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Segment Information - Summary of underwriting income or loss by segment (Details) $ in Thousands | 3 Months Ended | 9 Months Ended |
--- | --- | --- | ---
Sep. 30, 2021 USD ($) | Sep. 30, 2020 USD ($) | Sep. 30, 2021 USD ($) segment | Sep. 30, 2020 USD ($) | Dec. 31, 2020 USD ($)
Segment Reporting Information [Line Items] |  |  |  |  |  |
Gross premiums written |  | $ 3,207,415 | $ 2,681,032 | $ 9,890,912 | $ 7,831,554 |
Premiums ceded |  | (1,131,486) | (806,888) | (2,907,002) | (2,151,853) |
Net premiums written |  | 2,075,929 | 1,874,144 | 6,983,910 | 5,679,701 |
Change in unearned premiums |  | (146,592) | (103,052) | (985,242) | (498,811) |
Net premiums earned |  | 1,929,337 | 1,771,092 | 5,998,668 | 5,180,890 |
Other underwriting income (loss) |  | 7,274 | 5,413 | 18,913 | 18,932 |
Losses and loss adjustment expenses |  | (1,226,019) | (1,216,273) | (3,588,950) | (3,562,214) |
Acquisition expenses |  | (306,015) | (247,942) | (945,639) | (750,014) |
Other operating expenses |  | (230,832) | (215,686) | (736,808) | (659,479) |
Underwriting income (loss) |  | 173,745 | 96,604 | 746,184 | 228,115 |
Net investment income |  | 88,195 | 128,512 | 298,664 | 405,150 |
Net realized gains (losses) |  | (25,040) | 280,499 | 320,328 | 470,127 |
Equity in net income (loss) of investment funds accounted for using the equity method |  | 105,398 | 126,735 | 299,270 | 57,407 |
Other income (loss) |  | (3,960) | 0 | 1,151 | 65 |
Corporate expenses |  | (18,636) | (16,263) | (59,279) | (51,407) |
Transaction costs and other |  | (1,036) | (1,674) | (1,728) | (5,246) |
Amortization of intangible assets |  | (20,135) | (16,715) | (49,823) | (49,835) |
Interest expense |  | (33,176) | (41,343) | (107,222) | (105,037) |
Net foreign exchange gains (losses) |  | 36,078 | (44,885) | 38,366 | (11,425) |
Income (loss) before income taxes and income (loss) from operating affiliates |  | 301,433 | 511,470 | 1,485,911 | 937,914 |
Income tax expense (benefit) |  | (4,137) | (23,707) | (94,176) | (77,779) |
Income (loss) from operating affiliates |  | 124,119 | 919 | 224,052 | 6,262 |
Net income (loss) |  | 421,415 | 488,682 | 1,615,787 | 866,397 |
Amounts attributable to redeemable noncontrolling interests |  | (1,473) | (1,875) | (3,889) | (4,998) |
Amounts attributable to non-redeemable noncontrolling interests |  | 0 | (67,768) | (78,314) | 578 |
Net income (loss) available to Arch |  | 419,942 | 419,039 | 1,533,584 | 861,977 |
Preferred dividends |  | (16,090) | (10,403) | (38,159) | (31,209) |
Loss on redemption of preferred shares |  | (15,101) | 0 | (15,101) | 0 |
Net income (loss) available to Arch common shareholders |  | $ 388,751 | $ 408,636 | $ 1,480,324 | $ 830,768 |
Underwriting Ratios |  |  |  |  |  |
Loss ratio |  | 63.50% | 68.70% | 59.80% | 68.80% |
Acquisition expense ratio |  | 15.90% | 14.00% | 15.80% | 14.50% |
Other operating expense ratio |  | 12.00% | 12.20% | 12.30% | 12.70% |
Combined ratio |  | 91.40% | 94.90% | 87.90% | 96.00% |
Goodwill and intangible assets |  | $ 963,322 | $ 713,777 | $ 963,322 | $ 713,777 | $ 692,863
Operating segments | Underwriting Segments |  |  |  |  |  |
Segment Reporting Information [Line Items] |  |  |  |  |  |
Number of segments | segment |  |  |  | 3 |  |
Gross premiums written | [1] | 3,207,415 | 2,556,914 | $ 9,602,213 | 7,461,860 |
Premiums ceded |  | (1,131,486) | (830,086) | (2,973,005) | (2,222,031) |
Net premiums written |  | 2,075,929 | 1,726,828 | 6,629,208 | 5,239,829 |
Change in unearned premiums |  | (146,592) | (101,767) | (962,508) | (476,544) |
Net premiums earned |  | 1,929,337 | 1,625,061 | 5,666,700 | 4,763,285 |
Other underwriting income (loss) |  | 7,274 | 4,867 | 18,174 | 17,385 |
Losses and loss adjustment expenses |  | (1,226,019) | (1,100,460) | (3,329,908) | (3,230,939) |
