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Segment Information (Tables)
3 Months Ended
Mar. 31, 2022
Segment Reporting [Abstract]  
Analysis of underwriting income or loss by segment and reconciliation to net income available to common shareholders
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, 2022
 InsuranceReinsuranceMortgageSub-TotalOtherTotal
Gross premiums written (1)$1,719,605 $1,718,942 $364,839 $3,800,775 $— $3,800,775 
Premiums ceded(512,709)(579,818)(76,719)(1,166,635)— (1,166,635)
Net premiums written1,206,896 1,139,124 288,120 2,634,140 — 2,634,140 
Change in unearned premiums(180,200)(334,724)1,417 (513,507)— (513,507)
Net premiums earned1,026,696 804,400 289,537 2,120,633 — 2,120,633 
Other underwriting income (loss)— 836 5,061 5,897 — 5,897 
Losses and loss adjustment expenses(600,739)(454,700)54,604 (1,000,835)— (1,000,835)
Acquisition expenses(195,650)(171,996)(10,513)(378,159)— (378,159)
Other operating expenses(166,825)(69,776)(53,342)(289,943)— (289,943)
Underwriting income (loss)$63,482 $108,764 $285,347 457,593 — 457,593 
Net investment income80,436 — 80,436 
Net realized gains (losses)(292,414)— (292,414)
Equity in net income (loss) of investment funds accounted for using the equity method36,305 — 36,305 
Other income (loss)(9,025)— (9,025)
Corporate expenses (2)(31,935)— (31,935)
Transaction costs and other (2)(397)— (397)
Amortization of intangible assets(27,167)— (27,167)
Interest expense(32,708)— (32,708)
Net foreign exchange gains (losses)3,845 — 3,845 
Income (loss) before income taxes and income (loss) from operating affiliates184,533 — 184,533 
Income tax (expense) benefit(11,619)— (11,619)
Income (loss) from operating affiliates24,518 — 24,518 
Net income (loss)197,432 — 197,432 
Amounts attributable to redeemable noncontrolling interests(1,632)— (1,632)
Net income (loss) available to Arch195,800 — 195,800 
Preferred dividends(10,184)— (10,184)
Net income (loss) available to Arch common shareholders$185,616 $— $185,616 
Underwriting Ratios
Loss ratio58.5 %56.5 %(18.9)%47.2 %— %47.2 %
Acquisition expense ratio19.1 %21.4 %3.6 %17.8 %— %17.8 %
Other operating expense ratio16.2 %8.7 %18.4 %13.7 %— %13.7 %
Combined ratio93.8 %86.6 %3.1 %78.7 %— %78.7 %
Goodwill and intangible assets$249,423 $183,675 $493,329 $926,427 $— $926,427 
(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
March 31, 2021
 InsuranceReinsuranceMortgageSub-TotalOtherTotal
Gross premiums written (1)$1,415,886 $1,471,060 $391,246 $3,277,293 $216,523 $3,397,206 
Premiums ceded(421,047)(471,948)(56,051)(948,147)(37,212)(888,749)
Net premiums written994,839 999,112 335,195 2,329,146 179,311 2,508,457 
Change in unearned premiums(175,365)(354,212)1,122 (528,455)(31,580)(560,035)
Net premiums earned819,474 644,900 336,317 1,800,691 147,731 1,948,422 
Other underwriting income (loss)— (1,198)6,897 5,699 411 6,110 
Losses and loss adjustment expenses(535,747)(484,870)(63,689)(1,084,306)(118,794)(1,203,100)
Acquisition expenses(128,222)(118,025)(30,082)(276,329)(28,152)(304,481)
Other operating expenses(137,113)(60,514)(49,131)(246,758)(14,275)(261,033)
Underwriting income (loss)$18,392 $(19,707)$200,312 198,997 (13,079)185,918 
Net investment income78,729 20,127 98,856 
Net realized gains (losses)101,336 41,125 142,461 
Equity in net income (loss) of investment funds accounted for using the equity method71,686 — 71,686 
Other income (loss)(1,741)— (1,741)
Corporate expenses (2)(23,468)— (23,468)
Transaction costs and other (2)(1,201)(715)(1,916)
Amortization of intangible assets(14,402)— (14,402)
Interest expense(34,197)(4,149)(38,346)
Net foreign exchange gains (losses)21,505 (1,442)20,063 
Income (loss) before income taxes and income (loss) from operating affiliates397,244 41,867 439,111 
Income tax (expense) benefit(38,852)(8)(38,860)
Income (loss) from operating affiliates75,457 — 75,457 
Net income (loss)433,849 41,859 475,708 
Amounts attributable to redeemable noncontrolling interests117 (972)(855)
Amounts attributable to nonredeemable noncontrolling interests— (36,697)(36,697)
Net income (loss) available to Arch433,966 4,190 438,156 
Preferred dividends(10,403)— (10,403)
Net income (loss) available to Arch common shareholders$423,563 $4,190 $427,753 
Underwriting Ratios     
Loss ratio65.4 %75.2 %18.9 %60.2 %80.4 %61.7 %
Acquisition expense ratio15.6 %18.3 %8.9 %15.3 %19.1 %15.6 %
Other operating expense ratio16.7 %9.4 %14.6 %13.7 %9.7 %13.4 %
Combined ratio97.7 %102.9 %42.4 %89.2 %109.2 %90.7 %
Goodwill and intangible assets$276,211 $17,807 $377,841 $671,859 $7,650 $679,509 

(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.’