Segment Information (Tables)

9 Months Ended

Sep. 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
	September 30, 2022
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	1,862,026		$	1,639,061		$	362,409		$	3,860,683		$	—		$	3,860,683
Premiums ceded	(493,267)			(560,225)			(86,230)			(1,136,909)			—			(1,136,909)
Net premiums written	1,368,759			1,078,836			276,179			2,723,774			—			2,723,774
Change in unearned premiums	(181,851)			(77,062)			5,889			(253,024)			—			(253,024)
Net premiums earned	1,186,908			1,001,774			282,068			2,470,750			—			2,470,750
Other underwriting income (loss)	—			452			2,625			3,077			—			3,077
Losses and loss adjustment expenses	(822,663)			(927,911)			67,878			(1,682,696)			—			(1,682,696)
Acquisition expenses	(232,469)			(208,425)			(6,693)			(447,587)			—			(447,587)
Other operating expenses	(165,499)			(62,777)			(46,471)			(274,747)			—			(274,747)
Underwriting income (loss)	$	(33,723)		$	(196,887)		$	299,407		68,797			—			68,797
Net investment income										128,640			—			128,640
Net realized gains (losses)										(183,673)			—			(183,673)
Equity in net income (loss) of investment funds accounted for using the equity method										(18,861)			—			(18,861)
Other income (loss)										(13,684)			—			(13,684)
Corporate expenses (2)										(17,634)			—			(17,634)
Transaction costs and other (2)										(76)			—			(76)
Amortization of intangible assets										(26,104)			—			(26,104)
Interest expense										(33,063)			—			(33,063)
Net foreign exchange gains (losses)										90,509			—			90,509
Income (loss) before income taxes and income (loss) from operating affiliates										(5,149)			—			(5,149)
Income tax (expense) benefit										14,900			—			14,900
Income (loss) from operating affiliates										8,507			—			8,507
Net income (loss)										18,258			—			18,258
Amounts attributable to redeemable noncontrolling interests										(1,157)			—			(1,157)
Net income (loss) available to Arch										17,101			—			17,101
Preferred dividends										(10,184)			—			(10,184)
Net income (loss) available to Arch common shareholders										$	6,917		$	—		$	6,917
Underwriting Ratios
Loss ratio	69.3		%	92.6		%	(24.1)		%	68.1		%	—		%	68.1		%
Acquisition expense ratio	19.6		%	20.8		%	2.4		%	18.1		%	—		%	18.1		%
Other operating expense ratio	13.9		%	6.3		%	16.5		%	11.1		%	—		%	11.1		%
Combined ratio	102.8		%	119.7		%	(5.2)		%	97.3		%	—		%	97.3		%
Goodwill and intangible assets	$	224,525		$	140,800		$	441,330		$	806,655		$	—		$	806,655

(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
	September 30, 2021
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	1,596,619		$	1,251,760		$	360,934		$	3,207,415		$	—		$	3,207,415
Premiums ceded	(442,806)			(630,371)			(60,207)			(1,131,486)			—			(1,131,486)
Net premiums written	1,153,813			621,389			300,727			2,075,929			—			2,075,929
Change in unearned premiums	(215,143)			57,313			11,238			(146,592)			—			(146,592)
Net premiums earned	938,670			678,702			311,965			1,929,337			—			1,929,337
Other underwriting income (loss)	—			3,293			3,981			7,274			—			7,274
Losses and loss adjustment expenses	(668,630)			(545,846)			(11,543)			(1,226,019)			—			(1,226,019)
Acquisition expenses	(152,467)			(129,450)			(24,098)			(306,015)			—			(306,015)
Other operating expenses	(138,931)			(45,647)			(46,254)			(230,832)			—			(230,832)
Underwriting income (loss)	$	(21,358)		$	(38,948)		$	234,051		173,745			—			173,745
Net investment income										88,195			—			88,195
Net realized gains (losses)										(25,040)			—			(25,040)
Equity in net income (loss) of investment funds accounted for using the equity method										105,398			—			105,398
Other income (loss)										(3,960)			—			(3,960)
Corporate expenses (2)										(18,636)			—			(18,636)
Transaction costs and other (2)										(1,036)			—			(1,036)
Amortization of intangible assets										(20,135)			—			(20,135)
Interest expense										(33,176)			—			(33,176)
Net foreign exchange gains (losses)										36,078			—			36,078
Income (loss) before income taxes and income (loss) from operating affiliates										301,433			—			301,433
Income tax (expense) benefit										(4,137)			—			(4,137)
Income (loss) from operating affiliates										124,119			—			124,119
Net income (loss)										421,415			—			421,415
Amounts attributable to redeemable noncontrolling interests										(1,473)			—			(1,473)
Net income (loss) available to Arch										419,942			—			419,942
Preferred dividends										(16,090)			—			(16,090)
Loss on redemption of preferred shares										(15,101)			—			(15,101)
Net income (loss) available to Arch common shareholders										$	388,751		$	—		$	388,751
Underwriting Ratios
Loss ratio	71.2		%	80.4		%	3.7		%	63.5		%	—		%	63.5		%
Acquisition expense ratio	16.2		%	19.1		%	7.7		%	15.9		%	—		%	15.9		%
Other operating expense ratio	14.8		%	6.7		%	14.8		%	12.0		%	—		%	12.0		%
Combined ratio	102.2		%	106.2		%	26.2		%	91.4		%	—		%	91.4		%
Goodwill and intangible assets	$	261,103		$	176,128		$	526,091		$	963,322		$	—		$	963,322

(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.’

