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Segment Information
 3 Months Ended
Mar. 31, 2024
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 tax 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
March 31, 2024
 InsuranceReinsuranceMortgageTotal
Gross premiums written (1)$2,126 $3,467 $341 $5,933 
Premiums ceded (1)(584)(1,201)(64)(1,848)
Net premiums written1,542 2,266 277 4,085 
Change in unearned premiums(91)(600)28 (663)
Net premiums earned1,451 1,666 305 3,422 
Other underwriting income (loss)— 2 10 12 
Losses and loss adjustment expenses(854)(883)9 (1,728)
Acquisition expenses(276)(331)— (607)
Other operating expenses(235)(75)(53)(363)
Underwriting income (loss)$86 $379 $271 736 
Net investment income327 
Net realized gains (losses)67 
Equity in net income (loss) of investment funds accounted for using the equity method99 
Other income (loss)14 
Corporate expenses (2)(46)
Transaction costs and other (2)(7)
Amortization of intangible assets(21)
Interest expense(34)
Net foreign exchange gains (losses)31 
Income (loss) before income taxes and income (loss) from operating affiliates1,166 
Income tax (expense) benefit(101)
Income (loss) from operating affiliates55 
Net income (loss) available to Arch1,120 
Preferred dividends(10)
Net income (loss) available to Arch common shareholders$1,110 
Underwriting Ratios
Loss ratio58.9 %53.0 %(3.0)%50.5 %
Acquisition expense ratio19.0 %19.9 %— %17.7 %
Other operating expense ratio16.2 %4.5 %17.5 %10.6 %
Combined ratio94.1 %77.4 %14.5 %78.8 %
Goodwill and intangible assets$293 $121 $364 $778 
(1)    Certain assumed and ceded amounts related to intersegment transactions are included in individual segment results. Accordingly, the sum of such transactions for each segment does not agree to the total due to eliminations.
(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’
Three Months Ended
March 31, 2023
 InsuranceReinsuranceMortgageTotal
Gross premiums written (1)$1,979 $2,460 $343 $4,780 
Premiums ceded (1)(542)(734)(82)(1,356)
Net premiums written1,437 1,726 261 3,424 
Change in unearned premiums(180)(396)35 (541)
Net premiums earned1,257 1,330 296 2,883 
Other underwriting income (loss)— 4 6 10 
Losses and loss adjustment expenses(703)(766)(2)(1,471)
Acquisition expenses(245)(281)(7)(533)
Other operating expenses(195)(74)(50)(319)
Underwriting income (loss)$114 $213 $243 570 
Net investment income199 
Net realized gains (losses)17 
Equity in net income (loss) of investment funds accounted for using the equity method48 
Other income (loss)11 
Corporate expenses (2)(29)
Transaction costs and other (2)(1)
Amortization of intangible assets(23)
Interest expense(32)
Net foreign exchange gains (losses)(18)
Income (loss) before income taxes and income (loss) from operating affiliates742 
Income tax (expense) benefit(64)
Income (loss) from operating affiliates39 
Net income (loss)717 
Net (income) loss attributable to noncontrolling interests(2)
Net income (loss) available to Arch715 
Preferred dividends(10)
Net income (loss) available to Arch common shareholders$705 
Underwriting Ratios    
Loss ratio55.9 %57.6 %0.6 %51.0 %
Acquisition expense ratio19.5 %21.1 %2.5 %18.5 %
Other operating expense ratio15.5 %5.6 %16.9 %11.1 %
Combined ratio90.9 %84.3 %20.0 %80.6 %
Goodwill and intangible assets$228 $142 $415 $785 

(1)    Certain assumed and ceded amounts related to intersegment transactions are included in individual segment results. Accordingly, the sum of such transactions for each segment does not agree to the total due to eliminations.
(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’