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Segment Information
 9 Months Ended
Sep. 30, 2022
Segment Reporting [Abstract]  
Segment Information
The Company classifies its businesses into three underwriting segments — insurance, reinsurance and mortgage — and two other operating segments — corporate and ‘other.’ The Company determined its reportable segments using the management approach described in accounting guidance regarding disclosures about segments of an enterprise and related information. The accounting policies of the segments are the same as those used for the preparation of the Company’s consolidated financial statements. Intersegment business is allocated to the segment accountable for the underwriting results.
The Company’s insurance, reinsurance and mortgage segments each have managers who are responsible for the overall profitability of their respective segments and who are directly accountable to the Company’s chief operating decision makers, the Chief Executive Officer of Arch Capital, the Chief Financial Officer and Treasurer of Arch Capital and the President and Chief Underwriting Officer of Arch Capital. The chief operating decision makers do not assess performance, measure return on equity or make resource allocation decisions on a line of business basis. Management measures segment performance for its three underwriting segments based on underwriting income or loss. The Company does not manage its assets by underwriting segment, with the exception of goodwill and intangible assets, and accordingly, investment income is not allocated to each underwriting segment.
The insurance segment consists of the Company’s insurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include: construction and national accounts; excess and surplus casualty; lenders products; professional lines; programs; property, energy, marine and aviation; travel, accident and health; and other (consisting of alternative markets, excess workers' compensation and surety business).
The reinsurance segment consists of the Company’s reinsurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include: casualty; marine and aviation; other specialty; property catastrophe; property excluding property catastrophe (losses on a single risk, both excess of loss and pro rata); and other (consisting of life reinsurance, casualty clash and other).
The mortgage segment includes the Company’s U.S. primary mortgage insurance business, investment and services related to U.S. credit-risk transfer (“CRT”) which are predominately with government sponsored enterprises (“GSE’s”) and international mortgage insurance and reinsurance operations. Arch Mortgage Insurance Company and United Guaranty Residential Insurance Company (combined “Arch MI U.S.”) are approved as eligible mortgage insurers by Federal National Mortgage Association (“Fannie Mae”) and Federal Home Loan Mortgage Corporation (“Freddie Mac”), each a GSE. Arch MI U.S. also includes Arch Mortgage Guaranty Company, which is not a GSE-approved entity.
The corporate segment results include net investment income, net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings), equity in net income or loss of investments accounted for using the equity method, other income (loss), corporate expenses, transaction costs and other, amortization of intangible assets, interest expense, net foreign exchange gains or losses, income taxes, income or loss from operating affiliates and items related to the Company’s non-cumulative preferred shares. Such amounts exclude the results of the ‘other’ segment.
Through June 30, 2021, the ‘other’ segment included the results of Somers. In July 2021, the Company announced the completion of the previously disclosed acquisition of Somers by Greysbridge. Based on the governing documents of Greysbridge, the Company has concluded that, while it retains significant influence over Somers, Somers no longer constitutes a variable interest entity. Accordingly, effective July 1, 2021, Arch no longer consolidates the results of Somers in its consolidated financial statements. See note 11.
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, 2022
 InsuranceReinsuranceMortgageSub-TotalOtherTotal
Gross premiums written (1)$1,862,026 $1,639,061 $362,409 $3,860,683 $— $3,860,683 
Premiums ceded(493,267)(560,225)(86,230)(1,136,909)— (1,136,909)
Net premiums written1,368,759 1,078,836 276,179 2,723,774 — 2,723,774 
Change in unearned premiums(181,851)(77,062)5,889 (253,024)— (253,024)
Net premiums earned1,186,908 1,001,774 282,068 2,470,750 — 2,470,750 
Other underwriting income (loss)— 452 2,625 3,077 — 3,077 
Losses and loss adjustment expenses(822,663)(927,911)67,878 (1,682,696)— (1,682,696)
Acquisition expenses(232,469)(208,425)(6,693)(447,587)— (447,587)
Other operating expenses(165,499)(62,777)(46,471)(274,747)— (274,747)
Underwriting income (loss)$(33,723)$(196,887)$299,407 68,797 — 68,797 
Net investment income128,640 — 128,640 
Net realized gains (losses)(183,673)— (183,673)
Equity in net income (loss) of investment funds accounted for using the equity method(18,861)— (18,861)
Other income (loss)(13,684)— (13,684)
Corporate expenses (2)(17,634)— (17,634)
Transaction costs and other (2)(76)— (76)
Amortization of intangible assets(26,104)— (26,104)
Interest expense(33,063)— (33,063)
Net foreign exchange gains (losses)90,509 — 90,509 
Income (loss) before income taxes and income (loss) from operating affiliates(5,149)— (5,149)
Income tax (expense) benefit14,900 — 14,900 
Income (loss) from operating affiliates8,507 — 8,507 
Net income (loss)18,258 — 18,258 
Amounts attributable to redeemable noncontrolling interests(1,157)— (1,157)
Net income (loss) available to Arch17,101 — 17,101 
Preferred dividends(10,184)— (10,184)
Net income (loss) available to Arch common shareholders$6,917 $— $6,917 
Underwriting Ratios
Loss ratio69.3 %92.6 %(24.1)%68.1 %— %68.1 %
Acquisition expense ratio19.6 %20.8 %2.4 %18.1 %— %18.1 %
Other operating expense ratio13.9 %6.3 %16.5 %11.1 %— %11.1 %
Combined ratio102.8 %119.7 %(5.2)%97.3 %— %97.3 %
Goodwill and intangible assets$224,525 $140,800 $441,330 $806,655 $— $806,655 
(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.’
