Segment Information (Tables)

12 Months Ended

Dec. 31, 2022

Segment Reporting [Abstract]

Analysis of underwriting income (loss) by segment and reconciliation to net income (loss) 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, summary information regarding net premiums written and earned by major line of business and net premiums written by location:

	Year Ended December 31, 2022
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	6,930,864		$	6,948,438		$	1,454,971		$	15,326,447		$	—		$	15,326,447
Premiums ceded	(1,910,222)			(2,024,462)			(322,400)			(4,249,258)			—			(4,249,258)
Net premiums written	5,020,642			4,923,976			1,132,571			11,077,189			—			11,077,189
Change in unearned premiums	(461,307)			(964,595)			26,790			(1,399,112)			—			(1,399,112)
Net premiums earned	4,559,335			3,959,381			1,159,361			9,678,077			—			9,678,077
Other underwriting income	—			4,871			8,356			13,227			—			13,227
Losses and loss adjustment expenses	(2,782,945)			(2,568,843)			324,271			(5,027,517)			—			(5,027,517)
Acquisition expenses	(885,866)			(813,555)			(40,159)			(1,739,580)			—			(1,739,580)
Other operating expenses	(665,472)			(267,531)			(195,172)			(1,128,175)			—			(1,128,175)
Underwriting income	$	225,052		$	314,323		$	1,256,657		1,796,032			—			1,796,032
Net investment income										496,547			—			496,547
Net realized gains (losses)										(662,734)			—			(662,734)
Equity in net income (loss) of investments accounted for using the equity method										115,856			—			115,856
Other income (loss)										(26,165)			—			(26,165)
Corporate expenses										(94,390)			—			(94,390)
Transaction costs and other										(1,092)			—			(1,092)
Amortization of intangible assets										(106,200)			—			(106,200)
Interest expense										(130,266)			—			(130,266)
Net foreign exchange gains (losses)										100,905			—			100,905
Income (loss) before income taxes and income (loss) from operating affiliates										1,488,493			—			1,488,493
Income tax expense										(79,961)			—			(79,961)
Income (loss) from operating affiliates										73,891			—			73,891
Net income (loss)										1,482,423			—			1,482,423
Amounts attributable to redeemable noncontrolling interests										(5,490)			—			(5,490)
Net income (loss) available to Arch										1,476,933			—			1,476,933
Preferred dividends										(40,736)			—			(40,736)
Net income (loss) available to Arch common shareholders										$	1,436,197		$	—		$	1,436,197
Underwriting Ratios
Loss ratio	61.0		%	64.9		%	-28.0		%	51.9		%	—		%	51.9		%
Acquisition expense ratio	19.4		%	20.5		%	3.5		%	18.0		%	—		%	18.0		%
Other operating expense ratio	14.6		%	6.8		%	16.8		%	11.7		%	—		%	11.7		%
Combined ratio	95.0		%	92.2		%	-7.7		%	81.6		%	—		%	81.6		%
Goodwill and intangible assets	$	228,532		$	144,846		$	430,911		$	804,289		$	—		$	804,289
Total investable assets										$	28,065,497		$	—		$	28,065,497
Total assets										47,990,507			—			47,990,507
Total liabilities										35,069,605			—			35,069,605

(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.

