a) The following tables summarize the Company's available-for-sale investments. Commercial and residential 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, 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	1,858,845		21,450		(96,874)		1,783,421
Commercial mortgage-backed securities	2,371,406		8,605		(136,353)		2,243,658
Residential mortgage-backed securities	491,949		334		(21,861)		470,422
Corporate bonds	977,271		13,043		(71,915)		918,399
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, 2022
(dollars in thousands)	Amortized Cost		Gross Unrealized Holding Gains		Gross Unrealized Holding Losses		Estimated Fair Value
Fixed maturity securities:
U.S. Treasury securities	$	3,050,089	$	2,363	$	(138,493)	$	2,913,959
U.S. government-sponsored enterprises	871,463		154		(106,079)		765,538
Obligations of states, municipalities and political subdivisions	3,973,911		6,503		(247,231)		3,733,183
Foreign governments	1,473,658		2,843		(169,723)		1,306,778
Commercial mortgage-backed securities	2,109,721		395		(169,668)		1,940,448
Residential mortgage-backed securities	553,591		6		(26,804)		526,793
Corporate bonds	773,454		836		(104,154)		670,136
Total fixed maturity securities	12,805,887		13,100		(962,152)		11,856,835
Short-term investments	2,663,560		5,760		(58)		2,669,262
Investments, available-for-sale	$	15,469,447	$	18,860	$	(962,210)	$	14,526,097


	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	49,056		(128)		1,113,616		(96,746)		1,162,672		(96,874)
Commercial mortgage-backed securities	169,557		(1,792)		1,790,637		(134,561)		1,960,194		(136,353)
Residential mortgage-backed securities	20,420		(80)		431,705		(21,781)		452,125		(21,861)
Corporate bonds	34,340		(266)		615,501		(71,649)		649,841		(71,915)
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.


	December 31, 2022
	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	$	735,605	$	(30,583)	$	1,907,922	$	(107,910)	$	2,643,527	$	(138,493)
U.S. government-sponsored enterprises	413,495		(40,488)		331,391		(65,591)		744,886		(106,079)
Obligations of states, municipalities and political subdivisions	2,474,289		(164,537)		348,943		(82,694)		2,823,232		(247,231)
Foreign governments	900,322		(115,324)		300,423		(54,399)		1,200,745		(169,723)
Commercial mortgage-backed securities	1,611,603		(117,482)		305,217		(52,186)		1,916,820		(169,668)
Residential mortgage-backed securities	516,423		(25,232)		9,342		(1,572)		525,765		(26,804)
Corporate bonds	498,406		(74,595)		153,035		(29,559)		651,441		(104,154)
Total fixed maturity securities	7,150,143		(568,241)		3,356,273		(393,911)		10,506,416		(962,152)
Short-term investments	774,480		(58)		—		—		774,480		(58)
Total	$	7,924,623	$	(568,299)	$	3,356,273	$	(393,911)	$	11,280,896	$	(962,210)

At December 31, 2022, the Company held 1,400 available-for-sale securities in an unrealized loss position with a total estimated fair value of $11.3 billion and gross unrealized losses of $962.2 million. Of these 1,400 securities, 246 securities had been in a continuous unrealized loss position for one year or longer and had a total estimated fair value of $3.4 billion and gross unrealized losses of $393.9 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, 2023 or 2022.

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	$	1,192,021	$	1,179,344
Due after one year through five years	5,033,324		4,917,770
Due after five years through ten years	4,320,467		4,159,846
Due after ten years	1,523,119		1,401,692
	12,068,931		11,658,652
Commercial mortgage-backed securities	2,371,406		2,243,658
Residential mortgage-backed securities	491,949		470,422
Total fixed maturity securities	$	14,932,286	$	14,372,732

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, 2023 was 4.1 years.


	Years Ended December 31,
(dollars in thousands)	2023		2022		2021
Interest:
Fixed maturity securities	$	383,022	$	294,417	$	283,366
Short-term investments	106,747		33,493		2,475
Cash and cash equivalents	145,074		28,890		479
Dividends on equity securities	116,911		107,213		98,099
	751,754		464,013		384,419
Investment expenses	(17,222)		(17,258)		(17,002)
Net investment income	$	734,532	$	446,755	$	367,417

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 gains (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)	2023		2022		2021
Fixed maturity securities, short-term investments and other investments:
Net realized investment gains (losses)	$	(42,177)	$	(40,983)	$	37,908
Equity securities:
Change in fair value of securities sold during the period	34,684		(14,884)		25,902
Change in fair value of securities held at the end of the period	1,531,547		(1,539,866)		1,914,724
Total change in fair value	1,566,231		(1,554,750)		1,940,626
Net investment gains (losses)	$	1,524,054	$	(1,595,733)	$	1,978,534
Change in net unrealized gains (losses) on available-for-sale investments included in other comprehensive income (loss):
Fixed maturity securities	$	389,498	$	(1,474,890)	$	(504,133)
Short-term investments	1,060		11,014		(8,951)
Net increase (decrease)	$	390,558	$	(1,463,876)	$	(513,084)


	December 31,
(dollars in thousands)	2023		2022
Fixed maturity securities	$	3,102,899	$	2,773,386
Equity securities	1,004,347		843,719
Short-term investments	807,138		543,737
Restricted cash and cash equivalents	584,974		1,084,081
Total	$	5,499,358	$	5,244,923


	December 31,
(dollars in thousands)	2023		2022
Assets held in trust or on deposit to support underwriting activities	$	5,048,857	$	4,807,135
Assets pledged as security for letters of credit	450,501		437,788
Total	$	5,499,358	$	5,244,923

g) At December 31, 2023 and 2022, 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.