| Investments |
Investments a) The following tables summarize the Company's available-for-sale investments. Agency mortgage-backed securities include securities issued by U.S. government-sponsored enterprises and U.S. government agencies. The net unrealized holding gains (losses) in the tables below are presented before taxes.
| | | | | | | | | | | | | | | | | | | | | | | | | | | September 30, 2026 | | (dollars in thousands) | Amortized
Cost | | Gross
Unrealized
Holding
Gains | | Gross
Unrealized
Holding
Losses | | | | Estimated
Fair
Value | | Fixed maturity securities: | | | | | | | | | | | U.S. Treasury securities | $ | 5,950,970 | | | $ | 288 | | | $ | (158,604) | | | | | $ | 5,792,654 | | | U.S. government-sponsored enterprises | 1,704,119 | | | 793 | | | (122,563) | | | | | 1,582,349 | | | Obligations of states, municipalities, and political subdivisions | 3,619,917 | | | 572 | | | (244,861) | | | | | 3,375,628 | | | Foreign governments, agencies, and supranationals | 3,542,488 | | | 25,387 | | | (190,045) | | | | | 3,377,830 | | | Agency mortgage-backed securities | 3,116,267 | | | 95 | | | (166,613) | | | | | 2,949,749 | | | Non-agency mortgage-backed securities | 44,236 | | | — | | | (974) | | | | | 43,262 | | | Corporate and university bonds | 204,892 | | | 39 | | | (31,341) | | | | | 173,590 | | | Total fixed maturity securities | 18,182,889 | | | 27,174 | | | (915,001) | | | | | 17,295,062 | | | Short-term investments | 2,771,422 | | | 2,791 | | | (5,121) | | | | | 2,769,092 | | | Investments, available-for-sale | $ | 20,954,311 | | | $ | 29,965 | | | $ | (920,122) | | | | | $ | 20,064,154 | |
| | | | | | | | | | | | | | | | | | | | | | | | | December 31, 2025 | | (dollars in thousands) | Amortized
Cost | | Gross
Unrealized
Holding
Gains | | Gross
Unrealized
Holding
Losses | | Estimated
Fair
Value | | Fixed maturity securities: | | | | | | | | | U.S. Treasury securities | $ | 5,877,779 | | | $ | 63,769 | | | $ | (13,641) | | | $ | 5,927,907 | | | U.S. government-sponsored enterprises | 1,678,599 | | | 19,378 | | | (57,743) | | | 1,640,234 | | | Obligations of states, municipalities, and political subdivisions | 3,743,154 | | | 34,871 | | | (105,557) | | | 3,672,468 | | | Foreign governments, agencies, and supranationals | 3,359,014 | | | 89,595 | | | (73,694) | | | 3,374,915 | | | Agency mortgage-backed securities | 2,935,758 | | | 24,903 | | | (59,541) | | | 2,901,120 | | | Non-agency mortgage-backed securities | 66,296 | | | — | | | (538) | | | 65,758 | | | Corporate and university bonds | 235,318 | | | 368 | | | (20,102) | | | 215,584 | | | Total fixed maturity securities | 17,895,918 | | | 232,884 | | | (330,816) | | | 17,797,986 | | | Short-term investments | 2,029,650 | | | 4,632 | | | (620) | | | 2,033,662 | | | Investments, available-for-sale | $ | 19,925,568 | | | $ | 237,516 | | | $ | (331,436) | | | $ | 19,831,648 | |
b) The following tables summarize gross unrealized investment losses on available-for-sale investments by the length of time that securities have continuously been in an unrealized loss position.