	Year Ended December 31, 2021
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	5,867,734		$	5,093,930		$	1,507,825		$	12,463,788		$	457,465		$	12,752,487
Premiums ceded	(1,719,541)			(1,839,556)			(246,757)			(3,800,153)			(102,763)			(3,734,150)
Net premiums written	4,148,193			3,254,374			1,261,068			8,663,635			354,702			9,018,337
Change in unearned premiums	(521,725)			(413,931)			22,351			(913,305)			(22,734)			(936,039)
Net premiums earned	3,626,468			2,840,443			1,283,419			7,750,330			331,968			8,082,298
Other underwriting income	—			3,669			17,665			21,334			739			22,073
Losses and loss adjustment expenses	(2,344,365)			(1,924,719)			(56,677)			(4,325,761)			(259,042)			(4,584,803)
Acquisition expenses, net	(606,265)			(536,754)			(97,418)			(1,240,437)			(62,741)			(1,303,178)
Other operating expenses	(558,906)			(212,810)			(194,010)			(965,726)			(32,869)			(998,595)
Underwriting income (loss)	$	116,932		$	169,829		$	952,979		1,239,740			(21,945)			1,217,795
Net investment income										346,808			42,310			389,118
Net realized gains (losses)										299,207			80,638			379,845
Equity in net income (loss) of investments accounted for using the equity method										366,402			—			366,402
Other income (loss)										10,244			—			10,244
Corporate expenses										(77,119)			—			(77,119)
Transaction costs and other										(1,103)			(935)			(2,038)
Amortization of intangible assets										(82,057)			(898)			(82,955)
Interest expense										(131,060)			(8,410)			(139,470)
Net foreign exchange gains (losses)										42,854			(1,325)			41,529
Income (loss) before income taxes and income (loss) from operating affiliates										2,013,916			89,435			2,103,351
Income tax expense										(128,348)			(234)			(128,582)
Income (loss) from operating affiliates										264,693			—			264,693
Net income (loss)										2,150,261			89,201			2,239,462
Amounts attributable to redeemable noncontrolling interests										(2,346)			(1,953)			(4,299)
Amounts attributable to nonredeemable noncontrolling interests										—			(78,314)			(78,314)
Net income (loss) available to Arch										2,147,915			8,934			2,156,849
Preferred dividends										(48,343)			—			(48,343)
Loss on redemption of preferred shares										(15,101)			—			(15,101)
Net income (loss) available to Arch common shareholders										$	2,084,471		$	8,934		$	2,093,405
Underwriting Ratios
Loss ratio	64.6		%	67.8		%	4.4		%	55.8		%	78.0		%	56.7		%
Acquisition expense ratio	16.7		%	18.9		%	7.6		%	16.0		%	18.9		%	16.1		%
Other operating expense ratio	15.4		%	7.5		%	15.1		%	12.5		%	9.9		%	12.4		%
Combined ratio	96.7		%	94.2		%	27.1		%	84.3		%	106.8		%	85.2		%
Goodwill and intangible assets	$	256,434		$	183,523		$	505,026		$	944,983		$	—		$	944,983
Total investable assets										$	27,442,153		$	—		$	27,442,153
Total assets										45,100,945			—			45,100,945
Total liabilities										31,545,816			—			31,545,816

(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.

	Year Ended December 31, 2020
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	4,688,562		$	3,472,086		$	1,473,999		$	9,632,691		$	728,546		$	10,088,068
Premiums ceded	(1,525,655)			(1,014,716)			(194,149)			(2,732,564)			(190,957)			(2,650,352)
Net premiums written	3,162,907			2,457,370			1,279,850			6,900,127			537,589			7,437,716
Change in unearned premiums	(291,487)			(295,141)			118,085			(468,543)			22,762			(445,781)
Net premiums earned	2,871,420			2,162,229			1,397,935			6,431,584			560,351			6,991,935
Other underwriting income	(31)			4,454			20,316			24,739			2,045			26,784
Losses and loss adjustment expenses	(2,092,453)			(1,628,320)			(528,344)			(4,249,117)			(440,482)			(4,689,599)
Acquisition expenses, net	(418,483)			(354,048)			(134,240)			(906,771)			(98,071)			(1,004,842)
Other operating expenses	(489,153)			(168,011)			(162,202)			(819,366)			(55,810)			(875,176)
Underwriting income (loss)	$	(128,700)		$	16,304		$	593,465		481,069			(31,967)			449,102
Net investment income										401,908			117,700			519,608
Net realized gains (losses)										813,781			9,679			823,460
Equity in net income (loss) of investments accounted for using the equity method										146,693			—			146,693
Other income (loss)										29			—			29
Corporate expenses										(68,492)			—			(68,492)
Transaction costs and other										(9,456)			(4,040)			(13,496)
Amortization of intangible assets										(69,031)			—			(69,031)
Interest expense										(120,214)			(23,242)			(143,456)
Net foreign exchange gains (losses)										(80,161)			(3,473)			(83,634)
Income (loss) before income taxes and income (loss) from operating affiliates										1,496,126			64,657			1,560,783
Income tax expense										(111,812)			(26)			(111,838)
Income (loss) from operating affiliates										16,766			—			16,766
Net income										1,401,080			64,631			1,465,711
Amounts attributable to redeemable noncontrolling interests										(2,997)			(4,117)			(7,114)
Amounts attributable to nonredeemable noncontrolling interests										—			(53,076)			(53,076)
Net income (loss) available to Arch										1,398,083			7,438			1,405,521
Preferred dividends										(41,612)			—			(41,612)
Net income (loss) available to Arch common shareholders										$	1,356,471		$	7,438		$	1,363,909
Underwriting Ratios
Loss ratio	72.9		%	75.3		%	37.8		%	66.1		%	78.6		%	67.1		%
Acquisition expense ratio	14.6		%	16.4		%	9.6		%	14.1		%	17.5		%	14.4		%
Other operating expense ratio	17.0		%	7.8		%	11.6		%	12.7		%	10.0		%	12.5		%
Combined ratio	104.5		%	99.5		%	59.0		%	92.9		%	106.1		%	94.0		%
Goodwill and intangible assets	$	280,978		$	18,963		$	385,272		$	685,213		$	7,650		$	692,863
Total investable assets										$	26,856,295		$	2,657,612		$	29,513,907
Total assets										39,791,983			3,490,314			43,282,297
Total liabilities										26,789,149			2,505,707			29,294,856

