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Segment Information
 9 Months Ended
Sep. 30, 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 and the Chief Financial Officer and Treasurer are the Company’s chief operating decision makers. The Company’s 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 reportable segments based on underwriting income or loss. The Company does not manage its assets by segment, with the exception of goodwill and intangible assets, and accordingly, investment income is not allocated to each segment.
The Company determined its 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 segment primarily consists of commercial insurance lines of business, with a focus on specialty insurance products. These products are mainly offered in North America, Bermuda, the United Kingdom, continental Europe and Australia. Products offered in North America include: commercial automobile; commercial multi‐peril; other liability—claims made, which includes financial and professional lines; other liability—occurrence, which includes admitted and excess and surplus casualty lines; property and short-tail specialty; workers compensation; and other. Products offered across the Company’s International units include: property and short-tail specialty; and casualty and other.
The Company’s reinsurance segment offers reinsurance products on a worldwide basis. Product lines of business include: casualty; marine and aviation; other specialty; property catastrophe; property excluding property catastrophe; and other.
The Company’s mortgage segment consists of U.S. primary mortgage insurance business written predominantly on loans sold to the Federal National Mortgage Association (“Fannie Mae”) and the Federal Home Loan Mortgage Corporation (“Freddie Mac”), each a government sponsored entity ("GSE") and also through non GSE approved entities (combined “Arch MI U.S.”); reinsurance and underwriting services related to U.S. credit-risk transfer (“CRT”) business which are predominately with the GSEs and other U.S. mortgage reinsurance transactions; and international mortgage insurance and reinsurance business covering loans primarily in Australia and Europe.
The Company’s results also 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 or losses on derivative instruments, changes in the allowance for credit losses on financial assets and gains or losses realized from the acquisition or disposition of subsidiaries), 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
September 30, 2024
 InsuranceReinsuranceMortgageTotal
Gross premiums written (1)$2,341 $2,763 $339 $5,440 
Premiums ceded (1)(521)(818)(57)(1,393)
Net premiums written1,820 1,945 282 4,047 
Change in unearned premiums(55)(53)31 (77)
Net premiums earned1,765 1,892 313 3,970 
Other underwriting income (loss)— 2 3 5 
Losses and loss adjustment expenses(1,087)(1,317)1 (2,403)
Acquisition expenses(308)(374)1 (681)
Other operating expenses(250)(54)(49)(353)
Underwriting income (loss)$120 $149 $269 538 
Net investment income399 
Net realized gains (losses)169 
Equity in net income (loss) of investment funds accounted for using the equity method171 
Other income (loss)8 
Corporate expenses (2)(19)
Transaction costs and other (2)(30)
Amortization of intangible assets(88)
Interest expense(35)
Net foreign exchange gains (losses)(63)
Income (loss) before income taxes and income (loss) from operating affiliates1,050 
Income tax (expense) benefit(98)
Income (loss) from operating affiliates36 
Net income (loss) available to Arch988 
Preferred dividends(10)
Net income (loss) available to Arch common shareholders$978 
Underwriting Ratios
Loss ratio61.6 %69.6 %(0.4)%60.5 %
Acquisition expense ratio17.4 %19.8 %(0.4)%17.2 %
Other operating expense ratio14.1 %2.9 %15.6 %8.9 %
Combined ratio93.1 %92.3 %14.8 %86.6 %
Goodwill and intangible assets$1,025 $113 $348 $1,486 
(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
September 30, 2023
 InsuranceReinsuranceMortgageTotal
Gross premiums written (1)$2,043 $2,138 $347 $4,527 
Premiums ceded (1)(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) 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 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.’
Nine Months Ended
September 30, 2024
 InsuranceReinsuranceMortgageTotal
Gross premiums written (1)$6,569 $9,171 $1,020 $16,755 
Premiums ceded (1)(1,649)(3,013)(185)(4,842)
Net premiums written4,920 6,158 835 11,913 
Change in unearned premiums(226)(820)90 (956)
Net premiums earned4,694 5,338 925 10,957 
Other underwriting income (loss)— 5 15 20 
Losses and loss adjustment expenses(2,789)(3,206)37 (5,958)
Acquisition expenses(872)(1,050)1 (1,921)
Other operating expenses(718)(193)(151)(1,062)
Underwriting income (loss)$315 $894 $827 2,036 
Net investment income1,090 
Net realized gains (losses)358 
Equity in net income (loss) of investment funds accounted for using the equity method437 
Other income (loss)30 
Corporate expenses (2)(88)
Transaction costs and other (2)(55)
Amortization of intangible assets(136)
Interest expense(104)
Net foreign exchange gains (losses)(31)
Income (loss) before income taxes and income (loss) from operating affiliates3,537 
Income tax (expense) benefit(296)
Income (loss) from operating affiliates136 
Net income (loss) available to Arch3,377 
Preferred dividends(30)
Net income (loss) available to Arch common shareholders$3,347 
Underwriting Ratios
Loss ratio59.4 %60.1 %(4.0)%54.4 %
Acquisition expense ratio18.6 %19.7 %(0.1)%17.5 %
Other operating expense ratio15.3 %3.6 %16.3 %9.7 %
Combined ratio93.3 %83.4 %12.2 %81.6 %
(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.’
Nine Months Ended
September 30, 2023
 InsuranceReinsuranceMortgageTotal
Gross premiums written (1)$5,977 $7,142 $1,037 $14,152 
Premiums ceded (1)(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) 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 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.’