The gross unrecognized gains and losses on, amortized cost, allowance for credit losses, carrying amount, and fair value of, those investments classified as held-to-maturity at September 30, 2020 are summarized as follows:

	Amortized Cost		Allowance for Credit Losses			Carrying Amount		Gross Unrecognized Gains		Gross Unrecognized Losses			Fair Value
	(in thousands)
States and political subdivisions	$	471,913	$	(38	)	$	471,875	$	30,756	$	(8	)	$	502,623
Corporate bonds		70,721		(242	)		70,479		3,106		—			73,585
U.S. agency-based mortgage-backed securities		8,070		—			8,070		644		—			8,714
U.S. Treasury securities and obligations of U.S. government agencies		21,914		—			21,914		326		—			22,240
Asset-backed securities		178		(8	)		170		7		—			177
Totals	$	572,796	$	(288	)	$	572,508	$	34,839	$	(8	)	$	607,339

The gross unrealized gains and losses on, and the amortized cost, allowance for credit losses, and fair value of, those investments classified as available-for-sale at September 30, 2020 are summarized as follows:

	Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses			Fair Value		Allowance for Credit Losses
	(in thousands)
States and political subdivisions	$	257,169	$	18,235	$	(33	)	$	275,371	$	—
Corporate bonds		91,162		5,492		(25	)		96,629		—
U.S. agency-based mortgage-backed securities		23,850		460		—			24,310		—
U.S. Treasury securities and obligations of U.S. government agencies		28,882		1,045		—			29,927		—
Totals	$	401,063	$	25,232	$	(58	)	$	426,237	$	—

The gross unrealized gains and losses on, and the cost of equity securities at September 30, 2020 are summarized as follows:

The gross unrealized gains and losses on, and the amortized cost and fair value of, those investments classified as held-to-maturity at December 31, 2019 are summarized as follows:

	Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses			Fair Value
	(in thousands)
States and political subdivisions	$	466,270	$	19,570	$	(193	)	$	485,647
Corporate bonds		109,241		1,684		—			110,925
U.S. agency-based mortgage-backed securities		10,967		544		—			11,511
U.S. Treasury securities and obligations of U.S. government agencies		12,723		330		(12	)		13,041
Asset-backed securities		220		—		(1	)		219
Totals	$	599,421	$	22,128	$	(206	)	$	621,343

The gross unrealized gains and losses on, and the amortized cost and fair value of, those investments classified as available-for-sale at December 31, 2019 are summarized as follows:

	Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses			Fair Value
	(in thousands)
States and political subdivisions	$	225,895	$	11,906	$	(26	)	$	237,775
Corporate bonds		130,453		3,326		(1	)		133,778
U.S. agency-based mortgage-backed securities		29,499		64		(96	)		29,467
U.S. Treasury securities and obligations of U.S. government agencies		39,851		317		(42	)		40,126
Totals	$	425,698	$	15,613	$	(165	)	$	441,146

The gross unrealized gains and losses on, and the cost of equity securities at December 31, 2019 are summarized as follows:

A summary of the carrying amounts and fair value of investments in fixed maturity securities, classified as held-to-maturity, by contractual maturity, is as follows:

	September 30, 2020				December 31, 2019
	Carrying Amount		Fair Value		Carrying Amount		Fair Value
	(in thousands)
Maturity:
Within one year	$	63,982	$	64,630	$	49,967	$	50,348
After one year through five years		182,355		190,897		198,025		202,109
After five years through ten years		94,035		99,644		110,460		113,877
After ten years		223,896		243,277		229,782		243,279
U.S. agency-based mortgage-backed securities		8,070		8,714		10,967		11,511
Asset-backed securities		170		177		220		219
Totals	$	572,508	$	607,339	$	599,421	$	621,343

A summary of the amortized cost and fair value of investments in fixed maturity securities, classified as available-for-sale, by contractual maturity, is as follows:

	September 30, 2020				December 31, 2019
	Amortized Cost		Fair Value		Amortized Cost		Fair Value
	(in thousands)
Maturity:
Within one year	$	61,469	$	62,203	$	27,160	$	27,194
After one year through five years		90,936		96,406		144,142		146,469
After five years through ten years		56,622		60,484		47,175		49,419
After ten years		168,186		182,834		177,722		188,597
U.S. agency-based mortgage-backed securities		23,850		24,310		29,499		29,467
Totals	$	401,063	$	426,237	$	425,698	$	441,146

The following table summarizes the fair value and gross unrealized losses on securities classified as available-for-sale, aggregated by major investment category and length of time that the individual securities have been in a continuous unrealized loss position as of September 30, 2020:

	Less Than 12 Months				12 Months or Greater				Total
	Fair Value of Investments with Unrealized Losses		Gross Unrealized Losses		Fair Value of Investments with Unrealized Losses		Gross Unrealized Losses		Fair Value of Investments with Unrealized Losses		Gross Unrealized Losses
	(in thousands)
September 30, 2020
Available-for-Sale
Fixed maturity securities:
States and political subdivisions	$	4,329	$	33	$	—	$	—	$	4,329	$	33
Corporate bonds		2,511		25		—		—		2,511		25
Total available-for-sale securities	$	6,840	$	58	$	—	$	—	$	6,840	$	58

At September 30, 2020, we held 8 individual fixed maturity securities classified as available-for-sale that were in an unrealized loss position, of which none were in a continuous unrealized loss position for longer than 12 months.