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | September 30, 2026 | | Less than 12 months | | 12 months or longer | | Total | | (dollars in thousands) | Estimated
Fair
Value | | Gross
Unrealized
Holding Losses | | Estimated
Fair
Value | | Gross
Unrealized
Holding Losses | | Estimated
Fair
Value | | Gross Unrealized Holding Losses | | Fixed maturity securities: | | | | | | | | | | | | | U.S. Treasury securities | $ | 4,389,125 | | | $ | (113,882) | | | $ | 986,030 | | | $ | (44,722) | | | $ | 5,375,155 | | | $ | (158,604) | | | U.S. government-sponsored enterprises | 789,093 | | | (32,862) | | | 722,508 | | | (89,701) | | | 1,511,601 | | | (122,563) | | | Obligations of states, municipalities, and political subdivisions | 1,754,504 | | | (83,762) | | | 1,455,084 | | | (161,099) | | | 3,209,588 | | | (244,861) | | | Foreign governments, agencies, and supranationals | 1,491,510 | | | (68,271) | | | 1,038,467 | | | (121,774) | | | 2,529,977 | | | (190,045) | | | Agency mortgage-backed securities | 1,662,303 | | | (78,033) | | | 1,230,123 | | | (88,580) | | | 2,892,426 | | | (166,613) | | | Non-agency mortgage-backed securities | 5,760 | | | (102) | | | 37,502 | | | (872) | | | 43,262 | | | (974) | | | Corporate and university bonds | 6,626 | | | (272) | | | 164,275 | | | (31,069) | | | 170,901 | | | (31,341) | | | Total fixed maturity securities | 10,098,921 | | | (377,184) | | | 5,633,989 | | | (537,817) | | | 15,732,910 | | | (915,001) | | | Short-term investments | 2,537,436 | | | (5,121) | | | — | | | — | | | 2,537,436 | | | (5,121) | | | Total | $ | 12,636,357 | | | $ | (382,305) | | | $ | 5,633,989 | | | $ | (537,817) | | | $ | 18,270,346 | | | $ | (920,122) | |
At September 30, 2026, the Company held 1,663 available-for-sale securities in an unrealized loss position with a total estimated fair value of $18.3 billion and gross unrealized losses of $920.1 million. Of these 1,663 securities, 716 securities had been in a continuous unrealized loss position for one year or longer and had a total estimated fair value of $5.6 billion and gross unrealized losses of $537.8 million.
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | December 31, 2025 | | Less than 12 months | | 12 months or longer | | Total | | (dollars in thousands) | Estimated
Fair
Value | | Gross Unrealized Holding Losses | | Estimated
Fair
Value | | Gross Unrealized Holding Losses | | Estimated
Fair
Value | | Gross Unrealized Holding Losses | | Fixed maturity securities: | | | | | | | | | | | | | U.S. Treasury securities | $ | 197,135 | | | $ | (470) | | | $ | 1,275,453 | | | $ | (13,171) | | | $ | 1,472,588 | | | $ | (13,641) | | | U.S. government-sponsored enterprises | 108,490 | | | (112) | | | 802,349 | | | (57,631) | | | 910,839 | | | (57,743) | | | Obligations of states, municipalities, and political subdivisions | 184,124 | | | (970) | | | 1,871,154 | | | (104,587) | | | 2,055,278 | | | (105,557) | | | Foreign governments, agencies, and supranationals | 214,787 | | | (1,008) | | | 1,181,298 | | | (72,686) | | | 1,396,085 | | | (73,694) | | | Agency mortgage-backed securities | 156,553 | | | (701) | | | 1,446,048 | | | (58,840) | | | 1,602,601 | | | (59,541) | | | Non-agency mortgage-backed securities | 5,889 | | | (6) | | | 59,869 | | | (532) | | | 65,758 | | | (538) | | | Corporate and university bonds | 20,488 | | | (174) | | | 180,290 | | | (19,928) | | | 200,778 | | | (20,102) | | | Total fixed maturity securities | 887,466 | | | (3,441) | | | 6,816,461 | | | (327,375) | | | 7,703,927 | | | (330,816) | | | Short-term investments | 59,179 | | | (620) | | | — | | | — | | | 59,179 | | | (620) | | | Total | $ | 946,645 | | | $ | (4,061) | | | $ | 6,816,461 | | | $ | (327,375) | | | $ | 7,763,106 | | | $ | (331,436) | |
At December 31, 2025, the Company held 948 available-for-sale securities in an unrealized loss position with a total estimated fair value of $7.8 billion and gross unrealized losses of $331.4 million. Of these 948 securities, 851 securities had been in a continuous unrealized loss position for one year or longer and had a total estimated fair value of $6.8 billion and gross unrealized losses of $327.4 million. The Company completes a detailed analysis each quarter to assess whether the decline in the fair value of any investment below its cost basis is the result of a credit loss. All available-for-sale securities with unrealized losses are reviewed. The Company considers many factors in completing its quarterly review of securities with unrealized losses for credit-related impairment to determine whether a credit loss exists, including the extent to which fair value is below cost, the implied yield to maturity, rating downgrades of the security, and whether or not the issuer has failed to make scheduled principal or interest payments. The Company also takes into consideration information about the financial condition of the issuer and industry factors that could negatively impact the issuer.