Three Months Ended
September 30, 2021
 InsuranceReinsuranceMortgageSub-TotalOtherTotal
Gross premiums written (1)$1,596,619 $1,251,760 $360,934 $3,207,415 $— $3,207,415 
Premiums ceded(442,806)(630,371)(60,207)(1,131,486)— (1,131,486)
Net premiums written1,153,813 621,389 300,727 2,075,929 — 2,075,929 
Change in unearned premiums(215,143)57,313 11,238 (146,592)— (146,592)
Net premiums earned938,670 678,702 311,965 1,929,337 — 1,929,337 
Other underwriting income (loss)— 3,293 3,981 7,274 — 7,274 
Losses and loss adjustment expenses(668,630)(545,846)(11,543)(1,226,019)— (1,226,019)
Acquisition expenses(152,467)(129,450)(24,098)(306,015)— (306,015)
Other operating expenses(138,931)(45,647)(46,254)(230,832)— (230,832)
Underwriting income (loss)$(21,358)$(38,948)$234,051 173,745 — 173,745 
Net investment income88,195 — 88,195 
Net realized gains (losses)(25,040)— (25,040)
Equity in net income (loss) of investment funds accounted for using the equity method105,398 — 105,398 
Other income (loss)(3,960)— (3,960)
Corporate expenses (2)(18,636)— (18,636)
Transaction costs and other (2)(1,036)— (1,036)
Amortization of intangible assets(20,135)— (20,135)
Interest expense(33,176)— (33,176)
Net foreign exchange gains (losses)36,078 — 36,078 
Income (loss) before income taxes and income (loss) from operating affiliates301,433 — 301,433 
Income tax (expense) benefit(4,137)— (4,137)
Income (loss) from operating affiliates124,119 — 124,119 
Net income (loss)421,415 — 421,415 
Amounts attributable to redeemable noncontrolling interests(1,473)— (1,473)
Net income (loss) available to Arch419,942 — 419,942 
Preferred dividends(16,090)— (16,090)
Loss on redemption of preferred shares(15,101)— (15,101)
Net income (loss) available to Arch common shareholders$388,751 $— $388,751 
Underwriting Ratios     
Loss ratio71.2 %80.4 %3.7 %63.5 %— %63.5 %
Acquisition expense ratio16.2 %19.1 %7.7 %15.9 %— %15.9 %
Other operating expense ratio14.8 %6.7 %14.8 %12.0 %— %12.0 %
Combined ratio102.2 %106.2 %26.2 %91.4 %— %91.4 %
Goodwill and intangible assets$261,103 $176,128 $526,091 $963,322 $— $963,322 

(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, 2022
 InsuranceReinsuranceMortgageSub-TotalOtherTotal
Gross premiums written (1)$5,286,798 $5,151,401 $1,099,144 $11,531,185 $— $11,531,185 
Premiums ceded(1,482,886)(1,770,807)(241,097)(3,488,632)— (3,488,632)
Net premiums written3,803,912 3,380,594 858,047 8,042,553 — 8,042,553 
Change in unearned premiums(488,164)(646,421)9,190 (1,125,395)— (1,125,395)
Net premiums earned3,315,748 2,734,173 867,237 6,917,158 — 6,917,158 
Other underwriting income (loss)— 5,814 6,130 11,944 — 11,944 
Losses and loss adjustment expenses(2,053,161)(1,920,189)187,163 (3,786,187)— (3,786,187)
Acquisition expenses(641,807)(569,915)(27,343)(1,239,065)— (1,239,065)
Other operating expenses(493,412)(198,606)(150,064)(842,082)— (842,082)
Underwriting income (loss)$127,368 $51,277 $883,123 $1,061,768 $— $1,061,768 
Net investment income315,468 — 315,468 
Net realized gains (losses)(742,666)— (742,666)
Equity in net income (loss) of investment funds accounted for using the equity method75,505 — 75,505 
Other income (loss)(34,486)— (34,486)
Corporate expenses (2)(76,928)— (76,928)
