733,108 
U.S. government and government agencies4,916,592 4,805,581 111,011 
Non-U.S. government securities2,078,757 2,078,757 
Asset backed securities1,683,753 1,678,791 4,962 
Total17,263,036 4,805,581 12,443,388 14,067 
Short-term investments956,546 904,804 51,742 
Equity securities, at fair value850,283 789,596 4,798 55,889 
Derivative instruments (4)48,946 48,946 
Fair value option:
Corporate bonds488,402 487,470 932 
Non-U.S. government bonds50,465 50,465 
Mortgage backed securities11,947 11,947 
Municipal bonds377 377 
Commercial mortgage backed securities1,134 1,134 
Asset backed securities200,163 200,163 
U.S. government and government agencies1,962 1,852 110 
Short-term investments377,014 333,320 43,694 
Equity securities102,697 43,962 641 58,094 
Other investments1,418,273 53,287 1,296,169 68,817 
Other investments measured at net asset value (2)1,011,043 
Total3,663,477 432,421 2,092,170 127,843 
Total assets measured at fair value$22,782,288 $6,932,402 $14,641,044 $197,799 
Liabilities measured at fair value:
Contingent consideration liabilities$(7,998)$$$(7,998)
Securities sold but not yet purchased (3)(66,257)(66,257)
Derivative instruments (4)(39,750)(39,750)
Total liabilities measured at fair value$(114,005)$$(106,007)$(7,998)
   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$5,537,548
 $
 $5,529,407
 $8,141
Mortgage backed securities541,193
 
 540,884
 309
Municipal bonds1,013,395
 
 1,013,395
 
Commercial mortgage backed securities729,442
 
 729,438
 4
U.S. government and government agencies3,758,698
 3,657,181
 101,517
 
Non-U.S. government securities1,771,338
 
 1,771,338
 
Asset backed securities1,600,896
 
 1,600,896
 
Total14,952,510
 3,657,181
 11,286,875
 8,454
        
Equity securities353,794
 321,927
 31,867
 
        
Short-term investments955,880
 875,881
 79,999
 
        
Derivative instruments (4)73,893
 
 73,893
 
        
Fair value option:       
Corporate bonds852,585
 
 846,827
 5,758
Non-U.S. government bonds79,066
 
 79,066
 
Mortgage backed securities16,731
 
 16,731
 
Municipal bonds7,144
 
 7,144
 
Asset backed securities178,790
 
 178,790
 
U.S. government and government agencies111,246
 111,138
 108
 
Short-term investments322,177
 278,579
 43,598
 
Equity securities103,893
 48,827
 55,066
 
Other investments1,254,220
 39,107
 1,152,408
 62,705
Other investments measured at net asset value (2)1,057,719
      
Total3,983,571
 477,651
 2,379,738
 68,463
        
Total assets measured at fair value$20,319,648
 $5,332,640
 $13,852,372
 $76,917
        
Liabilities measured at fair value: 
  
  
  
Contingent consideration liabilities$(66,665) $
 $
 $(66,665)
Securities sold but not yet purchased (3)(7,790) 
 (7,790) 
Derivative instruments (4)(20,664) 
 (20,664) 
Total liabilities measured at fair value$(95,119) $
 $(28,454) $(66,665)


(1)
(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 7note 6, “—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 8.

(2)    In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.
(3)    Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets.
(4)    See note 9.

ARCH CAPITAL 323520192020 THIRD QUARTER FORM 10-Q

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

The following table presents a reconciliation of the beginning and ending balances for all financial assets and liabilities measured at fair value on a recurring basis using Level 3 inputs:
AssetsLiabilities
sAvailable For SaleFair Value OptionFair Value
 Structured Securities (1)Corporate
Bonds
Corporate
Bonds
Other
Investments
Equity
Securities
Equity
Securities
Contingent Consideration Liabilities
Three Months Ended September 30, 2020  
Balance at beginning of period$3,450 $857 $998 $46,453 $61,447 $51,981 $(1,250)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)(75)(5,872)(34)885 2,076 (946)
Included in other comprehensive income191 6,936 
Purchases, issuances, sales and settlements
Purchases22,436 
Issuances
Sales(3,588)(8,349)
Settlements(11)620 
Transfers in and/or out of Level 3(1,908)
Balance at end of period$3,555 $13 $964 $66,186 $63,523 $42,686 $(630)
Three Months Ended September 30, 2019  
Balance at beginning of period$290 $7,642 $26,103 $95,273 $56,145 $51,212 $(7,825)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)(1,227)(411)127 (26)(79)
Included in other comprehensive income(301)
Purchases, issuances, sales and settlements
Purchases3,713 12,119 
Issuances
Sales(2,097)(80)(27,982)
Settlements(18)(456)560 
Transfers in and/or out of Level 35,449 1,860 (13,052)
Balance at end of period$5,721 $8,745 $22,779 $85,443 $56,272 $35,323 $(7,344)
Nine Months Ended September 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)(130)(5,865)(34)(129)5,429 7,132 (72)
Included in other comprehensive income(118)397 
Purchases, issuances, sales and settlements
Purchases66 22,460 3,464 
Issuances
Sales(27,946)(23,799)
Settlements(1,413)(1,462)7,440 
Transfers in and/or out of Level 3(1,908)2,984 
Balance at end of period$3,555 $13 $964 $66,186 $63,523 $42,686 $(630)
Nine Months Ended September 30, 2019  
Balance at beginning of year$313 $8,141 $5,758 $62,705 $$$(66,665)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)1,757 (1,566)(11,727)127 (26)(1,410)
Included in other comprehensive income(317)
Purchases, issuances, sales and settlements
Purchases429 3,713 12,119 
Issuances(548)
Sales(1,757)(5,332)(228)(27,982)
Settlements(46)(1,368)(600)61,279 
Transfers in and/or out of Level 35,449 1,860 23,919 31,580 56,145 51,212 
Balance at end of period$5,721 $8,745 $22,779 $85,443 $56,272 $35,323 $(7,344)
 AssetsLiabilities
sAvailable 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 September 30, 2019   
        
  
Balance at beginning of period$290
 $7,642
 $26,103
 $95,273
 $56,145
 $51,212
 $(7,825)
Total gains or (losses) (realized/unrealized)          

  
Included in earnings (2)
 
 (1,227) (411) 127
 (26) (79)
Included in other comprehensive income
 (301) 
 
 
 
 
Purchases, issuances, sales and settlements          

  
Purchases
 
 
 3,713
 
 12,119
 
Issuances
 
 
 
 
 
 
Sales
 
 (2,097) (80) 
 (27,982) 
Settlements(18) (456) 
 
 
 
 560
Transfers in and/or out of Level 35,449
 1,860
 
 (13,052) 
 
 
Balance at end of period$5,721
 $8,745
 $22,779
 $85,443
 $56,272
 $35,323
 $(7,344)
              
Three Months Ended September 30, 2018   
        
  
Balance at beginning of period$376
 $8,773
 $11,335
 $58,214
 $
 $
 $(63,930)
Total gains or (losses) (realized/unrealized)          

  
Included in earnings (2)
 (1) (503) (1,459) 
 
 (1,711)
Included in other comprehensive income2
 (32) 
 
 
 
 
Purchases, issuances, sales and settlements          

  
Purchases
 
 
 6,250
 
 
 
Issuances
 
 
 
 
 
 
Sales
 
 
 (74) 
 
 
Settlements(33) (456) (1,226) 
 
 
 
Transfers in and/or out of Level 3
 
 
 
 
 
 
Balance at end of period$345
 $8,284
 $9,606
 $62,931
 $
 $
 $(65,641)
              
Nine Months Ended September 30, 2019   
        
  
Balance at beginning of year$313
 $8,141
 $5,758
 $62,705
 $
 $
 $(66,665)
Total gains or (losses) (realized/unrealized)          

  
Included in earnings (2)1,757
 
 (1,566) (11,727) 127
 (26) (1,410)
Included in other comprehensive income5
 (317) 
 
 
 
 
Purchases, issuances, sales and settlements          

  
Purchases
 429
 
 3,713
 
 12,119
 
Issuances
 
 
 
 
 
 (548)
Sales(1,757) 
 (5,332) (228) 
 (27,982) 
Settlements(46) (1,368) 
 (600) 
 
 61,279
Transfers in and/or out of Level 35,449
 1,860
 23,919
 31,580
 56,145
 51,212
 
Balance at end of period$5,721
 $8,745
 $22,779
 $85,443
 $56,272
 $35,323
 $(7,344)
              
Nine Months Ended September 30, 2018   
        
  
Balance at beginning of year$5,927
 $9,460
 $12,217
 $59,167
 $
 $
 $(60,996)
Total gains or (losses) (realized/unrealized)          

  
Included in earnings (2)4
 (1) (1,115) (1,838) 
 
 (4,645)
Included in other comprehensive income(6) (200) 
 
 
 
 
Purchases, issuances, sales and settlements          

  
Purchases
 393
 
 6,250
 
 
 
Issuances
 
 
 
 
 
 
Sales(5,003) 
 
 (148) 
 
 
Settlements(577) (1,368) (1,496) (500) 
 
 
Transfers in and/or out of Level 3
 
 
 
 
 
 
Balance at end of period$345
 $8,284
 $9,606
 $62,931
 $
 $
 $(65,641)
(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

(2)    Gains or losses were included in net realized gains (losses).
(1)Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.
(2)Gains or losses were included in net realized gains (losses).

ARCH CAPITAL 333620192020 THIRD QUARTER FORM 10-Q

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

Financial Instruments Disclosed, But Not Carried, At Fair Value
The Company uses various financial instruments in the normal course of its business. The carrying values of cash, accrued investment income, receivable for securities sold, certain other assets, payable for securities purchased and certain other liabilities approximated their fair values at September 30, 2019,2020, due to their respective short maturities. As these financial instruments are not actively traded, their respective fair values are classified within Level 2.
At September 30, 2020, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.86 billion and had a fair value of $3.51 billion. At December 31, 2019, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $1.87 billion and had a fair value of $2.35 billion. At December 31, 2018, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $1.73 billion and had a fair value of $1.88$2.34 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.
8.9.    Derivative Instruments

The Company’s investment strategy allows for the use of derivative instruments. The Company’s derivative instruments are recorded on its consolidated balance sheets at fair value. The Company utilizes exchange traded U.S. Treasury note, Eurodollar and other futures contracts and commodity futures to manage portfolio duration or replicate investment positions in its portfolios and the Company routinely utilizes foreign currency forward contracts, currency options, index futures contracts and other derivatives as part of its total return objective. In addition, certain of the Company’s investments are managed in portfolios which incorporate the use of foreign currency forward contracts which are intended to provide an economic hedge against foreign currency movements. 
In addition, the Company purchases to-be-announced mortgage backed securities (“TBAs”) as part of its investment strategy. TBAs represent commitments to purchase a future issuance of agency mortgage backed securities. For the period between purchase of a TBA and issuance of the underlying security, the Company’s position is accounted for as a derivative. The Company purchases TBAs in both long and short positions to enhance investment performance and as part of its overall investment strategy.
The following table summarizes information on the fair values and notional values of the Company’s derivative instruments:
 Estimated Fair Value
 Asset DerivativesLiability DerivativesNotional
Value (1)
September 30, 2020
Futures contracts (2)$23,605 $(9,357)$2,804,901 
Foreign currency forward contracts (2)11,428 (3,256)990,726 
TBAs (3)
Other (2)95,461 (69,844)6,231,827 
Total$130,494 $(82,457)
December 31, 2019
Futures contracts (2)$10,065 $(13,722)$4,104,559 
Foreign currency forward contracts (2)5,352 (5,327)686,878 
TBAs (3)55,010 53,229 
Other (2)33,529 (20,701)4,356,300 
Total$103,956 $(39,750)
 Estimated Fair Value  
 Asset Derivatives Liability Derivatives 
Notional
Value (1)
September 30, 2019     
Futures contracts (2)$15,148
 $(20,515) $3,987,260
Foreign currency forward contracts (2)5,316
 (8,616) 965,348
TBAs (3)54,961
 
 53,229
Other (2)31,183
 (24,609) 3,983,466
Total$106,608
 $(53,740)  
      
December 31, 2018     
Futures contracts (2)$51,800
 $(2,115) $3,153,518
Foreign currency forward contracts (2)8,147
 (7,796) 1,008,907
TBAs (3)8,292
 
 8,132
Other (2)13,946
 (10,753) 2,213,981
Total$82,185
 $(20,664)  
(1)    Represents the absolute notional value of all outstanding contracts, consisting of long and short positions.
(1)Represents the absolute notional value of all outstanding contracts, consisting of long and short positions.
(2)The fair value of asset derivatives are included in ‘other assets’ and the fair value of liability derivatives are included in ‘other liabilities.’
(3)The fair value of TBAs are included in ‘fixed maturities available for sale, at fair value.’
(2)    The fair value of asset derivatives are included in ‘other assets’ and the fair value of liability derivatives are included in ‘other liabilities.’
(3)    The fair value of TBAs are included in ‘fixed maturities available for sale, at fair value.’
The Company did not hold any derivatives which were designated as hedging instruments at September 30, 20192020 or December 31, 2018.2019.
The Company’s derivative instruments can be traded under master netting agreements, which establish terms that apply to all derivative transactions with a counterparty. In the event of a bankruptcy or other stipulated event of default, such agreements provide that the non-defaulting party may elect to terminate all outstanding derivative transactions, in which case all individual derivative positions (loss or gain) with a counterparty are closed out and netted and replaced with a single amount, usually referred to as the termination amount, which is expressed in a single currency. The resulting single net amount, where positive, is payable to the party “in-the-money” regardless of whether or not it is the defaulting party, unless the parties have agreed that only the non-defaulting party is entitled to receive a termination payment where the net amount is positive and is in its favor. Contractual close-out netting reduces derivatives credit exposure from gross to net exposure. The remaining derivatives included in the table above were not subject to a master netting agreement.
At September 30, 2019,2020, asset derivatives and liability derivatives of $105.5$109.7 million and $52.7$74.6 million, respectively, were subject to a master netting agreement, compared to $80.4$97.8 million and $18.9$37.8 million, respectively, at December 31, 2018.2019. The remaining derivatives included in the preceding table were not subject to a master netting agreement.

ARCH CAPITAL 343720192020 THIRD QUARTER FORM 10-Q

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

Realized and unrealized contract gains and losses on the Company’s derivative instruments are reflected in ‘net realized gains (losses)’ in the consolidated statements of income, as summarized in the following table:
Derivatives not designated as September 30,
hedging instruments: 2019 2018
     
Three Months Ended    
Net realized gains (losses):    
Futures contracts $46,194
 $(15,399)
Foreign currency forward contracts 2,044
 (5,458)
TBAs 269
 (3)
Other (5,614) 3,304
Total $42,893
 $(17,556)
     
Nine Months Ended    
Net realized gains (losses):    
Futures contracts $140,503
 $(10,609)
Foreign currency forward contracts (17,030) (13,074)
TBAs 507
 (100)
Other 18,750
 118
Total $142,730
 $(23,665)

Derivatives not designated asSeptember 30,
hedging instruments:20202019
Three Months Ended
Net realized gains (losses):
Futures contracts$10,945 $46,194 
Foreign currency forward contracts10,813 2,044 
TBAs120 269 
Other(1,509)(5,614)
Total$20,369 $42,893 
Nine Months Ended
Net realized gains (losses):
Futures contracts$105,282 $140,503 
Foreign currency forward contracts3,466 (17,030)
TBAs1,129 507 
Other36,845 18,750 
Total$146,722 $142,730 
9.10.    Commitments and Contingencies

Senior Notes
On June 30, 2020, Arch Capital completed a public offering of $1.0 billion aggregate principal amount of its 3.635% senior notes with a scheduled maturity of June 30, 2050 (the “2050 notes”). The 2050 notes are Arch Capital’s senior unsecured obligations and rank equally with all of its existing and future senior unsecured indebtedness. Interest payments on the 2050 notes are due semi-annually in arrears on June 30 and December 30, beginning on December 30, 2020, to holders of record on the preceding June 15 or December 15, as the case may be. Interest will be calculated on the basis of a 360-day year of twelve 30-day months. Subject to conditions of redemption, Arch Capital may redeem the 2050 notes at any time and from time to time prior to December 30, 2049, in whole or in part, at a redemption price equal to the “make-whole” redemption price, plus accrued and unpaid interest thereon to, but excluding, the redemption date. Arch Capital is planning to use the net proceeds for general corporate purposes.
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 $1.90$1.91 billion at September 30, 2019,2020, compared to $1.77$1.69 billion at December 31, 2018.2019.
Interest Paid
Interest paid on the Company’s senior notes and other borrowings were $68.6$60.6 million for the nine months ended September 30, 2019,2020, consistent with $67.6$68.6 million for the 20182019 period.
Letter of Credit
11.    Variable Interest Entities and Revolving Credit Facilities
In September 2019, Watford entered into an unsecured letter of credit agreement. Watford has access to a $100 million letter of credit facility expiring on September 20, 2020. The Company does not guarantee or provide credit support for Watford, and the Company’s financial exposure to Watford is limited to its investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from the reinsurance transactions.
10.    Leases

In the ordinary course of business, the Company renews and enters into new leases for office property and equipment. At the lease inception date, the Company determines whether a contract contains a lease and its classification as a finance or operating lease. Primarily all of the Company’s leases are classified as operating leases. The Company’s operating leases have remaining lease terms of up to 11 years, some of which include options to extend the lease term. The Company considers these options when determining the lease term and measuring its lease liability and right-of-use asset. In addition, the Company’s lease agreements do not contain any material residual value guarantees or material restrictive covenants.
Short-term operating leases with an initial term of twelve months or less were excluded on the Company's consolidated balance sheet and represent an inconsequential amount of operating lease expense.
As most leases do not provide an implicit rate, the Company uses its incremental borrowing rate based on the information available at the lease commencement date in determining the present value of lease payments.
Additional information regarding the Company’s operating leases is as follows:
  September 30,
  2019
   
Three Months Ended  
Operating lease costs $7,751
Cash payments included in the measurement of lease liabilities reported in operating cash flows $8,031
Right-of-use assets obtained in exchange for new lease liabilities $2,897
Right-of-use assets (1) $131,424
Operating lease liability (1) $147,326
Weighted average discount rate 3.9%
Weighted average remaining lease term 6.3 years
   
Nine Months Ended  
Operating lease costs

 $22,611
Cash payments included in the measurement of lease liabilities reported in operating cash flows $22,616
Right-of-use assets obtained in exchange for new lease liabilities $7,009
Right-of-use assets (1) $131,424
Operating lease liability (1) $147,326
Weighted average discount rate 3.9%
Weighted average remaining lease term 6.3 years
(1)The right-of-use assets are included in ‘other assets’ while the operating lease liability is included in ‘other liabilities.’


Noncontrolling Interests
ARCH CAPITAL 352019 THIRD QUARTER FORM 10-Q

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

The following table presents the contractual maturities of the Company's operating lease liabilities at September 30, 2019:
Years Ending December 31,  
2019 (remainder) $1,693
2020 31,541
2021 30,392
2022 27,096
2023 22,290
2024 and thereafter 55,080
Total undiscounted lease liability $168,092
Less: present value adjustment (20,767)
Operating lease liability $147,325


At December 31, 2018, the future minimum rental commitments, exclusive of escalation clauses and maintenance costs and net of rental income, for all of the Company’s operating leases was as follows:
2019$31,088
202030,491
202129,351
202226,068
202321,408
2024 and thereafter54,745
Total$193,151

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, and a warrant to purchase up to 975,503 additional common shares. The warrants expire on March 31, 2020. The exercise price of the warrants is determined on the date of exercise based on certain targeted returns for existing common shareholders.equity. Watford’s common shares are listed on the Nasdaq Select Global Market under the ticker symbol “WTRE”. As of September 30, 2020, the Company owns approximately 13% of Watford’s outstanding common equity.
OnIn July 2, 2019, Watford completed an offering of $175.0 million in aggregate principal amount of its 6.5% senior notes, due July 2, 2029 (“Watford Senior Notes”). Interest on the Watford Senior Notes will be paidis payable semi-annually in arrears on each January 2 and July 2 commencing on January 2, 2020. The $172.4 million net proceeds from the offering were used to redeem a portion of Watford’s outstanding preference shares (“Watford Preference Shares”). The Company purchased $35.0 million in aggregate principal amount of the Watford Senior Notes.
Watford is considered a VIE and the Company concluded that it is the primary beneficiary of Watford. As such, the results of Watford are included in the Company’s consolidated financial statements.
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.
ARCH CAPITAL 382020 THIRD QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
The following table provides the carrying amount and balance sheet caption in which the assets and liabilities of Watford are reported:
September 30,December 31,
20202019
Assets
Investments accounted for using the fair value option$1,937,037 $1,898,091 
Fixed maturities available for sale, at fair value649,781 745,708 
Equity securities, at fair value52,807 65,338 
Cash195,333 102,437 
Accrued investment income16,234 14,025 
Premiums receivable263,748 273,657 
Reinsurance recoverable on unpaid and paid losses and LAE263,293 170,973 
Ceded unearned premiums131,885 132,577 
Deferred acquisition costs58,583 64,044 
Receivable for securities sold1,730 16,287 
Goodwill and intangible assets7,650 7,650 
Other assets75,139 60,070 
Total assets of consolidated VIE$3,653,220 $3,550,857 
Liabilities
Reserve for losses and loss adjustment expenses$1,429,656 $1,263,628 
Unearned premiums459,476 438,907 
Reinsurance balances payable68,339 77,066 
Revolving credit agreement borrowings210,687 484,287 
Senior notes172,621 172,418 
Payable for securities purchased76,567 18,180 
Other liabilities (1)316,599 171,714 
Total liabilities of consolidated VIE$2,733,945 $2,626,200 
Redeemable noncontrolling interests$52,375 $52,305 
 September 30, December 31,
 2019 2018
Assets   
Investments accounted for using the fair value option$2,048,295
 $2,312,003
Fixed maturities available for sale, at fair value678,094
 393,351
Equity securities, at fair value43,488
 32,206
Cash80,390
 63,529
Accrued investment income18,277
 19,461
Premiums receivable302,265
 227,301
Reinsurance recoverable on unpaid and paid losses and LAE144,437
 86,445
Ceded unearned premiums129,909
 61,587
Deferred acquisition costs67,241
 80,858
Receivable for securities sold25,283
 24,507
Goodwill and intangible assets7,650
 7,650
Other assets66,165
 63,959
Total assets of consolidated VIE$3,611,494
 $3,372,857
    
Liabilities   
Reserve for losses and loss adjustment expenses$1,164,945
 $1,032,760
Unearned premiums454,148
 390,114
Reinsurance balances payable79,264
 21,034
Revolving credit agreement borrowings490,720
 455,682
Senior notes172,350
 
Payable for securities purchased40,586
 60,142
Other liabilities (1)196,431
 302,524
Total liabilities of consolidated VIE$2,598,444
 $2,262,256
    
Redeemable noncontrolling interests$52,281
 $220,992
(1)    Includes certain borrowings related to investing activities.

(1)Includes certain borrowings related to investing activities.
For the nine months ended September 30, 2019,2020, Watford generated $133.6 million of cash provided by operating activities, $242.0 million of cash provided by investing activities and $279.7 million of cash used for financing activities, compared to $177.2 million of cash provided by operating activities, $181.2 million of cash used for investing activities and $22.2 million of cash provided by financing activities compared to $174.3 million of cash provided by operating activities, $208.3 million of cash used for investing activities and $24.2 million of cash used for financing activities for the nine months ended September 30, 2018.2019.

