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Unaudited Condensed Quarterly Financial Information
 12 Months Ended
Dec. 31, 2020
Quarterly Financial Information Disclosure [Abstract]  
Unaudited Condensed Quarterly Financial Information Unaudited Condensed Quarterly Financial Information
The following table summarizes the 2020 and 2019 unaudited condensed quarterly financial information:
Fourth
Quarter
Third
Quarter
Second
Quarter
First
Quarter
Year Ended December 31, 2020
Net premiums written$1,758,015 $1,874,144 $1,668,311 $2,137,246 
Net premiums earned1,811,045 1,771,092 1,665,354 1,744,444 
Net investment income114,458 128,512 131,485 145,153 
Net realized gains (losses)353,333 280,499 556,588 (366,960)
Underwriting income (loss)220,987 96,604 (22,539)154,050 
Net income (loss) attributable to Arch543,544 419,039 298,821 144,117 
Preferred dividends(10,403)(10,403)(10,403)(10,403)
Net income (loss) available to Arch common shareholders533,141 408,636 288,418 133,714 
Net income (loss) per common share -- basic$1.32 $1.01 $0.72 $0.33 
Net income (loss) per common share -- diluted$1.30 $1.00 $0.71 $0.32 
Year Ended December 31, 2019
Net premiums written$1,455,453 $1,613,457 $1,444,898 $1,525,259 
Net premiums earned1,515,882 1,438,023 1,463,727 1,368,866 
Net investment income154,263 161,488 155,038 156,949 
Net realized gains (losses)40,830 61,355 120,757 140,256 
Underwriting income (loss)251,421 231,262 293,134 260,148 
Net income (loss) attributable to Arch326,384 392,453 468,954 448,528 
Preferred dividends(10,403)(10,403)(10,403)(10,403)
Net income (loss) available to Arch common shareholders315,981 382,050 458,551 438,125 
Net income (loss) per common share -- basic$0.78 $0.95 $1.14 $1.09 
Net income (loss) per common share -- diluted$0.76 $0.92 $1.12 $1.07