Segment Information (Tables)

6 Months Ended

Jun. 30, 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
	June 30, 2022
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	1,705,167		$	1,793,398		$	371,896		$	3,869,727		$	—		$	3,869,727
Premiums ceded	(476,910)			(630,764)			(78,148)			(1,185,088)			—			(1,185,088)
Net premiums written	1,228,257			1,162,634			293,748			2,684,639			—			2,684,639
Change in unearned premiums	(126,113)			(234,635)			1,884			(358,864)			—			(358,864)
Net premiums earned	1,102,144			927,999			295,632			2,325,775			—			2,325,775
Other underwriting income (loss)	—			4,526			(1,556)			2,970			—			2,970
Losses and loss adjustment expenses	(629,759)			(537,578)			64,681			(1,102,656)			—			(1,102,656)
Acquisition expenses	(213,688)			(189,494)			(10,137)			(413,319)			—			(413,319)
Other operating expenses	(161,088)			(66,053)			(50,251)			(277,392)			—			(277,392)
Underwriting income (loss)	$	97,609		$	139,400		$	298,369		535,378			—			535,378
Net investment income										106,392			—			106,392
Net realized gains (losses)										(266,579)			—			(266,579)
Equity in net income (loss) of investment funds accounted for using the equity method										58,061			—			58,061
Other income (loss)										(11,777)			—			(11,777)
Corporate expenses (2)										(27,359)			—			(27,359)
Transaction costs and other (2)										(261)			—			(261)
Amortization of intangible assets										(27,207)			—			(27,207)
Interest expense										(32,795)			—			(32,795)
Net foreign exchange gains (losses)										87,775			—			87,775
Income (loss) before income taxes and income (loss) from operating affiliates										421,628			—			421,628
Income tax (expense) benefit										(22,323)			—			(22,323)
Income (loss) from operating affiliates										4,640			—			4,640
Net income (loss)										403,945			—			403,945
Amounts attributable to redeemable noncontrolling interests										399			—			399
Net income (loss) available to Arch										404,344			—			404,344
Preferred dividends										(10,184)			—			(10,184)
Net income (loss) available to Arch common shareholders										$	394,160		$	—		$	394,160
Underwriting Ratios
Loss ratio	57.1		%	57.9		%	(21.9)		%	47.4		%	—		%	47.4		%
Acquisition expense ratio	19.4		%	20.4		%	3.4		%	17.8		%	—		%	17.8		%
Other operating expense ratio	14.6		%	7.1		%	17.0		%	11.9		%	—		%	11.9		%
Combined ratio	91.1		%	85.4		%	(1.5)		%	77.1		%	—		%	77.1		%
Goodwill and intangible assets	$	236,661		$	166,437		$	464,916		$	868,014		$	—		$	868,014

(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, 2021
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	1,368,867		$	1,358,020		$	391,511		$	3,117,505		$	240,942		$	3,286,291
Premiums ceded	(405,312)			(433,288)			(55,665)			(893,372)			(65,551)			(886,767)
Net premiums written	963,555			924,732			335,846			2,224,133			175,391			2,399,524
Change in unearned premiums	(98,128)			(187,708)			(1,625)			(287,461)			8,846			(278,615)
Net premiums earned	865,427			737,024			334,221			1,936,672			184,237			2,120,909
Other underwriting income (loss)	—			1,053			4,148			5,201			328			5,529
Losses and loss adjustment expenses	(545,880)			(463,823)			(9,880)			(1,019,583)			(140,248)			(1,159,831)
Acquisition expenses	(136,852)			(133,585)			(30,117)			(300,554)			(34,589)			(335,143)
Other operating expenses	(133,342)			(44,695)			(48,312)			(226,349)			(18,594)			(244,943)
Underwriting income (loss)	$	49,353		$	95,974		$	250,060		395,387			(8,866)			386,521
Net investment income										89,430			22,183			111,613
Net realized gains (losses)										163,394			39,513			202,907
Equity in net income (loss) of investment funds accounted for using the equity method										122,186			—			122,186
Other income (loss)										6,852			—			6,852
Corporate expenses (2)										(17,175)			—			(17,175)
Transaction costs and other (2)										1,444			(220)			1,224
Amortization of intangible assets										(14,388)			(898)			(15,286)
Interest expense										(31,439)			(4,261)			(35,700)
Net foreign exchange gains (losses)										(17,892)			117			(17,775)
Income (loss) before income taxes and income (loss) from operating affiliates										697,799			47,568			745,367
Income tax (expense) benefit										(50,953)			(226)			(51,179)
Income (loss) from operating affiliates										24,476			—			24,476
Net income (loss)										671,322			47,342			718,664
Amounts attributable to redeemable noncontrolling interests										(580)			(981)			(1,561)
Amounts attributable to nonredeemable noncontrolling interests										—			(41,617)			(41,617)
Net income (loss) available to Arch										670,742			4,744			675,486
Preferred dividends										(11,666)			—			(11,666)
Net income (loss) available to Arch common shareholders										$	659,076		$	4,744		$	663,820
Underwriting Ratios
Loss ratio	63.1		%	62.9		%	3.0		%	52.6		%	76.1		%	54.7		%
Acquisition expense ratio	15.8		%	18.1		%	9.0		%	15.5		%	18.8		%	15.8		%
Other operating expense ratio	15.4		%	6.1		%	14.5		%	11.7		%	10.1		%	11.5		%
Combined ratio	94.3		%	87.1		%	26.5		%	79.8		%	105.0		%	82.0		%
Goodwill and intangible assets	$	270,262		$	16,168		$	370,405		$	656,835		$	10,318		$	667,153