ARCH CAPITAL 362019 THIRD QUARTER FORM 10-Q

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

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 89%87% at September 30, 2019.2020. The portion of Watford’s income or loss attributable to third party investors is recorded in the consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests.’
The following table sets forth activity in the non-redeemable noncontrolling interests:
September 30,
 20202019
Three Months Ended
Balance, beginning of period$679,089 $855,347 
Additional paid in capital attributable to noncontrolling interests243 205 
Amounts attributable to noncontrolling interests67,768 136 
Other comprehensive income (loss) attributable to noncontrolling interests10,820 (764)
Balance, end of period$757,920 $854,924 
Nine Months Ended
Balance, beginning of year$762,777 $791,560 
Additional paid in capital attributable to noncontrolling interests715 2,279 
Repurchases attributable to non-redeemable noncontrolling interests (1)
(2,867)
Amounts attributable to noncontrolling interests(578)54,819 
Other comprehensive income (loss) attributable to noncontrolling interests(2,127)6,266 
Balance, end of period$757,920 $854,924 
 September 30,
 2019 2018
Three Months Ended   
Balance, beginning of period$855,347
 $861,153
Additional paid in capital attributable to noncontrolling interests205
 
Amounts attributable to noncontrolling interests136
 16,759
Other comprehensive income (loss) attributable to noncontrolling interests(764) (1,158)
Balance, end of period$854,924
 $876,754
    
Nine Months Ended   
Balance, beginning of year$791,560
 $843,411
Additional paid in capital attributable to noncontrolling interests2,279
 
Amounts attributable to noncontrolling interests54,819
 36,251
Other comprehensive income (loss) attributable to noncontrolling interests6,266
 (2,908)
Balance, end of period$854,924
 $876,754
(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.
OnIn August 1, 2019, Watford redeemed 6,919,998 of its 9,065,200 issued and outstanding Watford Preference Shares. The Watford Preference Shares were redeemed at a total redemption price of $25.19748 per share, inclusive of all declared and unpaid dividends, with accumulation of any undeclared dividends on or after June 30, 2019. In addition, the Company received $11.5 million pursuant to the redemption of Watford Preference Shares.
ARCH CAPITAL 392020 THIRD QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
The following table sets forth activity in the redeemable non-controlling interests:
 September 30,
 2019 2018
Three Months Ended   
Balance, beginning of period$206,475
 $206,105
Redemption of noncontrolling interests(157,709) 
Accretion of preference share issuance costs23
 94
Balance, end of period$48,789
 $206,199
    
Nine Months Ended   
Balance, beginning of year$206,292
 $205,922
Redemption of noncontrolling interests(157,709) 
Accretion of preference share issuance costs206
 277
Balance, end of period$48,789
 $206,199

September 30,
 20202019
Three Months Ended
Balance, beginning of period$55,986 $206,475 
Redemption of noncontrolling interests(157,709)
Accretion of preference share issuance costs23 23 
Other1,826 
Balance, end of period$57,835 $48,789 
Nine Months Ended
Balance, beginning of year$55,404 $206,292 
Redemption of noncontrolling interests(157,709)
Accretion of preference share issuance costs70 206 
Other2,361 
Balance, end of period$57,835 $48,789 
The portion of Watford’s income or loss attributable to third party investors, recorded in the Company’s consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests,’ are summarized in the table below:
September 30,September 30,
2019 2018 20202019
Three Months Ended   Three Months Ended
Amounts attributable to non-redeemable noncontrolling interests$(136) $(16,759)Amounts attributable to non-redeemable noncontrolling interests$(67,768)$(136)
Dividends attributable to redeemable noncontrolling interests(6,600) (4,599)
Amounts attributable to redeemable noncontrolling interestsAmounts attributable to redeemable noncontrolling interests(1,875)(6,600)
Net (income) loss attributable to noncontrolling interests$(6,736) $(21,358)Net (income) loss attributable to noncontrolling interests$(69,643)$(6,736)
   
Nine Months Ended   Nine Months Ended
Amounts attributable to non-redeemable noncontrolling interests$(54,819) $(36,251)Amounts attributable to non-redeemable noncontrolling interests$578 $(54,819)
Dividends attributable to redeemable noncontrolling interests(15,778) (13,769)
Amounts attributable to redeemable noncontrolling interestsAmounts attributable to redeemable noncontrolling interests(4,998)(15,778)
Net (income) loss attributable to noncontrolling interests$(70,597) $(50,020)Net (income) loss attributable to noncontrolling interests$(4,420)$(70,597)


ARCH CAPITAL 372019 THIRD QUARTER FORM 10-Q

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

Bellemeade Re
The Company has entered into various aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda (the “Bellemeade Agreements”). At the time the Bellemeade Agreements were entered into, the applicability of the accounting guidance that addresses VIEs was evaluated. As a result of the evaluation of the Bellemeade Agreements, the Company concluded that these entities are VIEs. However, given that the ceding insurers do not have the unilateral power to direct those activities that are significant to their economic performance, the Company does not consolidate such entities in its consolidated financial statements.
The following table presents the total assets of the Bellemeade entities, as well as the Company’s maximum exposure to loss associated with these VIEs, calculated as the maximum historical observable spread between the one month LIBOR, the basis for the contractual payments to bond holders, and short term invested trust asset yields.
Maximum Exposure to Loss
Bellemeade Entities (Issue Date)Total VIE AssetsOn-Balance Sheet (Asset) LiabilityOff-Balance SheetTotal
Sep 30, 2020
Bellemeade 2017-1 Ltd. (Oct-17)$145,573 $(432)$2,104 $1,672 
Bellemeade 2018-1 Ltd. (Apr-18)250,095 (1,592)4,821 3,229 
Bellemeade 2018-2 Ltd. (Aug-18)187,362 (641)1,695 1,054 
Bellemeade 2018-3 Ltd. (Oct-18)302,563 (2,477)7,261 4,784 
Bellemeade 2019-1 Ltd. (Mar-19)219,256 (1,062)8,944 7,882 
Bellemeade 2019-2 Ltd. (Apr-19)398,316 (1,090)11,369 10,279 
Bellemeade 2019-3 Ltd. (Jul-19)528,084 (975)9,156 8,181 
Bellemeade 2019-4 Ltd. (Oct-19)468,737 (1,179)12,722 11,543 
Bellemeade 2020-1 Ltd. (Jun-20) (1)406,534 (701)7,590 6,889 
Bellemeade 2020-2 Ltd. (Sep-20) (2)423,420 (322)9,081 8,759 
Total$3,329,940 $(10,471)$74,743 $64,272 
Dec 31, 2019
Bellemeade 2017-1 Ltd. (Oct-17)$216,429 $(442)$2,794 $2,352 
Bellemeade 2018-1 Ltd. (Apr-18)328,482 (1,574)5,757 4,183 
Bellemeade 2018-2 Ltd. (Aug-18)437,009 (877)2,524 1,647 
Bellemeade 2018-3 Ltd. (Oct-18)426,806 (1,113)3,937 2,824 
Bellemeade 2019-1 Ltd. (Mar-19)257,358 (226)3,027 2,801 
Bellemeade 2019-2 Ltd. (Apr-19)525,959 (78)2,579 2,501 
Bellemeade 2019-3 Ltd. (Jul-19)656,523 (585)9,273 8,688 
Bellemeade 2019-4 Ltd. (Oct-19)577,267 (302)12,193 11,891 
Total$3,425,833 $(5,197)$42,084 $36,887 
(1)  An additional $79 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.
   Maximum Exposure to Loss
Bellemeade Entities (Issue Date)Total VIE Assets On-Balance Sheet (Asset) Liability Off-Balance Sheet Total
Sep 30, 2019       
Bellemeade 2015-1 Ltd. (Jul-15)$6,046
 $
 $2
 $2
Bellemeade 2017-1 Ltd. (Oct-17)249,737
 (345) 3,526
 3,181
Bellemeade 2018-1 Ltd. (Apr-18)362,603
 (1,351) 7,035
 5,684
Bellemeade 2018-2 Ltd. (Aug-18)507,534
 (829) 3,395
 2,566
Bellemeade 2018-3 Ltd. (Oct-18)488,430
 (916) 4,600
 3,684
Bellemeade 2019-1 Ltd. (Mar-19)293,595
 (210) 4,533
 4,323
Bellemeade 2019-2 Ltd. (Apr-19)621,022
 (367) 15,161
 14,794
Bellemeade 2019-3 Ltd. (July-19)

700,920
 (468) 11,888
 11,420
Total$3,229,887
 $(4,486) $50,140
 $45,654
Dec 31, 2018       
Bellemeade 2015-1 Ltd. (Jul-15)$43,246
 $112
 $498
 $610
Bellemeade 2017-1 Ltd. (Oct-17)304,373
 165
 1,312
 1,477
Bellemeade 2018-1 Ltd. (Apr-18)374,460
 132
 3,539
 3,671
Bellemeade 2018-2 Ltd. (Aug-18)653,278
 874
 4,005
 4,879
Bellemeade 2018-3 Ltd. (Oct-18)506,110
 469
 1,836
 2,305
Total$1,881,467
 $1,752
 $11,190
 $12,942

See note 16.(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.

ARCH CAPITAL 384020192020 THIRD QUARTER FORM 10-Q

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

12.    Other Comprehensive Income (Loss)


The following tables present details about amounts reclassified from accumulated other comprehensive income and the tax effects allocated to each component of other comprehensive income (loss):
    Amounts Reclassified from AOCI
  Consolidated Statement of Income Three Months Ended Nine Months Ended
Details About Line Item That Includes September 30, September 30,
AOCI Components Reclassification 2019 2018 2019 2018
           
Unrealized appreciation on available-for-sale investments        
  Net realized gains (losses) $43,124
 $(23,888) $114,642
 $(130,409)
  Other-than-temporary impairment losses (1,163) (492) (2,521) (1,124)
  Total before tax 41,961
 (24,380) 112,121
 (131,533)
  Income tax (expense) benefit (3,218) 1,177
 (7,812) 9,226
  Net of tax $38,743
 $(23,203) $104,309
 $(122,307)

Amounts Reclassified from AOCI
Consolidated Statement of IncomeThree Months EndedNine Months Ended
Details AboutLine Item That IncludesSeptember 30,September 30,
AOCI ComponentsReclassification2020201920202019
Unrealized appreciation on available-for-sale investments
Net realized gains (losses)$87,871 $43,124 $416,432 $114,642 
Provision for credit losses1,333 (4,762)
Other-than-temporary impairment losses(1,163)(533)(2,521)
Total before tax89,204 41,961 411,137 112,121 
Income tax (expense) benefit(9,401)(3,218)(42,714)(7,812)
Net of tax$79,803 $38,743 $368,423 $104,309 
 Before Tax Amount Tax Expense (Benefit) Net of Tax Amount
Three Months Ended September 30, 2019     
Unrealized appreciation (decline) in value of investments:     
Unrealized holding gains (losses) arising during period$70,449
 $11,159
 $59,290
Portion of other-than-temporary impairment losses recognized in other comprehensive income (loss)
 
 
Less reclassification of net realized gains (losses) included in net income41,961
 3,218
 38,743
Foreign currency translation adjustments(16,507) (83) (16,424)
Other comprehensive income (loss)$11,981
 $7,858
 $4,123
      
Three Months Ended September 30, 2018     
Unrealized appreciation (decline) in value of investments:     
Unrealized holding gains (losses) arising during period$(57,812) $(4,504) $(53,308)
Portion of other-than-temporary impairment losses recognized in other comprehensive income (loss)
 
 
Less reclassification of net realized gains (losses) included in net income(24,380) (1,177) (23,203)
Foreign currency translation adjustments2,167
 104
 2,063
Other comprehensive income (loss)$(31,265) $(3,223) $(28,042)
      
Nine Months Ended September 30, 2019     
Unrealized appreciation (decline) in value of investments:     
Unrealized holding gains (losses) arising during period$573,513
 $65,863
 $507,650
Portion of other-than-temporary impairment losses recognized in other comprehensive income (loss)
 
 
Less reclassification of net realized gains (losses) included in net income112,121
 7,812
 104,309
Foreign currency translation adjustments(6,454) 187
 (6,641)
Other comprehensive income (loss)$454,938
 $58,238
 $396,700
      
Nine Months Ended September 30, 2018     
Unrealized appreciation (decline) in value of investments:     
Unrealized holding gains (losses) arising during period$(335,789) $(30,533) $(305,256)
Portion of other-than-temporary impairment losses recognized in other comprehensive income (loss)
 
 
Less reclassification of net realized gains (losses) included in net income(131,533) (9,226) (122,307)
Foreign currency translation adjustments(9,102) 148
 (9,250)
Other comprehensive income (loss)$(213,358) $(21,159) $(192,199)



Before Tax AmountTax Expense (Benefit)Net of Tax Amount
Three Months Ended September 30, 2020
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period$119,265 $8,483 $110,782 
Less reclassification of net realized gains (losses) included in net income89,204 9,401 79,803 
Foreign currency translation adjustments16,918 209 16,709 
Other comprehensive income (loss)$46,979 $(709)$47,688 
Three Months Ended September 30, 2019
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period$70,449 $11,159 $59,290 
Less reclassification of net realized gains (losses) included in net income41,961 3,218 38,743 
Foreign currency translation adjustments(16,507)(83)(16,424)
Other comprehensive income (loss)$11,981 $7,858 $4,123 
Nine Months Ended September 30, 2020
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period$611,390 $65,099 $546,291 
Less reclassification of net realized gains (losses) included in net income411,137 42,714 368,423 
Foreign currency translation adjustments(5,911)(182)(5,729)
Other comprehensive income (loss)$194,342 $22,203 $172,139 
Nine Months Ended September 30, 2019
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period$573,513 $65,863 $507,650 
Less reclassification of net realized gains (losses) included in net income112,121 7,812 104,309 
Foreign currency translation adjustments(6,454)187 (6,641)
Other comprehensive income (loss)$454,938 $58,238 $396,700 
ARCH CAPITAL 394120192020 THIRD QUARTER FORM 10-Q

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

13.    Guarantor Financial Information

The following tables present condensed financial information for Arch Capital, Arch Capital Group (U.S.) Inc. (“Arch-U.S.”), a 100% owned subsidiary of Arch Capital, and Arch Capital’s other subsidiaries. The senior notes of Arch-U.S. due November 1, 2043 are fully and unconditionally guaranteed by Arch Capital.
 
September 30, 2019
Condensed Consolidating Balance SheetArch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated
Assets         
Total investments$41
 $918,720
 $22,737,556
 $(38,982) $23,617,335
Cash12,696
 72,727
 794,676
 
 880,099
Investments in subsidiaries11,454,186
 4,189,656
 
 (15,643,842) 
Due from subsidiaries and affiliates106
 2
 1,899,559
 (1,899,667) 
Premiums receivable
 
 2,446,539
 (828,353) 1,618,186
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses
 
 8,490,131
 (5,321,936) 3,168,195
Contractholder receivables
 
 2,094,683
 
 2,094,683
Ceded unearned premiums
 
 2,149,492
 (981,234) 1,168,258
Deferred acquisition costs
 
 674,559
 (52,531) 622,028
Goodwill and intangible assets
 
 624,500
 
 624,500
Other assets21,336
 25,586
 1,875,817
 (143,420) 1,779,319
 Total assets$11,488,365
 $5,206,691
 $43,787,512
 $(24,909,965) $35,572,603
           
Liabilities         
Reserve for losses and loss adjustment expenses$
 $
 $17,486,844
 $(5,097,460) $12,389,384
Unearned premiums
 
 5,224,606
 (981,234) 4,243,372
Reinsurance balances payable
 
 1,430,244
 (828,353) 601,891
Contractholder payables
 
 2,094,683
 
 2,094,683
Collateral held for insured obligations
 
 205,449
 

 205,449
Senior notes297,228
 494,803
 1,114,355
 (35,000) 1,871,386
Revolving credit agreement borrowings
 
 490,720
 
 490,720
Due to subsidiaries and affiliates8
 542,103
 1,357,556
 (1,899,667) 
Other liabilities33,033
 55,585
 1,946,208
 (420,917) 1,613,909
 Total liabilities330,269
 1,092,491
 31,350,665
 (9,262,631) 23,510,794
           
Redeemable noncontrolling interests
 
 52,281
 (3,492) 48,789
           
Shareholders’ Equity         
Total shareholders’ equity available to Arch11,158,096
 4,114,200
 11,529,642
 (15,643,842) 11,158,096
Non-redeemable noncontrolling interests
 
 854,924
 
 854,924
 Total shareholders’ equity11,158,096
 4,114,200
 12,384,566
 (15,643,842) 12,013,020
          
 Total liabilities, noncontrolling interests and shareholders’ equity$11,488,365
 $5,206,691
 $43,787,512
 $(24,909,965) $35,572,603







Income Taxes
ARCH CAPITAL 402019 THIRD QUARTER FORM 10-Q

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


  December 31, 2018
Condensed Consolidating Balance SheetArch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated
Assets         
Total investments$104
 $452,674
 $21,307,206
 $(14,700) $21,745,284
Cash6,125
 5,940
 634,491
 
 646,556
Investments in subsidiaries9,735,256
 3,999,243
 
 (13,734,499) 
Due from subsidiaries and affiliates9
 2
 1,802,686
 (1,802,697) 
Premiums receivable
 
 1,834,389
 (535,239) 1,299,150
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses
 
 8,618,660
 (5,699,288) 2,919,372
Contractholder receivables
 
 2,079,111
 
 2,079,111
Ceded unearned premiums
 
 1,730,262
 (754,793) 975,469
Deferred acquisition costs
 
 618,535
 (48,961) 569,574
Goodwill and intangible assets
 
 634,920
 
 634,920
Other assets12,588
 80,949
 1,466,438
 (211,082) 1,348,893
 Total assets$9,754,082
 $4,538,808
 $40,726,698
 $(22,801,259) $32,218,329
           
Liabilities         
Reserve for losses and loss adjustment expenses$
 $
 $17,345,142
 $(5,491,845) $11,853,297
Unearned premiums
 
 4,508,429
 (754,793) 3,753,636
Reinsurance balances payable
 
 928,346
 (535,239) 393,107
Contractholder payables
 
 2,079,111
 
 2,079,111
Collateral held for insured obligations
 
 236,630
 
 236,630
Senior notes297,150
 494,723
 941,655
 
 1,733,528
Revolving credit agreement borrowings
 
 455,682
 
 455,682
Due to subsidiaries and affiliates
 536,805
 1,265,892
 (1,802,697) 
Other liabilities17,105
 26,270
 1,699,768
 (467,484) 1,275,659
 Total liabilities314,255
 1,057,798
 29,460,655
 (9,052,058) 21,780,650
           
Redeemable noncontrolling interests
 
 220,992
 (14,700) 206,292
           
Shareholders’ Equity         
Total shareholders’ equity available to Arch9,439,827
 3,481,010
 10,253,491
 (13,734,501) 9,439,827
Non-redeemable noncontrolling interests
 
 791,560
 
 791,560
 Total shareholders’ equity9,439,827
 3,481,010
 11,045,051
 (13,734,501) 10,231,387
          
 Total liabilities, noncontrolling interests and shareholders’ equity$9,754,082
 $4,538,808
 $40,726,698
 $(22,801,259) $32,218,329


ARCH CAPITAL 412019 THIRD QUARTER FORM 10-Q

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


  Three Months Ended September 30, 2019
Condensed Consolidating Statement of Income and Comprehensive IncomeArch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated
Revenues         
Net premiums earned$
 $
 $1,438,023
 $
 $1,438,023
Net investment income81
 2,899
 181,621
 (23,113) 161,488
Net realized gains (losses)
 1,880
 66,683
 (6,045) 62,518
Net impairment losses recognized in earnings
 
 (1,163) 
 (1,163)
Other underwriting income
 
 3,326
 
 3,326
Equity in net income (loss) of investment funds accounted for using the equity method
 600
 16,530
 
 17,130
Other income (loss)(153) 
 1,491
 
 1,338
 Total revenues(72) 5,379
 1,706,511
 (29,158) 1,682,660
           
Expenses         
Losses and loss adjustment expenses
 
 802,455
 
 802,455
Acquisition expenses
 
 211,120
 
 211,120
Other operating expenses
 
 196,512
 
 196,512
Corporate expenses15,066
 1,631
 364
 
 17,061
Amortization of intangible assets
 
 20,003
 
 20,003
Interest expense5,539
 12,019
 36,712
 (22,942) 31,328
Net foreign exchange (gains) losses1
 
 (25,405) (7,720) (33,124)
 Total expenses20,606
 13,650
 1,241,761
 (30,662) 1,245,355
           
Income (loss) before income taxes(20,678) (8,271) 464,750
 1,504
 437,305
Income tax (expense) benefit
 1,647
 (39,763) 
 (38,116)
Income (loss) before equity in net income of subsidiaries(20,678) (6,624) 424,987
 1,504
 399,189
Equity in net income of subsidiaries413,131
 124,814
 
 (537,945) 
Net income392,453
 118,190
 424,987
 (536,441) 399,189
Net (income) loss attributable to noncontrolling interests
 
 (6,906) 170
 (6,736)
Net income available to Arch392,453
 118,190
 418,081
 (536,271) 392,453
Preferred dividends(10,403) 
 
 
 (10,403)
Net income available to Arch common shareholders$382,050
 $118,190
 $418,081
 $(536,271) $382,050
           
Comprehensive income available to Arch$397,340
 $138,832
 $427,238
 $(566,070) $397,340


ARCH CAPITAL 422019 THIRD QUARTER FORM 10-Q

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


  Three Months Ended September 30, 2018
Condensed Consolidating Statement of Income and Comprehensive IncomeArch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated
Revenues         
Net premiums earned$
 $
 $1,290,878
 $
 $1,290,878
Net investment income2
 1,202
 165,289
 (22,469) 144,024
Net realized gains (losses)
 (64) (51,641) 
 (51,705)
Net impairment losses recognized in earnings
 
 (492) 
 (492)
Other underwriting income
 
 5,823
 
 5,823
Equity in net income (loss) of investment funds accounted for using the equity method
 
 15,982
 
 15,982
Other income (loss)(195) 
 (531) 
 (726)
 Total revenues(193) 1,138
 1,425,308
 (22,469) 1,403,784
           
Expenses         
Losses and loss adjustment expenses
 
 699,420
 
 699,420
Acquisition expenses
 
 201,602
 
 201,602
Other operating expenses
 
 161,098
 
 161,098
Corporate expenses15,170
 446
 (1,281) 
 14,335
Amortization of intangible assets
 
 26,315
 
 26,315
Interest expense5,536
 12,075
 34,276
 (22,157) 29,730
Net foreign exchange (gains) losses
 
 (10,426) (412) (10,838)
 Total expenses20,706
 12,521
 1,111,004
 (22,569) 1,121,662
           
Income (loss) before income taxes(20,899) (11,383) 314,304
 100
 282,122
Income tax (expense) benefit
 2,276
 (35,632) 
 (33,356)
Income (loss) before equity in net income of subsidiaries(20,899) (9,107) 278,672
 100
 248,766
Equity in net income of subsidiaries248,307
 92,906
 
 (341,213) 
Net income (loss)227,408
 83,799
 278,672
 (341,113) 248,766
Net (income) loss attributable to noncontrolling interests
 
 (21,669) 311
 (21,358)
Net income (loss) available to Arch227,408
 83,799
 257,003
 (340,802) 227,408
Preferred dividends(10,402) 
 
 
 (10,402)
Net income (loss) available to Arch common shareholders$217,006
 $83,799
 $257,003
 $(340,802) $217,006
           
Comprehensive income available to Arch$200,524
 $77,389
 $230,565
 $(307,954) $200,524



ARCH CAPITAL 432019 THIRD QUARTER FORM 10-Q

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

  Nine Months Ended September 30, 2019
Condensed Consolidating Statement of Income and Comprehensive IncomeArch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated
Revenues��        
Net premiums earned$
 $
 $4,270,616
 $
 $4,270,616
Net investment income165
 9,425
 532,031
 (68,146) 473,475
Net realized gains (losses)
 16,223
 320,356
 (11,690) 324,889
Net impairment losses recognized in earnings
 
 (2,521) 
 (2,521)
Other underwriting income
 
 18,104
 
 18,104
Equity in net income (loss) of investment funds accounted for using the equity method
 536
 95,997
 
 96,533
Other income (loss)(634) 
 4,184
 
 3,550
 Total revenues(469) 26,184
 5,238,767
 (79,836) 5,184,646
           
Expenses         
Losses and loss adjustment expenses
 
 2,288,530
 
 2,288,530
Acquisition expenses
 
 619,057
 
 619,057
Other operating expenses
 
 596,589
 
 596,589
Corporate expenses46,666
 5,912
 696
 
 53,274
Amortization of intangible assets
 
 60,214
 
 60,214
Interest expense16,615
 35,966
 104,430
 (67,338) 89,673
Net foreign exchange (gains) losses3
 
 (26,715) (4,985) (31,697)
 Total expenses63,284
 41,878
 3,642,801
 (72,323) 3,675,640
           
Income (loss) before income taxes(63,753) (15,694) 1,595,966
 (7,513) 1,509,006
Income tax (expense) benefit
 3,491
 (131,965) 
 (128,474)
Income (loss) before equity in net income of subsidiaries(63,753) (12,203) 1,464,001
 (7,513) 1,380,532
Equity in net income of subsidiaries1,373,688
 410,115
 
 (1,783,803) 
Net income1,309,935
 397,912
 1,464,001
 (1,791,316) 1,380,532
Net (income) loss attributable to noncontrolling interests
 
 (71,405) 808
 (70,597)
Net income available to Arch1,309,935
 397,912
 1,392,596
 (1,790,508) 1,309,935
Preferred dividends(31,209) 
 
 
 (31,209)
Net income available to Arch common shareholders$1,278,726
 $397,912
 $1,392,596
 $(1,790,508) $1,278,726
           
Comprehensive income available to Arch$1,700,369
 $608,108
 $1,779,463
 $(2,387,571) $1,700,369


ARCH CAPITAL 442019 THIRD QUARTER FORM 10-Q

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


  Nine Months Ended September 30, 2018
Condensed Consolidating Statement of Income and Comprehensive IncomeArch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated
Revenues         
Net premiums earned$
 $
 $3,862,540
 $
 $3,862,540
Net investment income37
 2,020
 471,588
 (67,229) 406,416
Net realized gains (losses)29
 (71) (239,272) 
 (239,314)
Net impairment losses recognized in earnings
 
 (1,124) 
 (1,124)
Other underwriting income
 
 15,046
 
 15,046
Equity in net income (loss) of investment funds accounted for using the equity method
 
 52,523
 
 52,523
Other income (loss)2,066
 
 395
 
 2,461
 Total revenues2,132
 1,949
 4,161,696
 (67,229) 4,098,548
           
Expenses         
Losses and loss adjustment expenses
 
 2,062,433
 
 2,062,433
Acquisition expenses
 
 595,816
 
 595,816
Other operating expenses
 
 512,294
 
 512,294
Corporate expenses47,981
 1,205
 2,973
 
 52,159
Amortization of intangible assets
 
 79,523
 
 79,523
Interest expense16,609
 36,014
 104,359
 (66,272) 90,710
Net foreign exchange (gains) losses29
 
 (37,347) (7,505) (44,823)
 Total expenses64,619
 37,219
 3,320,051
 (73,777) 3,348,112
           
Income (loss) before income taxes(62,487) (35,270) 841,645
 6,548
 750,436
Income tax (expense) benefit
 7,704
 (86,643) 
 (78,939)
Income (loss) before equity in net income of subsidiaries(62,487) (27,566) 755,002
 6,548
 671,497
Equity in net income of subsidiaries683,964
 266,053
 
 (950,017) 
Net income621,477
 238,487
 755,002
 (943,469) 671,497
Net (income) loss attributable to noncontrolling interests
 
 (50,976) 956
 (50,020)
Net income available to Arch621,477
 238,487
 704,026
 (942,513) 621,477
Preferred dividends(31,242) 
 
 
 (31,242)
Loss on redemption of preferred shares(2,710) 
 
 
 (2,710)
Net income available to Arch common shareholders$587,525
 $238,487
 $704,026
 $(942,513) $587,525
           
Comprehensive income available to Arch$432,186
 $153,992
 $522,448
 $(676,440) $432,186




ARCH CAPITAL 452019 THIRD QUARTER FORM 10-Q

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


  Nine Months Ended September 30, 2019
Condensed Consolidating Statement
of Cash Flows
Arch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated
Operating Activities         
 Net Cash Provided By (Used For) Operating Activities$42,221
 $525,712
 $1,554,406
 $(579,200) $1,543,139
Investing Activities         
Purchases of fixed maturity investments
 (868,773) (23,313,996) 172,146
 (24,010,623)
Purchases of equity securities
 (74,502) (520,292) 70,743
 (524,051)
Purchases of other investments
 (28,557) (986,368) 
 (1,014,925)
Proceeds from the sales of fixed maturity investments
 482,804
 22,373,404
 (148,354) 22,707,854
Proceeds from the sales of equity securities
 7,441
 434,432
 (70,743) 371,130
Proceeds from the sales, redemptions and maturities of other investments
 1,057
 826,460
 
 827,517
Proceeds from redemptions and maturities of fixed maturity investments
 
 394,719
 
 394,719
Net settlements of derivative instruments
 
 92,423
 
 92,423
Net (purchases) sales of short-term investments63
 31,605
 97,410
 
 129,078
Change in cash collateral related to securities lending
 
 6,990
 
 6,990
Contributions to subsidiaries(2,121) 
 (70,125) 72,246
 
Issuance of intercompany loans
 
 (53,828) 53,828
 
Purchases of fixed assets(32) 
 (27,603) 
 (27,635)
Other
 (10,000) (192,953) 
 (202,953)
 Net Cash Provided By (Used For) Investing Activities(2,090) (458,925) (939,327) 149,866
 (1,250,476)
Financing Activities         
Purchases of common shares under share repurchase program(2,871) 
 
 
 (2,871)
Proceeds from common shares issued, net518
 
 72,246
 (72,246) 518
Proceeds from intercompany borrowings
 
 53,828
 (53,828) 
Proceeds from borrowings
 
 235,083
 (35,000) 200,083
Repayments of intercompany borrowings
 
 
 
 
Repayments of borrowings
 
 (27,538) 
 (27,538)
Change in cash collateral related to securities lending
 
 (6,990) 
 (6,990)
Change in third party investment in redeemable noncontrolling interests
 
 (173,082) 11,208
 (161,874)
Dividends paid to redeemable noncontrolling interests
 
 (12,217) 809
 (11,408)
Dividends paid to parent (1)
 
 (578,391) 578,391
 
Other
 
 (5,207) 
 (5,207)
Preferred dividends paid(31,209) 
 
 
 (31,209)
 Net Cash Provided By (Used For) Financing Activities(33,562) 
 (442,268) 429,334
 (46,496)
Effects of exchange rates changes on foreign currency cash and restricted cash
 
 (8,335) 
 (8,335)
Increase (decrease) in cash and restricted cash6,569
 66,787
 164,476
 
 237,832
Cash and restricted cash, beginning of year6,159
 5,940
 712,544
 
 724,643
Cash and restricted cash, end of period$12,728
 $72,727
 $877,020
 $
 $962,475

(1)     Dividends received by parent are included in net cash provided by (used for) operating activities.


ARCH CAPITAL 462019 THIRD QUARTER FORM 10-Q

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


  Nine Months Ended September 30, 2018
Condensed Consolidating Statement
of Cash Flows
Arch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated
Operating Activities         
 Net Cash Provided By (Used For) Operating Activities$222,097
 $176,851
 $1,622,248
 $(900,209) $1,120,987
Investing Activities         
Purchases of fixed maturity investments
 (214,449) (25,229,184) 605,716
 (24,837,917)
Purchases of equity securities
 
 (819,342) 
 (819,342)
Purchases of other investments
 
 (1,543,332) 
 (1,543,332)
Proceeds from the sales of fixed maturity investments
 111,533
 23,804,386
 (605,716) 23,310,203
Proceeds from the sales of equity securities
 
 866,919
 
 866,919
Proceeds from the sales, redemptions and maturities of other investments
 
 1,178,035
 
 1,178,035
Proceeds from redemptions and maturities of fixed maturity investments
 
 724,021
 
 724,021
Net settlements of derivative instruments
 
 765
 
 765
Net (purchases) sales of short-term investments96,397
 (49,031) 506,949
 
 554,315
Change in cash collateral related to securities lending
 
 137,073
 
 137,073
Contributions to subsidiaries
 (2,500) (29,646) 32,146
 
Purchases of fixed assets(71) 
 (18,979) 
 (19,050)
Other(4) 
 58,231
 
 58,227
 Net Cash Provided By (Used For) Investing Activities96,322
 (154,447) (364,104) 32,146
 (390,083)
Financing Activities         
Redemption of preferred shares(92,555) 
 
 
 (92,555)
Purchases of common shares under share repurchase program(184,529) 
 
 
 (184,529)
Proceeds from common shares issued, net(12,029) 
 32,146
 (32,146) (12,029)
Proceeds from borrowings
 
 167,259
 
 167,259
Repayments of borrowings
 
 (427,000) 
 (427,000)
Change in cash collateral related to securities lending
 
 (137,073) 
 (137,073)
Dividends paid to redeemable noncontrolling interests
 
 (14,447) 956
 (13,491)
Dividends paid to parent (1)
 
 (899,253) 899,253
 
Other
 
 (6,084) 
 (6,084)
Preferred dividends paid(31,242) 
 
 
 (31,242)
 Net Cash Provided By (Used For) Financing Activities(320,355) 
 (1,284,452) 868,063
 (736,744)
Effects of exchange rates changes on foreign currency cash and restricted cash
 
 (11,625) 
 (11,625)
Increase (decrease) in cash and restricted cash(1,936) 22,404
 (37,933) 
 (17,465)
Cash and restricted cash, beginning of year10,048
 30,380
 686,856
 
 727,284
Cash and restricted cash, end of period$8,112
 $52,784
 $648,923
 $
 $709,819

(1)     Dividends received by parent are included in net cash provided by (used for) operating activities.




ARCH CAPITAL 472019 THIRD QUARTER FORM 10-Q

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

14.    Income Taxes

The Company’s income tax provision on income before income taxes resulted in an expenseeffective tax rate of 8.5%8.2% for the nine months ended September 30, 2019,2020, compared to an expense of 10.5%8.5% for the 20182019 period.
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. For interim reporting purposes, the Company has calculated its annual effective tax rate for the full year of 2019 by treating excess tax benefits in the U.S. that arise from the accounting for stock based compensation as a discrete item. As such, this amount is not included when projecting the Company’s full year annual effective tax rate but rather is accounted for at the U.S. Federal statutory rate of 21% after applying the projected full year annual effective tax rate to actual nine months results before the discrete item. The impact of the discrete item resulted in a benefit of 0.4% for the nine months ended September 30, 2019.
The Company had a net deferred tax liabilityasset of $55.9$29.7 million at September 30, 2019,2020, compared to a net deferred tax assetliability of $22.5$53.5 million at December 31, 2018.2019. The change is primarily a result of fluctuations in the appreciation of the Company’s fixed maturities from December 31, 2018 to September 30, 2019.contingency reserve. In addition, the Company paid $47.1$146.8 million and recovered $34.0$47.1 million of income taxes for the nine months ended September 30, 20192020 and 2018,2019, respectively.
15.14.    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 September 30, 2019,2020, the Company was not a party to any litigation or arbitration which is expected by management to have a material adverse effect on the Company’s results of operations and financial condition and liquidity.

15.    Transactions with Related Parties
In 2017, the Company acquired approximately 25% of Premia Holdings Ltd. Premia Holdings Ltd. is the parent of Premia Reinsurance Ltd., a multi-line Bermuda reinsurance company (together with Premia Holdings Ltd., “Premia”). Premia’s strategy is to reinsure or acquire companies or reserve portfolios in the non-life property and casualty insurance and reinsurance run-off market. Arch Re Bermuda and certain Arch co-investors invested $100.0 million and acquired approximately 25% of Premia as well as warrants to purchase additional common equity. Arch has appointed 2 directors to serve on the 7 person board of directors of Premia. Arch Re Bermuda is providing a 25% quota share reinsurance treaty on certain business written by Premia.
In the 2019 fourth quarter, Barbican Group Holdings Limited (“Barbican”), a wholly owned subsidiary of the Company, entered into certain reinsurance and related transactions with Premia pursuant to which Premia assumed a transfer of liability for the 2018 and prior years of account of Barbican as of July 1, 2019. Barbicanrecorded reinsurance recoverable on unpaid and paid losses and funds held liability of $175.8 million and $150.2 million, respectively, at September 30, 2020, compared to $177.7 million and $180.0 million, respectively, at December 31, 2019. 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.

ARCH CAPITAL 422020 THIRD QUARTER FORM 10-Q

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


Bellemeade Re 2019-42020-3 Ltd.
In October 2019,November 2020, the Company’s first-lien U.S. mortgage insurance subsidiaries entered into an aggregate excess of loss reinsurance agreement with Bellemeade Re 2019-42020-3 Ltd. (“Bellemeade 2019-4”2020-3”), a special purpose reinsurance company domiciled in Bermuda. The Bellemeade 2019-42020-3 agreement provides for up to $577.3$451.8 million of aggregate excess of loss reinsurance coverage at inception in excess of $162.4$173.8 million of aggregate losses for new delinquencies on a portfolio of in-force policies primarily issued in the first half of 2019.from June 1 through August 31, 2020. The coverage
amount decreases over a ten-year period as the underlying covered mortgages amortize.
Bellemeade 2019-42020-3 financed the coverage through the issuance of mortgage insurance-linked notes in an aggregate amount of approximately $577.3$418.2 million to unrelated investors (the “Notes”). and an additional $33.7 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers. The maturity date of the Notes is October 25, 2029.2030. The Notes will be redeemed prior to maturity upon the occurrence of a mandatory termination event or if the ceding insurers trigger a termination of the reinsurance agreement following the occurrence of an optional termination event. All of the proceeds paid to Bellemeade 2019-42020-3 from the sale of the Notes were deposited into a reinsurance trust as security for Bellemeade 2019-4’s2020-3’s obligations. At all times, funds in the reinsurance trust account are required to be invested in high credit quality money market funds.
Catastrophic Events
Watford
In November 2020, the 2019 fourth quarter, Typhoon Hagibis, the ongoing wildfiresCompany announced a revised definitive agreement under which it will acquire, in Californiapartnership with funds managed by Warburg Pincus LLC (“Warburg Pincus”) and other catastrophic events may have an impact on the Company’s financial results. It is too early to reasonably estimate losses for these events given the significant uncertainties and the early stageKelso & Company (“Kelso”), all of the damage assessment process, among other factors.
Share Repurchases
At September 30, 2019,common shares of Watford for $35.00 per share or approximately $160.9 million$700 million. The transaction is expected to close in the first quarter of share repurchases were available under Arch Capital’s share repurchase program. From October 1 through October 31, 2019,2021 and remains subject to customary closing conditions, including regulatory and shareholder approvals. Under the merger agreement, the Company did not repurchase any common shares. On November 8, 2019,assigned its current interests and obligations in Watford to a newly formed subsidiary which will acquire the boardoutstanding shares of directorsWatford. At closing, the Company will own approximately 40% of ACGL increased the aggregate purchase amount authorized under the share repurchase program to $1.0 billion. Repurchases under this authorization may be effected from time to time in open market or privately negotiated transactions through December 31, 2021. The timingWatford, Warburg Pincus and amount of the repurchase transactions under this authorizationKelso will depend on a variety of factors, including market conditions and corporate and regulatory considerations.

each own approximately 30%.

ARCH CAPITAL 432020 THIRD QUARTER FORM 10-Q

ARCH CAPITAL 482019 THIRD QUARTER FORM 10-Q

ITEM 2.     MANAGEMENT’S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS OF OPERATIONS


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, 20182019 (“20182019 Form 10-K”). In addition, readers should review “Risk Factors” set forth in Item 1A of Part I of our 20182019 Form 10-K.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 Bermuda public limited liability company with approximately $12.89$15.2 billion in capital at September 30, 20192020 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 objective is to achieve an average operating return on average equity of 15% or greater over the insurance cycle, whichIn keeping with our longstanding underwriting approach we believe to be an attractive return to our common shareholders given the risks we assume. We continue to look for opportunities to find acceptable books of business to underwrite without sacrificing underwriting discipline and continue to write a portion of our overall book in catastrophe-exposed business which has the potential to increase the volatility of our operating results. From an operating perspective, the 2020 third quarter reflected the benefits of rate improvements as all three of our underwriting segments are seeing attractive opportunities to grow at acceptable rates of return.
Across all linesConsequently, these rate improvements have enabled us to continue to expand writings in our property casualty segments as risk adjusted returns are increasingly achieved. We know from experience that this is an opportune time to significantly expand our participation into this hardening market. In the insurance business, renewalsegment, our rate increases for the third quarter averaged over 11% and we believe that this trend of increasing rates experienced a modest increase as net premiums grewwill continue through 2021. To support this growth, we raised an additional $1.0 billion of capital in the 2019 third quarter. Reinsurance pricing tendsform of long-term senior notes at the end of June 2020 and continue to followdeploy capital to those lines that provide the best expected returns.
COVID-19 has continued to significantly impact social and economic activity in the U.S. and global markets. We are committed to the safety of our employees, including restricting travel and instituting an extensive work from home
policy. These actions have helped prevent a major disruption to our clients and operations. The impact of the primary insurance industry although catastrophespread of COVID-19, a developing recession and large attritionalrelated levels of unemployment has changed some of our outlook for 2020, but we are navigating this period with a strong capital base. The extent to which COVID-19 impacts our business, results of operations and financial results depends on numerous evolving factors including, but not limited to: the magnitude and duration of COVID-19, the extent to which it will impact macroeconomic conditions, the speed of the anticipated recovery and governmental, business and individual reactions to the pandemic. Given the continuing evolution of the COVID-19 outbreak and the response to curb its spread, currently we are not able to estimate the future effects of the COVID-19 outbreak to our results of operations, financial condition, or liquidity.
For the 2020 third quarter and nine months ended September 30, 2020, we recorded $11.9 million and $271.6 million, respectively, for COVID-19 losses across our property casualty segments. We continue to have limited information to accurately quantify our potential exposure to the pandemic in certain areas but have established IBNR reserves for occurrences based on policy terms and conditions including limits, sub-limits, and deductibles. These reserves were recorded across a number of lines of business, such as trade credit, travel, workers compensation and property where we have limited exposure to policies that do not contain a specific pandemic exclusion and/or explicitly afford business interruption coverage under a pandemic. Given the Japanese typhoons this year, inunusual circumstances and breadth of the reinsurance market can disproportionately affect results and create opportunities.pandemic, we have classified COVID-19 losses as a catastrophe.
For our U.S. primary mortgage operations, reported delinquencies were 4.69% at September 30, 2020, compared to 5.14% at June 30, 2020. Delinquencies continue to be better than our expectations at the beginning of the COVID-19 pandemic. We believe that property facultativethe mortgage insurance industry is benefiting from solid credit quality of loan originations in the years after the 2008 Great Financial Crisis, a favorable supply and marine businessesdemand imbalance in housing and government intervention. However, delinquency rates remain at elevated levels, reflecting the impact of the recession and forbearance programs under the CARES Act to borrowers experiencing a hardship during COVID-19. Forbearance allows for mortgage payments to be suspended for up to 360 days along with a suspension of foreclosures and evictions. See “Results of Operations—Mortgage Segment” for further details on our mortgage operations.
ARCH CAPITAL 442020 THIRD QUARTER FORM 10-Q

Record mortgage originations fueled by low mortgage rates are examplescontinuing to create surges in both purchase and refinancing activity. There remains significant uncertainty on the economy’s health and the lack of improving markets.a full understanding on how COVID-19 may impact individual borrowers and, as such, caution is warranted on predicting how this will ultimately affect our results of operations.

Our underwriting teams continueWe believe that delinquency rates could increase in the future from the current level, as additional borrowers may request forbearance on their mortgage loans under the CARES Act. We would record loss reserves on these delinquencies which would result in elevated levels of incurred losses over the coming quarters. Over time, we would expect many of these delinquencies to executecure and revert back to performing loans as the economy returns to a disciplined strategy by emphasizing smallless-stressed state. At this time, we do not have enough visibility to predictably forecast the rate at which forbearance delinquencies will be reported to us, cure or ultimately turn into claims on an annual, let alone a quarterly basis. That said, based on our current analysis which tells us that the pandemic will represent an earnings event for our mortgage segment and medium-sized accounts over large accounts, shrinking premiums in more commoditized lines such as general liability and by utilizing reinsurance purchases to reduce volatility on large account, high capacity business. The spread between rate changes and loss trendnot a capital event, our current expectation continues to be a key variable in assessing expected returns and can be difficult to quantify precisely, particularly in specialty lines.
Ourthat our pre-tax underwriting income for the entire mortgage segment continueswill be significantly lower than in 2019. However, there is likely to experience generally favorable market conditions. Although pricing remains competitivebe variability in underwriting income between quarters based on the U.S., borrower credit quality andtiming of receipt of notice of defaults. For further discussion of the general economy remain strong. Our results continue to reflect our success in making high quality credit underwriting risk decisions and building customer relationships.potential impacts of COVID-19, see “ITEM 1A—Risk Factors”.
Arch remains 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,“GSEs. in 2018. Such programs have continued to generate business. In addition, we completed Bellemeade risk transfers in March, April, JulyJune, September and October 2019,November 2020, increasing our protection for mortgage tail risk. The Bellemeade structures provide approximately $3.9 billion of aggregate reinsurance coverage.

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 $28.75 at September 30, 2020, compared to $27.62 at June 30, 2020 and $25.61 at September 30, 2019, compared to $24.64 at June 30, 2019 and $21.15 at September 30, 2018.2019. The 3.9%4.1% increase for the 20192020 third quarter reflected strong underwriting results and the impact of a decrease in interest ratestotal return on our fixed income securitiesinvestments, partially offset by the impact of catastrophic events including COVID-19 on underwriting results, while the 21.1% 12.2% increase 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

ARCH CAPITAL 492019 THIRD QUARTER FORM 10-Q


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,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 loss on redemption of preferred shares 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 4.2% for the 2020 third quarter, compared to 10.3% for the 2019 third quarter, compared to 11.4%and 3.9% for the 2018 third quarter, and 12.0% for the nine months ended September 30, 2019,2020, compared to 11.4%12.0% for the 20182019 period. The 2019 and 2018lower 2020 returns reflected favorable mortgage insurancethe impact of elevated catastrophic activity including COVID-19 on underwriting performance, strongresults and lower investment returns and a low level of catastrophic activity.income than in the 2019 periods.
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
ARCH CAPITAL 452020 THIRD QUARTER FORM 10-Q

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):
2020 Third Quarter2.30 %2.41 %
2019 Third Quarter1.00 %0.70 %
Nine Months Ended September 30, 20205.19 %3.67 %
Nine Months Ended September 30, 20196.20 %5.79 %
 
Arch
Portfolio
 
Benchmark
Return
Pre-tax total return (before investment expenses):   
2019 Third Quarter1.00 % 0.70 %
2018 Third Quarter0.31 % 0.36 %
    
Nine Months Ended September 30, 20196.20 % 5.79 %
Nine Months Ended September 30, 2018(0.19)% (0.46)%

Total return for the 2019 periods2020 third quarter reflected the impact of a decline inlower interest rates which increasedon our fixed income portfolio. In addition, returns from our equity and alternative investments contributed approximately 40% of the total return onfor the quarter. The total return for the nine months ended September 30, 2020 outperformed our investment grade fixed income portfolio, aided by favorable returns on equities.benchmark return index.
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 September 30, 2019,2020, the benchmark return index had an average credit quality of “Aa3” by Moody’s Investors Service (“Moody’s”), and an estimated duration of 2.973.06 years.
The benchmark return index included weightings to the following indices:
%
ICE BoAML 1-10 Year AAAA - AAAA U.S. Corporate Index21.00%
ICE BoAML 1-5 Year U.S. Treasury Index15.00
MSCI ACWI Net Total Return USD Index8.60 
ICE BoAML 3-5 Year Fixed Rate Asset Backed Securities Index7.00
ICE BoAML 1-10 Year U.S. Municipal SecuritiesS&P Leveraged Loan Total Return Index5.005.20 
Bloomberg Barclays CMBS Invest Grade Aaa Total Return Index5.00
MSCI ACWI Net Total Return USD Index5.00
Hedge Fund Research HFRX Fixed Income Credit Index5.00
Hedge Fund Research HFRX Equal Weighted Strategies5.00
ICE BoAML 1-10 Year BBB U.S. Corporate Index4.00
ICE BoAML U.S. Mortgage Backed Securities Index4.00 
ICE BoAML 1-5 Year U.K. Gilt Index4.00 
ICE BoAML German Government 1-10 Year Index4.003.50 
ICE BoAML U.S. Mortgage Backed Securities Index4.00
ICE BoAML 0-3 Month U.S. Treasury Bill Index4.003.25 
ICE BoAML 1-51-10 Year U.K. GiltU.S. Municipal Securities Index3.503.00 
ICE BoAML 5-10 Year U.S. Treasury Index3.00
ICE BoAML 1-5 Year Australian GovernmentsAustralia Government Index3.002.75 
ICE BoAML U.S. High Yield Constrained Index2.50
S&P Leveraged Loan Total Return Index2.50
ICE BoAML 1-5 Year Canada Government Index1.002.00 
Bloomberg Barclays Global High Yield Total Return Index1.50 
Hedge Fund Research HFRX ED Distressed Restructuring Index (Flagship Funds)1.50 
Dow Jones Global ex-US Select Real Estate Securities Total Return Net Index0.90 
FTSE Nareit All Mortgage Capped Index Total Return USD0.90 
Bloomberg Barclays CMBS: Erisa Eligible Unhedged USD0.90 
ICE BoAML 20+ Year Canada Government Index0.50
Total100.00%
COMMENT ON NON-GAAP FINANCIAL MEASURES

Throughout this filing, we present our operations in the way we believe will be the most meaningful and useful to investors, analysts, rating agencies and others who use our financial information in evaluating the performance of our company. This presentation includes the use of after-tax operating income available to Arch common shareholders, which is defined as net income available to Arch common shareholders, excluding net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings,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 loss on redemption of preferred shares and income taxes, and the use of annualized operating return on average common equity. The presentation

ARCH CAPITAL 502019 THIRD QUARTER FORM 10-Q


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
ARCH CAPITAL 462020 THIRD QUARTER FORM 10-Q

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, 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 and transaction costs and other and loss on redemption of preferred shares in any particular period are not indicative of the performance of, or trends in, our business. Although net realized gains or losses, net impairment losses recognized in earnings, 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 ourthe 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. The loss on redemption of preferred shares related to the redemption of our Series C preferred shares in January 2018 and had no impact on shareholders' equity or cash flows. Due to these reasons, we exclude net realized gains
or losses, 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 and transaction costs and other and loss on redemption of preferred shares 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 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

ARCH CAPITAL 512019 THIRD QUARTER FORM 10-Q


from the ‘other’ segment. The ‘other’ segment includes 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 generally accepted
ARCH CAPITAL 472020 THIRD QUARTER FORM 10-Q

accounting principles, Watford is considered a variable interest entity and we concluded that we are the primary beneficiary of Watford. As such, we consolidate the results of Watford in our consolidated financial statements, although we only own approximately 11%13% 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.