Acquisition expenses |  | (306,015) | (223,524) | (882,898) | (681,248) |
Other operating expenses |  | (230,832) | (201,067) | (703,939) | (616,956) |
Underwriting income (loss) |  | $ 173,745 | $ 104,877 | $ 768,129 | $ 251,527 |
Underwriting Ratios |  |  |  |  |  |
Loss ratio |  | 63.50% | 67.70% | 58.80% | 67.80% |
Acquisition expense ratio |  | 15.90% | 13.80% | 15.60% | 14.30% |
Other operating expense ratio |  | 12.00% | 12.40% | 12.40% | 13.00% |
Combined ratio |  | 91.40% | 93.90% | 86.80% | 95.10% |
Goodwill and intangible assets |  | $ 963,322 | $ 706,127 | $ 963,322 | $ 706,127 |
Operating segments | Insurance |  |  |  |  |  |
Segment Reporting Information [Line Items] |  |  |  |  |  |
Gross premiums written | [1] | 1,596,619 | 1,206,328 | 4,381,372 | 3,444,335 |
Premiums ceded |  | (442,806) | (382,167) | (1,269,165) | (1,119,165) |
Net premiums written |  | 1,153,813 | 824,161 | 3,112,207 | 2,325,170 |
Change in unearned premiums |  | (215,143) | (105,007) | (488,636) | (202,188) |
Net premiums earned |  | 938,670 | 719,154 | 2,623,571 | 2,122,982 |
Other underwriting income (loss) |  | 0 | (31) | 0 | (31) |
Losses and loss adjustment expenses |  | (668,630) | (525,321) | (1,750,257) | (1,550,632) |
Acquisition expenses |  | (152,467) | (102,420) | (417,541) | (317,428) |
Other operating expenses |  | (138,931) | (122,541) | (409,386) | (370,947) |
Underwriting income (loss) |  | $ (21,358) | $ (31,159) | $ 46,387 | $ (116,056) |
Underwriting Ratios |  |  |  |  |  |
Loss ratio |  | 71.20% | 73.00% | 66.70% | 73.00% |
Acquisition expense ratio |  | 16.20% | 14.20% | 15.90% | 15.00% |
Other operating expense ratio |  | 14.80% | 17.00% | 15.60% | 17.50% |
Combined ratio |  | 102.20% | 104.20% | 98.20% | 105.50% |
Goodwill and intangible assets |  | $ 261,103 | $ 282,146 | $ 261,103 | $ 282,146 |
Operating segments | Reinsurance |  |  |  |  |  |
Segment Reporting Information [Line Items] |  |  |  |  |  |
Gross premiums written | [1] | 1,251,760 | 1,004,590 | 4,080,840 | 2,934,174 |
Premiums ceded |  | (630,371) | (400,388) | (1,535,607) | (967,698) |
Net premiums written |  | 621,389 | 604,202 | 2,545,233 | 1,966,476 |
Change in unearned premiums |  | 57,313 | (49,704) | (484,607) | (388,321) |
Net premiums earned |  | 678,702 | 554,498 | 2,060,626 | 1,578,155 |
Other underwriting income (loss) |  | 3,293 | 298 | 3,148 | 1,767 |
Losses and loss adjustment expenses |  | (545,846) | (422,084) | (1,494,539) | (1,235,586) |
Acquisition expenses |  | (129,450) | (85,388) | (381,060) | (255,516) |
Other operating expenses |  | (45,647) | (41,818) | (150,856) | (125,831) |
Underwriting income (loss) |  | $ (38,948) | $ 5,506 | $ 37,319 | $ (37,011) |
Underwriting Ratios |  |  |  |  |  |
Loss ratio |  | 80.40% | 76.10% | 72.50% | 78.30% |
Acquisition expense ratio |  | 19.10% | 15.40% | 18.50% | 16.20% |
Other operating expense ratio |  | 6.70% | 7.50% | 7.30% | 8.00% |
Combined ratio |  | 106.20% | 99.00% | 98.30% | 102.50% |
Goodwill and intangible assets |  | $ 176,128 | $ 20,319 | $ 176,128 | $ 20,319 |
Operating segments | Mortgage |  |  |  |  |  |
Segment Reporting Information [Line Items] |  |  |  |  |  |
Gross premiums written | [1] | 360,934 | 346,248 | 1,143,691 | 1,084,337 |
Premiums ceded |  | (60,207) | (47,783) | (171,923) | (136,154) |
Net premiums written |  | 300,727 | 298,465 | 971,768 | 948,183 |
Change in unearned premiums |  | 11,238 | 52,944 | 10,735 | 113,965 |
Net premiums earned |  | 311,965 | 351,409 | 982,503 | 1,062,148 |
Other underwriting income (loss) |  | 3,981 | 4,600 | 15,026 | 15,649 |
Losses and loss adjustment expenses |  | (11,543) | (153,055) | (85,112) | (444,721) |
Acquisition expenses |  | (24,098) | (35,716) | (84,297) | (108,304) |
Other operating expenses |  | (46,254) | (36,708) | (143,697) | (120,178) |
Underwriting income (loss) |  | $ 234,051 | $ 130,530 | $ 684,423 | $ 404,594 |
Underwriting Ratios |  |  |  |  |  |
