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Segment Information (Tables)
 3 Months Ended
Mar. 31, 2020
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, 2020
 
Insurance
 
Reinsurance
 
Mortgage
 
Sub-Total
 
Other
 
Total
 
 
 
 
 
 
 
 
 
 
 
 
Gross premiums written (1)
$
1,207,645

 
$
1,122,519

 
$
368,945

 
$
2,698,537

 
$
234,902

 
$
2,832,830

Premiums ceded
(378,897
)
 
(325,339
)
 
(44,327
)
 
(747,991
)
 
(48,202
)
 
(695,584
)
Net premiums written
828,748

 
797,180

 
324,618

 
1,950,546

 
186,700

 
2,137,246

Change in unearned premiums
(112,829
)
 
(253,720
)
 
20,408

 
(346,141
)
 
(46,661
)
 
(392,802
)
Net premiums earned
715,919

 
543,460

 
345,026

 
1,604,405

 
140,039

 
1,744,444

Other underwriting income (loss)
—

 
2,120

 
4,599

 
6,719

 
133

 
6,852

Losses and loss adjustment expenses
(507,108
)
 
(430,069
)
 
(67,566
)
 
(1,004,743
)
 
(110,676
)
 
(1,115,419
)
Acquisition expenses
(107,337
)
 
(79,606
)
 
(38,536
)
 
(225,479
)
 
(21,804
)
 
(247,283
)
Other operating expenses
(129,649
)
 
(45,297
)
 
(45,896
)
 
(220,842
)
 
(13,702
)
 
(234,544
)
Underwriting income (loss)
$
(28,175
)
 
$
(9,392
)
 
$
197,627

 
160,060

 
(6,010
)
 
154,050

 
 
 
 
 
 
 
 
 
 
 
 
Net investment income
 
 
 
 
 
 
113,028

 
32,125

 
145,153

Net realized gains (losses)
 
 
 
 
 
 
(72,109
)
 
(294,851
)
 
(366,960
)
Equity in net income (loss) of investment funds accounted for using the equity method
 
 
 
 
 
 
(4,209
)
 
—

 
(4,209
)
Other income (loss)
 
 
 
 
 
 
8,548

 
—

 
8,548

Corporate expenses (2)
 
 
 
 
 
 
(18,201
)
 
—

 
(18,201
)
Transaction costs and other (2)
 
 
 
 
 
 
(2,595
)
 
—

 
(2,595
)
Amortization of intangible assets
 
 
 
 
 
 
(16,631
)
 
—

 
(16,631
)
Interest expense
 
 
 
 
 
 
(25,245
)
 
(7,310
)
 
(32,555
)
Net foreign exchange gains (losses)
 
 
 
 
 
 
63,307

 
9,364

 
72,671

Income (loss) before income taxes
 
 
 
 
 
 
205,953

 
(266,682
)
 
(60,729
)
Income tax expense
 
 
 
 
 
 
(27,945
)
 
—

 
(27,945
)
Net income (loss)
 
 
 
 
 
 
178,008

 
(266,682
)
 
(88,674
)
Amounts attributable to redeemable noncontrolling interests
 
 
 
 
 
 
(57
)
 
(1,096
)
 
(1,153
)
Amounts attributable to nonredeemable noncontrolling interests
 
 
 
 
 
 
—

 
233,944

 
233,944

Net income (loss) available to Arch
 
 
 
 
 
 
177,951

 
(33,834
)
 
144,117

Preferred dividends
 
 
 
 
 
 
(10,403
)
 
—

 
(10,403
)
Net income (loss) available to Arch common shareholders
 
 
 
 
 
 
$
167,548

 
$
(33,834
)
 
$
133,714

 
 
 
 
 
 
 
 
 
 
 
 
Underwriting Ratios
 
 
 
 
 
 
 
 
 
 
 
Loss ratio
70.8
%
 
79.1
%
 
19.6
%
 
62.6
%
 
79.0
%
 
63.9
%
Acquisition expense ratio
15.0
%
 
14.6
%
 
11.2
%
 
14.1
%
 
15.6
%
 
14.2
%
Other operating expense ratio
18.1
%
 
8.3
%
 
13.3
%
 
13.8
%
 
9.8
%
 
13.4
%
Combined ratio
103.9
%
 
102.0
%
 
44.1
%
 
90.5
%
 
104.4
%
 
91.5
%
 
 
 
 
 
 
 
 
 
 
 