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, on the capital held in the business, and compares the return generated by our investment portfolio against benchmark returns which we measured our portfolio against during the periods.
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 approximate 11%percentage ownership of Watford’s common equity.equity during such period.
Three Months EndedNine Months Ended
September 30,September 30,
2020201920202019
Net income available to Arch common shareholders$408,636 $382,050 $830,768 $1,278,726 
Net realized (gains) losses(219,726)(77,959)(517,007)(316,882)
Equity in net (income) loss of investment funds accounted for using the equity method(126,735)(17,130)(57,407)(96,533)
Net foreign exchange (gains) losses39,462 (30,160)17,003 (29,100)
Transaction costs and other1,674 1,995 5,246 5,363 
Income tax
expense (1)
17,010 2,156 48,088 12,708 
After-tax operating income available to Arch common shareholders$120,321 $260,952 $326,691 $854,282 
Beginning common shareholders’ equity$11,211,825 $9,977,352 $10,717,371 $8,659,827 
Ending common shareholders’ equity11,671,997 10,378,096 11,671,997 10,378,096 
Average common shareholders’ equity$11,441,911 $10,177,724 $11,194,684 $9,518,962 
Annualized return on average common equity %14.3 15.0 9.9 17.9 
Annualized operating return on average
common equity %
4.2 10.3 3.9 12.0 
(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.
 Three Months Ended Nine Months Ended
 September 30, September 30,
 2019 2018 2019 2018
Net income available to Arch common shareholders$382,050
 $217,006
 $1,278,726
 $587,525
Net realized (gains) losses(79,122) 47,528
 (319,403) 220,718
Net impairment losses recognized in earnings1,163
 492
 2,521
 1,124
Equity in net (income) loss of investment funds accounted for using the equity method(17,130) (15,982) (96,533) (52,523)
Net foreign exchange (gains) losses(30,160) (7,539) (29,100) (39,021)
Transaction costs and other1,995
 1,091
 5,363
 8,829
Loss on redemption of preferred shares
 
 
 2,710
Income tax expense (benefit) (1)2,156
 (316) 12,708
 (9,343)
After-tax operating income available to Arch common shareholders$260,952
 $242,280
 $854,282
 $720,019
        
Beginning common shareholders’ equity$9,977,352
 $8,383,755
 $8,659,827
 $8,324,047
Ending common shareholders’ equity10,378,096
 8,575,148
 10,378,096
 8,575,148
Average common shareholders’ equity$10,177,724
 $8,479,452
 $9,518,962
 $8,449,598
        
Annualized return on average common equity %15.0
 10.2
 17.9
 9.3
Annualized operating return on average
common equity %
10.3
 11.4
 12.0
 11.4
(1)Income tax expense (benefit) on net realized gains or losses, 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 loss on redemption of preferred shares reflects the relative mix reported by jurisdiction and the varying tax rates in each jurisdiction.

ARCH CAPITAL 524820192020 THIRD QUARTER FORM 10-Q


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 President and Chief Executive Officer of Arch Capital and the Chief Financial 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 September 30, Three Months Ended September 30,
2019 2018 % Change 20202019
Change
Gross premiums written$1,005,874
 $836,820
 20.2
Gross premiums written$1,206,328 $1,005,874 19.9 
Premiums ceded(302,034) (259,968)  Premiums ceded(382,167)(302,034)
Net premiums written703,840
 576,852
 22.0
Net premiums written824,161 703,840 17.1 
Change in unearned premiums(98,504) (15,794)  Change in unearned premiums(105,007)(98,504)
Net premiums earned605,336
 561,058
 7.9
Net premiums earned719,154 605,336 18.8 
Other underwriting income (loss)Other underwriting income (loss)(31)—  
Losses and loss adjustment expenses(422,782) (409,435)  
Losses and loss adjustment expenses(525,321)(422,782) 
Acquisition expenses(91,259) (88,255)  
Acquisition expenses(102,420)(91,259) 
Other operating expenses(115,408) (90,081)  
Other operating expenses(122,541)(115,408) 
Underwriting income (loss)$(24,113) $(26,713)  n/m
Underwriting income (loss)$(31,159)$(24,113)(29.2)
     
Underwriting Ratios 
  
 % Point
Change
Underwriting Ratios  % Point
Change
Loss ratio69.8% 73.0% (3.2)Loss ratio73.0 %69.8 %3.2 
Acquisition expense ratio15.1% 15.7% (0.6)Acquisition expense ratio14.2 %15.1 %(0.9)
Other operating expense ratio19.1% 16.1% 3.0
Other operating expense ratio17.0 %19.1 %(2.1)
Combined ratio104.0% 104.8% (0.8)Combined ratio104.2 %104.0 %0.2 
Nine Months Ended September 30, Nine Months Ended September 30,
2019 2018 % Change 20202019%
Change
Gross premiums written$2,867,753
 $2,429,570
 18.0
Gross premiums written$3,444,335 $2,867,753 20.1 
Premiums ceded(914,751) (752,413)  Premiums ceded(1,119,165)(914,751)
Net premiums written1,953,002
 1,677,157
 16.4
Net premiums written2,325,170 1,953,002 19.1 
Change in unearned premiums(201,719) (30,913)  Change in unearned premiums(202,188)(201,719)
Net premiums earned1,751,283
 1,646,244
 6.4
Net premiums earned2,122,982 1,751,283 21.2 
Other underwriting income (loss)Other underwriting income (loss)(31)—  
Losses and loss adjustment expenses(1,168,677) (1,120,630)  
Losses and loss adjustment expenses(1,550,632)(1,168,677) 
Acquisition expenses(265,177) (264,094)  
Acquisition expenses(317,428)(265,177) 
Other operating expenses(338,327) (274,735)  
Other operating expenses(370,947)(338,327) 
Underwriting income (loss)$(20,898) $(13,215)  n/m
Underwriting income (loss)$(116,056)$(20,898)(455.3)
     
Underwriting Ratios 
  
 % Point
Change
Underwriting Ratios  % Point
Change
Loss ratio66.7% 68.1% (1.4)Loss ratio73.0 %66.7 %6.3 
Acquisition expense ratio15.1% 16.0% (0.9)Acquisition expense ratio15.0 %15.1 %(0.1)
Other operating expense ratio19.3% 16.7% 2.6
Other operating expense ratio17.5 %19.3 %(1.8)
Combined ratio101.1% 100.8% 0.3
Combined ratio105.5 %101.1 %4.4 
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
ARCH CAPITAL 492020 THIRD QUARTER FORM 10-Q

managers with unique expertise and niche products offering

ARCH CAPITAL 532019 THIRD QUARTER FORM 10-Q


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 stand alonestandalone 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 September 30,
Three Months Ended September 30, 20202019
2019 2018 Amount%Amount%
Amount % Amount %
Professional Lines$137,569
 19.5
 $113,100
 19.6
Property, energy, marine and aviationProperty, energy, marine and aviation$152,193 18.5 $97,966 13.9 
Professional linesProfessional lines199,163 24.2 137,569 19.5 
Programs120,039
 17.1
 103,928
 18.0
Programs123,768 15.0 120,039 17.1 
Property, energy, marine and aviation97,966
 13.9
 60,909
 10.6
Construction and national accounts98,522
 14.0
 71,888
 12.5
Construction and national accounts88,790 10.8 98,522 14.0 
Excess and surplus casualtyExcess and surplus casualty78,889 9.6 62,843 8.9 
Travel, accident and health75,192
 10.7
 79,450
 13.8
Travel, accident and health28,972 3.5 75,192 10.7 
Excess and surplus casualty62,843
 8.9
 44,829
 7.8
Lenders products31,005
 4.4
 25,995
 4.5
Lenders products60,830 7.4 31,005 4.4 
Other80,704
 11.5
 76,753
 13.3
Other91,556 11.1 80,704 11.5 
Total$703,840
 100.0
 $576,852
 100.0
Total$824,161 100.0 $703,840 100.0 
20192020 Third Quarter versus 2018 Third Quarter2019 Period. . Gross premiums written by the insurance segment in the 20192020 third quarter were 20.2%19.9% higher than in the 20182019 third quarter, while net premiums written were 22.0%17.1% higher. Approximately thirty percentThe higher level of the growth in net premiums written resulted from our acquisition of renewal rights of a U.K. commercial lines book of business on January 1, 2019. The remainder was due to growth in existing accounts and ratereflected increases across most lines of business.business, due in part to new business opportunities, rate increases and growth in existing accounts, partially offset by a decrease in travel business, reflecting the ongoing impact of the COVID-19 global pandemic.
Nine Months Ended September 30,
Nine Months Ended September 30, 20202019
2019 2018 Amount%Amount%
Amount % Amount %
Professional Lines$388,482
 19.9
 $341,187
 20.3
Property, energy, marine and aviationProperty, energy, marine and aviation$439,579 18.9 $272,271 13.9 
Professional linesProfessional lines526,180 22.6 388,482 19.9 
Programs329,882
 16.9
 300,662
 17.9
Programs341,230 14.7 329,882 16.9 
Property, energy, marine and aviation272,271
 13.9
 175,157
 10.4
Construction and national accounts254,765
 13.0
 236,700
 14.1
Construction and national accounts261,933 11.3 254,765 13.0 
Excess and surplus casualtyExcess and surplus casualty209,011 9.0 166,474 8.5 
Travel, accident and health239,833
 12.3
 223,196
 13.3
Travel, accident and health183,015 7.9 239,833 12.3 
Excess and surplus casualty166,474
 8.5
 126,793
 7.6
Lenders products75,793
 3.9
 70,269
 4.2
Lenders products117,812 5.1 75,793 3.9 
Other225,502
 11.5
 203,193
 12.1
Other246,410 10.6 225,502 11.5 
Total$1,953,002
 100.0
 $1,677,157
 100.0
Total$2,325,170 100.0 $1,953,002 100.0 
Nine Months Ended September 30, 2020 versus 2019 versus 2018 periodPeriod. Gross premiums written by the insurance segment for the nine months ended September 30, 20192020 were 18.0%20.1% higher than in the 20182019 period, while net premiums written were 16.4%19.1% higher. The higher than in the 2018 period. Growth inlevel of net premiums written primarily resulted from our acquisition of renewal rights of a U.K. commercialreflected increases in most lines book of business, on January 1, 2019, with the remainder reflectingprimarily due to new business opportunities, rate increases and growth in existing accounts and rate increases across most linesaccounts. Such amounts were partially offset by a decrease in travel business, primarily due to the ongoing impact of business.COVID-19.
Net Premiums Earned.
The following tables set forth our insurance segment’s net premiums earned by major line of business:
 Three Months Ended September 30,
 20202019
 Amount%Amount%
Property, energy, marine and aviation$133,827 18.6 $80,246 13.3 
Professional lines168,502 23.4 135,343 22.4 
Programs104,861 14.6 104,432 17.3 
Construction and national accounts95,386 13.3 81,472 13.5 
Excess and surplus casualty69,978 9.7 53,991 8.9 
Travel, accident and health36,726 5.1 81,952 13.5 
Lenders products33,401 4.6 (5,724)(0.9)
Other76,473 10.6 73,624 12.2 
Total$719,154 100.0 $605,336 100.0 
 Three Months Ended September 30,
 2019 2018
 Amount % Amount %
Professional Lines$135,343
 22.4
 $115,271
 20.5
Programs104,432
 17.3
 96,509
 17.2
Property, energy, marine and aviation80,246
 13.3
 53,857
 9.6
Construction and national accounts81,472
 13.5
 80,381
 14.3
Travel, accident and health81,952
 13.5
 81,405
 14.5
Excess and surplus casualty53,991
 8.9
 43,401
 7.7
Lenders products (1)(5,724) (0.9) 24,254
 4.3
Other73,624
 12.2
 65,980
 11.8
Total$605,336
 100.0
 $561,058
 100.0
(1)Reflects a change in earning patterns on certain business in the 2019 third quarter.

ARCH CAPITAL 545020192020 THIRD QUARTER FORM 10-Q


Nine Months Ended September 30,
Nine Months Ended September 30, 20202019
2019 2018 Amount%Amount%
Amount % Amount %
Professional Lines$365,801
 20.9
 $343,515
 20.9
Property, energy, marine and aviationProperty, energy, marine and aviation$365,791 17.2 $208,879 11.9 
Professional linesProfessional lines475,014 22.4 365,801 20.9 
Programs304,605
 17.4
 288,853
 17.5
Programs322,203 15.2 304,605 17.4 
Property, energy, marine and aviation208,879
 11.9
 153,300
 9.3
Construction and national accounts234,198
 13.4
 239,377
 14.5
Construction and national accounts286,691 13.5 234,198 13.4 
Excess and surplus casualtyExcess and surplus casualty196,041 9.2 144,218 8.2 
Travel, accident and health237,163
 13.5
 222,994
 13.5
Travel, accident and health166,218 7.8 237,163 13.5 
Excess and surplus casualty144,218
 8.2
 129,994
 7.9
Lenders products (1)41,078
 2.3
 70,231
 4.3
Lenders productsLenders products81,855 3.9 41,078 2.3 
Other215,341
 12.3
 197,980
 12.0
Other229,169 10.8 215,341 12.3 
Total$1,751,283
 100.0
 $1,646,244
 100.0
Total$2,122,982 100.0 $1,751,283 100.0 
(1)Reflects a change in earning patterns on certain business in the 2019 third quarter.
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 in the 20192020 third quarter were 7.9%18.8% higher than in the 20182019 third quarter. For the nine months ended September 30, 2019,2020, net premiums earned were 6.4%21.2% higher than in the 20182019 period. Net premiums earned reflect changes in net premiums written over the previous five quarters.
Losses and Loss Adjustment Expenses.
The table below shows the components of the insurance segment’s loss ratio:
Three Months Ended Nine Months EndedThree Months EndedNine Months Ended
September 30, September 30,September 30,September 30,
2019 2018 2019 2018 2020201920202019
Current year70.5 % 74.1 % 67.4 % 69.0 %Current year73.3 %70.5 %73.3 %67.4 %
Prior period reserve development(0.7)% (1.1)% (0.7)% (0.9)%Prior period reserve development(0.3)%(0.7)%(0.3)%(0.7)%
Loss ratio69.8 % 73.0 % 66.7 % 68.1 %Loss ratio73.0 %69.8 %73.0 %66.7 %
Current Year Loss Ratio.
2020 Third Quarter versus 2019 Period. The insurance segment’s current year loss ratio in the 20192020 third quarter was 3.62.8 points lowerhigher than in the 20182019 third quarter. The 2020 third quarter andloss ratio reflected 4.310.3 points of current year catastrophic activity, primarily related to Hurricane Dorian,Hurricanes Isaias, Laura and Sally, including 0.5 points related to COVID-19 exposure, compared to 5.84.3 points inof catastrophic activity for the 20182019 third quarter primarily related to Hurricane Florence.quarter.
Nine Months Ended September 30, 2020 versus 2019 Period. The insurance segment’s current year loss ratio for the nine months ended September 30, 20192020 was 1.65.9 points lowerhigher than in the 2018 period and2019 period. The loss ratio for the nine months ended September 30, 2020 reflected 1.69.9 points of current year catastrophic activity, including 5.5 points for exposure related to COVID-19, compared to 2.51.6 points of catastrophic
activity in the 20182019 period. The balance of the change in the 20192020 loss ratios resulted, in part, from changes in mix of business, and the level of large attritional losses.losses and the effect of rate increases.
Prior Period Reserve Development.
The insurance segment’s net favorable development was $2.3 million, or 0.3 points, for the 2020 third quarter, compared to $4.4 million, or 0.7 points, for the 2019 third quarter, compared toand $5.9 million, or 1.1 points, for the 2018 third quarter, and $11.4 million, or 0.70.3 points, for the nine months ended September 30, 2019,2020, compared to $14.1$11.4 million, or 0.90.7 points, for the 20182019 period. The 2019 third quarter loss ratio reflected a lower level of large attritional losses than in the 2018 third quarter. 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.
20192020 Third Quarter versus 2018 Third Quarter2019 Period. . The insurance segment’s underwriting expense ratio was 31.2% in the 2020 third quarter, compared to 34.2% in the 2019 third quarter, compared to 31.8% inwith the 2018 third quarter. Operating expenses increased in the 2019 third quarterdecrease primarily due to our 2019 acquisitions, which increased the operating expense ratio. The resulting increase in the expense ratio was partially offset by the growth in net premiums earned.
Nine Months Ended September 30, 2020 versus 2019 versus 2018 periodPeriod. The insurance segment’s underwriting expense ratio was 34.4%32.5% for the nine months ended September 30, 2019,2020, compared to 32.7%34.4% for the 2018 period. Operating expenses increased for2019 period, with the nine months ended September 30, 2019decrease primarily due to our 2019 acquisitions.growth in net premiums earned.
Reinsurance Segment 
The following tables set forth our reinsurance segment’s underwriting results:
Three Months Ended September 30, Three Months Ended September 30,
2019 2018 % Change 20202019% Change
Gross premiums written$662,572
 $435,396
 52.2
Gross premiums written$1,004,590 $662,572 51.6 
Premiums ceded(226,096) (123,705)  Premiums ceded(400,388)(226,096)
Net premiums written436,476
 311,691
 40.0
Net premiums written604,202 436,476 38.4 
Change in unearned premiums(72,621) (18,418)  Change in unearned premiums(49,704)(72,621)
Net premiums earned363,855
 293,273
 24.1
Net premiums earned554,498 363,855 52.4 
Other underwriting income(1,208) 1,387
  
Other underwriting income (loss)Other underwriting income (loss)298 (1,208) 
Losses and loss adjustment expenses(270,379) (183,413)  
Losses and loss adjustment expenses(422,084)(270,379) 
Acquisition expenses(62,393) (50,367)  
Acquisition expenses(85,388)(62,393) 
Other operating expenses(32,533) (29,936)  
Other operating expenses(41,818)(32,533) 
Underwriting income$(2,658) $30,944
 (108.6)
Underwriting income (loss)Underwriting income (loss)$5,506 $(2,658)307.1 
     
Underwriting Ratios    % Point
Change
Underwriting Ratios% Point
Change
Loss ratio74.3% 62.5% 11.8
Loss ratio76.1 %74.3 %1.8 
Acquisition expense ratio17.1% 17.2% (0.1)Acquisition expense ratio15.4 %17.1 %(1.7)
Other operating expense ratio8.9% 10.2% (1.3)Other operating expense ratio7.5 %8.9 %(1.4)
Combined ratio100.3% 89.9% 10.4
Combined ratio99.0 %100.3 %(1.3)

ARCH CAPITAL 555120192020 THIRD QUARTER FORM 10-Q


Nine Months Ended September 30, Nine Months Ended September 30,
2019 2018 % Change 20202019% Change
Gross premiums written$1,890,974
 $1,503,206
 25.8
Gross premiums written$2,934,174 $1,890,974 55.2 
Premiums ceded(627,120) (455,682)  Premiums ceded(967,698)(627,120)
Net premiums written1,263,854
 1,047,524
 20.7
Net premiums written1,966,476 1,263,854 55.6 
Change in unearned premiums(186,450) (134,761)  Change in unearned premiums(388,321)(186,450)
Net premiums earned1,077,404
 912,763
 18.0
Net premiums earned1,578,155 1,077,404 46.5 
Other underwriting income4,393
 2,490
  
Other underwriting income1,767 4,393  
Losses and loss adjustment expenses(751,147) (555,044)  
Losses and loss adjustment expenses(1,235,586)(751,147) 
Acquisition expenses(173,504) (148,828)  
Acquisition expenses(255,516)(173,504) 
Other operating expenses(102,197) (101,185)  
Other operating expenses(125,831)(102,197) 
Underwriting income (loss)$54,949
 $110,196
 (50.1)Underwriting income (loss)$(37,011)$54,949 (167.4)
     
Underwriting Ratios    % Point
Change
Underwriting Ratios% Point
Change
Loss ratio69.7% 60.8% 8.9
Loss ratio78.3 %69.7 %8.6 
Acquisition expense ratio16.1% 16.3% (0.2)Acquisition expense ratio16.2 %16.1 %0.1 
Other operating expense ratio9.5% 11.1% (1.6)Other operating expense ratio8.0 %9.5 %(1.5)
Combined ratio95.3% 88.2% 7.1
Combined ratio102.5 %95.3 %7.2 
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 include fire, explosion, collapse, riot, vandalism, wind, tornado,
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 September 30,
Three Months Ended September 30, 20202019
2019 2018 Amount%Amount%
Amount % Amount %
Casualty$178,802
 41.0
 $98,788
 31.7
Other specialty94,072
 21.6
 105,535
 33.9
Property excluding property catastrophe118,671
 27.2
 83,222
 26.7
Property excluding property catastrophe$223,880 37.1 $118,671 27.2 
Property catastrophe23,597
 5.4
 9,053
 2.9
Property catastrophe42,125 7.0 23,597 5.4 
Other specialtyOther specialty159,969 26.5 94,072 21.6 
CasualtyCasualty142,401 23.6 178,802 41.0 
Marine and aviation10,181
 2.3
 6,011
 1.9
Marine and aviation27,839 4.6 10,181 2.3 
Other11,153
 2.6
 9,082
 2.9
Other7,988 1.3 11,153 2.6 
Total$436,476
 100.0
 $311,691
 100.0
Total$604,202 100.0 $436,476 100.0 
20192020 Third Quarter versus 2018 Third Quarter2019 Period. . Gross premiums written by the reinsurance segment in the 20192020 third quarter were 52.2%51.6% higher than in the 20182019 third quarter, while net premiums written were 40.0%38.4% higher. The growth in grosshigher level of net premiums written primarily reflected increases in property and other specialty lines, mainly due to new business opportunities in casualty and property lines, partially offset by a decline in other specialty business, driven by reductions in motor and agriculture business. The growth in net premiums written is less than the growth in gross premiums written because a high proportion of the property business is subject to retrocessions.rate increases.
Nine Months Ended September 30,
Nine Months Ended September 30, 20202019
2019 2018 Amount%Amount%
Amount % Amount %
Casualty$425,311
 33.7
 $297,077
 28.4
Other specialty363,723
 28.8
 399,608
 38.1
Property excluding property catastrophe317,461
 25.1
 246,268
 23.5
Property excluding property catastrophe$546,443 27.8 $317,461 25.1 
Property catastrophe73,574
 5.8
 51,730
 4.9
Property catastrophe248,893 12.7 73,574 5.8 
Other specialtyOther specialty562,296 28.6 363,723 28.8 
CasualtyCasualty438,330 22.3 425,311 33.7 
Marine and aviation41,758
 3.3
 26,084
 2.5
Marine and aviation109,996 5.6 41,758 3.3 
Other42,027
 3.3
 26,757
 2.6
Other60,518 3.1 42,027 3.3 
Total$1,263,854
 100.0
 $1,047,524
 100.0
Total$1,966,476 100.0 $1,263,854 100.0 
Nine Months Ended September 30, 2020 versus 2019 versus 2018 periodPeriod. Gross premiums written by the reinsurance segment for the nine months ended September 30, 20192020 were 25.8%55.2% higher than in the 20182019 period, while net premiums written were 20.7%55.6% higher than in the 20182019 period. The increase in net premiums written reflected growth across all lines of business due to new business and rate increases. The 2020 period was affected by the presence of an $88 million loss portfolio transfer contract, written and fully earned in the period in the
ARCH CAPITAL 522020 THIRD QUARTER FORM 10-Q

other specialty line of business. The growth in net premiums written is less than the growthalso reflected increases in gross premiums written because a high

ARCH CAPITAL 562019 THIRD QUARTER FORM 10-Q


proportion of the property business is subject to retrocessions. The increase in net premiums written for the nine months ended September 30, 2019 reflected growth from select new business opportunities across most lines of business, partially offset by a declineprimarily due to growth in other specialty business.existing accounts, 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 September 30,
 20202019
 Amount%Amount%
Property excluding property catastrophe$163,081 29.4 $90,358 24.8 
Property catastrophe69,524 12.5 22,617 6.2 
Other specialty141,201 25.5 112,349 30.9 
Casualty136,421 24.6 116,242 31.9 
Marine and aviation26,744 4.8 11,798 3.2 
Other17,527 3.2 10,491 2.9 
Total$554,498 100.0 $363,855 100.0 
 Three Months Ended September 30,
 2019 2018
 Amount % Amount %
Casualty$116,242
 31.9
 $77,496
 26.4
Other specialty112,349
 30.9
 108,311
 36.9
Property excluding property catastrophe90,358
 24.8
 71,358
 24.3
Property catastrophe22,617
 6.2
 18,190
 6.2
Marine and aviation11,798
 3.2
 8,672
 3.0
Other10,491
 2.9
 9,246
 3.2
Total$363,855
 100.0
 $293,273
 100.0
Nine Months Ended September 30,
Nine Months Ended September 30, 20202019
2019 2018 Amount%Amount%
Amount % Amount %
Casualty$311,030
 28.9
 $231,877
 25.4
Other specialty370,443
 34.4
 361,676
 39.6
Property excluding property catastrophe259,629
 24.1
 210,961
 23.1
Property excluding property catastrophe$399,752 25.3 $259,629 24.1 
Property catastrophe59,886
 5.6
 52,293
 5.7
Property catastrophe177,750 11.3 59,886 5.6 
Other specialtyOther specialty467,592 29.6 370,443 34.4 
CasualtyCasualty404,248 25.6 311,030 28.9 
Marine and aviation35,355
 3.3
 28,150
 3.1
Marine and aviation76,562 4.9 35,355 3.3 
Other41,061
 3.8
 27,806
 3.0
Other52,251 3.3 41,061 3.8 
Total$1,077,404
 100.0
 $912,763
 100.0
Total$1,578,155 100.0 $1,077,404 100.0 
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. ForNet premiums earned by the 2019reinsurance segment in the 2020 third quarter net premiums earned were 24.1%52.4% higher than in the 20182019 third quarter. For the nine months ended September 30, 2019,2020, net premiums earned were 18.0%46.5% higher than in the 20182019 period.
Other Underwriting Income (Loss).
Other underwriting income (loss)for the 2020 third quarter was $0.3 million, compared to a loss of $1.2 million for the 2019 third quarter, was a loss of $1.2 million, compared to anand income of $1.4 million for the 2018 third quarter, and an income of $4.4$1.8 million for the nine months ended September 30, 2019,2020, compared to $2.5income of $4.4 million of income for the 20182019 period.
Losses and Loss Adjustment Expenses.
The table below shows the components of the reinsurance segment’s loss ratio:
Three Months Ended Nine Months EndedThree Months EndedNine Months Ended
September 30, September 30,September 30,September 30,
2019 2018 2019 2018 2020201920202019
Current year78.5 % 74.2 % 72.1 % 72.2 %Current year83.7 %78.5 %84.2 %72.1 %
Prior period reserve development(4.2)% (11.7)% (2.4)% (11.4)%Prior period reserve development(7.6)%(4.2)%(5.9)%(2.4)%
Loss ratio74.3 % 62.5 % 69.7 % 60.8 %Loss ratio76.1 %74.3 %78.3 %69.7 %
Current Year Loss Ratio.
2020 Third Quarter versus 2019 Period. The reinsurance segment’s current year loss ratio in the 20192020 third quarter was 4.35.2 points higher than in the 20182019 third quarter. The 2020 third quarter andloss ratio reflected 12.226.1 points of current year catastrophic activity, primarily related to Hurricanes Laura and Sally the Derecho Windstorm, including 1.5 points related to COVID-19. The 2019 third quarter included 12.2 points of catastrophic activity, primarily related to Hurricane Dorian and Typhoon Faxai compared to 9.5 points in the 2018 third quarter, primarily related to Hurricane Florence and Typhoon Jebi.TheFaxai.
Nine Months Ended September 30, 2020 versus 2019 Period. The reinsurance segment’s current year loss ratio for the nine months ended September 30, 20192020 was 0.112.1 points lowerhigher than in the 2018 period and2019 period. The loss ratio for the nine months ended September 30, 2020 reflected 5.321.6 points of current year catastrophic activity, including 9.8 points for exposure related to COVID-19, compared to 4.05.3 points infor the 20182019 period. The balance of the change in the 20192020 loss ratios resulted, in part, from changes in mix of business, and the level of attritional losses.losses and the effect of rate increases.
Prior Period Reserve Development.
The reinsurance segment’s net favorable development was $42.0 million, or 7.6 points, for the 2020 third quarter, compared to $15.3 million, or 4.2 points, for the 2019 third quarter, compared to $34.3and $93.8 million, or 11.7 points, for the 2018 third quarter, and $26.3 million, or 2.45.9 points, for the nine months ended September 30, 2019,2020, compared to $103.9$26.3 million, or 11.42.4 points, for the 20182019 period. Seenote 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.
20192020 Third Quarter versus 2018 Third Quarter2019 Period. The underwriting expense ratio for the reinsurance segment was 22.9% in the 2020 third quarter, compared to 26.0% in the 2019 third quarter, with the decrease primarily due to growth in net premiums earned.
ARCH CAPITAL 532020 THIRD QUARTER FORM 10-Q

Nine Months Ended September 30, 2020 versus 2019 Period. The underwriting expense ratio for the reinsurance segment was 26.0% in the 2019 third quarter, compared to 27.4% in the 2018 third quarter, reflecting growth in net premiums earned and changes in mix of business.
Nine Months Ended September 30, 2019 versus 2018 period. The underwriting expense ratio for the reinsurance segment was 25.6%24.2% for the nine months ended September 30, 2019,2020, compared to 27.4%25.6% for the 2018 period.2019 period, with the decrease primarily due to growth in net premiums earned.
Mortgage Segment 
Our mortgage operations include U.S. and international mortgage insurance and reinsurance operations as well as

ARCH CAPITAL 572019 THIRD QUARTER FORM 10-Q


participation in GSE credit risk-sharing transactions. Our mortgage group includes direct mortgage insurance in the U.S. primarily through Arch Mortgage Insurance Company and United Guaranty Residential Insurance 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 MI Europe”Insurance EU”) and, 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 September 30,
 20202019% Change
Gross premiums written$346,248 $375,092 (7.7)
Premiums ceded(47,783)(57,703)
Net premiums written298,465 317,389 (6.0)
Change in unearned premiums52,944 25,611 
Net premiums earned351,409 343,000 2.5 
Other underwriting income4,600 3,955 
Losses and loss adjustment expenses(153,055)(13,080)
Acquisition expenses(35,716)(34,396)
Other operating expenses(36,708)(37,003)
Underwriting income$130,530 $262,476 (50.3)
Underwriting Ratios% Point
Change
Loss ratio43.6 %3.8 %39.8 
Acquisition expense ratio10.2 %10.0 %0.2 
Other operating expense ratio10.4 %10.8 %(0.4)
Combined ratio64.2 %24.6 %39.6 
 Three Months Ended September 30,
 2019 2018 % Change
Gross premiums written$375,092
 $350,559
 7.0
Premiums ceded(57,703) (57,226)  
Net premiums written317,389
 293,333
 8.2
Change in unearned premiums25,611
 7,591
  
Net premiums earned343,000
 300,924
 14.0
Other underwriting income3,955
 3,733
  
Losses and loss adjustment expenses(13,080) (9,615)  
Acquisition expenses(34,396) (33,361)  
Other operating expenses(37,003) (31,122)  
Underwriting income$262,476
 $230,559
 13.8
      
Underwriting Ratios 
  
 % Point
Change
Loss ratio3.8% 3.2% 0.6
Acquisition expense ratio10.0% 11.1% (1.1)
Other operating expense ratio10.8% 10.3% 0.5
Combined ratio24.6% 24.6% 
Nine Months Ended September 30, Nine Months Ended September 30,
2019 2018 % Change 20202019% Change
Gross premiums written$1,095,607
 $1,002,727
 9.3
Gross premiums written$1,084,337 $1,095,607 (1.0)
Premiums ceded(149,358) (154,230)  Premiums ceded(136,154)(149,358)
Net premiums written946,249
 848,497
 11.5
Net premiums written948,183 946,249 0.2 
Change in unearned premiums72,436
 23,147
  Change in unearned premiums113,965 72,436 
Net premiums earned1,018,685
 871,644
 16.9
Net premiums earned1,062,148 1,018,685 4.3 
Other underwriting income11,867
 10,464
  
Other underwriting income15,649 11,867  
Losses and loss adjustment expenses(50,226) (74,672)  
Losses and loss adjustment expenses(444,721)(50,226) 
Acquisition expenses(98,722) (87,665)  
Acquisition expenses(108,304)(98,722) 
Other operating expenses(116,697) (108,622)  
Other operating expenses(120,178)(116,697) 
Underwriting income$764,907
 $611,149
 25.2
Underwriting income$404,594 $764,907 (47.1)
     
Underwriting Ratios 
  
 % Point
Change
Underwriting Ratios  % Point
Change
Loss ratio4.9% 8.6% (3.7)Loss ratio41.9 %4.9 %37.0 
Acquisition expense ratio9.7% 10.1% (0.4)Acquisition expense ratio10.2 %9.7 %0.5 
Other operating expense ratio11.5% 12.5% (1.0)Other operating expense ratio11.3 %11.5 %(0.2)
Combined ratio26.1% 31.2% (5.1)Combined ratio63.4 %26.1 %37.3 
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 September 30, Three Months Ended September 30,
2019 2018 20202019
Amount % Amount % Amount%Amount%
Underwriting location:       Underwriting location:
United States$260,202
 82.0
 $240,959
 82.1
United States$245,971 82.4 $260,202 82.0 
Other57,187
 18.0
 52,374
 17.9
Other52,494 17.6 57,187 18.0 
Total$317,389
 100.0
 $293,333
 100.0
Total$298,465 100.0 $317,389 100.0 
20192020 Third Quarter versus 2018 Third Quarter2019 Period. . Gross premiums written by the mortgage segment in the 20192020 third quarter were 7.0% higher7.7% lower than in the 20182019 third quarter, while net premiums written were 8.2% higher. The growth6.0% lower, primarily reflecting a reduction in net premiums written primarily reflected an increase in monthly premium business due to growth inU.S. primary mortgage insurance in force indue to mortgage refinance activity and a lower contribution from single premium policies. Net premiums written for the 2020 third quarter also reflected a lower level of ceded premiums on U.S. primary mortgage insurance business.
Nine Months Ended September 30,
20202019
Amount%Amount%
Nine Months Ended September 30,
2019 2018
Amount % Amount %
Underwriting location:       Underwriting location:
United States$774,356
 81.8
 $691,851
 81.5
United States$771,203 81.3 $774,356 81.8 
Other171,893
 18.2
 156,646
 18.5
Other176,980 18.7 171,893 18.2 
Total$946,249
 100.0
 $848,497
 100.0
Total$948,183 100.0 $946,249 100.0 
Nine Months Ended September 30, 2020 versus 2019 versus 2018 periodPeriod. Gross premiums written by the mortgage segment for the nine months ended September 30, 20192020 were 9.3% higher1.0% lower than in the 20182019 period, while net premiums written were 11.5% higher. The growth in net premiums written primarily reflected an increase in monthly premium business due to growth in insurance in force in the U.S. In addition, net premiums written for the nine months ended September 30, 2020 were 0.2% higher than in the 2019 included $17.1 million due to the novationperiod.
ARCH CAPITAL 542020 THIRD QUARTER FORM 10-Q

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, of which the Arch MI U.S. portfolio of mortgage loansinsurance policies was 78.6%62.5% at September 30, 2019,2020, reflecting the higher level of mortgage refinancing activity, compared to 81.5%75.7% at December 31, 2018.2019.
Arch MI U.S. generated $25.3 billion ofThe following tables provide details on the new insurance written (“NIW”) in the 2019 third quarter, compared to $21.4 billion in the 2018 third quarter.generated by Arch MI U.S. NIW represents the original principal balance of all loans that received coverage during the period. Monthly premium policies contributed 92.3%
(U.S. Dollars in millions)Three Months Ended September 30,
20202019
Amount%Amount%
Total new insurance written (NIW) (1)$32,787 $25,313 
Credit quality (FICO):
>=740$21,160 64.5 $15,204 60.1 
680-73910,562 32.2 8,725 34.5 
620-6791,065 3.2 1,384 5.5 
Total$32,787 100.0 $25,313 100.0 
Loan-to-value (LTV):
95.01% and above$2,561 7.8 $3,182 12.6 
90.01% to 95.00%13,967 42.6 10,409 41.1 
85.01% to 90.00%10,052 30.7 7,762 30.7 
85.00% and below6,207 18.9 3,960 15.6 
Total$32,787 100.0 $25,313 100.0 
Monthly vs. single:
Monthly$31,928 97.4 $23,358 92.3 
Single859 2.6 1,955 7.7 
Total$32,787 100.0 $25,313 100.0 
Purchase vs. refinance:
Purchase$24,256 74.0 $19,068 75.3 
Refinance8,531 26.0 6,245 24.7 
Total$32,787 100.0 $25,313 100.0 
(1)Represents the original principal balance of NIW inall loans that received coverage during the 2019 third quarter, compared to 92.6% forperiod.
(U.S. Dollars in millions)Nine Months Ended September 30,
20202019
Amount%Amount%
Total new insurance written (NIW) (1)$74,116 $53,681 
Credit quality (FICO):
>=740$47,080 63.5 $31,416 58.5 
680-73924,130 32.6 18,905 35.2 
620-6792,906 3.9 3,360 6.3 
Total$74,116 100.0 $53,681 100.0 
Loan-to-value (LTV):
95.01% and above$6,177 8.3 $7,520 14.0 
90.01% to 95.00%30,569 41.2 22,881 42.6 
85.01% to 90.00%23,521 31.7 15,937 29.7 
85.00% and below13,849 18.7 7,343 13.7 
Total$74,116 100.0 $53,681 100.0 
Monthly vs. single:
Monthly$71,011 95.8 $49,556 92.3 
Single3,105 4.2 4,125 7.7 
Total$74,116 100.0 $53,681 100.0 
Purchase vs. refinance:
Purchase$51,511 69.5 $44,349 82.6 
Refinance22,605 30.5 9,332 17.4 
Total$74,116 100.0 $53,681 100.0 
(1)Represents the 2018 third quarter.

ARCH CAPITAL 582019 THIRD QUARTER FORM 10-Q


The following tables provide details onall loans that received coverage during the NIW generated by Arch MI U.S.:period.
(U.S. Dollars in millions)Three Months Ended September 30,
2019 2018
 Amount % Amount %
Total new insurance written (NIW) (1)$25,313
   $21,425
  
        
Credit quality (FICO):       
>=740$15,204
 60.1
 $12,013
 56.1
680-7398,725
 34.5
 7,728
 36.1
620-6791,384
 5.5
 1,684
 7.9
Total$25,313
 100.0
 $21,425
 100.0
        
Loan-to-value (LTV):       
95.01% and above$3,182
 12.6
 $3,231
 15.1
90.01% to 95.00%10,409
 41.1
 9,689
 45.2
85.01% to 90.00%7,762
 30.7
 6,264
 29.2
85.01% and below3,960
 15.6
 2,241
 10.5
Total$25,313
 100.0
 $21,425
 100.0
        
Monthly vs. single:       
Monthly$23,358
 92.3
 $19,842
 92.6
Single1,955
 7.7
 1,583
 7.4
Total$25,313
 100.0
 $21,425
 100.0
        
Purchase vs. refinance:       
Purchase$19,068
 75.3
 $20,397
 95.2
Refinance6,245
 24.7
 1,028
 4.8
Total$25,313
 100.0
 $21,425
 100.0
(1)Represents the original principal balance of all loans that received coverage during the period.
(U.S. Dollars in millions)Nine Months Ended September 30,
2019 2018
 Amount % Amount %
Total new insurance written (NIW) (1)$53,681
   $52,742
  
        
Credit quality (FICO):       
>=740$31,416
 58.5
 $29,933
 56.8
680-73918,905
 35.2
 18,952
 35.9
620-6793,360
 6.3
 3,857
 7.3
Total$53,681
 100.0
 $52,742
 100.0
        
Loan-to-value (LTV):       
95.01% and above$7,520
 14.0
 $7,328
 13.9
90.01% to 95.00%22,881
 42.6
 24,030
 45.6
85.01% to 90.00%15,937
 29.7
 15,817
 30.0
85.01% and below7,343
 13.7
 5,567
 10.6
Total$53,681
 100.0
 $52,742
 100.0
        
Monthly vs. single:       
Monthly$49,556
 92.3
 $49,046
 93.0
Single4,125
 7.7
 3,696
 7.0
Total$53,681
 100.0
 $52,742
 100.0
        
Purchase vs. refinance:       
Purchase$44,349
 82.6
 $49,556
 94.0
Refinance9,332
 17.4
 3,186
 6.0
Total$53,681
 100.0
 $52,742
 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 September 30,
 20202019
 Amount%Amount%
Underwriting location:
United States$290,451 82.7 $287,064 83.7 
Other60,958 17.3 55,936 16.3 
Total$351,409 100.0 $343,000 100.0 
 Three Months Ended September 30,
 2019 2018
 Amount % Amount %
Underwriting location:       
United States$287,064
 83.7
 $256,231
 85.1
Other55,936
 16.3
 44,693
 14.9
Total$343,000
 100.0
 $300,924
 100.0
 Nine Months Ended September 30,
 2019 2018
 Amount % Amount %
Underwriting location:       
United States$843,599
 82.8
 $742,269
 85.2
Other175,086
 17.2
 129,375
 14.8
Total$1,018,685
 100.0
 $871,644
 100.0
2020 Third Quarter versus 2019 Period. Net premiums earned for the 20192020 third quarter were 14.0%2.5% higher than in the 20182019 third quarter. Forquarter, and reflected a higher level of single premiums earned as a result of policy terminations due to mortgage refinance activity, which more than offset the reduction in U.S. primary mortgage insurance in force noted above.
ARCH CAPITAL 552020 THIRD QUARTER FORM 10-Q

 Nine Months Ended September 30,
 20202019
 Amount%Amount%
Underwriting location:
United States$884,265 83.3 $843,599 82.8 
Other177,883 16.7 175,086 17.2 
Total$1,062,148 100.0 $1,018,685 100.0 
Nine Months Ended September 30, 2020 versus 2019 Period. Net premiums earned for the nine months ended September 30, 2019, net premiums earned2020 were 16.9%4.3% higher than in the 2018 period. The increases were2019 period, primarily reflecting a higher level of single premiums earned as a result of policy terminations due to growth in U.S. insurance in force.mortgage refinance activity.
Other Underwriting Income.
Other underwriting income, which is primarily related to older GSE credit risk-sharing transactions receiving derivative accounting treatment and to a lesser extent contract underwriting fees, was $4.6 million for the 2020 third quarter, compared to $4.0 million for the 2019 third quarter, compared to $3.7 million for the 2018 third quarter. and $11.9 million for the nine months ended September 30, 2019, compared to $10.5 million for the 2018 period.
Losses and Loss Adjustment Expenses.
The table below shows the components of the mortgage segment’s loss ratio:
Three Months Ended Nine Months EndedThree Months EndedNine Months Ended
September 30, September 30,September 30,September 30,
2019 2018 2019 2018 2020201920202019
Current year13.4 % 16.0 % 14.0 % 17.2 %Current year44.9 %13.4 %42.9 %14.0 %
Prior period reserve development(9.6)% (12.8)% (9.1)% (8.6)%Prior period reserve development(1.3)%(9.6)%(1.0)%(9.1)%
Loss ratio3.8 % 3.2 % 4.9 % 8.6 %Loss ratio43.6 %3.8 %41.9 %4.9 %
Current Year Loss Ratio.
2020 Third Quarter versus 2019 Period. The mortgage segment’s current year loss ratio was 2.631.5 points lowerhigher in the 20192020 third quarter than in the 20182019 third quarter. The percentage of loans in default on U.S. primary mortgage business was 4.69% at September 30, 2020, compared to 1.48% at September 30, 2019. For U.S. primary mortgage insurance, loss reserving under GAAP is based on reported delinquencies.
Nine Months Ended September 30, 2020 versus 2019 Period. The mortgage segment’s current year loss ratio was 3.228.9 points lowerhigher for the nine months ended September 30, 20192020 than for the 20182019 period. The lower current year loss ratios
Incurred losses for the 2019
2020 periods reflected elevated delinquency rates due, in part, to financial stress from the COVID-19 pandemic. Segregating estimated losses due to COVID-19 from the overall mortgage segment estimated losses would require knowledge of the number of delinquencies specifically attributable to COVID-19. As this

ARCH CAPITAL 592019 THIRD QUARTER FORM 10-Q


periods reflectexercise cannot be performed accurately, the current favorable macroeconomic environment.Company is not reporting COVID-19 provisions separately from its overall loss provisions.
Prior Period Reserve Development.
The mortgage segment’s net favorable development was $4.5 million, or 1.3 points, for the 2020 third quarter, compared to $33.0 million, or 9.6 points, for the 2019 third quarter, compared to $38.6and $10.8 million, or 12.8 points, for the 2018 third quarter, and $92.5 million, or 9.11.0 points, for the nine months ended September 30, 2019,2020, compared to $74.9$92.5 million, or 8.69.1 points, for the 20182019 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.
20192020 Third Quarter versus 2018 Third Quarter2019 Period. The underwriting expense ratio for the mortgage segment was 20.6% in the 2020 third quarter, consistent with 20.8% in the 2019 third quarter.
Nine Months Ended September 30, 2020 versus 2019 Period. The underwriting expense ratio for the mortgage segment was 20.8% in the 2019 third quarter, compared to 21.4% in the 2018 third quarter. The lower ratio in the 2019 third quarter primarily resulted from the higher level of net premiums earned.
Nine Months Ended September 30, 2019 versus 2018 period. The underwriting expense ratio for the mortgage segment was 21.2%21.5% for the nine months ended September 30, 2019, compared to 22.6%2020, consistent with 21.2% for the 20182019 period. The lower ratio in the 2019 period primarily resulted from the higher level of net premiums earned.
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 includedrecognized in earnings,earnings), equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses and income taxes. Such amounts exclude the results of the ‘other’ segment.
ARCH CAPITAL 562020 THIRD QUARTER FORM 10-Q

Net Investment Income.
The components of net investment income were derived from the following sources:
Three Months EndedNine Months Ended
September 30,September 30,
 2020201920202019
Fixed maturities$84,608 $109,953 $277,862 $331,939 
Equity securities6,659 3,581 18,312 9,321 
Short-term investments1,162 3,432 5,444 11,178 
Other (1)24,594 24,170 62,898 67,229 
Gross investment income117,023 141,136 364,516 419,667 
Investment expenses (2)(17,166)(14,262)(50,600)(48,506)
Net investment income$99,857 $126,874 $313,916 371,161 
 Three Months Ended Nine Months Ended
 September 30, September 30,
 2019 2018 2019 2018
Fixed maturities$109,955
 $103,252
 $331,941
 $294,658
Equity securities3,581
 3,426
 9,321
 10,408
Short-term investments3,432
 4,417
 11,178
 12,591
Other (1)24,170
 18,030
 67,229
 56,501
Gross investment income141,138
 129,125
 419,669
 374,158
Investment expenses (2)(14,262) (14,797) (48,506) (51,826)
Net investment income$126,876
 $114,328
 $371,163
 322,332
(1)    Amounts include dividends and other distributions on investment funds, term loan investments, funds held balances, cash balances and other items.
(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 0.31% of average invested assets for the 2019 third quarter, compared to 0.29% for the 2018 third quarter, and 0.33% for the nine months ended September 30, 2019, compared to 0.36% for the 2018 period.
(2)    Investment expenses were approximately 0.32% of average invested assets for the 2020 third quarter, consistent with 0.31% for the 2019 third quarter, and 0.31% for the nine months ended September 30, 2020, compared to 0.33% for the 2019 period.
The higherlower level of net investment income for the 20192020 periods primarily reflected growthrelated to lower yields available in average investable assets, the reinvestment of fixed income securities at slightly higher available yields and the shift from municipal bonds to corporates.financial market. The pre-tax investment income yield, calculated based on amortized cost and on an annualized basis, was 1.76% for the 2020 third quarter, compared to 2.58% for the 2019 third quarter, compare to 2.45% for the 2018 third quarter, and 2.62%1.94% for the nine months ended September 30, 2019,2020, compared to 2.31%2.62% for the 20182019 period.
Corporate Expenses.
Corporate expenses were $16.3 million for the 2020 third quarter, compared to $15.1 million for the 2019 third quarter, compared to $13.2 million for the 2018 third quarter, and $47.9$51.4 million for the nine months ended September 30, 2019,2020, compared to $43.3$47.9 million for the 20182019 period. The increase in corporate expenses in the 2019 periods primarily reflected higher compensationprofessional fees and other costs.
Transaction Costs and Other.
Transaction costs and other were $1.7 million for the 2020 third quarter, compared to $2.0 million for the 2019 third quarter, compared to $1.1 million for the 2018 third quarter, and $5.4$5.2 million for the nine months ended September 30, 2019, compared to $8.82020, consistent with $5.4 million for the 20182019 period. Amounts in the 20192020 period are primarily related to recent acquisition activity. Amounts for 2018 periods were primarily attributable to the write off of intangible assets related to insurance licenses for a subsidiary of UGC which was merged into another subsidiary.