(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
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	3,424,772		$	3,512,340		$	736,735		$	7,670,502		$	—		$	7,670,502
Premiums ceded	(989,619)			(1,210,582)			(154,867)			(2,351,723)			—			(2,351,723)
Net premiums written	2,435,153			2,301,758			581,868			5,318,779			—			5,318,779
Change in unearned premiums	(306,313)			(569,359)			3,301			(872,371)			—			(872,371)
Net premiums earned	2,128,840			1,732,399			585,169			4,446,408			—			4,446,408
Other underwriting income (loss)	—			5,362			3,505			8,867			—			8,867
Losses and loss adjustment expenses	(1,230,498)			(992,278)			119,285			(2,103,491)			—			(2,103,491)
Acquisition expenses	(409,338)			(361,490)			(20,650)			(791,478)			—			(791,478)
Other operating expenses	(327,913)			(135,829)			(103,593)			(567,335)			—			(567,335)
Underwriting income (loss)	$	161,091		$	248,164		$	583,716		$	992,971		$	—		$	992,971
Net investment income										186,828			—			186,828
Net realized gains (losses)										(558,993)			—			(558,993)
Equity in net income (loss) of investment funds accounted for using the equity method										94,366			—			94,366
Other income (loss)										(20,802)			—			(20,802)
Corporate expenses (2)										(59,294)			—			(59,294)
Transaction costs and other (2)										(658)			—			(658)
Amortization of intangible assets										(54,374)			—			(54,374)
Interest expense										(65,503)			—			(65,503)
Net foreign exchange gains (losses)										91,620			—			91,620
Income (loss) before income taxes and income (loss) from operating affiliates										606,161			—			606,161
Income tax (expense) benefit										(33,942)			—			(33,942)
Income (loss) from operating affiliates										29,158			—			29,158
Net income (loss)										601,377			—			601,377
Amounts attributable to redeemable noncontrolling interests										(1,233)			—			(1,233)
Net income (loss) available to Arch										600,144			—			600,144
Preferred dividends										(20,368)			—			(20,368)
Net income (loss) available to Arch common shareholders										$	579,776		$	—		$	579,776
Underwriting Ratios
Loss ratio	57.8		%	57.3		%	(20.4)		%	47.3		%	—		%	47.3		%
Acquisition expense ratio	19.2		%	20.9		%	3.5		%	17.8		%	—		%	17.8		%
Other operating expense ratio	15.4		%	7.8		%	17.7		%	12.8		%	—		%	12.8		%
Combined ratio	92.4		%	86.0		%	0.8		%	77.9		%	—		%	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.’

	Six Months Ended
	June 30, 2021
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	2,784,753		$	2,829,080		$	782,757		$	6,394,798		$	457,465		$	6,683,497
Premiums ceded	(826,359)			(905,236)			(111,716)			(1,841,519)			(102,763)			(1,775,516)
Net premiums written	1,958,394			1,923,844			671,041			4,553,279			354,702			4,907,981
Change in unearned premiums	(273,493)			(541,920)			(503)			(815,916)			(22,734)			(838,650)
Net premiums earned	1,684,901			1,381,924			670,538			3,737,363			331,968			4,069,331
Other underwriting income (loss)	—			(145)			11,045			10,900			739			11,639
Losses and loss adjustment expenses	(1,081,627)			(948,693)			(73,569)			(2,103,889)			(259,042)			(2,362,931)
Acquisition expenses	(265,074)			(251,610)			(60,199)			(576,883)			(62,741)			(639,624)
Other operating expenses	(270,455)			(105,209)			(97,443)			(473,107)			(32,869)			(505,976)
Underwriting income (loss)	$	67,745		$	76,267		$	450,372		$	594,384		$	(21,945)		$	572,439
Net investment income										168,159			42,310			210,469
Net realized gains (losses)										264,730			80,638			345,368
Equity in net income (loss) of investment funds accounted for using the equity method										193,872			—			193,872
Other income (loss)										5,111			—			5,111
Corporate expenses (2)										(40,643)			—			(40,643)
Transaction costs and other (2)										243			(935)			(692)
Amortization of intangible assets										(28,790)			(898)			(29,688)
Interest expense										(65,636)			(8,410)			(74,046)
Net foreign exchange gains (losses)										3,613			(1,325)			2,288
Income (loss) before income taxes and income (loss) from operating affiliates										1,095,043			89,435			1,184,478
Income tax (expense) benefit										(89,805)			(234)			(90,039)
Income (loss) from operating affiliates										99,933			—			99,933
Net income (loss)										1,105,171			89,201			1,194,372
Amounts attributable to redeemable noncontrolling interests										(463)			(1,953)			(2,416)
Amounts attributable to nonredeemable noncontrolling interests										—			(78,314)			(78,314)
Net income (loss) available to Arch										1,104,708			8,934			1,113,642
Preferred dividends										(22,069)			—			(22,069)
Net income (loss) available to Arch common shareholders										$	1,082,639		$	8,934		$	1,091,573
Underwriting Ratios
Loss ratio	64.2		%	68.7		%	11.0		%	56.3		%	78.0		%	58.1		%
Acquisition expense ratio	15.7		%	18.2		%	9.0		%	15.4		%	18.9		%	15.7		%
Other operating expense ratio	16.1		%	7.6		%	14.5		%	12.7		%	9.9		%	12.4		%
Combined ratio	96.0		%	94.5		%	34.5		%	84.4		%	106.8		%	86.2		%

(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.’