 
Goodwill and intangible assets
$
268,296

 
$
2,516

 
$
426,988

 
$
697,800

 
$
7,650

 
$
705,450

(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, 2019
 
Insurance
 
Reinsurance
 
Mortgage
 
Sub-Total
 
Other
 
Total
 
 
 
 
 
 
 
 
 
 
 
 
Gross premiums written (1)
$
941,954

 
$
682,855

 
$
356,050

 
$
1,980,453

 
$
186,689

 
$
2,077,879

Premiums ceded
(320,622
)
 
(231,567
)
 
(48,798
)
 
(600,581
)
 
(41,302
)
 
(552,620
)
Net premiums written
621,332

 
451,288

 
307,252

 
1,379,872

 
145,387

 
1,525,259

Change in unearned premiums
(67,827
)
 
(104,923
)
 
15,650

 
(157,100
)
 
707

 
(156,393
)
Net premiums earned
553,505

 
346,365

 
322,902

 
1,222,772

 
146,094

 
1,368,866

Other underwriting income (loss)
—

 
4,377

 
3,856

 
8,233

 
592

 
8,825

Losses and loss adjustment expenses
(356,723
)
 
(239,810
)
 
(11,149
)
 
(607,682
)
 
(110,850
)
 
(718,532
)
Acquisition expenses
(82,824
)
 
(54,326
)
 
(31,672
)
 
(168,822
)
 
(29,026
)
 
(197,848
)
Other operating expenses
(113,396
)
 
(35,704
)
 
(39,875
)
 
(188,975
)
 
(12,188
)
 
(201,163
)
Underwriting income (loss)
$
562

 
$
20,902

 
$
244,062

 
265,526

 
(5,378
)
 
260,148

 
 
 
 
 
 
 
 
 
 
 
 
Net investment income
 
 
 
 
 
 
121,249

 
35,700

 
156,949

Net realized gains (losses)
 
 
 
 
 
 
111,124

 
29,132

 
140,256

Equity in net income (loss) of investment funds accounted for using the equity method
 
 
 
 
 
 
46,867

 
—

 
46,867

Other income (loss)
 
 
 
 
 
 
1,083

 
—

 
1,083

Corporate expenses (2)
 
 
 
 
 
 
(16,772
)
 
—

 
(16,772
)
Transaction costs and other (2)
 
 
 
 
 
 
(1,190
)
 
—

 
(1,190
)
Amortization of intangible assets
 
 
 
 
 
 
(20,417
)
 
—

 
(20,417
)
Interest expense
 
 
 
 
 
 
(23,482
)
 
(5,583
)
 
(29,065
)
Net foreign exchange gains (losses)
 
 
 
 
 
 
5,175

 
(1,650
)
 
3,525

Income before income taxes
 
 
 
 
 
 
489,163

 
52,221

 
541,384

Income tax expense
 
 
 
 
 
 
(45,886
)
 
—

 
(45,886
)
Net income
 
 
 
 
 
 
443,277

 
52,221

 
495,498

Amounts attributable to redeemable noncontrolling interests
 
 
 
 
 
 
—

 
(4,588
)
 
(4,588
)
Amounts attributable to nonredeemable noncontrolling interests
 
 
 
 
 
 
—

 
(42,382
)
 
(42,382
)
Net income available to Arch
 
 
 
 
 
 
443,277

 
5,251

 
448,528

Preferred dividends
 
 
 
 
 
 
(10,403
)
 
—

 
(10,403
)
Net income available to Arch common shareholders
 
 
 
 
 
 
$
432,874

 
$
5,251

 
$
438,125

 
 
 
 
 
 
 
 
 
 
 
 
Underwriting Ratios
 

 
 

 
 

 
 
 
 

 
 

Loss ratio
64.4
%
 
69.2
%
 
3.5
%
 
49.7
%
 
75.9
%
 
52.5
%
Acquisition expense ratio
15.0
%
 
15.7
%
 
9.8
%
 
13.8
%
 
19.9
%
 
14.5
%
Other operating expense ratio
20.5
%
 
10.3
%
 
12.3
%
 
15.5
%
 
8.3
%
 
14.7
%
Combined ratio
99.9
%
 
95.2
%
 
25.6
%
 
79.0
%
 
104.1
%
 
81.7
%
 
 
 
 
 
 
 
 
 
 
 
 
Goodwill and intangible assets
$
156,735

 
$
—

 
$
494,830

 
$
651,565

 
$
7,650

 
$
659,215


(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.’