Segment Information (Tables)

9 Months Ended

Sep. 30, 2023

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, 2023
	Insurance			Reinsurance			Mortgage			Total
Gross premiums written (1)	$	2,043		$	2,138		$	347		$	4,527
Premiums ceded	(521)			(576)			(76)			(1,172)
Net premiums written	1,522			1,562			271			3,355
Change in unearned premiums	(110)			(19)			22			(107)
Net premiums earned	1,412			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 income										269
Net realized gains (losses)										(248)
Equity in net income (loss) of investment funds accounted for using the equity method										59
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 affiliates										741
Income tax (expense) benefit										(72)
Income (loss) from operating affiliates										54
Net income (loss)										723
Net (income) loss attributable to noncontrolling interests										—
Net income (loss) available to Arch										723
Preferred dividends										(10)
Net income (loss) available to Arch common shareholders										$	713
Underwriting Ratios
Loss ratio	57.5		%	56.4		%	(12.1)		%	50.7		%
Acquisition expense ratio	19.1		%	19.7		%	0.6		%	17.7		%
Other operating expense ratio	14.3		%	3.9		%	16.2		%	9.5		%
Combined ratio	90.9		%	80.0		%	4.7		%	77.9		%
Goodwill and intangible assets	$	220		$	132		$	387		$	739

(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, 2022
	Insurance			Reinsurance			Mortgage			Total
Gross premiums written (1)	$	1,862		$	1,639		$	362		$	3,861
Premiums ceded	(493)			(560)			(86)			(1,137)
Net premiums written	1,369			1,079			276			2,724
Change in unearned premiums	(182)			(77)			6			(253)
Net premiums earned	1,187			1,002			282			2,471
Other underwriting income (loss)	—			—			3			3
Losses and loss adjustment expenses	(823)			(928)			68			(1,683)
Acquisition expenses	(233)			(208)			(7)			(448)
Other operating expenses	(165)			(63)			(47)			(275)
Underwriting income (loss)	$	(34)		$	(197)		$	299		68
Net investment income										129
Net realized gains (losses)										(184)
Equity in net income (loss) of investment funds accounted for using the equity method										(19)
Other income (loss)										(14)
Corporate expenses (2)										(18)
Transaction costs and other (2)										—
Amortization of intangible assets										(26)
Interest expense										(33)
Net foreign exchange gains (losses)										91
Income (loss) before income taxes and income (loss) from operating affiliates										(6)
Income tax (expense) benefit										15
Income (loss) from operating affiliates										9
Net income (loss)										18
Net (income) loss attributable to noncontrolling interests										(1)
Net income (loss) available to Arch										17
Preferred dividends										(10)
Net income (loss) available to Arch common shareholders										$	7
Underwriting Ratios
Loss ratio	69.3		%	92.6		%	(24.1)		%	68.1		%
Acquisition expense ratio	19.6		%	20.8		%	2.4		%	18.1		%
Other operating expense ratio	13.9		%	6.3		%	16.5		%	11.1		%
Combined ratio	102.8		%	119.7		%	(5.2)		%	97.3		%
Goodwill and intangible assets	$	225		$	141		$	441		$	807

(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, 2023
	Insurance			Reinsurance			Mortgage			Total
Gross premiums written (1)	$	5,977		$	7,142		$	1,037		$	14,152
Premiums ceded	(1,564)			(2,145)			(240)			(3,945)
Net premiums written	4,413			4,997			797			10,207
Change in unearned premiums	(416)			(781)			86			(1,111)
Net premiums earned	3,997			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 income										710
Net realized gains (losses)										(354)
Equity in net income (loss) of investment funds accounted for using the equity method										176
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 affiliates										2,197
Income tax (expense) benefit										(203)
Income (loss) from operating affiliates										115
Net income (loss)										2,109
Net (income) loss attributable to noncontrolling interests										—
Net income (loss) available to Arch										2,109
Preferred dividends										(30)
Net income (loss) available to Arch common shareholders										$	2,079
Underwriting Ratios
Loss ratio	57.0		%	56.4		%	(5.3)		%	50.7		%
Acquisition expense ratio	19.5		%	20.7		%	1.8		%	18.3		%
Other operating expense ratio	14.8		%	4.8		%	16.7		%	10.4		%
Combined ratio	91.3		%	81.9		%	13.2		%	79.4		%

(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			Total
Gross premiums written (1)	$	5,287		$	5,151		$	1,099		$	11,532
Premiums ceded	(1,483)			(1,770)			(241)			(3,489)
Net premiums written	3,804			3,381			858			8,043
Change in unearned premiums	(488)			(647)			10			(1,125)
Net premiums earned	3,316			2,734			868			6,918
Other underwriting income (loss)	—			6			6			12
Losses and loss adjustment expenses	(2,054)			(1,920)			187			(3,787)
Acquisition expenses	(643)			(569)			(27)			(1,239)
Other operating expenses	(493)			(199)			(150)			(842)
Underwriting income (loss)	$	126		$	52		$	884		1,062
Net investment income										315
Net realized gains (losses)										(743)
Equity in net income (loss) of investment funds accounted for using the equity method										75
Other income (loss)										(35)
Corporate expenses (2)										(78)
Transaction costs and other (2)										—
Amortization of intangible assets										(80)
Interest expense										(99)
Net foreign exchange gains (losses)										183
Income (loss) before income taxes and income (loss) from operating affiliates										600
Income tax (expense) benefit										(19)
Income (loss) from operating affiliates										39
Net income (loss)										620
Net (income) loss attributable to noncontrolling interests										(3)
Net income (loss) available to Arch										617
Preferred dividends										(30)
Net income (loss) available to Arch common shareholders										$	587
Underwriting Ratios
Loss ratio	61.9		%	70.2		%	(21.6)		%	54.7		%
Acquisition expense ratio	19.4		%	20.8		%	3.2		%	17.9		%
Other operating expense ratio	14.9		%	7.3		%	17.3		%	12.2		%
Combined ratio	96.2		%	98.3		%	(1.1)		%	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.’