Loss ratio |  | 3.70% | 43.60% | 8.70% | 41.90% |
Acquisition expense ratio |  | 7.70% | 10.20% | 8.60% | 10.20% |
Other operating expense ratio |  | 14.80% | 10.40% | 14.60% | 11.30% |
Combined ratio |  | 26.20% | 64.20% | 31.90% | 63.40% |
Goodwill and intangible assets |  | $ 526,091 | $ 403,662 | $ 526,091 | $ 403,662 |
Operating segments | Corporate and Other Segments |  |  |  |  |  |
Segment Reporting Information [Line Items] |  |  |  |  |  |
Number of segments | segment |  |  |  | 2 |  |
Operating segments | Corporate |  |  |  |  |  |
Segment Reporting Information [Line Items] |  |  |  |  |  |
Net investment income |  | 88,195 | 99,857 | $ 256,354 | 313,916 |
Net realized gains (losses) |  | (25,040) | 210,984 | 239,690 | 523,964 |
Equity in net income (loss) of investment funds accounted for using the equity method |  | 105,398 | 126,735 | 299,270 | 57,407 |
Other income (loss) |  | (3,960) | 0 | 1,151 | 65 |
Corporate expenses | [2] | (18,636) | (16,263) | (59,279) | (51,407) |
Transaction costs and other | [2] | (1,036) | (1,674) | (793) | (5,246) |
Amortization of intangible assets |  | (20,135) | (16,715) | (48,925) | (49,835) |
Interest expense |  | (33,176) | (36,224) | (98,812) | (86,599) |
Net foreign exchange gains (losses) |  | 36,078 | (38,681) | 39,691 | (17,812) |
Income (loss) before income taxes and income (loss) from operating affiliates |  | 301,433 | 432,896 | 1,396,476 | 935,980 |
Income tax expense (benefit) |  | (4,137) | (23,638) | (93,942) | (78,112) |
Income (loss) from operating affiliates |  | 124,119 | 919 | 224,052 | 6,262 |
Net income (loss) |  | 421,415 | 410,177 | 1,526,586 | 864,130 |
Amounts attributable to redeemable noncontrolling interests |  | (1,473) | (882) | (1,936) | (1,873) |
Amounts attributable to non-redeemable noncontrolling interests |  | 0 | 0 | 0 | 0 |
Net income (loss) available to Arch |  | 419,942 | 409,295 | 1,524,650 | 862,257 |
Preferred dividends |  | (16,090) | (10,403) | (38,159) | (31,209) |
Loss on redemption of preferred shares |  | (15,101) |  | (15,101) |  |
Net income (loss) available to Arch common shareholders |  | 388,751 | 398,892 | 1,471,390 | 831,048 |
Operating segments | Other |  |  |  |  |  |
Segment Reporting Information [Line Items] |  |  |  |  |  |
Gross premiums written | [1] | 0 | 197,480 | 457,465 | 590,309 |
Premiums ceded |  | 0 | (50,164) | (102,763) | (150,437) |
Net premiums written |  | 0 | 147,316 | 354,702 | 439,872 |
Change in unearned premiums |  | 0 | (1,285) | (22,734) | (22,267) |
Net premiums earned |  | 0 | 146,031 | 331,968 | 417,605 |
Other underwriting income (loss) |  | 0 | 546 | 739 | 1,547 |
Losses and loss adjustment expenses |  | 0 | (115,813) | (259,042) | (331,275) |
Acquisition expenses |  | 0 | (24,418) | (62,741) | (68,766) |
Other operating expenses |  | 0 | (14,619) | (32,869) | (42,523) |
Underwriting income (loss) |  | 0 | (8,273) | (21,945) | (23,412) |
Net investment income |  | 0 | 28,655 | 42,310 | 91,234 |
Net realized gains (losses) |  | 0 | 69,515 | 80,638 | (53,837) |
Equity in net income (loss) of investment funds accounted for using the equity method |  | 0 | 0 | 0 | 0 |
Other income (loss) |  | 0 | 0 | 0 | 0 |
Corporate expenses | [2] | 0 | 0 | 0 | 0 |
Transaction costs and other | [2] | 0 | 0 | (935) | 0 |
Amortization of intangible assets |  | 0 | 0 | (898) | 0 |
Interest expense |  | 0 | (5,119) | (8,410) | (18,438) |
Net foreign exchange gains (losses) |  | 0 | (6,204) | (1,325) | 6,387 |
Income (loss) before income taxes and income (loss) from operating affiliates |  | 0 | 78,574 | 89,435 | 1,934 |
Income tax expense (benefit) |  | 0 | (69) | (234) | 333 |
Income (loss) from operating affiliates |  | 0 | 0 | 0 | 0 |
Net income (loss) |  | 0 | 78,505 | 89,201 | 2,267 |
Amounts attributable to redeemable noncontrolling interests |  | 0 | (993) | (1,953) | (3,125) |