If the decline in fair value of an available-for-sale security below its amortized cost is considered to be the result of a credit loss, the Company compares the estimated present value of the cash flows expected to be collected to the amortized cost of the security. The extent to which the estimated present value of the cash flows expected to be collected is less than the amortized cost of the security represents the credit loss, which is recorded as an allowance and recognized in net income. The allowance is limited to the difference between the fair value and the amortized cost of the security. Any remaining decline in fair value represents the non-credit portion of the impairment, which is recognized in other comprehensive income. The Company did not have an allowance for credit losses for any available-for-sale securities as of September 30, 2026 or December 31, 2025. As of September 30, 2026 and December 31, 2025, gross unrealized losses on available-for-sale securities were the result of declines in the fair value of the investments due to increases in interest rates, which are expected to reverse as the securities mature, and foreign currency movements related to available-for-sale securities denominated in a foreign currency.
Quarterly, the Company also considers whether it intends to sell an available-for-sale security or if it is more likely than not that it will be required to sell a security before recovery of its amortized cost. In these instances, a decline in fair value is recognized in net income based on the fair value of the security at the time of assessment, resulting in a new cost basis for the security.
c) The amortized cost and estimated fair value of fixed maturity securities at September 30, 2026 are shown below by contractual maturity.
| | | | | | | | | | | | | (dollars in thousands) | Amortized
Cost | | Estimated
Fair Value | | Due in one year or less | $ | 2,084,296 | | | $ | 2,083,791 | | | Due after one year through five years | 6,576,638 | | | 6,341,782 | | | Due after five years through ten years | 5,156,621 | | | 4,836,669 | | | Due after ten years | 1,204,831 | | | 1,039,809 | | | 15,022,386 | | | 14,302,051 | | Mortgage-backed securities | 3,160,503 | | | 2,993,011 | | | Total fixed maturity securities | $ | 18,182,889 | | | $ | 17,295,062 | |
d) The following table presents the components of net investment income.
| | | | | | | | | | | | | | | | | | | | | | | | | Quarter Ended September 30, | | Nine Months Ended September 30, | | (dollars in thousands) | 2026 | | 2025 | | 2026 | | 2025 | | Interest: | | | | | | | | | Fixed maturity securities | $ | 171,041 | | | $ | 155,645 | | | $ | 504,561 | | | $ | 444,819 | | | Short-term investments | 21,981 | | | 19,406 | | | 56,784 | | | 58,659 | | | Cash and cash equivalents and restricted cash and cash equivalents | 30,054 | | | 37,483 | | | 89,307 | | | 112,980 | | | Dividends on equity securities | 38,182 | | | 35,762 | | | 131,345 | | | 110,769 | | | 261,258 | | | 248,296 | | | 781,997 | | | 727,227 | | | Investment expenses | (3,143) | | | (2,621) | | | (11,869) | | | (14,448) | | | Net investment income | $ | 258,115 | | | $ | 245,675 | | | $ | 770,128 | | | $ | 712,779 | |
e) The following table presents the components of net investment gains (losses) included in net income and the change in net unrealized losses included in other comprehensive income (loss). Gross realized investment gains and losses on fixed maturity securities and short-term investments were not material to the consolidated financial statements and are presented on a net basis in the following table.
| | | | | | | | | | | | | | | | | | | | | | | | | Quarter Ended September 30, | | Nine Months Ended September 30, | | (dollars in thousands) | 2026 | | 2025 | | 2026 | | 2025 | Fixed maturity securities and short-term investments: | | | | | | | | | Net realized investment gains (losses) | $ | (523) | | | $ | 4,695 | | | $ | (1,413) | | | $ | (13,702) | | | Equity securities: | | | | | | | | | Change in fair value of securities sold during the period | (177) | | | (1,795) | | | 20,750 | | | 1,345 | | | Change in fair value of securities held at the end of the period | (280,209) | | | 429,986 | | | 139,717 | | | 876,395 | | | Total change in fair value | (280,386) | | | 428,191 | | | 160,467 | | | 877,740 | | | Net investment gains (losses) | $ | (280,909) | | | $ | 432,886 | | | $ | 159,054 | | | $ | 864,038 | | | Change in net unrealized losses on available-for-sale investments included in other comprehensive income (loss): | | | | | | | | | Fixed maturity securities | $ | (551,827) | | | $ | 60,844 | | | $ | (789,895) | | | $ | 585,862 | | | Short-term investments | 1,411 | | | (1,021) | | | (6,342) | | | 9,517 | | | Net increase (decrease) | $ | (550,416) | | | $ | 59,823 | | | $ | (796,237) | | | $ | 595,379 | |
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