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Segment Information (Tables) | 9 Months Ended
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Sep. 30, 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
| September 30, 2020
| Insurance |  | Reinsurance |  | Mortgage |  | Sub-Total |  | Other |  | Total
Gross premiums written (1) | $ | 1,206,328 |  |  | $ | 1,004,590 |  |  | $ | 346,248 |  |  | $ | 2,556,914 |  |  | $ | 197,480 |  |  | $ | 2,681,032 |
Premiums ceded | (382,167) |  |  | (400,388) |  |  | (47,783) |  |  | (830,086) |  |  | (50,164) |  |  | (806,888) |
Net premiums written | 824,161 |  |  | 604,202 |  |  | 298,465 |  |  | 1,726,828 |  |  | 147,316 |  |  | 1,874,144 |
Change in unearned premiums | (105,007) |  |  | (49,704) |  |  | 52,944 |  |  | (101,767) |  |  | (1,285) |  |  | (103,052) |
Net premiums earned | 719,154 |  |  | 554,498 |  |  | 351,409 |  |  | 1,625,061 |  |  | 146,031 |  |  | 1,771,092 |
Other underwriting income (loss) | (31) |  |  | 298 |  |  | 4,600 |  |  | 4,867 |  |  | 546 |  |  | 5,413 |
Losses and loss adjustment expenses | (525,321) |  |  | (422,084) |  |  | (153,055) |  |  | (1,100,460) |  |  | (115,813) |  |  | (1,216,273) |
Acquisition expenses | (102,420) |  |  | (85,388) |  |  | (35,716) |  |  | (223,524) |  |  | (24,418) |  |  | (247,942) |
Other operating expenses | (122,541) |  |  | (41,818) |  |  | (36,708) |  |  | (201,067) |  |  | (14,619) |  |  | (215,686) |
Underwriting income (loss) | $ | (31,159) |  |  | $ | 5,506 |  |  | $ | 130,530 |  |  | 104,877 |  |  | (8,273) |  |  | 96,604 |
Net investment income |  |  |  |  |  |  | 99,857 |  |  | 28,655 |  |  | 128,512 |
Net realized gains (losses) |  |  |  |  |  |  | 210,984 |  |  | 69,515 |  |  | 280,499 |
Equity in net income (loss) of investment funds accounted for using the equity method |  |  |  |  |  |  | 126,735 |  |  | — |  |  | 126,735 |
Other income (loss) |  |  |  |  |  |  | 919 |  |  | — |  |  | 919 |
Corporate expenses (2) |  |  |  |  |  |  | (16,263) |  |  | — |  |  | (16,263) |
Transaction costs and other (2) |  |  |  |  |  |  | (1,674) |  |  | — |  |  | (1,674) |
Amortization of intangible assets |  |  |  |  |  |  | (16,715) |  |  | — |  |  | (16,715) |
Interest expense |  |  |  |  |  |  | (36,224) |  |  | (5,119) |  |  | (41,343) |
Net foreign exchange gains (losses) |  |  |  |  |  |  | (38,681) |  |  | (6,204) |  |  | (44,885) |
Income (loss) before income taxes |  |  |  |  |  |  | 433,815 |  |  | 78,574 |  |  | 512,389 |
Income tax (expense) benefit |  |  |  |  |  |  | (23,638) |  |  | (69) |  |  | (23,707) |
Net income (loss) |  |  |  |  |  |  | 410,177 |  |  | 78,505 |  |  | 488,682 |
Amounts attributable to redeemable noncontrolling interests |  |  |  |  |  |  | (882) |  |  | (993) |  |  | (1,875) |
Amounts attributable to nonredeemable noncontrolling interests |  |  |  |  |  |  | — |  |  | (67,768) |  |  | (67,768) |
Net income (loss) available to Arch |  |  |  |  |  |  | 409,295 |  |  | 9,744 |  |  | 419,039 |
Preferred dividends |  |  |  |  |  |  | (10,403) |  |  | — |  |  | (10,403) |
Net income (loss) available to Arch common shareholders |  |  |  |  |  |  | $ | 398,892 |  |  | $ | 9,744 |  |  | $ | 408,636 |
Underwriting Ratios |  |  |  |  |  |  |  |  |  |  |
Loss ratio | 73.0 | % |  | 76.1 | % |  | 43.6 | % |  | 67.7 | % |  | 79.3 | % |  | 68.7 | %
Acquisition expense ratio | 14.2 | % |  | 15.4 | % |  | 10.2 | % |  | 13.8 | % |  | 16.7 | % |  | 14.0 | %
Other operating expense ratio | 17.0 | % |  | 7.5 | % |  | 10.4 | % |  | 12.4 | % |  | 10.0 | % |  | 12.2 | %
Combined ratio | 104.2 | % |  | 99.0 | % |  | 64.2 | % |  | 93.9 | % |  | 106.0 | % |  | 94.9 | %
Goodwill and intangible assets | $ | 282,146 |  |  | $ | 20,319 |  |  | $ | 403,662 |  |  | $ | 706,127 |  |  | $ | 7,650 |  |  | $ | 713,777 |
(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, 2019
| Insurance |  | Reinsurance |  | Mortgage |  | Sub-Total |  | Other |  | Total
Gross premiums written (1) | $ | 1,005,874 |  |  | $ | 662,572 |  |  | $ | 375,092 |  |  | $ | 2,043,292 |  |  | $ | 249,960 |  |  | $ | 2,181,121 |
Premiums ceded | (302,034) |  |  | (226,096) |  |  | (57,703) |  |  | (585,587) |  |  | (94,208) |  |  | (567,664) |
Net premiums written | 703,840 |  |  | 436,476 |  |  | 317,389 |  |  | 1,457,705 |  |  | 155,752 |  |  | 1,613,457 |
Change in unearned premiums | (98,504) |  |  | (72,621) |  |  | 25,611 |  |  | (145,514) |  |  | (29,920) |  |  | (175,434) |
Net premiums earned | 605,336 |  |  | 363,855 |  |  | 343,000 |  |  | 1,312,191 |  |  | 125,832 |  |  | 1,438,023 |
Other underwriting income (loss) | — |  |  | (1,208) |  |  | 3,955 |  |  | 2,747 |  |  | 579 |  |  | 3,326 |
Losses and loss adjustment expenses | (422,782) |  |  | (270,379) |  |  | (13,080) |  |  | (706,241) |  |  | (96,214) |  |  | (802,455) |
Acquisition expenses | (91,259) |  |  | (62,393) |  |  | (34,396) |  |  | (188,048) |  |  | (23,072) |  |  | (211,120) |
Other operating expenses | (115,408) |  |  | (32,533) |  |  | (37,003) |  |  | (184,944) |  |  | (11,568) |  |  | (196,512) |
Underwriting income (loss) | $ | (24,113) |  |  | $ | (2,658) |  |  | $ | 262,476 |  |  | 235,705 |  |  | (4,443) |  |  | 231,262 |
Net investment income |  |  |  |  |  |  | 126,874 |  |  | 34,614 |  |  | 161,488 |
Net realized gains (losses) |  |  |  |  |  |  | 80,014 |  |  | (18,659) |  |  | 61,355 |
Equity in net income (loss) of investment funds accounted for using the equity method |  |  |  |  |  |  | 17,130 |  |  | — |  |  | 17,130 |
Other income (loss) |  |  |  |  |  |  | 1,338 |  |  | — |  |  | 1,338 |
Corporate expenses (2) |  |  |  |  |  |  | (15,066) |  |  | — |  |  | (15,066) |
Transaction costs and other (2) |  |  |  |  |  |  | (1,995) |  |  | — |  |  | (1,995) |
Amortization of intangible assets |  |  |  |  |  |  | (20,003) |  |  | — |  |  | (20,003) |
Interest expense |  |  |  |  |  |  | (23,237) |  |  | (8,091) |  |  | (31,328) |
Net foreign exchange gains (losses) |  |  |  |  |  |  | 29,794 |  |  | 3,330 |  |  | 33,124 |
Income (loss) before income taxes |  |  |  |  |  |  | 430,554 |  |  | 6,751 |  |  | 437,305 |
Income tax (expense) benefit |  |  |  |  |  |  | (38,116) |  |  | — |  |  | (38,116) |
Net income (loss) |  |  |  |  |  |  | 392,438 |  |  | 6,751 |  |  | 399,189 |
Amounts attributable to redeemable noncontrolling interests |  |  |  |  |  |  | — |  |  | (6,600) |  |  | (6,600) |
Amounts attributable to nonredeemable noncontrolling interests |  |  |  |  |  |  | — |  |  | (136) |  |  | (136) |
Net income (loss) available to Arch |  |  |  |  |  |  | 392,438 |  |  | 15 |  |  | 392,453 |
Preferred dividends |  |  |  |  |  |  | (10,403) |  |  | — |  |  | (10,403) |
Net income (loss) available to Arch common shareholders |  |  |  |  |  |  | $ | 382,035 |  |  | $ | 15 |  |  | $ | 382,050 |
Underwriting Ratios |  |  |  |  |  |  |  |  |  |  |
Loss ratio | 69.8 | % |  | 74.3 | % |  | 3.8 | % |  | 53.8 | % |  | 76.5 | % |  | 55.8 | %
Acquisition expense ratio | 15.1 | % |  | 17.1 | % |  | 10.0 | % |  | 14.3 | % |  | 18.3 | % |  | 14.7 | %
Other operating expense ratio | 19.1 | % |  | 8.9 | % |  | 10.8 | % |  | 14.1 | % |  | 9.2 | % |  | 13.7 | %
Combined ratio | 104.0 | % |  | 100.3 | % |  | 24.6 | % |  | 82.2 | % |  | 104.0 | % |  | 84.2 | %
Goodwill and intangible assets | $ | 158,990 |  |  | $ | — |  |  | $ | 457,860 |  |  | $ | 616,850 |  |  | $ | 7,650 |  |  | $ | 624,500 |
(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, 2020
| Insurance |  | Reinsurance |  | Mortgage |  | Sub-Total |  | Other |  | Total
Gross premiums written (1) | $ | 3,444,335 |  |  | $ | 2,934,174 |  |  | $ | 1,084,337 |  |  | $ | 7,461,860 |  |  | $ | 590,309 |  |  | $ | 7,831,554 |
Premiums ceded | (1,119,165) |  |  | (967,698) |  |  | (136,154) |  |  | (2,222,031) |  |  | (150,437) |  |  | (2,151,853) |
Net premiums written | 2,325,170 |  |  | 1,966,476 |  |  | 948,183 |  |  | 5,239,829 |  |  | 439,872 |  |  | 5,679,701 |
Change in unearned premiums | (202,188) |  |  | (388,321) |  |  | 113,965 |  |  | (476,544) |  |  | (22,267) |  |  | (498,811) |
Net premiums earned | 2,122,982 |  |  | 1,578,155 |  |  | 1,062,148 |  |  | 4,763,285 |  |  | 417,605 |  |  | 5,180,890 |
Other underwriting income (loss) | (31) |  |  | 1,767 |  |  | 15,649 |  |  | 17,385 |  |  | 1,547 |  |  | 18,932 |
Losses and loss adjustment expenses | (1,550,632) |  |  | (1,235,586) |  |  | (444,721) |  |  | (3,230,939) |  |  | (331,275) |  |  | (3,562,214) |
Acquisition expenses | (317,428) |  |  | (255,516) |  |  | (108,304) |  |  | (681,248) |  |  | (68,766) |  |  | (750,014) |
Other operating expenses | (370,947) |  |  | (125,831) |  |  | (120,178) |  |  | (616,956) |  |  | (42,523) |  |  | (659,479) |
Underwriting income (loss) | $ | (116,056) |  |  | $ | (37,011) |  |  | $ | 404,594 |  |  | 251,527 |  |  | (23,412) |  |  | 228,115 |
Net investment income |  |  |  |  |  |  | 313,916 |  |  | 91,234 |  |  | 405,150 |
Net realized gains (losses) |  |  |  |  |  |  | 523,964 |  |  | (53,837) |  |  | 470,127 |
Equity in net income (loss) of investment funds accounted for using the equity method |  |  |  |  |  |  | 57,407 |  |  | — |  |  | 57,407 |
Other income (loss) |  |  |  |  |  |  | 6,327 |  |  | — |  |  | 6,327 |
Corporate expenses (2) |  |  |  |  |  |  | (51,407) |  |  | — |  |  | (51,407) |
Transaction costs and other (2) |  |  |  |  |  |  | (5,246) |  |  | — |  |  | (5,246) |
Amortization of intangible assets |  |  |  |  |  |  | (49,835) |  |  | — |  |  | (49,835) |
Interest expense |  |  |  |  |  |  | (86,599) |  |  | (18,438) |  |  | (105,037) |
Net foreign exchange gains (losses) |  |  |  |  |  |  | (17,812) |  |  | 6,387 |  |  | (11,425) |
Income (loss) before income taxes |  |  |  |  |  |  | 942,242 |  |  | 1,934 |  |  | 944,176 |
Income tax (expense) benefit |  |  |  |  |  |  | (78,112) |  |  | 333 |  |  | (77,779) |
Net income (loss) |  |  |  |  |  |  | 864,130 |  |  | 2,267 |  |  | 866,397 |
Dividends attributable to redeemable noncontrolling interests |  |  |  |  |  |  | (1,873) |  |  | (3,125) |  |  | (4,998) |
Amounts attributable to nonredeemable noncontrolling interests |  |  |  |  |  |  | — |  |  | 578 |  |  | 578 |
Net income (loss) available to Arch |  |  |  |  |  |  | 862,257 |  |  | (280) |  |  | 861,977 |
Preferred dividends |  |  |  |  |  |  | (31,209) |  |  | — |  |  | (31,209) |
Net income (loss) available to Arch common shareholders |  |  |  |  |  |  | $ | 831,048 |  |  | $ | (280) |  |  | $ | 830,768 |
Underwriting Ratios |  |  |  |  |  |  |  |  |  |  |
Loss ratio | 73.0 | % |  | 78.3 | % |  | 41.9 | % |  | 67.8 | % |  | 79.3 | % |  | 68.8 | %
Acquisition expense ratio | 15.0 | % |  | 16.2 | % |  | 10.2 | % |  | 14.3 | % |  | 16.5 | % |  | 14.5 | %
Other operating expense ratio | 17.5 | % |  | 8.0 | % |  | 11.3 | % |  | 13.0 | % |  | 10.2 | % |  | 12.7 | %
Combined ratio | 105.5 | % |  | 102.5 | % |  | 63.4 | % |  | 95.1 | % |  | 106.0 | % |  | 96.0 | %
(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, 2019
| Insurance |  | Reinsurance |  | Mortgage |  | Sub-Total |  | Other |  | Total
Gross premiums written (1) | $ | 2,867,753 |  |  | $ | 1,890,974 |  |  | $ | 1,095,607 |  |  | $ | 5,853,574 |  |  | $ | 598,627 |  |  | $ | 6,196,809 |
Premiums ceded | (914,751) |  |  | (627,120) |  |  | (149,358) |  |  | (1,690,469) |  |  | (178,118) |  |  | (1,613,195) |
Net premiums written | 1,953,002 |  |  | 1,263,854 |  |  | 946,249 |  |  | 4,163,105 |  |  | 420,509 |  |  | 4,583,614 |
Change in unearned premiums | (201,719) |  |  | (186,450) |  |  | 72,436 |  |  | (315,733) |  |  | 2,735 |  |  | (312,998) |
Net premiums earned | 1,751,283 |  |  | 1,077,404 |  |  | 1,018,685 |  |  | 3,847,372 |  |  | 423,244 |  |  | 4,270,616 |
Other underwriting income (loss) | — |  |  | 4,393 |  |  | 11,867 |  |  | 16,260 |  |  | 1,844 |  |  | 18,104 |
Losses and loss adjustment expenses | (1,168,677) |  |  | (751,147) |  |  | (50,226) |  |  | (1,970,050) |  |  | (318,480) |  |  | (2,288,530) |
Acquisition expenses | (265,177) |  |  | (173,504) |  |  | (98,722) |  |  | (537,403) |  |  | (81,654) |  |  | (619,057) |
Other operating expenses | (338,327) |  |  | (102,197) |  |  | (116,697) |  |  | (557,221) |  |  | (39,368) |  |  | (596,589) |
Underwriting income (loss) | $ | (20,898) |  |  | $ | 54,949 |  |  | $ | 764,907 |  |  | 798,958 |  |  | (14,414) |  |  | 784,544 |
Net investment income |  |  |  |  |  |  | 371,161 |  |  | 102,314 |  |  | 473,475 |
Net realized gains (losses) |  |  |  |  |  |  | 316,201 |  |  | 6,167 |  |  | 322,368 |