	Nine Months Ended
	September 30, 2022
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	5,286,798		$	5,151,401		$	1,099,144		$	11,531,185		$	—		$	11,531,185
Premiums ceded	(1,482,886)			(1,770,807)			(241,097)			(3,488,632)			—			(3,488,632)
Net premiums written	3,803,912			3,380,594			858,047			8,042,553			—			8,042,553
Change in unearned premiums	(488,164)			(646,421)			9,190			(1,125,395)			—			(1,125,395)
Net premiums earned	3,315,748			2,734,173			867,237			6,917,158			—			6,917,158
Other underwriting income (loss)	—			5,814			6,130			11,944			—			11,944
Losses and loss adjustment expenses	(2,053,161)			(1,920,189)			187,163			(3,786,187)			—			(3,786,187)
Acquisition expenses	(641,807)			(569,915)			(27,343)			(1,239,065)			—			(1,239,065)
Other operating expenses	(493,412)			(198,606)			(150,064)			(842,082)			—			(842,082)
Underwriting income (loss)	$	127,368		$	51,277		$	883,123		$	1,061,768		$	—		$	1,061,768
Net investment income										315,468			—			315,468
Net realized gains (losses)										(742,666)			—			(742,666)
Equity in net income (loss) of investment funds accounted for using the equity method										75,505			—			75,505
Other income (loss)										(34,486)			—			(34,486)
Corporate expenses (2)										(76,928)			—			(76,928)
Transaction costs and other (2)										(734)			—			(734)
Amortization of intangible assets										(80,478)			—			(80,478)
Interest expense										(98,566)			—			(98,566)
Net foreign exchange gains (losses)										182,129			—			182,129
Income (loss) before income taxes and income (loss) from operating affiliates										601,012			—			601,012
Income tax (expense) benefit										(19,042)			—			(19,042)
Income (loss) from operating affiliates										37,665			—			37,665
Net income (loss)										619,635			—			619,635
Amounts attributable to redeemable noncontrolling interests										(2,390)			—			(2,390)
Net income (loss) available to Arch										617,245			—			617,245
Preferred dividends										(30,552)			—			(30,552)
Net income (loss) available to Arch common shareholders										$	586,693		$	—		$	586,693
Underwriting Ratios
Loss ratio	61.9		%	70.2		%	(21.6)		%	54.7		%	—		%	54.7		%
Acquisition expense ratio	19.4		%	20.8		%	3.2		%	17.9		%	—		%	17.9		%
Other operating expense ratio	14.9		%	7.3		%	17.3		%	12.2		%	—		%	12.2		%
Combined ratio	96.2		%	98.3		%	(1.1)		%	84.8		%	—		%	84.8		%

(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.’

	Nine Months Ended
	September 30, 2021
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	4,381,372		$	4,080,840		$	1,143,691		$	9,602,213		$	457,465		$	9,890,912
Premiums ceded	(1,269,165)			(1,535,607)			(171,923)			(2,973,005)			(102,763)			(2,907,002)
Net premiums written	3,112,207			2,545,233			971,768			6,629,208			354,702			6,983,910
Change in unearned premiums	(488,636)			(484,607)			10,735			(962,508)			(22,734)			(985,242)
Net premiums earned	2,623,571			2,060,626			982,503			5,666,700			331,968			5,998,668
Other underwriting income (loss)	—			3,148			15,026			18,174			739			18,913
Losses and loss adjustment expenses	(1,750,257)			(1,494,539)			(85,112)			(3,329,908)			(259,042)			(3,588,950)
Acquisition expenses	(417,541)			(381,060)			(84,297)			(882,898)			(62,741)			(945,639)
Other operating expenses	(409,386)			(150,856)			(143,697)			(703,939)			(32,869)			(736,808)
Underwriting income (loss)	$	46,387		$	37,319		$	684,423		$	768,129		$	(21,945)		$	746,184
Net investment income										256,354			42,310			298,664
Net realized gains (losses)										239,690			80,638			320,328
Equity in net income (loss) of investment funds accounted for using the equity method										299,270			—			299,270
Other income (loss)										1,151			—			1,151
Corporate expenses (2)										(59,279)			—			(59,279)
Transaction costs and other (2)										(793)			(935)			(1,728)
Amortization of intangible assets										(48,925)			(898)			(49,823)
Interest expense										(98,812)			(8,410)			(107,222)
Net foreign exchange gains (losses)										39,691			(1,325)			38,366
Income (loss) before income taxes and income (loss) from operating affiliates										1,396,476			89,435			1,485,911
Income tax (expense) benefit										(93,942)			(234)			(94,176)
Income (loss) from operating affiliates										224,052			—			224,052
Net income (loss)										1,526,586			89,201			1,615,787
Amounts attributable to redeemable noncontrolling interests										(1,936)			(1,953)			(3,889)
Amounts attributable to nonredeemable noncontrolling interests										—			(78,314)			(78,314)
Net income (loss) available to Arch										1,524,650			8,934			1,533,584
Preferred dividends										(38,159)			—			(38,159)
Loss on redemption of preferred shares										(15,101)			—			(15,101)
Net income (loss) available to Arch common shareholders										$	1,471,390		$	8,934		$	1,480,324
Underwriting Ratios
Loss ratio	66.7		%	72.5		%	8.7		%	58.8		%	78.0		%	59.8		%
Acquisition expense ratio	15.9		%	18.5		%	8.6		%	15.6		%	18.9		%	15.8		%
Other operating expense ratio	15.6		%	7.3		%	14.6		%	12.4		%	9.9		%	12.3		%
Combined ratio	98.2		%	98.3		%	31.9		%	86.8		%	106.8		%	87.9		%

(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.’