Amounts attributable to non-redeemable noncontrolling interests |  | 0 | (67,768) | (78,314) | 578 |
Net income (loss) available to Arch |  | 0 | 9,744 | 8,934 | (280) |
Preferred dividends |  | 0 | 0 | 0 | 0 |
Loss on redemption of preferred shares |  | 0 |  | 0 |  |
Net income (loss) available to Arch common shareholders |  | $ 0 | $ 9,744 | $ 8,934 | $ (280) |
Underwriting Ratios |  |  |  |  |  |
Loss ratio |  | 0.00% | 79.30% | 78.00% | 79.30% |
Acquisition expense ratio |  | 0.00% | 16.70% | 18.90% | 16.50% |
Other operating expense ratio |  | 0.00% | 10.00% | 9.90% | 10.20% |
Combined ratio |  | 0.00% | 106.00% | 106.80% | 106.00% |
Goodwill and intangible assets |  | $ 0 | $ 7,650 | $ 0 | $ 7,650 |
[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 The acquisition expense ratio is obtained by dividing acquisition costs, net of certain fee income, by net premiums earned. + References No definition available. + Details
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- Definition The combined ratio is defined as the sum of the loss ratio, acquisition expense ratio and the other operating expense ratio. + References No definition available. + Details
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- Definition Other operating expense ratio is obtained by dividing other operating expenses by net premiums earned. + References No definition available. + Details
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- Definition Income (loss) from agency and brokerage operations (includes sales of annuities and supplemental contracts); service charges, commissions, and fees from the sale of insurance and related services; and management fees from separate accounts, deferred annuities, and universal life products, and other underwriting related income (loss). + References No definition available. + Details
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- Definition Aggregate revenue less cost of goods and services sold or operating expenses directly attributable to the revenue generation activity. + References No definition available. + Details
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- Definition The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 230 -SubTopic 10 -Section 45 -Paragraph 28 -Subparagraph (b) -URI http://asc.fasb.org/extlink&oid=123570139&loc=d3e3602-108585 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 30 -Section 50 -Paragraph 2 -Subparagraph (a)(2) -URI http://asc.fasb.org/extlink&oid=66006027&loc=d3e16323-109275 Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 30 -Section 45 -Paragraph 2 -URI http://asc.fasb.org/extlink&oid=6388964&loc=d3e16225-109274 + Details
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- Definition This element represents acquisition-related costs incurred to effect a business combination which costs have been expensed during the period. Such costs include finder's fees; advisory, legal, accounting, valuation, and other professional or consulting fees; general administrative costs, including the costs of maintaining an internal acquisitions department; and may include costs of registering and issuing debt and equity securities. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 805 -SubTopic 10 -Section 25 -Paragraph 23 -URI http://asc.fasb.org/extlink&oid=123586518&loc=d3e1043-128460 + Details
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- Definition Amount of written premiums ceded to other entities. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 944 -SubTopic 605 -Section 50 -Paragraph 1 -Subparagraph (b)(3) -URI http://asc.fasb.org/extlink&oid=6486672&loc=d3e27261-158547 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 944 -SubTopic 605 -Section 50 -Paragraph 1 -Subparagraph (c)(2) -URI http://asc.fasb.org/extlink&oid=6486672&loc=d3e27261-158547 + Details
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