Equity in net income (loss) of investment funds accounted for using the equity method |  |  |  |  |  |  | 96,533 |  |  | — |  |  | 96,533 |
Other income (loss) |  |  |  |  |  |  | 3,550 |  |  | — |  |  | 3,550 |
Corporate expenses (2) |  |  |  |  |  |  | (47,911) |  |  | — |  |  | (47,911) |
Transaction costs and other (2) |  |  |  |  |  |  | (5,363) |  |  | — |  |  | (5,363) |
Amortization of intangible assets |  |  |  |  |  |  | (60,214) |  |  | — |  |  | (60,214) |
Interest expense |  |  |  |  |  |  | (70,094) |  |  | (19,579) |  |  | (89,673) |
Net foreign exchange gains (losses) |  |  |  |  |  |  | 28,779 |  |  | 2,918 |  |  | 31,697 |
Income (loss) before income taxes |  |  |  |  |  |  | 1,431,600 |  |  | 77,406 |  |  | 1,509,006 |
Income tax (expense) benefit |  |  |  |  |  |  | (128,454) |  |  | (20) |  |  | (128,474) |
Net income (loss) |  |  |  |  |  |  | 1,303,146 |  |  | 77,386 |  |  | 1,380,532 |
Dividends attributable to redeemable noncontrolling interests |  |  |  |  |  |  | — |  |  | (15,778) |  |  | (15,778) |
Amounts attributable to nonredeemable noncontrolling interests |  |  |  |  |  |  | — |  |  | (54,819) |  |  | (54,819) |
Net income (loss) available to Arch |  |  |  |  |  |  | 1,303,146 |  |  | 6,789 |  |  | 1,309,935 |
Preferred dividends |  |  |  |  |  |  | (31,209) |  |  | — |  |  | (31,209) |
Net income (loss) available to Arch common shareholders |  |  |  |  |  |  | $ | 1,271,937 |  |  | $ | 6,789 |  |  | $ | 1,278,726 |
Underwriting Ratios |  |  |  |  |  |  |  |  |  |  |
Loss ratio | 66.7 | % |  | 69.7 | % |  | 4.9 | % |  | 51.2 | % |  | 75.2 | % |  | 53.6 | %
Acquisition expense ratio | 15.1 | % |  | 16.1 | % |  | 9.7 | % |  | 14.0 | % |  | 19.3 | % |  | 14.5 | %
Other operating expense ratio | 19.3 | % |  | 9.5 | % |  | 11.5 | % |  | 14.5 | % |  | 9.3 | % |  | 14.0 | %
Combined ratio | 101.1 | % |  | 95.3 | % |  | 26.1 | % |  | 79.7 | % |  | 103.8 | % |  | 82.1 | %
(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.’

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- Definition Tabular disclosure of the profit or loss and total assets for each reportable segment. An entity discloses certain information on each reportable segment if the amounts (a) are included in the measure of segment profit or loss reviewed by the chief operating decision maker or (b) are otherwise regularly provided to the chief operating decision maker, even if not included in that measure of segment profit or loss. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 280 -SubTopic 10 -Section 50 -Paragraph 22 -URI http://asc.fasb.org/extlink&oid=120311839&loc=d3e8736-108599 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 280 -SubTopic 10 -Section 50 -Paragraph 25 -URI http://asc.fasb.org/extlink&oid=120311839&loc=d3e8813-108599 Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 20 -Section 50 -Paragraph 1 -URI http://asc.fasb.org/extlink&oid=121556970&loc=d3e13816-109267 Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 280 -SubTopic 10 -Section 50 -Paragraph 30 -URI http://asc.fasb.org/extlink&oid=120311839&loc=d3e8906-108599 + Details
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