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Segment Information
 6 Months Ended
Jun. 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 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.
The following tables summarize the Company’s underwriting income or loss by segment, together with a reconciliation of underwriting income or loss to net income available to Arch common shareholders:
Three Months Ended
June 30, 2023
 InsuranceReinsuranceMortgageTotal
Gross premiums written (1)$1,955 $2,544 $347 $4,845 
Premiums ceded(501)(835)(82)(1,417)
Net premiums written1,454 1,709 265 3,428 
Change in unearned premiums(126)(366)29 (463)
Net premiums earned1,328 1,343 294 2,965 
Other underwriting income (loss)— 3 3 6 
Losses and loss adjustment expenses(761)(743)13 (1,491)
Acquisition expenses(264)(290)(7)(561)
Other operating expenses(195)(68)(50)(313)
Underwriting income (loss)$108 $245 $253 606 
Net investment income242 
Net realized gains (losses)(123)
Equity in net income (loss) of investment funds accounted for using the equity method69 
Other income (loss)3 
Corporate expenses (2)(20)
Transaction costs and other (2)(1)
Amortization of intangible assets(24)
Interest expense(33)
Net foreign exchange gains (losses)(5)
Income (loss) before income taxes and income (loss) from operating affiliates714 
Income tax (expense) benefit(67)
Income (loss) from operating affiliates22 
Net income (loss)669 
Net (income) loss attributable to noncontrolling interests2 
Net income (loss) available to Arch671 
Preferred dividends(10)
Net income (loss) available to Arch common shareholders$661 
Underwriting Ratios
Loss ratio57.3 %55.3 %(4.5)%50.3 %
Acquisition expense ratio19.9 %21.6 %2.4 %18.9 %
Other operating expense ratio14.7 %5.0 %17.1 %10.6 %
Combined ratio91.9 %81.9 %15.0 %79.8 %
Goodwill and intangible assets$228 $146 $401 $775 
(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
June 30, 2022
 InsuranceReinsuranceMortgageTotal
Gross premiums written (1)$1,705 $1,793 $372 $3,870 
Premiums ceded(477)(630)(78)(1,185)
Net premiums written1,228 1,163 294 2,685 
Change in unearned premiums(126)(235)2 (359)
Net premiums earned1,102 928 296 2,326 
Other underwriting income (loss)— 5 (2)3 
Losses and loss adjustment expenses(630)(538)65 (1,103)
Acquisition expenses(214)(189)(10)(413)
Other operating expenses(161)(66)(50)(277)
Underwriting income (loss)$97 $140 $299 536 
Net investment income106 
Net realized gains (losses)(267)
Equity in net income (loss) of investment funds accounted for using the equity method58 
Other income (loss)(12)
Corporate expenses (2)(28)
Transaction costs and other (2)— 
Amortization of intangible assets(27)
Interest expense(33)
Net foreign exchange gains (losses)88 
Income (loss) before income taxes and income (loss) from operating affiliates421 
Income tax (expense) benefit(22)
Income (loss) from operating affiliates5 
Net income (loss)404 
Net (income) loss attributable to noncontrolling interests— 
Net income (loss) available to Arch404 
Preferred dividends(10)
Net income (loss) available to Arch common shareholders$394 
Underwriting Ratios    
Loss ratio57.1 %57.9 %(21.9)%47.4 %
Acquisition expense ratio19.4 %20.4 %3.4 %17.8 %
Other operating expense ratio14.6 %7.1 %17.0 %11.9 %
Combined ratio91.1 %85.4 %(1.5)%77.1 %
Goodwill and intangible assets$237 $166 $465 $868 

(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.’
Six Months Ended
June 30, 2023
 InsuranceReinsuranceMortgageTotal
Gross premiums written (1)$3,934 $5,004 $690 $9,625 
Premiums ceded(1,043)(1,569)(164)(2,773)
Net premiums written2,891 3,435 526 6,852 
Change in unearned premiums(306)(762)64 (1,004)
Net premiums earned2,585 2,673 590 5,848 
Other underwriting income (loss)— 7 9 16 
Losses and loss adjustment expenses(1,464)(1,509)11 (2,962)
Acquisition expenses(509)(571)(14)(1,094)
Other operating expenses(390)(142)(100)(632)
Underwriting income (loss)$222 $458 $496 $1,176 
Net investment income441 
Net realized gains (losses)(106)
Equity in net income (loss) of investment funds accounted for using the equity method117 
Other income (loss)14 
Corporate expenses (2)(49)
Transaction costs and other (2)(2)
Amortization of intangible assets(47)
Interest expense(65)
Net foreign exchange gains (losses)(23)
Income (loss) before income taxes and income (loss) from operating affiliates1,456 
Income tax (expense) benefit(131)
Income (loss) from operating affiliates61 
Net income (loss)1,386 
Net (income) loss attributable to noncontrolling interests— 
Net income (loss) available to Arch1,386 
Preferred dividends(20)
Net income (loss) available to Arch common shareholders$1,366 
Underwriting Ratios
Loss ratio56.6 %56.5 %(1.9)%50.6 %
Acquisition expense ratio19.7 %21.3 %2.4 %18.7 %
Other operating expense ratio15.1 %5.3 %17.0 %10.8 %
Combined ratio91.4 %83.1 %17.5 %80.1 %
(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.’
Six Months Ended
June 30, 2022
 InsuranceReinsuranceMortgageTotal
Gross premiums written (1)$3,425 $3,512 $737 $7,671 
Premiums ceded(990)(1,210)(155)(2,352)
Net premiums written2,435 2,302 582 5,319 
Change in unearned premiums(306)(570)4 (872)
Net premiums earned2,129 1,732 586 4,447 
Other underwriting income (loss)— 6 3 9 
Losses and loss adjustment expenses(1,231)(992)119 (2,104)
Acquisition expenses(410)(361)(20)(791)
Other operating expenses(328)(136)(103)(567)
Underwriting income (loss)$160 $249 $585 $994 
Net investment income186 
Net realized gains (losses)(559)
Equity in net income (loss) of investment funds accounted for using the equity method94 
Other income (loss)(21)
Corporate expenses (2)(60)
Transaction costs and other (2)— 
Amortization of intangible assets(54)
Interest expense(66)
Net foreign exchange gains (losses)92 
Income (loss) before income taxes and income (loss) from operating affiliates606 
Income tax (expense) benefit(34)
Income (loss) from operating affiliates30 
Net income (loss)602 
Net (income) loss attributable to noncontrolling interests(2)
Net income (loss) available to Arch600 
Preferred dividends(20)
Net income (loss) available to Arch common shareholders$580 
Underwriting Ratios
Loss ratio57.8 %57.3 %(20.4)%47.3 %
Acquisition expense ratio19.2 %20.9 %3.5 %17.8 %
Other operating expense ratio15.4 %7.8 %17.7 %12.8 %
Combined ratio92.4 %86.0 %0.8 %77.9 %
(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.’