(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.

Summary of information regarding net premiums written and earned by major line of business and net premiums written by location

The following tables provide summary information regarding net premiums earned by major line of business and net premiums written by underwriting location:

INSURANCE SEGMENT	Year Ended December 31,
	2022		2021		2020
Net premiums earned (1)
Professional lines	$	1,314,236	$	942,817	$	655,872
Property, energy, marine and aviation	772,388		667,892		506,182
Programs	589,860		506,867		432,854
Travel, accident and health	491,847		255,590		190,944
Construction and national accounts	432,020		416,107		398,999
Excess and surplus casualty	393,353		318,027		270,620
Warranty and lenders solutions	127,222		153,958		114,687
Other	438,409		365,210		301,262
Total	$	4,559,335	$	3,626,468	$	2,871,420
Net premiums written by underwriting location (1)
United States	$	3,340,038	$	2,813,039	$	2,158,415
Europe	1,405,719		1,125,192		856,572
Other	274,885		209,962		147,920
Total	$	5,020,642	$	4,148,193	$	3,162,907

REINSURANCE SEGMENT	Year Ended December 31,
	2022		2021		2020
Net premiums earned (1)
Other specialty	$	1,377,880	$	818,801	$	626,409
Property excluding property catastrophe	1,091,440		836,573		562,208
Casualty	854,543		666,754		549,056
Property catastrophe	366,991		280,738		237,736
Marine and aviation	159,401		152,955		109,624
Other	109,126		84,622		77,196
Total	$	3,959,381	$	2,840,443	$	2,162,229
Net premiums written by underwriting location (1)
United States	$	1,246,507	$	828,504	$	687,622
Bermuda	2,561,771		1,557,294		1,001,990
Europe and other	1,115,698		868,576		767,758
Total	$	4,923,976	$	3,254,374	$	2,457,370

MORTGAGE SEGMENT	Year Ended December 31,
	2022		2021		2020
Net premiums earned by underwriting location
United States	$	815,519	$	970,507	$	1,158,563
Other	343,842		312,912		239,372
Total	$	1,159,361	$	1,283,419	$	1,397,935
Net premiums written by underwriting location
United States	$	780,256	$	914,477	$	1,021,950
Other	352,315		346,591		257,900
Total	$	1,132,571	$	1,261,068	$	1,279,850

(1)    Segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions.

OTHER SEGMENT	Year Ended December 31,
	2022		2021		2020
Net premiums earned (1)
Casualty	$	—	$	138,551	$	245,272
Other specialty	—		118,356		186,717
Property catastrophe	—		15,235		23,037
Property excluding property catastrophe	—		6,578		1,130
Marine and aviation	—		190		429
Other	—		53,058		103,766
Total	$	—	$	331,968	$	560,351
Net premiums written by underwriting location (1)
United States	$	—	$	63,403	$	115,471
Europe	—		91,499		97,753
Bermuda	—		199,800		324,365
Total	$	—	$	354,702	$	537,589

(1)    Segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions.