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.


	December 31, 2024
(dollars in thousands)	Amortized Cost		Gross Unrealized Holding Gains		Gross Unrealized Holding Losses		Estimated Fair Value
Fixed maturity securities:
U.S. Treasury securities	$	5,147,365	$	8,962	$	(68,469)	$	5,087,858
U.S. government-sponsored enterprises	1,445,171		2,976		(101,911)		1,346,236
Obligations of states, municipalities and political subdivisions	3,813,146		5,866		(199,520)		3,619,492
Foreign governments, agencies and supranationals	2,909,561		4,264		(207,302)		2,706,523
Agency mortgage-backed securities	2,771,589		2,096		(123,872)		2,649,813
Non-agency mortgage-backed securities	122,373		—		(4,343)		118,030
Corporate and university bonds	248,518		76		(31,007)		217,587
Total fixed maturity securities	16,457,723		24,240		(736,424)		15,745,539
Short-term investments	2,530,941		548		(6,579)		2,524,910
Investments, available-for-sale	$	18,988,664	$	24,788	$	(743,003)	$	18,270,449


	December 31, 2023
(dollars in thousands)	Amortized Cost		Gross Unrealized Holding Gains		Gross Unrealized Holding Losses		Estimated Fair Value
Fixed maturity securities:
U.S. Treasury securities	$	3,811,293	$	35,824	$	(62,404)	$	3,784,713
U.S. government-sponsored enterprises	1,225,426		7,292		(89,904)		1,142,814
Obligations of states, municipalities and political subdivisions	4,196,096		14,787		(181,578)		4,029,305
Foreign governments, agencies and supranationals	2,554,874		34,352		(142,008)		2,447,218
Agency mortgage-backed securities	2,507,682		8,939		(135,611)		2,381,010
Non-agency mortgage-backed securities	355,673		—		(22,603)		333,070
Corporate and university bonds	281,242		141		(26,781)		254,602
Total fixed maturity securities	14,932,286		101,335		(660,889)		14,372,732
Short-term investments	2,564,620		7,155		(393)		2,571,382
Investments, available-for-sale	$	17,496,906	$	108,490	$	(661,282)	$	16,944,114


	December 31, 2024
	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	$	1,593,711	$	(27,213)	$	1,444,869	$	(41,256)	$	3,038,580	$	(68,469)
U.S. government-sponsored enterprises	415,333		(10,938)		691,781		(90,973)		1,107,114		(101,911)
Obligations of states, municipalities and political subdivisions	1,133,275		(21,242)		2,024,298		(178,278)		3,157,573		(199,520)
Foreign governments, agencies and supranationals	1,056,877		(29,890)		1,246,215		(177,412)		2,303,092		(207,302)
Agency mortgage-backed securities	757,562		(13,880)		1,710,436		(109,992)		2,467,998		(123,872)
Non-agency mortgage-backed securities	—		—		118,030		(4,343)		118,030		(4,343)
Corporate and university bonds	2,107		(137)		212,404		(30,870)		214,511		(31,007)
Total fixed maturity securities	4,958,865		(103,300)		7,448,033		(633,124)		12,406,898		(736,424)
Short-term investments	163,503		(6,579)		—		—		163,503		(6,579)
Total	$	5,122,368	$	(109,879)	$	7,448,033	$	(633,124)	$	12,570,401	$	(743,003)

At December 31, 2024, the Company held 1,485 available-for-sale securities in an unrealized loss position with a total estimated fair value of $12.6 billion and gross unrealized losses of $743.0 million. Of these 1,485 securities, 966 securities had been in a continuous unrealized loss position for one year or longer and had a total estimated fair value of $7.4 billion and gross unrealized losses of $633.1 million.


	December 31, 2023
	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	$	317,027	$	(2,147)	$	1,507,784	$	(60,257)	$	1,824,811	$	(62,404)
U.S. government-sponsored enterprises	145,143		(2,134)		723,537		(87,770)		868,680		(89,904)
Obligations of states, municipalities and political subdivisions	679,124		(3,881)		2,332,281		(177,697)		3,011,405		(181,578)
Foreign governments, agencies and supranationals	83,396		(394)		1,492,912		(141,614)		1,576,308		(142,008)
Agency mortgage-backed securities	189,977		(1,872)		1,889,272		(133,739)		2,079,249		(135,611)
Non-agency mortgage-backed securities	—		—		333,070		(22,603)		333,070		(22,603)
Corporate and university bonds	—		—		236,205		(26,781)		236,205		(26,781)
Total fixed maturity securities	1,414,667		(10,428)		8,515,061		(650,461)		9,929,728		(660,889)
Short-term investments	52,601		(393)		—		—		52,601		(393)
Total	$	1,467,268	$	(10,821)	$	8,515,061	$	(650,461)	$	9,982,329	$	(661,282)

At December 31, 2023, the Company held 1,386 available-for-sale securities in an unrealized loss position with a total estimated fair value of $10.0 billion and gross unrealized losses of $661.3 million. Of these 1,386 securities, 1,131 securities had been in a continuous unrealized loss position for one year or longer and had a total estimated fair value of $8.5 billion and gross unrealized losses of $650.5 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 December 31, 2024 or 2023.

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.


(dollars in thousands)	Amortized Cost		Estimated Fair Value
Due in one year or less	$	1,593,149	$	1,571,022
Due after one year through five years	6,071,013		5,901,682
Due after five years through ten years	4,647,538		4,406,225
Due after ten years	1,252,061		1,098,767
	13,563,761		12,977,696
Mortgage-backed securities	2,893,962		2,767,843
Total fixed maturity securities	$	16,457,723	$	15,745,539

Expected maturities may differ from contractual maturities because borrowers may have the right to call or prepay obligations with or without penalties, and the holders may have the right to put the securities back to the issuer. Based on expected maturities, the estimated average duration of fixed maturity securities at December 31, 2024 was 3.9 years.


	Years Ended December 31,
(dollars in thousands)	2024		2023		2022
Interest:
Fixed maturity securities	$	510,044	$	383,022	$	294,417
Short-term investments	124,575		106,747		33,493
Cash and cash equivalents and restricted cash and cash equivalents	161,488		145,074		28,890
Dividends on equity securities	142,367		116,911		107,213
	938,474		751,754		464,013
Investment expenses	(17,978)		(17,222)		(17,258)
Net investment income	$	920,496	$	734,532	$	446,755

e) The following table presents the components of net investment gains (losses) included in net income (loss) and the pre-tax change in net unrealized losses included in other comprehensive income (loss). Gross realized investment gains and losses on fixed maturity securities, short-term investments and other investments were not material to the consolidated financial statements and are presented on a net basis in the following table.


	Years Ended December 31,
(dollars in thousands)	2024		2023		2022
Fixed maturity securities, short-term investments and other investments:
Net realized investment gains (losses)	$	4,423	$	(42,177)	$	(40,983)
Equity securities:
Change in fair value of securities sold during the period	(14,966)		34,684		(14,884)
Change in fair value of securities held at the end of the period	1,817,762		1,531,547		(1,539,866)
Total change in fair value	1,802,796		1,566,231		(1,554,750)
Net investment gains (losses)	$	1,807,219	$	1,524,054	$	(1,595,733)
Change in net unrealized losses on available-for-sale investments included in other comprehensive income (loss):
Fixed maturity securities	$	(152,630)	$	389,498	$	(1,474,890)
Short-term investments	(12,793)		1,060		11,014
Net increase (decrease)	$	(165,423)	$	390,558	$	(1,463,876)


	December 31,
(dollars in thousands)	2024		2023
Fixed maturity securities	$	3,027,863	$	3,102,899
Equity securities	915,242		1,004,347
Short-term investments	704,201		807,138
Restricted cash and cash equivalents	499,581		584,974
Total	$	5,146,887	$	5,499,358


	December 31,
(dollars in thousands)	2024		2023
Assets held in trust or on deposit to support underwriting activities	$	4,727,799	$	5,048,857
Assets pledged as security for letters of credit	419,088		450,501
Total	$	5,146,887	$	5,499,358

g) At December 31, 2024 and 2023, investments in securities issued by the U.S. Treasury, U.S. government agencies and U.S. government-sponsored enterprises were the only investments in any one issuer that exceeded 10% of shareholders' equity.