ARCH CAPITAL 602019 THIRD QUARTER FORM 10-Q


Amortization of Intangible Assets.
Amortization of intangible assets for the 2020 third quarter was $16.7 million, compared to $20.0 million for the 2019 third quarter, was $20.0 million, compared to $26.3 million for the 2018 third quarter, and $60.2$49.8 million for the nine months ended
September 30, 2019,2020, compared to $79.5$60.2 million for the 20182019 period. Such expenses are primarily related to the UGC acquisition while the 2019 periods also included amortization relatedand other acquisitions in late 2018 to the previously announced acquisitions of (i) renewal rights of a U.K. commercial lines book of business on January 1, 2019; and (ii) McNeil & Co. on December 6, 2018.2019. See the consolidated financial statements contained in our 20182019 Form 10-K for disclosures on our amortization pattern.
Interest Expense.
Interest expense was $36.2 million for the 2020 third quarter, compared to the $23.2 million for the 2019 third quarter compared to the $24.7 million for the 2018 third quarter, and $70.1$86.6 million for the nine months ended September 30, 2019,2020, compared to $76.6$70.1 million for the 20182019 period. The lowerhigher level of interest expense mainly resulted from the issuance of $1.0 billion of 3.635% senior notes in June 2020. The increase in the 2019 periods2020 period also reflected the paydown of revolving credit agreement borrowingsan increase in the second half of 2018.
Loss on Redemption of Preferred Shares.
In January 2018, we redeemed all remaining 6.75% Series C preferred shares and, in accordance with GAAP, recorded a loss of $2.7 million to remove original issuance costsinterest expense related to the redeemed shares from additional paid-in capital. Such adjustment had no impact on total shareholders’ equity or cash flows.funds held liabilities.
Net Realized Gains or Losses.
We recorded net realized gains of $81.2$211.0 million for the 20192020 third quarter, compared to net realized lossesgains of $47.0$80.0 million for the 20182019 third quarter, and net realized gains of $318.7$524.0 million for the nine months ended September 30, 2019,2020, compared to net realized lossesgains of $218.4$316.2 million for the 20182019 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 re-measurement of contingent consideration liability amounts.changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings. See note 6,7, “Investment Information—Net Realized Gains (Losses),” to our consolidated financial statements for additional information. See
Net Impairment Losses Recognized in Earnings.
Equity in Net Income (Loss) of Investment Funds Accounted for Using the Equity Method.
We recorded $17.1$126.7 million of equity in net income related to investment funds accounted for using the equity method in the 20192020 third quarter, compared to $16.0$17.1 million of income for the 20182019 third quarter, and $96.5$57.4 million of income for the nine months ended September 30, 2019,2020, compared to $52.5$96.5 million for the 20182019 period. Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds. Investment
ARCH CAPITAL 572020 THIRD QUARTER FORM 10-Q

funds accounted for using the equity method totaled $1.58$1.88 billion at September 30, 2019,2020, compared to $1.49$1.66 billion at December 31, 2018.2019. See note 6,7, “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 gainslosses for the 20192020 third quarter were $29.8$38.7 million, compared to net foreign exchange gains for the 20182019 third quarter of $7.1$29.8 million. Net foreign exchange gainslosses for the nine months ended September 30, 20192020 were $28.8$17.8 million, compared to net foreign exchange gains for the 20182019 period of $38.3$28.8 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 resulted in an expense of 5.4% for the 2020 third quarter, compared to 8.9% for the 2019 third quarter and 9.0%8.3% for the nine months ended September 30, 2019,2020, compared to 12.9% for the 2018 third quarter and 11.3% for the nine months ended September 30, 2018 . The effective tax rates9.0% for the 2019 third quarter and nine months ended September 30, 2019 included a discrete income tax benefitperiod. Such amounts exclude the results of $1.3 million and $5.6 million, respectively, related to share based compensation.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.
Other Segment 
The ‘other’ segment includes the results of Watford. Pursuant to generally accepted accounting principles, Watford is considered a variable interest entity and we concluded that we are the primary beneficiary of Watford. As such, we consolidate

ARCH CAPITAL 612019 THIRD QUARTER FORM 10-Q


the results of Watford in our consolidated financial statements, although we only own approximately 11%13% of Watford’s common equity. See note 11, “Variable Interest Entities and Noncontrolling Interests,” and note 4, “Segment Information,” 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 20182019 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 September 30, 2019,2020, total investable assets held by Arch were $21.57$25.7 billion, excluding the $2.73$2.7 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
September 30, 2020
Fixed maturities (2)$18,294,480 71.1 
Short-term investments (2)2,157,410 8.4 
Cash781,065 3.0 
Equity securities (2)1,479,702 5.8 
Other investments (2)1,276,867 5.0 
Investments accounted for using the equity method1,883,702 7.3 
Securities transactions entered into but not settled at the balance sheet date(148,725)(0.6)
Total investable assets held by Arch$25,724,501 100.0 
Average effective duration (in years)3.21 
Average S&P/Moody’s credit ratings (3)AA/Aa2
Embedded book yield (4)1.71 %
December 31, 2019
Fixed maturities (2)$16,894,021 75.8 
Short-term investments (2)1,004,257 4.5 
Cash623,793 2.8 
Equity securities (2)827,842 3.7 
Other investments (2)1,336,920 6.0 
Investments accounted for using the equity method1,660,396 7.5 
Securities transactions entered into but not settled at the balance sheet date(61,553)(0.3)
Total investable assets held by Arch$22,285,676 100.0 
Average effective duration (in years)3.40 
Average S&P/Moody’s credit ratings (3)AA/Aa2
Embedded book yield (4)2.55 %
Investable assets (1):
Estimated
Fair Value
 
% of
Total
September 30, 2019   
Fixed maturities (2)$16,586,794
 76.9
Short-term investments (2)785,358
 3.6
Cash799,709
 3.7
Equity securities (2)559,054
 2.6
Other investments (2)1,369,554
 6.4
Investments accounted for using the equity method1,575,832
 7.3
Securities transactions entered into but not settled at the balance sheet date(110,213) (0.5)
Total investable assets held by Arch$21,566,088
 100.0
    
Average effective duration (in years)3.64
  
Average S&P/Moody’s credit ratings (3)AA/Aa2
  
Embedded book yield (4)2.70%  
    
December 31, 2018   
Fixed maturities (2)$14,881,902
 76.1
Short-term investments (2)995,926
 5.1
Cash583,027
 3.0
Equity securities (2)368,843
 1.9
Other investments (2)1,261,525
 6.4
Investments accounted for using the equity method1,493,791
 7.6
Securities transactions entered into but not settled at the balance sheet date(18,153) (0.1)
Total investable assets held by Arch$19,566,861
 100.0
    
Average effective duration (in years)3.38
  
Average S&P/Moody’s credit ratings (3)AA/Aa2
  
Embedded book yield (4)2.89%  
(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.
(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 at fair value under the fair value option.
(3)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”).
(4)Before investment expenses.
(2)Includes investments carried at fair value under the fair value option.
(3)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”).
(4)Before investment expenses.
At September 30, 2019,2020, approximately $15.40$18.7 billion, or 71.4%72.8%, of total investable assets held by Arch were internally managed, compared to $14.08$15.8 billion, or 72.0%70.9%, at December 31, 2018.2019.

ARCH CAPITAL 625820192020 THIRD QUARTER FORM 10-Q


The following table summarizes our fixed maturities and fixed maturities pledged under securities lending agreements (“Fixed Maturities”) by type:
Estimated
Fair Value
% of
Total
Estimated
Fair Value
 
% of
Total
September 30, 2019 
  
September 30, 2020September 30, 2020 
Corporate bonds$6,494,654
 39.2
Corporate bonds$8,137,582 44.5 
Mortgage backed securities528,227
 3.2
Residential mortgage backed securitiesResidential mortgage backed securities703,393 3.8 
Municipal bonds652,296
 3.9
Municipal bonds525,617 2.9 
Commercial mortgage backed securities754,306
 4.5
Commercial mortgage backed securities375,510 2.1 
U.S. government and government agencies4,830,839
 29.1
U.S. government and government agencies4,662,260 25.5 
Non-U.S. government securities1,800,032
 10.9
Non-U.S. government securities2,196,827 12.0 
Asset backed securities1,526,440
 9.2
Asset backed securities1,693,291 9.3 
Total$16,586,794
 100.0
Total$18,294,480 100.0 
   
December 31, 2018 
  
December 31, 2019December 31, 2019 
Corporate bonds$5,735,526
 38.5
Corporate bonds$6,561,354 38.8 
Mortgage backed securities535,763
 3.6
Residential mortgage backed securitiesResidential mortgage backed securities541,800 3.2 
Municipal bonds1,012,308
 6.8
Municipal bonds880,119 5.2 
Commercial mortgage backed securities729,442
 4.9
Commercial mortgage backed securities734,244 4.3 
U.S. government and government agencies3,601,269
 24.2
U.S. government and government agencies4,632,947 27.4 
Non-U.S. government securities1,713,891
 11.5
Non-U.S. government securities1,995,813 11.8 
Asset backed securities1,553,703
 10.4
Asset backed securities1,547,744 9.2 
Total$14,881,902
 100.0
Total$16,894,021 100.0 
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
September 30, 2020
U.S. government and gov’t agencies (1)$5,360,798 29.3 
AAA3,352,902 18.3 
AA2,087,245 11.4 
A3,895,053 21.3 
BBB2,542,233 13.9 
BB504,570 2.8 
B231,774 1.3 
Lower than B54,118 0.3 
Not rated265,787 1.5 
Total$18,294,480 100.0 
December 31, 2019
U.S. government and gov’t agencies (1)$5,215,489 30.9 
AAA3,392,341 20.1 
AA2,115,828 12.5 
A3,849,458 22.8 
BBB1,495,467 8.9 
BB355,803 2.1 
B216,663 1.3 
Lower than B56,865 0.3 
Not rated196,107 1.2 
Total$16,894,021 100.0 
(1)Includes U.S. government-sponsored agency residential mortgage-backed securities and agency commercial mortgage-backed securities.
 Estimated Fair Value 
% of
Total
September 30, 2019   
U.S. government and gov’t agencies (1)$5,403,271
 32.6
AAA3,240,708
 19.5
AA1,879,728
 11.3
A3,648,581
 22.0
BBB1,576,052
 9.5
BB362,117
 2.2
B210,824
 1.3
Lower than B61,205
 0.4
Not rated204,308
 1.2
Total$16,586,794
 100.0
    
December 31, 2018   
U.S. government and gov’t agencies (1)$4,194,676
 28.2
AAA3,551,039
 23.9
AA2,129,336
 14.3
A3,069,656
 20.6
BBB1,251,205
 8.4
BB275,201
 1.8
B183,614
 1.2
Lower than B61,271
 0.4
Not rated165,904
 1.1
Total$14,881,902
 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
Severity of gross unrealized losses:Estimated Fair ValueGross
Unrealized
Losses
% of
Total Gross
Unrealized
Losses
September 30, 2019     
September 30, 2020September 30, 2020
0-10%$4,084,228
 $(70,410) 82.6
0-10%$4,535,833 $(62,221)78.3 
10-20%79,286
 (12,714) 14.9
10-20%58,233 (10,279)12.9 
20-30%3,701
 (1,121) 1.3
20-30%9,417 (2,839)3.6 
Greater than 30%1,480
 (999) 1.2
Greater than 30%3,132 (4,079)5.1 
Total$4,168,695
 $(85,244) 100.0
Total$4,606,615 $(79,418)100.0 
     
December 31, 2018     
December 31, 2019December 31, 2019
0-10%$8,722,837
 $(190,170) 92.5
0-10%$4,136,798 $(49,072)95.3 
10-20%87,188
 (13,012) 6.3
10-20%12,405 (1,796)3.5 
20-30%3,359
 (1,058) 0.5
20-30%830 (273)0.5 
Greater than 30%2,363
 (1,266) 0.6
Greater than 30%315 (363)0.7 
Total$8,815,747
 $(205,506) 100.0
Total$4,150,348 $(51,504)100.0 
The following table summarizes our top ten exposures to fixed income corporate issuers by fair value at September 30, 2019,2020, excluding guaranteed amounts and covered bonds:
 Estimated Fair Value 
Credit
Rating (1)
Bank of America Corporation$241,428
 A-/A2
Apple Inc.213,331
 AA+/Aa1
JPMorgan Chase & Co.209,254
 A-/A2
Wells Fargo & Company201,534
 A-/A1
Citigroup Inc.184,850
 A/A1
Morgan Stanley141,891
 BBB+/A3
Nestlé S.A.113,597
 AA-/Aa2
BP p.l.c.110,616
 A-/A1
The Goldman Sachs Group, Inc.109,147
 BBB+/A3
Deere & Company105,217
 A/A2
Total$1,630,865
  
(1)Average credit ratings as assigned by S&P and Moody’s, respectively.Estimated Fair ValueCredit
Rating (1)
Bank of America Corporation$320,603 A-/A2
Wells Fargo & Company259,752 BBB+/A2
Nestlé S.A.228,219 AA-/Aa3
JPMorgan Chase & Co.227,543 A-/A2
Johnson & Johnson220,521 AAA/Aaa
Apple Inc.169,793 AA+/Aa1
Citigroup Inc.145,195 BBB+/A3
Morgan Stanley134,680 BBB+/A3
Comcast Corporation120,210 A-/A3
BP p.l.c.120,177 A-/A1
Total$1,946,693 
(1)Average credit ratings as assigned by S&P and Moody’s, respectively.

ARCH CAPITAL 635920192020 THIRD QUARTER FORM 10-Q

Table of Contents

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”):
AgenciesInvestment GradeBelow Investment GradeTotal
Sep 30, 2020
RMBS$669,672 $4,371 $29,350 $703,393 
CMBS28,865 326,774 19,871 375,510 
ABS— 1,579,166 114,125 1,693,291 
Total$698,537 $1,910,311 $163,346 $2,772,194 
Dec 31, 2019
RMBS$503,929 $7,770 $30,101 $541,800 
CMBS78,612 629,424 26,208 734,244 
ABS— 1,483,449 64,295 1,547,744 
Total$582,541 $2,120,643 $120,604 $2,823,788 
 Agencies Investment Grade Below Investment Grade Total
Sep 30, 2019       
RMBS$478,427
 $15,437
 $34,363
 $528,227
CMBS94,004
 636,384
 23,918
 754,306
ABS
 1,458,377
 68,063
 1,526,440
Total$572,431
 $2,110,198
 $126,344
 $2,808,973
        
Dec 31, 2018       
RMBS$488,862
 $15,410
 $31,491
 $535,763
CMBS104,547
 602,865
 22,030
 729,442
ABS
 1,485,150
 68,553
 1,553,703
Total$593,409
 $2,103,425
 $122,074
 $2,818,908
The following table summarizes our equity securities, which include investments in exchange traded funds:
At
September 30,
2020
December 31,
2019
Equities (1)$494,159 $375,067 
Exchange traded funds
Fixed income (2)602,133 7,237 
Equity and other (3)383,410 445,538 
Total$1,479,702 $827,842 
(1)Primarily in consumer non-cyclical, consumer cyclical, technology, communications and financial stocks at September 30, 2019, our structured securities included $38.3 million par value2020.
(2)Primarily in sub-prime securities with a fair value of $30.6 millioncorporate, MBS and average credit quality ratings from S&P/Moody’s of “CCC-/Caa3,” compared to $38.2 million par value with a fair value of $31.7 million and average credit quality ratings of “CCC-/Caa3”municipal strategies at December 31, 2018.
At September 30, 2019, our investment portfolio included $559.1 million of equity securities, compared to $368.8 million2020.
(3)Primarily in utilities, large cap stocks and foreign equities at December 31, 2018. Our equity portfolio includes publicly traded common stocks in the natural resources, energy, consumer staples and other sectors and exchange-traded funds.September 30, 2020.

The following table summarizes our other investments, which are included in investments accounted for using the fair value option, by strategy:
September 30,
2019
 December 31,
2018
September 30,
2020
December 31,
2019
Lending$624,699
 $524,112
Lending$575,623 $602,841 
Term loan investments289,902
 281,486
Term loan investments309,496 264,083 
Energy113,791
 117,509
Energy65,330 97,402 
Credit related funds165,444
 152,510
Credit related funds98,121 123,020 
Investment grade fixed income83,649
 101,902
Investment grade fixed income114,784 151,594 
Infrastructure49,602
 45,371
Infrastructure60,579 61,786 
Private equity25,027
 24,383
Private equity34,983 18,915 
Real estate17,440
 14,252
Real estate17,951 17,279 
Total$1,369,554
 $1,261,525
Total$1,276,867 $1,336,920 
For details on our investments accounted for using the equity method, see note 6,7, “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 8,9, “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 7,8, “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:
September 30,
2019
 December 31,
2018
September 30,
2020
December 31,
2019
Investments accounted for using the fair value option:   Investments accounted for using the fair value option:
Other investments$1,070,566
 $1,050,414
Other investments$893,030 $1,092,396 
Fixed maturities563,214
 922,819
Fixed maturities632,664 416,592 
Short-term investments357,611
 282,131
Short-term investments350,391 329,303 
Equity securities56,905
 56,638
Equity securities60,951 59,799 
Total2,048,296
 2,312,002
Total1,937,036 1,898,090 
Fixed maturities available for sale, at fair value639,112
 393,351
Fixed maturities available for sale, at fair value608,022 706,875 
Equity securities, at fair value43,487
 32,206
Equity securities, at fair value52,807 65,337 
Cash80,390
 63,529
Cash195,333 102,437 
Securities sold but not yet purchased(65,736) (7,790)Securities sold but not yet purchased(24,909)(66,257)
Securities transactions entered into but not settled at the balance sheet date(15,302) (35,635)Securities transactions entered into but not settled at the balance sheet date(74,837)(1,893)
Total investable assets included in ‘other’ segment$2,730,247
 $2,757,663
Total investable assets included in ‘other’ segment$2,693,452 $2,704,589 

ARCH CAPITAL 646020192020 THIRD QUARTER FORM 10-Q

Table of Contents

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 EndedNine Months Ended
September 30,September 30,
2020201920202019
Premiums written:
Direct$1,667,449 $1,438,943 $4,841,874 $4,176,274 
Assumed1,013,583 742,178 2,989,680 2,020,535 
Ceded(806,888)(567,664)(2,151,853)(1,613,195)
Net$1,874,144 $1,613,457 $5,679,701 $4,583,614 
Premiums earned:
Direct$1,618,583 $1,375,384 $4,723,630 $3,977,005 
Assumed880,024 593,129 2,387,286 1,701,307 
Ceded(727,515)(530,490)(1,930,026)(1,407,696)
Net$1,771,092 $1,438,023 $5,180,890 $4,270,616 
Losses and LAE:
Direct$1,131,696 $741,871 $3,279,737 $2,063,168 
Assumed635,199 366,904 1,689,176 1,093,541 
Ceded(550,622)(306,320)(1,406,699)(868,179)
Net$1,216,273 $802,455 $3,562,214 $2,288,530 
 Three Months Ended Nine Months Ended
 September 30, September 30,
 2019 2018 2019 2018
Premiums written:       
Direct$1,438,943
 $1,242,276
 $4,176,274
 $3,601,410
Assumed742,178
 489,052
 2,020,535
 1,664,676
Ceded(567,664) (397,775) (1,613,195) (1,221,093)
Net$1,613,457
 $1,333,553
 $4,583,614
 $4,044,993
        
Premiums earned:       
Direct$1,375,384
 $1,223,445
 $3,977,005
 $3,545,493
Assumed593,129
 466,361
 1,701,307
 1,446,815
Ceded(530,490) (398,928) (1,407,696) (1,129,768)
Net$1,438,023
 $1,290,878
 $4,270,616
 $3,862,540
        
Losses and LAE:       
Direct$741,871
 $718,921
 $2,063,168
 $1,807,860
Assumed366,904
 198,248
 1,093,541
 759,527
Ceded(306,320) (217,749) (868,179) (504,954)
Net$802,455
 $699,420
 $2,288,530
 $2,062,433
Reinsurance Recoverables
The following table summarizes our reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums) at September 30, 2019 and December 31, 2018:
 September 30,
2019
 December 31,
2018
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses$3,168,195
 $2,919,372
% due from carriers with A.M. Best rating of “A-” or better58.6% 63.0%
% due from unrated fully collateralized reinsurers (1)15.5% 12.9%
% due from all other carriers with no A.M. Best rating (2)25.9% 24.1%
Largest balance due from any one carrier as % of total shareholders’ equity1.7% 2.7%
(1)Such amount is fully collateralized through reinsurance trusts.
(2)Over 90% of such amount is collateralized through reinsurance trusts or letters of credit.
Growth in items not rated in 2019 is primarily due to recoverables from a third party reinsurer related to a retroactive reinsurance transaction to reinsure liabilities associated with certain U.S. insurance exposures. Such amounts are fully collateralized. See note 5, “Reserve6, “Allowance for Expected Credit Losses, and Loss
Adjustment Expenses,” to our consolidated financial statements for additional information.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.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 September 30, 2019:2020:
September 30, 2020
Initial Coverage at IssuanceCurrent CoverageRemaining Retention, Net
Bellemeade 2017-1 Ltd. (1)$368,114 $145,573 $130,138 
Bellemeade 2018-1 Ltd. (2)374,460 250,095 129,515 
Bellemeade 2018-2 Ltd. (3)653,278 187,362 308,439 
Bellemeade 2018-3 Ltd. (4)506,110 302,563 137,695 
Bellemeade 2019-1 Ltd. (5)341,790 219,256 133,014 
Bellemeade 2019-2 Ltd. (6)621,022 398,316 173,083 
Bellemeade 2019-3 Ltd. (7)700,920 528,084 185,645 
Bellemeade 2019-4 Ltd. (8)577,267 468,737 124,732 
Bellemeade 2020-1 Ltd. (9)528,540 473,817 763,650 
Bellemeade 2020-2 Ltd. (10)449,167 449,167 246,055 
Total$5,120,668 $3,422,970 $2,331,966 
 Initial Coverage at Issuance Coverage at Sept. 30, 2019 First Layer Retention
Bellemeade 2015-1 Ltd. (1)$300,000
 $6,046
 $129,900
Bellemeade 2017-1 Ltd. (2)368,100
 249,737
 165,700
Bellemeade 2018-1 Ltd. (3)374,460
 362,603
 168,510
Bellemeade 2018-2 Ltd. (4)653,278
 507,534
 352,258
Bellemeade 2018-3 Ltd. (5)506,110
 488,430
 179,331
Bellemeade 2019-1 Ltd. (6)341,790
 293,595
 208,046
Bellemeade 2019-2 Ltd. (7)621,022
 621,022
 221,794
Bellemeade 2019-3 Ltd. (8)700,920
 700,920
 232,093
(1)    Issued in October 2017, covering in-force policies issued between January 1, 2017 and June 30, 2017.
(1)Issued in July 2015, covering in-force policies issued between January 1, 2009 and March 31, 2013.
(2)Issued in October 2017, covering in-force policies issued between January 1, 2017 and June 30, 2017.
(3)Issued in April 2018, covering in-force policies issued between July 1, 2017 and December 31, 2017.
(4)Issued in August 2018, covering in-force policies issued between April 1, 2013 and December 31, 2015.
(5)Issued in October 2018, covering in-force policies issued between January 1, 2018 and June 30, 2018.
(6)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.
(7)Issued in April 2019, covering in-force policies issued between July 1, 2018 and December 31, 2018.
(8)
(2)    Issued in April 2018, covering in-force policies issued between July 1, 2017 and December 31, 2017.
(3)    Issued in August 2018, covering in-force policies issued between April 1, 2013 and December 31, 2015.
(4)    Issued in October 2018, covering in-force policies issued between January 1, 2018 and June 30, 2018.
(5)    Issued in March 2019, covering in-force policies primarily issued between 2005-2008 under United Guaranty Residential Insurance Company (“UGRIC”); as well as policies issued through 2015 under both UGRIC and Arch Mortgage Insurance Company.
(6)    Issued in April 2019, covering in-force policies issued between July 1, 2018 and December 31, 2018.
(7)    Issued in July 2019, covering in-force policies issued in 2016.