Transaction costs and other (2)(734)— (734)
Amortization of intangible assets(80,478)— (80,478)
Interest expense(98,566)— (98,566)
Net foreign exchange gains (losses)182,129 — 182,129 
Income (loss) before income taxes and income (loss) from operating affiliates601,012 — 601,012 
Income tax (expense) benefit(19,042)— (19,042)
Income (loss) from operating affiliates37,665 — 37,665 
Net income (loss)619,635 — 619,635 
Amounts attributable to redeemable noncontrolling interests(2,390)— (2,390)
Net income (loss) available to Arch617,245 — 617,245 
Preferred dividends(30,552)— (30,552)
Net income (loss) available to Arch common shareholders$586,693 $— $586,693 
Underwriting Ratios
Loss ratio61.9 %70.2 %(21.6)%54.7 %— %54.7 %
Acquisition expense ratio19.4 %20.8 %3.2 %17.9 %— %17.9 %
Other operating expense ratio14.9 %7.3 %17.3 %12.2 %— %12.2 %
Combined ratio96.2 %98.3 %(1.1)%84.8 %— %84.8 %
(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, 2021
 InsuranceReinsuranceMortgageSub-TotalOtherTotal
Gross premiums written (1)$4,381,372 $4,080,840 $1,143,691 $9,602,213 $457,465 $9,890,912 
Premiums ceded(1,269,165)(1,535,607)(171,923)(2,973,005)(102,763)(2,907,002)
Net premiums written3,112,207 2,545,233 971,768 6,629,208 354,702 6,983,910 
Change in unearned premiums(488,636)(484,607)10,735 (962,508)(22,734)(985,242)
Net premiums earned2,623,571 2,060,626 982,503 5,666,700 331,968 5,998,668 
Other underwriting income (loss)— 3,148 15,026 18,174 739 18,913 
Losses and loss adjustment expenses(1,750,257)(1,494,539)(85,112)(3,329,908)(259,042)(3,588,950)
Acquisition expenses(417,541)(381,060)(84,297)(882,898)(62,741)(945,639)
Other operating expenses(409,386)(150,856)(143,697)(703,939)(32,869)(736,808)
Underwriting income (loss)$46,387 $37,319 $684,423 $768,129 $(21,945)$746,184 
Net investment income256,354 42,310 298,664 
Net realized gains (losses)239,690 80,638 320,328 
Equity in net income (loss) of investment funds accounted for using the equity method299,270 — 299,270 
Other income (loss)1,151 — 1,151 
Corporate expenses (2)(59,279)— (59,279)
Transaction costs and other (2)(793)(935)(1,728)
Amortization of intangible assets(48,925)(898)(49,823)
Interest expense(98,812)(8,410)(107,222)
Net foreign exchange gains (losses)39,691 (1,325)38,366 
Income (loss) before income taxes and income (loss) from operating affiliates1,396,476 89,435 1,485,911 
Income tax (expense) benefit(93,942)(234)(94,176)
Income (loss) from operating affiliates224,052 — 224,052 
Net income (loss)1,526,586 89,201 1,615,787 
Amounts attributable to redeemable noncontrolling interests(1,936)(1,953)(3,889)
Amounts attributable to nonredeemable noncontrolling interests— (78,314)(78,314)
Net income (loss) available to Arch1,524,650 8,934 1,533,584 
Preferred dividends(38,159)— (38,159)
Loss on redemption of preferred shares(15,101)— (15,101)
Net income (loss) available to Arch common shareholders$1,471,390 $8,934 $1,480,324 
Underwriting Ratios
Loss ratio66.7 %72.5 %8.7 %58.8 %78.0 %59.8 %
Acquisition expense ratio15.9 %18.5 %8.6 %15.6 %18.9 %15.8 %
Other operating expense ratio15.6 %7.3 %14.6 %12.4 %9.9 %12.3 %
Combined ratio98.2 %98.3 %31.9 %86.8 %106.8 %87.9 %
(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.’