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Segment Information
 9 Months Ended
Sep. 30, 2023
Segment Reporting [Abstract]  
Segment Information
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, the Chief Financial Officer and Treasurer and the President and Chief Underwriting Officer are the Company’s chief operating decision makers. They 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 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 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; professional lines; programs; property, energy, marine and aviation; travel, accident and health; warranty and lenders solutions; 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 (“GSEs”) 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 realized and unrealized changes in the fair value of equity securities and assets accounted for using the fair value option, realized and unrealized gains and losses on derivative instruments and changes in the allowance for credit losses on financial assets), equity in net income or loss of investment funds 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 items, income or loss from operating affiliates and items related to the Company’s non cumulative preferred shares.

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, 2023
 InsuranceReinsuranceMortgageTotal
Gross premiums written (1)$2,043 $2,138 $347 $4,527 
Premiums ceded(521)(576)(76)(1,172)
Net premiums written1,522 1,562 271 3,355 
Change in unearned premiums(110)(19)22 (107)
Net premiums earned1,412 1,543 293 3,248 
Other underwriting income (loss)— 2 3 5 
Losses and loss adjustment expenses(812)(870)35 (1,647)
Acquisition expenses(269)(304)(2)(575)
Other operating expenses(202)(61)(47)(310)
Underwriting income (loss)$129 $310 $282 721 
Net investment income269 
Net realized gains (losses)(248)
Equity in net income (loss) of investment funds accounted for using the equity method59 
Other income (loss)(4)
Corporate expenses (2)(20)
Transaction costs and other (2)— 
Amortization of intangible assets(24)
Interest expense(34)
Net foreign exchange gains (losses)22 
Income (loss) before income taxes and income (loss) from operating affiliates741 
Income tax (expense) benefit(72)
Income (loss) from operating affiliates54 
Net income (loss)723 
Net (income) loss attributable to noncontrolling interests— 
Net income (loss) available to Arch723 
Preferred dividends(10)
Net income (loss) available to Arch common shareholders$713 
Underwriting Ratios
Loss ratio57.5 %56.4 %(12.1)%50.7 %
Acquisition expense ratio19.1 %19.7 %0.6 %17.7 %
Other operating expense ratio14.3 %3.9 %16.2 %9.5 %
Combined ratio90.9 %80.0 %4.7 %77.9 %
Goodwill and intangible assets$220 $132 $387 $739 
(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, 2022
 InsuranceReinsuranceMortgageTotal
Gross premiums written (1)$1,862 $1,639 $362 $3,861 
Premiums ceded(493)(560)(86)(1,137)
Net premiums written1,369 1,079 276 2,724 
Change in unearned premiums(182)(77)6 (253)
Net premiums earned1,187 1,002 282 2,471 
Other underwriting income (loss)— — 3 3 
Losses and loss adjustment expenses(823)(928)68 (1,683)
Acquisition expenses(233)(208)(7)(448)
Other operating expenses(165)(63)(47)(275)
Underwriting income (loss)$(34)$(197)$299 68 
Net investment income129 
Net realized gains (losses)(184)
Equity in net income (loss) of investment funds accounted for using the equity method(19)
Other income (loss)(14)
Corporate expenses (2)(18)
Transaction costs and other (2)— 
Amortization of intangible assets(26)
Interest expense(33)
Net foreign exchange gains (losses)91 
Income (loss) before income taxes and income (loss) from operating affiliates(6)
Income tax (expense) benefit15 
Income (loss) from operating affiliates9 
Net income (loss)18 
Net (income) loss attributable to noncontrolling interests(1)
Net income (loss) available to Arch17 
Preferred dividends(10)
Net income (loss) available to Arch common shareholders$7 
Underwriting Ratios    
Loss ratio69.3 %92.6 %(24.1)%68.1 %
Acquisition expense ratio19.6 %20.8 %2.4 %18.1 %
Other operating expense ratio13.9 %6.3 %16.5 %11.1 %
Combined ratio102.8 %119.7 %(5.2)%97.3 %
Goodwill and intangible assets$225 $141 $441 $807 

(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, 2023
 InsuranceReinsuranceMortgageTotal
Gross premiums written (1)$5,977 $7,142 $1,037 $14,152 
Premiums ceded(1,564)(2,145)(240)(3,945)
Net premiums written4,413 4,997 797 10,207 
Change in unearned premiums(416)(781)86 (1,111)
Net premiums earned3,997 4,216 883 9,096 
Other underwriting income (loss)— 9 12 21 
Losses and loss adjustment expenses(2,276)(2,379)46 (4,609)
Acquisition expenses(778)(875)(16)(1,669)
Other operating expenses(592)(203)(147)(942)
Underwriting income (loss)$351 $768 $778 1,897 
Net investment income710 
Net realized gains (losses)(354)
Equity in net income (loss) of investment funds accounted for using the equity method176 
Other income (loss)10 
Corporate expenses (2)(69)
Transaction costs and other (2)(2)
Amortization of intangible assets(71)
Interest expense(99)
Net foreign exchange gains (losses)(1)
Income (loss) before income taxes and income (loss) from operating affiliates2,197 
Income tax (expense) benefit(203)
Income (loss) from operating affiliates115 
Net income (loss)2,109 
Net (income) loss attributable to noncontrolling interests— 
Net income (loss) available to Arch2,109 
Preferred dividends(30)
Net income (loss) available to Arch common shareholders$2,079 
Underwriting Ratios
Loss ratio57.0 %56.4 %(5.3)%50.7 %
Acquisition expense ratio19.5 %20.7 %1.8 %18.3 %
Other operating expense ratio14.8 %4.8 %16.7 %10.4 %
Combined ratio91.3 %81.9 %13.2 %79.4 %
(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
 InsuranceReinsuranceMortgageTotal
Gross premiums written (1)$5,287 $5,151 $1,099 $11,532 
Premiums ceded(1,483)(1,770)(241)(3,489)
Net premiums written3,804 3,381 858 8,043 
Change in unearned premiums(488)(647)10 (1,125)
Net premiums earned3,316 2,734 868 6,918 
Other underwriting income (loss)— 6 6 12 
Losses and loss adjustment expenses(2,054)(1,920)187 (3,787)
Acquisition expenses(643)(569)(27)(1,239)
Other operating expenses(493)(199)(150)(842)
Underwriting income (loss)$126 $52 $884 1,062 
Net investment income315 
Net realized gains (losses)(743)
Equity in net income (loss) of investment funds accounted for using the equity method75 
Other income (loss)(35)
Corporate expenses (2)(78)
Transaction costs and other (2)— 
Amortization of intangible assets(80)
Interest expense(99)
Net foreign exchange gains (losses)183 
Income (loss) before income taxes and income (loss) from operating affiliates600 
Income tax (expense) benefit(19)
Income (loss) from operating affiliates39 
Net income (loss)620 
Net (income) loss attributable to noncontrolling interests(3)
Net income (loss) available to Arch617 
Preferred dividends(30)
Net income (loss) available to Arch common shareholders$587 
Underwriting Ratios
Loss ratio61.9 %70.2 %(21.6)%54.7 %
Acquisition expense ratio19.4 %20.8 %3.2 %17.9 %
Other operating expense ratio14.9 %7.3 %17.3 %12.2 %
Combined ratio96.2 %98.3 %(1.1)%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.’