In October 2019, we entered into an aggregate excess of loss reinsurance agreement with Bellemeade Re 2019-4 Ltd. Such agreement provides for up to $577.3 million of aggregate excess of loss reinsurance coverage at inception in excess of $162.4 million of aggregate losses for new delinquencies on a portfolio of in-force policies issued in the first half2016.
(8)    Issued in October 2019, covering in-force policies issued between January 1, 2019 and June 30, 2019.
(9)     Issued in June 2020, covering in-force policies issued between July 1, 2019 and December 31, 2019. $450 million was directly funded by Bellemeade 2020-1 Ltd. with an additional $79 million of 2019.
capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

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

ARCH CAPITAL 652019 THIRD QUARTER FORM 10-Q

Table of Contents

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, which is exacerbated by the fact that we have relatively limited historical experience upon which to base such estimates.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.
ARCH CAPITAL 612020 THIRD QUARTER FORM 10-Q

Table of Contents
At September 30, 20192020 and December 31, 2018,2019, our Loss Reserves, net of unpaid losses and loss adjustment expenses recoverable, by type and by operating segment were as follows:
September 30,
2020
December 31,
2019
Insurance segment:  
Case reserves$1,755,511 $1,601,627 
IBNR reserves3,840,659 3,403,051 
Total net reserves5,596,170 5,004,678 
Reinsurance segment:
Case reserves1,444,823 1,273,523 
Additional case reserves290,983 166,251 
IBNR reserves2,175,367 1,835,993 
Total net reserves3,911,173 3,275,767 
Mortgage segment:
Case reserves546,425 266,030 
IBNR reserves272,381 157,712 
Total net reserves (1)818,806 423,742 
Other segment:
Case reserves515,358 478,036 
Additional case reserves32,931 29,059 
IBNR reserves642,450 597,910 
Total net reserves1,190,739 1,105,005 
Total:  
Case reserves4,262,117 3,619,216 
Additional case reserves323,914 195,310 
IBNR reserves6,930,857 5,994,666 
Total net reserves$11,516,888 $9,809,192 
 September 30,
2019
 December 31,
2018
Insurance segment: 
  
Case reserves$1,506,217
 $1,489,644
IBNR reserves3,297,090
 3,266,796
Total net reserves4,803,307
 4,756,440
Reinsurance segment:   
Case reserves1,178,486
 1,082,917
Additional case reserves174,241
 191,002
IBNR reserves1,730,100
 1,578,907
Total net reserves3,082,827
 2,852,826
Mortgage segment:   
Case reserves285,458
 355,606
IBNR reserves155,432
 122,304
Total net reserves (1)440,890
 477,910
Other segment:   
Case reserves434,495
 364,052
Additional case reserves24,495
 36,512
IBNR reserves573,201
 551,266
Total net reserves1,032,191
 951,830
Total: 
  
Case reserves3,404,656
 3,292,219
Additional case reserves198,736
 227,514
IBNR reserves5,755,823
 5,519,273
Total net reserves$9,359,215
 $9,039,006
(1)At September 30, 2020, total net reserves include $593.2 million from U.S. primary mortgage insurance business, of which 27.8% represents policy years 2010 and prior and the remainder from later policy years. At December 31, 2019, total net reserves include $278.7 million from U.S. primary mortgage insurance business, of which 58.2% represents policy years 2010 and prior and the remainder from later policy years.
(1)At September 30, 2019, total net reserves include $309.9 million from U.S. mortgage insurance business, of which 61.8% represents policy years 2009 and prior and the remainder from later policy years. At December 31, 2018, total net reserves include $375.8 million from U.S. mortgage insurance business, of which 73.4% represents policy years 2009 and prior and the remainder from later policy years.
At September 30, 20192020 and December 31, 2018,2019, the insurance segment’s Loss Reserves by major line of business, net of unpaid losses and loss adjustment expenses recoverable, were as follows:
September 30,
2020
December 31,
2019
Insurance segment:
Professional lines (1)$1,439,717 $1,322,969 
Construction and national accounts1,352,674 1,248,750 
Excess and surplus casualty (2)665,666 564,254 
Programs663,465 571,926 
Property, energy, marine and aviation469,450 371,822 
Travel, accident and health115,116 109,613 
Lenders products38,190 28,233 
Other (3)851,892 787,111 
Total net reserves$5,596,170 $5,004,678 
(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.
 September 30,
2019
 December 31,
2018
Insurance segment:   
Professional lines (1)$1,259,731
 $1,247,914
Construction and national accounts1,223,245
 1,166,143
Excess and surplus casualty (2)524,981
 631,370
Programs548,552
 482,045
Property, energy, marine and aviation343,652
 388,710
Travel, accident and health99,564
 83,836
Lenders products29,836
 52,007
Other (3)773,746
 704,415
Total net reserves$4,803,307
 $4,756,440
(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 September 30, 20192020 and December 31, 2018,2019, the reinsurance segment’s Loss Reserves by major line of business, net of unpaid losses and loss adjustment expenses recoverable, were as follows:
September 30,
2020
December 31,
2019
Reinsurance segment:
Casualty (1)$1,920,125 $1,796,073 
Other specialty (2)860,154 649,309 
Property excluding property catastrophe585,110 471,775 
Marine and aviation190,955 160,930 
Property catastrophe250,602 113,565 
Other (3)104,227 84,115 
Total net reserves$3,911,173 $3,275,767 
 September 30,
2019
 December 31,
2018
Reinsurance segment:   
Casualty (1)$1,630,159
 $1,551,550
Other specialty (2)672,042
 582,420
Property excluding property catastrophe459,768
 422,612
Marine and aviation133,960
 130,683
Property catastrophe105,952
 90,635
Other (3)80,946
 74,926
Total net reserves$3,082,827
 $2,852,826
(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.
(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.
ARCH CAPITAL 662019 THIRD QUARTER FORM 10-Q

Table of Contents

Mortgage Operations Supplemental Information
The mortgage segment’s insurance in force (“IIF”) and risk in force (“RIF”) were as follows at September 30, 20192020 and December 31, 2018:2019:
(U.S. Dollars in millions)September 30, 2020December 31, 2019
Amount%Amount%
Insurance In Force (IIF) (1):
U.S. primary mortgage insurance$275,846 66.8 $287,150 68.7 
Mortgage reinsurance28,421 6.9 26,768 6.4 
Other (2)108,786 26.3 104,346 24.9 
Total$413,053 100.0 $418,264 100.0 
Risk In Force (RIF) (3):
U.S. primary mortgage insurance$69,620 91.0 $73,388 91.9 
Mortgage reinsurance2,145 2.8 2,129 2.7 
Other (2)4,750 6.2 4,380 5.5 
Total$76,515 100.0 $79,897 100.0 
(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.
(U.S. Dollars in millions)September 30, 2019 December 31, 2018
Amount % Amount %
Insurance In Force (IIF) (1):       
U.S. primary mortgage insurance$284,496
 69.7
 $276,538
 72.1
Mortgage reinsurance25,440
 6.2
 25,975
 6.8
Other (2)98,054
 24.0
 81,147
 21.2
Total$407,990
 100.0
 $383,660
 100.0
        
Risk In Force (RIF) (3):       
U.S. primary mortgage insurance$72,916
 92.0
 $70,995
 92.3
Mortgage reinsurance2,086
 2.6
 2,217
 2.9
Other (2)4,216
 5.3
 3,728
 4.8
Total$79,218
 100.0
 $76,940
 100.0
(1)ARCH CAPITALRepresents the aggregate dollar amount of each insured mortgage loan’s current principal balance. 622020 THIRD QUARTER FORM 10-Q
(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.

Table of Contents
The insurance in force and risk in force for our U.S. primary mortgage insurance business by policy year were as follows at September 30, 2019:2020:
(U.S. Dollars in millions)IIFRIFDelinquency
Amount%Amount%Rate (1)
Policy year:
2010 and prior$14,603 5.3 $3,320 4.8 11.59 %
20111,141 0.4 308 0.4 3.67 %
20124,467 1.6 1,228 1.8 2.92 %
20138,754 3.2 2,447 3.5 3.37 %
20149,613 3.5 2,647 3.8 4.02 %
201517,752 6.4 4,778 6.9 3.79 %
201629,299 10.6 7,753 11.1 4.89 %
201729,537 10.7 7,639 11.0 5.52 %
201832,788 11.9 8,304 11.9 6.66 %
201956,189 20.4 13,900 20.0 4.68 %
202071,703 26.0 17,296 24.8 1.01 %
Total$275,846 100.0 $69,620 100.0 4.69 %
(U.S. Dollars in millions)IIF RIF Delinquency
Amount % Amount % Rate (1)
Policy year:         
2009 and prior$17,943
 6.3
 $4,156
 5.7
 8.48%
2010442
 0.2
 117
 0.2
 3.21%
20111,919
 0.7
 533
 0.7
 1.46%
20126,919
 2.4
 1,929
 2.6
 0.81%
201313,552
 4.8
 3,782
 5.2
 0.94%
201414,950
 5.3
 4,111
 5.6
 1.04%
201527,984
 9.8
 7,431
 10.2
 0.79%
201644,091
 15.5
 11,445
 15.7
 0.88%
201747,430
 16.7
 12,136
 16.6
 0.82%
201857,472
 20.2
 14,511
 19.9
 0.62%
201951,794
 18.2
 12,765
 17.5
 0.09%
Total$284,496
 100.0
 $72,916
 100.0
 1.48%
(1)Represents the ending percentage of loans in default.
(1)Represents the ending percentage of loans in default.
The insurance in force and risk in force for our U.S. primary mortgage insurance business by policy year were as follows at December 31, 2018:2019:
(U.S. Dollars in millions)IIFRIFDelinquency
Amount%Amount%Rate (1)
Policy year:
2010 and prior$17,251 6.0 $3,990 5.4 8.79 %
20111,678 0.6 464 0.6 1.59 %
20126,293 2.2 1,753 2.4 0.89 %
201312,276 4.3 3,433 4.7 0.99 %
201413,714 4.8 3,778 5.1 1.16 %
201525,788 9.0 6,880 9.4 0.87 %
201640,898 14.2 10,670 14.5 1.03 %
201743,896 15.3 11,262 15.3 1.00 %
201851,776 18.0 13,086 17.8 0.86 %
201973,580 25.6 18,072 24.6 0.14 %
Total$287,150 100.0 $73,388 100.0 1.54 %
(1)Represents the ending percentage of loans in default.
(U.S. Dollars in millions)IIF RIF Delinquency
Amount % Amount % Rate (1)
Policy year:         
2009 and prior$21,210
 7.7
 $4,900
 6.9
 8.90%
2010646
 0.2
 175
 0.2
 2.62%
20112,530
 0.9
 701
 1.0
 1.57%
20129,650
 3.5
 2,664
 3.8
 0.78%
201316,823
 6.1
 4,676
 6.6
 0.89%
201418,274
 6.6
 4,947
 7.0
 0.97%
201533,781
 12.2
 8,849
 12.5
 0.69%
201652,324
 18.9
 13,407
 18.9
 0.77%
201754,287
 19.6
 13,793
 19.4
 0.55%
201867,013
 24.2
 16,883
 23.8
 0.15%
Total$276,538
 100.0
 $70,995
 100.0
 1.60%
(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 September 30, 20192020 and December 31, 2018:2019:
(U.S. Dollars in millions)September 30, 2020December 31, 2019
Amount%Amount%
Credit quality (FICO):
>=740$40,017 57.5 $42,301 57.6 
680-73924,236 34.8 25,240 34.4 
620-6795,016 7.2 5,444 7.4 
<620351 0.5 403 0.5 
Total$69,620 100.0 $73,388 100.0 
Weighted average FICO score743 743 
Loan-to-value (LTV):
95.01% and above$8,789 12.6 $9,064 12.4 
90.01% to 95.00%37,278 53.5 40,136 54.7 
85.01% to 90.00%19,870 28.5 20,890 28.5 
85.00% and below3,683 5.3 3,298 4.5 
Total$69,620 100.0 $73,388 100.0 
Weighted average LTV92.9 %93.0 %
Total RIF, net of external reinsurance$56,067 $58,512 
(U.S. Dollars in millions)September 30, 2019 December 31, 2018
Amount % Amount %
Credit quality (FICO):       
>=740$41,975
 57.6
 $41,066
 57.8
680-73925,013
 34.3
 23,954
 33.7
620-6795,501
 7.5
 5,485
 7.7
<620427
 0.6
 490
 0.7
Total$72,916
 100.0
 $70,995
 100.0
Weighted average FICO score743
   743
  
        
Loan-to-value (LTV):       
95.01% and above$8,948
 12.3
 $7,918
 11.2
90.01% to 95.00%40,086
 55.0
 39,370
 55.5
85.01% to 90.00%20,708
 28.4
 20,643
 29.1
85.00% and below3,174
 4.4
 3,064
 4.3
Total$72,916
 100.0
 $70,995
 100.0
Weighted average LTV93.1%   93.0%  
        
Total RIF, net of external reinsurance$57,768
   $55,755
  
(U.S. Dollars in millions)September 30, 2020December 31, 2019
Amount%Amount%
Total RIF by State:
Texas$5,536 8.0 $5,678 7.7 
California5,019 7.2 5,187 7.1 
Florida3,648 5.2 3,887 5.3 
Georgia2,890 4.2 2,753 3.8 
Illinois2,670 3.8 2,616 3.6 
Virginia2,540 3.6 2,881 3.9 
North Carolina2,516 3.6 2,470 3.4 
Minnesota2,489 3.6 2,514 3.4 
Massachusetts2,344 3.4 2,432 3.3 
Washington2,222 3.2 2,474 3.4 
Other37,746 54.2 40,496 55.2 
Total$69,620 100.0 $73,388 100.0 

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(U.S. Dollars in millions)September 30, 2019 December 31, 2018
Amount % Amount %
Total RIF by State:       
Texas$5,599
 7.7
 $5,491
 7.7
California4,984
 6.8
 4,505
 6.3
Florida3,821
 5.2
 3,541
 5.0
Virginia2,907
 4.0
 2,931
 4.1
Georgia2,667
 3.7
 2,573
 3.6
Illinois2,602
 3.6
 2,482
 3.5
Minnesota2,480
 3.4
 2,400
 3.4
North Carolina2,469
 3.4
 2,505
 3.5
Washington2,466
 3.4
 2,408
 3.4
Maryland2,443
 3.4
 2,407
 3.4
Others40,478
 55.5
 39,752
 56.0
Total$72,916
 100.0
 $70,995
 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)Nine Months Ended
September 30,
20202019
Roll-forward of insured loans in default:
Beginning delinquent number of loans20,163 20,665 
New notices87,760 28,728 
Cures(48,234)(27,877)
Paid claims(1,327)(2,273)
Ending delinquent number of loans (1)58,362 19,243 
Ending number of policies in force (1)1,245,408 1,304,263 
Delinquency rate (1)4.69 %1.48 %
Losses:
Number of claims paid1,327 2,273 
Total paid claims$55,559 $91,601 
Average per claim$41.9 $40.3 
Severity (2)93.3 %96.6 %
Average case reserve per default (in thousands)$10.1 $14.7 
(U.S. Dollars in thousands, except policy, loan and claim count)Nine Months Ended
September 30,
2019 2018
Roll-forward of insured loans in default:   
Beginning delinquent number of loans20,665
 27,068
New notices28,728
 27,258
Cures(27,877) (31,111)
Paid claims(2,273) (2,854)
Ending delinquent number of loans (1)19,243
 20,361
    
Ending number of policies in force (1)1,304,263
 1,270,728
    
Delinquency rate (1)1.48% 1.60%
    
Losses:   
Number of claims paid2,273
 2,854
Total paid claims$91,601
 $118,492
Average per claim$40.3
 $41.5
Severity (2)96.6% 102.0%
Average reserve per default (in thousands)$14.7
 $18.1
(1)Includes first lien primary and pool policies.
(1)Includes first lien primary and pool policies.
(2)Represents total paid claims divided by RIF of loans for which claims were paid.
(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 12.99.6 to 1 at September 30, 2019,2020, compared to 13.012.0 to 1 at December 31, 2018.2019.
Shareholders’ Equity and Book Value per Share
Total shareholders’ equity available to Arch was $11.16$12.5 billion at September 30, 2019,2020, compared to $9.44$11.5 billion at December 31, 2018.2019. The increase primarily reflected strongthe impact of investment returns, partially offset by the impact of a higher level of catastrophic activity (including COVID-19) on underwriting and investment returns.
The following table presents the calculation of book value per share:
(U.S. dollars in thousands, except 
share data)
September 30,
2020
December 31,
2019
Total shareholders’ equity available to Arch$12,451,997 $11,497,371 
Less preferred shareholders’ equity780,000 780,000 
Common shareholders’ equity available to Arch$11,671,997 $10,717,371 
Common shares and common share equivalents outstanding, net of treasury shares (1)406,018,958 405,619,201 
Book value per share$28.75 $26.42 
(U.S. dollars in thousands, except 
share data)
September 30,
2019
 December 31,
2018
Total shareholders’ equity available to Arch$11,158,096
 $9,439,827
Less preferred shareholders’ equity780,000
 780,000
Common shareholders’ equity available to Arch$10,378,096
 $8,659,827
Common shares and common share equivalents outstanding, net of treasury shares (1)405,230,531
 402,454,834
Book value per share$25.61
 $21.52
(1)Excludes the effects of 17,967,735 and 18,853,018 stock options and 1,064,759 and 1,586,779 restricted stock units outstanding at September 30, 2020 and December 31, 2019, respectively.
LIQUIDITY
(1)Excludes the effects of 19,170,417 and 20,076,593 stock options and 1,609,195 and 1,307,304 restricted stock units outstanding at September 30, 2019 and December 31, 2018, respectively.
LIQUIDITY

Our liquidity and capital resources were not materially impacted by COVID-19 during the third quarter of 2020. We raised an additional $1.0 billion of capital in the form of long-term senior notes at the end of June 2020. For further discussion of the risks related to our potential future impacts of COVID-19 on our liquidity and capital resources, see “ITEM 1A—Risk Factors”.

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 nine months ended September 30, 2019,2020, Arch Capital received dividends of $86.4$163.7 million from Arch Re Bermuda, our Bermuda-based reinsurer and insurer, which can pay approximately $2.54$2.9 billion to Arch Capital during the remainder of 20192020 without providing an affidavit to the Bermuda Monetary Authority (“BMA”). For the nine months ended September 30, 2019 Arch Capital Group (U.S.) Inc. (“Arch-U.S.”) received $465.0 million
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Table of dividends from Arch U.S. MI Holdings Inc., a subsidiary of Arch-U.S.Contents
We expect that our liquidity needs, including our anticipated (re)insurance obligations and operating and capital expenditure needs, for the next twelve months, at a minimum, 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.

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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.
Nine Months EndedNine Months Ended
September 30,September 30,
2019 2018 20202019
Total cash provided by (used for): 
  
Total cash provided by (used for):  
Operating activities$1,366,762
 $947,656
Operating activities$2,198,037 $1,366,762 
Investing activities(1,093,054) (181,774)Investing activities(2,850,392)(1,093,054)
Financing activities(45,757) (713,511)Financing activities845,612 (45,757)
Effects of exchange rate changes on foreign currency cash(6,981) (9,867)Effects of exchange rate changes on foreign currency cash(2,878)(6,981)
Increase (decrease) in cash and restricted cash$220,970
 $42,504
Increase (decrease) in cash and restricted cash$190,379 $220,970 
Cash provided by operating activities for the nine months ended September 30, 20192020 reflected a higher level of premiums collected than in the 20182019 period.
Cash used for investing activities for the nine months ended September 30, 20192020 was higher than in the 20182019 period, reflecting a higher level of securities purchased.purchased, and the investing of proceeds from our issuance of senior notes.
Cash used forprovided by financing activities for the nine months ended September 30, 2019 was lower than in2020, primarily reflected the 2018 period. The 2018 periodissuance of $1.0 billion of senior notes. Cash flows also reflected $250.0 million of paydowns on our revolving credit agreement borrowings, $184.5$75.5 million of repurchases under our share repurchase program and $92.6 million related to redemption of our Series C preferred shares.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)
Sep 30,
2020
Dec 31,
2019
Senior notes$2,723,189 $1,734,209 
Shareholders’ equity available to Arch:
Series E non-cumulative preferred shares$450,000 $450,000 
Series F non-cumulative preferred shares330,000 330,000 
Common shareholders’ equity11,671,997 10,717,371 
Total$12,451,997 $11,497,371 
Total capital available to Arch$15,175,186 $13,231,580 
Debt to total capital (%)17.9 13.1 
Preferred to total capital (%)5.1 5.9 
Debt and preferred to total capital (%)23.1 19.0 
(U.S. dollars in thousands, except 
share data)
Sep 30,
2019
 Dec 31,
2018
Debt:   
Senior notes, due May 2034$300,000
 $300,000
Arch-U.S. senior notes, due Nov 2043 (1)500,000
 500,000
Arch Finance senior notes, due Dec 2026 (1)500,000
 500,000
Arch Finance senior notes, due Dec 2046 (1)450,000
 450,000
Deferred debt costs on senior notes(15,963) (16,472)
Revolving credit agreement borrowings due Oct 2021 (2)
 
Total$1,734,037
 $1,733,528
    
Shareholders’ equity available to Arch:   
Series E non-cumulative preferred shares$450,000
 $450,000
Series F non-cumulative preferred shares330,000
 330,000
Common shareholders’ equity10,378,096
 8,659,827
Total$11,158,096
 $9,439,827
    
Total capital available to Arch$12,892,133
 $11,173,355
    
Debt to total capital (%)13.5
 15.5
Preferred to total capital (%)6.1
 7.0
Debt and preferred to total capital (%)19.5
 22.5
(1)Fully and unconditionally guaranteed by Arch Capital.
(2)$500 million unsecured facility for revolving loans and letters of credit.
On June 30, 2020, Arch Capital and Arch-U.S. are each holding companies and, accordingly, they conduct substantially allissued $1.0 billion of their operations through their operating subsidiaries. Arch Capital Finance LLC (“Arch Finance”) is a wholly owned subsidiary30 year senior notes. The net proceeds of Arch U.S. MI Holdings Inc. As a result, Arch Capital, Arch-U.S. and Arch Finance's cash flows and their ability to service their debt depends upon the earnings of their operating subsidiaries, or affiliates in the case of Arch Finance, and on their ability to distribute the earnings, loans or other payments from such subsidiaries or affiliatesoffering were contributed to Arch Capital, Arch-U.S. and Arch Finance, respectively.Re Bermuda to support our underwriting operations.
In addition, 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 September 30, 20192020 with an estimated PMIER sufficiency ratio of 154%158%, compared to 141%161% at December 31, 2018.


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Pursuant to our 2014 acquisition of the CMG Mortgage Insurance Company and its affiliated mortgage insurance companies, we made a contingent consideration payment of $61.5 million in April 2019. The maximum amount of remaining contingent consideration payments over the remaining earn-out period is $6.6 million.
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, 2018. As a result, the level of subject business ceded toIn 2019, certain reinsurance agreements between our insurance subsidiaries and Arch Re Bermuda were reinstated.
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GUARANTOR INFORMATION

The below table provides a description of our senior notes payable at September 30, 2020, excluding amounts attributable to the ‘other’ segment (i.e., Watford):

InterestPrincipalCarrying
Issuer/Due(Fixed)AmountAmount
Arch Capital:
May 1, 20347.350 %$300,000 $297,338 
June 30, 20503.635 %1,000,000988,447
Arch-U.S.:
Nov. 1, 2043 (1)5.144 %500,000494,915
Arch Finance:
Dec. 15, 2026 (1)4.011 %500,000497,109
Dec. 15, 2046 (1)5.031 %450,000445,380
Total$2,750,000 $2,723,189 
(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 the reported periods was substantially lower than in 2017Arch Capital (parent guarantor) and prior periods.Arch-U.S. (subsidiary issuer):
September 30, 2020December 31, 2019
Arch CapitalArch-U.S.Arch CapitalArch-U.S.
Assets
Total investments$158 $715,800 $42 $692,606 
Cash9,041 10,092 18,113 54,518 
Investments in subsidiaries13,745,334 4,743,177 11,786,861 4,347,806 
Due from subsidiaries and affiliates17 200,758 17 200,635 
Other assets19,357 31,328 20,461 32,187 
Total assets$13,773,907 $5,701,155 $11,825,494 $5,327,752 
Liabilities
Senior notes1,285,785 494,915 297,254 494,831 
Due to subsidiaries and affiliates— 542,103 — 536,805 
Other liabilities36,125 43,134 30,869 33,267 
Total liabilities1,321,910 1,080,152 328,123 1,064,903 
Shareholders' Equity
Total shareholders' equity available to Arch12,451,997 4,621,003 11,497,371 4,262,849 
Total shareholders' equity12,451,997 4,621,003 11,497,371 4,262,849 
Total liabilities and shareholders' equity$13,773,907 $5,701,155 $11,825,494 $5,327,752 
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Nine Months EndedYear Ended
September 30, 2020December 31, 2019
Arch CapitalArch-U.S.Arch CapitalArch-U.S.
Revenues
Net investment income$53 $13,104 $212 $14,270 
Net realized gains (losses)— 1,428 — 25,313 
Equity in net income (loss) of investments accounted for using the equity method— 2,308 — 779 
Other income (loss)(327)— (762)— 
Total revenues(274)16,840 (550)40,362 
Expenses
Corporate expenses47,802 5,642 62,701 7,221 
Interest expense25,762 35,645 22,154 47,951 
Net foreign exchange (gains) losses— — 
Total expenses73,567 41,287 84,856 55,172 
Income (loss) before income taxes(73,841)(24,447)(85,406)(14,810)
Income tax (expense) benefit— 5,429 — 3,696 
Income (loss) before equity in net income of subsidiaries(73,841)(19,018)(85,406)(11,114)
Equity in net income of subsidiaries935,818 272,253 1,721,725 564,657 
Net income available to Arch861,977 253,235 1,636,319 553,543 
Preferred dividends(31,209)— (41,612)— 
Net income available to Arch common shareholders$830,768 $253,235 $1,594,707 $553,543 
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 nine months ended September 30, 2019,2020, Arch Capital repurchased 0.12.6 million shares under the share repurchase program with an aggregate purchase price of $2.9$75.5 million. Since the inception of the share repurchase program through September 30, 2019,2020, Arch Capital has repurchased 386.3388.9 million common shares for an aggregate purchase price of $3.97$4.04 billion. At September 30, 2019,2020, approximately $160.9$924.5 million of share repurchases were available under the program. On November 8, 2019, the board of directors of ACGL increased the aggregate purchase amount authorized under the share repurchase program, to $1.0 billion. Repurchases under this authorizationwhich 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. We will continue to monitor our share price and, dependingDepending upon results of operations, market conditions and the development of the economy, as well as other factors, generally we will consider share repurchases on an opportunistic basis.basis from time to time. During the 2020 third quarter, we have not repurchased any shares under our share repurchase program.
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. CatastrophesNatural 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 totaltangible shareholders’ equity available to Arch.Arch (total shareholders’
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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 October 1, 2019,2020, our modeled peak zone catastrophe exposure was a windstorm affecting the Northeastern U.S.,Florida Tri-County, with a net probable maximum pre-tax loss of $414$918 million, followed by windstorms affecting Florida Tri-CountyNortheastern U.S. and the Gulf of Mexico regions with net probable maximum pre-tax losses of $398 million$674 and $357$644 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 hurricanes. As of October 1, 2019,2020, our modeled peak zone earthquake exposure (San Francisco earthquake) represented approximately 70%57% of our peak zone catastrophe exposure, and our modeled peak zone international exposure (Japan earthquake) was substantially less than both our peak zone windstorm and earthquake exposures.
Effective July 1, 2019,2020, our insurance operations had in effect a reinsurance program which provided coverage for certain property-catastrophe related losses equal to $275$243 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.

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Currently, we seek to limit our modeled RDS loss from a severe economic event to approximately 25% of total tangible shareholders’ equity available to Arch (total shareholders’ equity available to Arch less goodwill and intangible assets).Arch. We reserve the right to change this threshold at any time. Based on in-force exposure estimated as of October 1, 2019,2020, our modeled RDS loss was approximately 9%8% 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 afterbefore 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 total shareholders' equity or tangible shareholders’ equity from one or more catastrophic events or severe economic events due to several factors. These factors includinginclude 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 20182019 Form 10-K.10-K, updated where applicable in “ITEM 1A—Risk Factors”
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 20182019 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 September 30, 2019.2020. 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 September 30, 20192020 that affect the quantitative and qualitative disclosures presented in our 20182019 Form 10-K (see section captioned “Management’s Discussion and Analysis of Financial Condition and Results of Operations—Market
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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 interest rate sensitive securitiesFixed Income 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:Fixed Income Securities:
(U.S. dollars in
billions)
Interest Rate Shift in Basis Points(U.S. dollars in
billions)
Interest Rate Shift in Basis Points
-100 -50  +50 +100-100-50+50+100
Sep 30, 2019 
  
  
  
  
Sep 30, 2020Sep 30, 2020     
Total fair value$20.91
 $20.55
 $20.21
 $19.82
 $19.48
Total fair value$24.84 $24.45 $24.07 $23.68 $23.30 
Change from base3.5% 1.7%   (1.9)% (3.6)%Change from base3.2 %1.6 %(1.6)%(3.2)%
Change in unrealized value$0.71
 $0.34
   $(0.38) $(0.73)Change in unrealized value$0.77 $0.39 $(0.39)$(0.77)
         
Dec 31, 2018         
Dec 31, 2019Dec 31, 2019
Total fair value$19.23
 $18.91
 $18.62
 $18.30
 $17.98
Total fair value$21.54 $21.19 $20.83 $20.48 $20.13 
Change from base3.3% 1.6%   (1.7)% (3.4)%Change from base3.4 %1.7 %(1.7)%(3.4)%
Change in unrealized value$0.61
 $0.30
   $(0.32) $(0.63)Change in unrealized value$0.71 $0.35 $(0.35)$(0.71)
In addition, we consider the effect of credit spread movements on the market value of our fixed maturities, fixed maturities pledged under securities lending agreements, short-term investments and certain of our other investments and investment funds accounted for using the equity method which

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invest in fixed income securitiesFixed Income Securities and the corresponding change in unrealized appreciation.value. As credit spreads widen, the fair value of our fixed income securitiesFixed 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:Fixed Income Securities:
(U.S. dollars in
billions)
Credit Spread Shift in Percentage Points(U.S. dollars in
billions)
Credit Spread Shift in Percentage Points
-100 -50  +50 +100-100-50+50+100
Sep 30, 2019 
  
  
  
  
Sep 30, 2020Sep 30, 2020
Total fair value$20.59
 $20.41
 $20.21
 $20.01
 $19.82
Total fair value$24.74 $24.40 $24.07 $23.73 $23.39 
Change from base1.9% 1.0%   (1.0)% (1.9)%Change from base2.8 %1.4 %(1.4)%(2.8)%
Change in unrealized value$0.38
 $0.20
   $(0.20) $(0.38)Change in unrealized value$0.67 $0.34 $(0.34)$(0.67)
         
Dec 31, 2018         
Dec 31, 2019Dec 31, 2019
Total fair value$19.08
 $18.84
 $18.62
 $18.39
 $18.15
Total fair value$21.19 $21.02 $20.83 $20.65 $20.48 
Change from base2.5% 1.2%   (1.2)% (2.5)%Change from base1.7 %0.9 %(0.9)%(1.7)%
Change in unrealized value$0.47
 $0.22
   $(0.22) $(0.47)Change in unrealized value$0.35 $0.19 $(0.19)$(0.35)
Another method that attempts to measure portfolio risk is Value-at-Risk (“VaR”). VaR attempts to take into account a broad cross-section of risks facing a portfolio by utilizing relevant securities volatility data skewed towards the most recent months and quarters. VaR measures the amount of a portfolio at risk for outcomes 1.65 standard deviations from the mean based onworst expected loss under normal market conditions over a one yearspecific time horizon and is expressed asinterval at a percentage of the portfolio’s initial value. In other words,given confidence level. The 1-year 95th percentile parametric VaR reported herein estimates that 95% of the time, should the risks taken into account in the VaR model perform per their historical tendencies, the portfolio’sportfolio loss in any one year period is expected toa one-year horizon would be less than or equal to the calculated VaR,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 September 30, 2019,2020, our portfolio’s VaR was estimated to be 3.34%5.4% compared to an estimated 3.02%3.19% at December 31, 2018.2019. 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 September 30, 20192020 and December 31, 2018,2019, the fair value of our investments in equity securities (excluding securities included in Fixed Income Securities above) totaled $559.1$877.6 million and $368.8$827.8 million, 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 $55.9$87.8 million and $36.9$82.8 million at September 30, 20192020 and December 31, 2018,2019, respectively, and would have decreased book value per share by approximately $0.14$0.22 and $0.09,$0.20, respectively. An immediate hypothetical 10% increase in the value of each position would increase the fair value of such investments by approximately $55.9$87.8 million and $36.9$82.8 million at September 30, 20192020 and December 31, 2018,2019, respectively, and would have increased book value per share by approximately $0.14$0.22 and $0.09,$0.20, respectively.
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Investment-Related Derivatives. At September 30, 2019,2020, 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 $7.53$8.70 billion, compared to $4.95$8.04 billion at December 31, 2018.2019. If the underlying exposure of each investment-related derivative held at September 30, 20192020 depreciated by 100 basis points, it would have resulted in a reduction in net income of approximately $75.3$87.0 million, and a decrease in book value per share of approximately $0.19$0.21 per share, compared to $49.5$80.4 million and $0.12$0.20 per share, respectively, on investment-related derivatives held at December 31, 2018.2019. If the underlying exposure of each investment-related derivative held at September 30, 20192020 appreciated by 100 basis points, it would have resulted in an increase in net income of approximately $75.3$87.0 million, and an increase in book value per share of approximately $0.19$0.21 per share, compared to $49.5$80.4 million and $0.12$0.20 per share, respectively, on investment-related derivatives held at December 31, 2018.2019. See note 8,9, “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 8,9, “Derivative Instruments,” to our consolidated financial statements for additional information.

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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)
September 30,
2020
December 31,
2019
Net assets (liabilities), denominated in foreign currencies, excluding shareholders’ equity and derivatives$(336,400)$265,501 
Shareholders’ equity denominated in foreign currencies (1)773,491 744,690 
Net foreign currency forward contracts outstanding (2)368,379 81,731 
Net exposures denominated in foreign currencies$805,470 $1,091,922 
Pre-tax impact of a hypothetical 10% appreciation of the U.S. Dollar against foreign currencies:  
Shareholders’ equity$(80,547)$(109,192)
Book value per share$(0.20)$(0.27)
Pre-tax impact of a hypothetical 10% decline of the U.S. Dollar against foreign currencies:  
Shareholders’ equity$80,547 $109,192 
Book value per share$0.20 $0.27 
(U.S. dollars in thousands, except 
per share data)
September 30,
2019
 December 31,
2018
Net assets (liabilities), denominated in foreign currencies, excluding shareholders’ equity and derivatives$206,486
 $(561,311)
Shareholders’ equity denominated in foreign currencies (1)542,970
 478,678
Net foreign currency forward contracts outstanding (2)52,491
 241,442
Net exposures denominated in foreign currencies$801,947
 $158,809
    
Pre-tax impact of a hypothetical 10% appreciation of the U.S. Dollar against foreign currencies: 
  
Shareholders’ equity$(80,195) $(15,881)
Book value per share$(0.20) $(0.04)
    
Pre-tax impact of a hypothetical 10% decline of the U.S. Dollar against foreign currencies: 
  
Shareholders’ equity$80,195
 $15,881
Book value per share$0.20
 $0.04
(1)    Represents capital contributions held in the foreign currencies of our operating units.
(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.
(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“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.
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OTHER FINANCIAL INFORMATION

The consolidated financial statements as of September 30, 20192020 and for the three month and nine month periods ended September 30, 20192020 and 20182019 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 September 30, 20192020 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.

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PART II.  OTHER INFORMATION
ARCH CAPITAL 742019 THIRD QUARTER FORM 10-Q


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 September 30, 2019,2020, 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
Our business is subject to a number of risks, including those identified in Part I—Item 1A of our 2019 Form 10-K, that could have a material adverse effect on our business, results of operations, financial condition and/or liquidity and that could cause our operating results to vary significantly from period to period. The risks described in our 2019 Form 10-K are not the only risks we face. Additional risks and uncertainties not currently known to us or that we currently deem to be immaterial also could have a material adverse effect on our business, results of operations, financial condition and/or liquidity. Other than as described below, there have been no material changes fromto the risk factors previously disclosed in Part I—Item 1A of our Annual Report2019 Form 10-K.

The impact of COVID-19 and related risks could materially affect our results of operations, financial position and/or liquidity.
The continuing global pandemic related to the novel coronavirus COVID-19 has impacted the global economy, financial markets and our results of operations. In addition, COVID-19 could materially disrupt the business operations of third parties with whom we interact. The resurgence of the pandemic in many countries has resulted in continued disruption in global supply chains, and adversely impacted operations in many sectors of the economy. Because of the size and breadth of this pandemic, all of the direct and indirect consequences of COVID-19 are not yet known and may not emerge for some time.

The pandemic could have a significant effect on our Company’s business, results of operations, and current and future financial performance. We may experience higher levels of loss and claims activity in certain lines of business and our premiums written and earned could also be adversely affected by a suppression of global commercial activity that results in a reduction in insurable assets and other exposure. Conditions of the financial markets resulting from the virus may also have a negative effect on the value and quality of
the assets we hold within our portfolio of invested assets, thereby adversely affecting our investment income and increasing our credit and related risk. Certain lines of our business may require additional forms of collateral in the event of a decline in the fair value of securities and benchmarks to which those repayment mechanisms are linked. The continued impacts of the pandemic to the financial markets may also adversely affect our ability to fund through public or private equity offerings, debt financings, and through other means at acceptable terms. For a further discussion, see “We could face unanticipated losses from war, terrorism, cyber-attacks, pandemics and political instability, and these or other unanticipated losses could have a material adverse effect on our financial condition and results of operations” and “Emerging claim and coverage issues may adversely affect our business” included in “Part I—Item 1A—Risk Factors” in our 2019 Form 10-K10-K.

The disruption in the financial markets related to COVID-19 has contributed to net realized losses, primarily due to the impact of changes in fair value on our equity investments and, to a lesser extent, our fixed-income investment portfolio. Our corporate fixed income portfolio may be adversely impacted by ratings downgrades, increased bankruptcies and credit spread widening in distressed industries, such as energy, gaming, lodging and leisure, autos, airlines and retail. In addition, in recent years, many state and local governments have been operating under deficits or projected deficits. These deficits may be exacerbated by the costs of responding to COVID-19 and reduced tax revenues due to adverse economic conditions. The severity and duration of these deficits could have an adverse impact on the collectability and valuation of our municipal bond portfolio. Our investment portfolio also includes residential mortgage-backed securities, commercial mortgage-backed securities and commercial mortgage loans, all of which could be adversely impacted by declines in real estate valuations and/or financial market disruption, including a heightened collection risk on the underlying mortgages and on rent receivables. Further disruptions in global financial markets due to the continuing impact of COVID-19 could result in additional net realized investment losses, including potential impairments in our fixed income portfolio. In addition, declines in fixed income yields would result in decreases in net investment income from future investment activity, including re-investments. Furthermore, issuers of the investments we hold under the equity method of accounting report their financial information to us one month to three months following the end of the reporting period. Accordingly, the adverse impact of any disruptions in global financial markets on equity method income from these investments would likely not be reflected in our current quarter results and would instead be reported in the subsequent quarter. Further disruptions in global financial markets could adversely impact our net investment income in
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future periods from its non-fixed income investment portfolio. For further discussion of the risks related to our investment portfolio see “We may be adversely affected by changes in economic conditions, including interest rate changes” and “The determination of the amount of allowances and impairments taken on our investments is highly subjective and could materially impact our results of operations or financial position” included in “Part I—Item 1A—Risk Factors” in our 2019 Form 10-K.
Governmental, regulatory and rating actions in response to the COVID-19 pandemic may adversely affect our financial performance and our ability to conduct our businesses as we have in the past.

Federal, state and local government actions in the U.S. and other countries where we do business to address and mitigate the impact of COVID-19 may adversely affect us. For example, we are potentially subject to legislative and/or regulatory action that seeks to retroactively mandate coverage for losses which our insurance policies were not designed or priced to cover. Currently, in some states there is proposed legislation to require insurers to cover business interruption claims irrespective of terms, exclusions or other conditions included in the year endedpolicies that would otherwise preclude coverage. In addition, a number of states have instituted, and other states are considering instituting, changes designed to effectively expand workers' compensation coverage by creating presumptions of compensability of claims for certain types of workers. Regulatory restrictions or requirements could also impact pricing, risk selection and our rights and obligations with respect to our policies and insureds, including our ability to cancel policies or our right to collect premiums. Some state regulators have issued orders to review insurers’ rates to determine whether premium refunds are required, and regulators in other states could take similar actions. Many insurers, including us, have also voluntarily provided, and may further provide, premium refunds to their customers. It is also possible that changes in economic conditions and steps taken by federal, state and local governments in response to COVID-19 could require an increase in taxes at the federal, state and local levels, which would adversely impact our results of operations.
We expect the pandemic to result in a material increase in new defaults as borrowers fail to make timely payments on their mortgages, including as a result of entering mortgage forbearance programs that allow borrowers to defer mortgage payments, which may impact our eligible insurers’ ability to remain compliant with the Private Mortgage Insurers Eligibility Requirements (“PMIERs”) financial requirements. On March 18, 2020, the Federal Housing Finance Agency (“FHFA”) directed Fannie Mae and Freddie Mac (the “GSEs”), the primary purchasers of mortgages insured by the Company, to suspend foreclosures and evictions for at least
60 days and to provide payment forbearance to borrowers impacted by COVID-19. On March 27, 2020, the Coronavirus Aid, Relief, and Economic Security Act ("CARES Act") was enacted. The CARES Act suspends foreclosures and evictions for at least 60 days from March 18, 2020, on mortgages purchased or securitized by the GSEs. In addition, the CARES Act provides for payment forbearance for up to 360 days to borrowers experiencing a hardship during the COVID-19 emergency. FHFA directed Fannie Mae and Freddie Mac to extend the suspension of eviction and foreclosure-related activities through at least December 31, 2018.2020.
Consistent with the CARES Act, the GSEs will provide a forbearance plan to any borrower who requests a forbearance with an attestation of the financial hardship caused by the COVID-19 emergency. No additional documentation other than the borrower’s attestation to a financial hardship caused by the COVID-19 emergency is required. It is unclear how many borrowers will obtain forbearance plans, the length of assistance borrowers will require, and whether borrowers will be able to resume their mortgage payments thereafter. Increases in unemployment as well as borrowers entering into forbearance plans will result in higher notices of delinquency (“NODs”) which may have an adverse impact on our results or operations. In addition, as a result of COVID-19-related relief programs, the defaults related to the pandemic, if not cured, could remain in our defaulted loan inventory for a protracted period of time, potentially resulting in higher frequency (claim rate) and severity (amount of the claim) for those loans that ultimately result in a claim. Accordingly, extended or extensive forbearance programs and other changes in regulations or laws may adversely impact our mortgage insurance segment.
When a borrower obtains a forbearance plan and does not make mortgage payments for two consecutive months, the servicer will report the NOD with a special code that indicates the loan is subject to a COVID-19 related forbearance plan. Under PMIERs, eligible insurers are required to hold additional risk-based required assets for delinquent mortgages. However, this amount is reduced for mortgages backed by a property located in a FEMA Declared Major Disaster Area that are either 1) subject to a forbearance plan executed in response to a FEMA Declared Major Disaster Area eligible for Individual Assistance, or 2) has an initial default date occurring up to either (i) 30 days prior to or (ii) 90 days following the Major Disaster event. FEMA has issued Major Disaster Area declarations in all states related to COVID-19, noting the incident date as January 20, 2020. On June 30, 2020 as amended and restated thereafter on September 29, 2020, the GSEs published guidance clarifying the applicability of the reduced delinquent loan charges on loans with their first missed payments occurring between March 1, 2020 and December 31, 2020 in response to a hardship related to COVID-19. Additionally, through March
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31, 2021, the GSEs have temporarily required eligible insurers to obtain prior approval of dividends or entering into any new arrangements or altering any existing arrangements under tax sharing and intercompany expense-sharing agreements. The Company is reliant on the accurate reporting of servicers to correctly identify which NODs are subject to COVID-19 related forbearance plans and the reduced delinquent loan charge. In addition, the rating agencies continually review the financial strength ratings assigned to the Company and its subsidiaries, and the ratings are subject to change. The COVID-19 pandemic and its impact on financial results and condition, could cause one or more of the rating agencies to downgrade the ratings assigned to the Company and its subsidiaries.
The disruption and other effects caused by COVID-19 could adversely impact our business operations, which could adversely affect our financial performance and results.
To protect our employees and in response to the global and regional restrictions on interpersonal contact and travel because of the COVID-19 pandemic, our work force (other than a small percentage of workers performing services which require them to visit the office) is working remotely, placing increased demands on our IT systems. Remote working arrangements may increase the risk of cyber-security attacks or data security incidents. While we have continued to conduct our business effectively, there is no assurance that our ability to continue to function in this new environment will not be adversely affected by an extended period of limited access to our physical facilities or by other developments such as an extended disruption to our systems that support our remote work capability. We depend on third-party platforms and other infrastructure to provide certain of our products and services, and such third-party infrastructures face similar risks. In addition, the continuation of the COVID-19 pandemic may continue to adversely affect our business operations, including decreased worker productivity, our ability to carry on business development activities and unavailability of employees due to illness or quarantines, among others. For a further discussion, see “Our information technology systems may be unable to meet the demands of customers” and “Technology breaches or failures, including, but not limited to, those resulting from a malicious cyber-attack on us or our business partners and service providers, could disrupt or otherwise negatively impact our business and/or expose us to litigation” included in “Part I—Item 1A—Risk Factors” in our 2019 Form 10-K.
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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 20192020 third 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)
7/1/2019 - 7/31/2019 27,535
 $38.56
 
 $160,867
8/1/2019 - 8/31/2019 18,304
 39.17
 
 $160,867
9/1/2019 - 9/30/2019 22,686
 41.13
 
 $160,867
Total 68,525
 $39.57
 
  
(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 September 30, 2019 under Arch Capital’s share repurchase authorization, under which repurchases may be effected from time to time in open market or privately negotiated transactions. On November 8, 2019, the board of directors of ACGL increased the aggregate purchase amount authorized under the share repurchase program to $1.0 billion. Repurchases under this authorization may be effected from time to time in open market or privately negotiated transactions through December 31, 2021.

Issuer Purchases of Equity Securities
PeriodTotal Number of Shares
Purchased (1)
Average Price Paid per ShareTotal 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)
7/1/2020 - 7/31/2020472 $30.34 — $924,514 
8/1/2020 - 8/31/20201,964 32.26 — $924,514 
9/1/2020 -9/30/202017,296 30.29 — $924,514 
Total19,732 $30.49 — 

(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 September 30, 2020 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.
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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 20192020 third 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.
Disclosure of Certain Activities Under Section 13(r) of the Securities Exchange Act of 1934

Section 13(r) of the Securities Exchange Act of 1934, as amended, requires an issuer to disclose in its annual or quarterly reports whether it or an affiliate knowingly engaged in certain activities described in that section, including certain activities related to Iran during the period covered by the report.
Certain of our non-U.S. subsidiaries underwrite insurance and facultative reinsurance on a global basis to non-U.S. insureds and insurers, including for liability, marine, aviation and energy risks. Coverage provided to non-Iranian business may indirectly cover an exposure in Iran. For example, certain of our operations underwrite global marine hull and cargo policies that provide coverage for vessels navigating into and out of ports worldwide, including Iran. For the quarter ended September 30, 2019, there has been no material amount of premium allocated or apportioned to activities relating to Iran, and we are unable to attribute gross revenues or net profits from any such policies because they insure multiple voyages and fleets containing multiple ships. Such non-U.S. subsidiaries will continue to provide such coverage only to the extent permitted by applicable law.

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ITEM 6. EXHIBITS
ARCH CAPITAL 75Incorporated by Reference
Exhibit NumberExhibit DescriptionFormOriginal NumberDate FiledFiled Herewith
15X
31.1X
31.2X
32.1X
32.2X
101.INSXBRL Instance Document
101.SCHXBRL Taxonomy Extension Schema Document
101.CALXBRL Taxonomy Extension Calculation Linkbase Document
101.DEFXBRL Taxonomy Extension Definition Linkbase Document
101.LABXBRL Taxonomy Extension Label Linkbase Document
101.PREXBRL Taxonomy Extension Presentation Linkbase Document


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ITEM 6. EXHIBITS
Incorporated by Reference
Exhibit NumberExhibit DescriptionFormOriginal NumberDate FiledFiled Herewith
2.18-K2.1October 14, 2020
2.28-K2.1November 2, 2020
10.18-K10.1October 14, 2020
15X
31.1X
31.2X
32.1X
32.2X
101.INSXBRL Instance Document
101.SCHXBRL Taxonomy Extension Schema Document
101.CALXBRL Taxonomy Extension Calculation Linkbase Document
101.DEFXBRL Taxonomy Extension Definition Linkbase Document
101.LABXBRL Taxonomy Extension Label Linkbase Document
101.PREXBRL Taxonomy Extension Presentation Linkbase Document
ARCH CAPITAL 777620192020 THIRD QUARTER FORM 10-Q


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: November 8, 20195, 2020Marc Grandisson
President and Chief Executive Officer (Principal Executive Officer)
/s/ François Morin
Date: November 8, 20195, 2020François Morin
Executive Vice President, Chief Financial Officer and Treasurer (Principal Financial and Accounting Officer)

ARCH CAPITAL 787720192020 THIRD QUARTER FORM 10-Q