The following table summarizes the fair value and gross unrealized losses on securities, aggregated by major investment category and length of time that the individual securities have been in a continuous unrealized loss position as of December 31, 2019:

	Less Than 12 Months				12 Months or Greater				Total
	Fair Value of Investments with Unrealized Losses		Gross Unrealized Losses		Fair Value of Investments with Unrealized Losses		Gross Unrealized Losses		Fair Value of Investments with Unrealized Losses		Gross Unrealized Losses
	(in thousands)
December 31, 2019
Held-to-Maturity
Fixed maturity securities:
States and political subdivisions	$	21,074	$	193	$	—	$	—	$	21,074	$	193
U.S. Treasury securities and obligations of U.S. government agencies		—		—		3,243		12		3,243		12
Asset-backed securities		—		—		68		1		68		1
Total held-to-maturity securities		21,074		193		3,311		13		24,385		206
Available-for-Sale
Fixed maturity securities:
States and political subdivisions	$	4,140	$	26	$	—	$	—	$	4,140	$	26
Corporate bonds		6,426		1		—		—		6,426		1
U.S. agency-based mortgage-backed securities		13,007		95		1,152		1		14,159		96
U.S. Treasury securities and obligations of U.S. government agencies		—		—		17,068		42		17,068		42
Total available-for-sale securities		23,573		122		18,220		43		41,793		165
Total	$	44,647	$	315	$	21,531	$	56	$	66,178	$	371

The following table illustrates the changes in the allowance for credit losses by major security type of the investments classified as held-to-maturity for the quarter ended September 30, 2020.

	States and Political Subdivisions			Corporate Bonds			U.S. Agency-Based Mortgage-Backed Securities		U.S. Treasury Securities and Obligations of U.S. Government Agencies		Asset-Backed Securities			Totals
	(in thousands)
Balance at June 30, 2020	$	49		$	299		$	—	$	—	$	9		$	357
Provision for credit loss benefit		(11	)		(57	)		—		—		(1	)		(69	)
Allowance for securities purchased with credit deterioration		—			—			—		—		—			—
Securities charged off		—			—			—		—		—			—
Recoveries		—			—			—		—		—			—
Balance at September 30, 2020	$	38		$	242		$	—	$	—	$	8		$	288

The following table illustrates the changes in the allowance for credit losses by major security type of the investments classified as held-to-maturity for the nine months ended September 30, 2020.

	States and Political Subdivisions			Corporate Bonds			U.S. Agency-Based Mortgage-Backed Securities		U.S. Treasury Securities and Obligations of U.S. Government Agencies		Asset-Backed Securities			Totals
	(in thousands)
Balance at January 1, 2020	$	45		$	245		$	—	$	—	$	11		$	301
Provision for credit loss benefit		(7	)		(3	)		—		—		(3	)		(13	)
Allowance for securities purchased with credit deterioration		—			—			—		—		—			—
Securities charged off		—			—			—		—		—			—
Recoveries		—			—			—		—		—			—
Balance at September 30, 2020	$	38		$	242		$	—	$	—	$	8		$	288

The Company has established an allowance for credit losses on 400 held-to-maturity securities totaling $0.3 million. The majority of those securities were states and political subdivisions and corporate bonds at 369 and 28, respectively.

The Company has no allowance for credit losses on investments classified as available-for-sale for the period ended September 30, 2020.

The credit rating used for held-to-maturity fixed income securities is the rating for each security as published by Moody’s, S&P, and Fitch to determine the probability of default. If there are two ratings, the lower rating is used. If there are three ratings, the median rating is used. If there is one rating, that rating is used. For corporate fixed income securities the probability of default (given a rating) comes from Moody’s annual study of corporate bond defaults published each February. The maximum maturity using the default rate is 20 years (any maturity greater than 20 years will use the 20-year rate). For municipal fixed income securities the probability of default (given a rating) comes from Moody’s annual study of municipal bond defaults published each July/August.

The calculation of the credit loss allowance takes the amortized cost of the fixed income security and assumes default and recovery based on the average recovery rates from the Moody’s default studies. The amortized cost of the security, minus the amount recovered, is the estimated full amount the Company could lose in a default scenario. Then this amount is multiplied by the probability of default to determine the allowance for credit loss. The lower the security is rated, the higher likelihood of default, and therefore a higher allowance for credit loss. The longer to the maturity date of a security, the higher the default risk.

The table below presents the amortized cost of held-to-maturity securities aggregated by credit quality indicator as of September 30, 2020.

	States and Political Subdivisions		Corporate Bonds		U.S. Agency-Based Mortgage-Backed Securities		U.S. Treasury Securities and Obligations of U.S. Government Agencies		Asset-Backed Securities		Totals
	Amortized cost
	(in thousands)
AAA/AA/A ratings	$	469,485	$	30,085	$	8,070	$	21,914	$	124	$	529,678
Baa/BBB ratings		2,428		40,636		—		—		18		43,082
B ratings		—		—		—		—		36		36
Total	$	471,913	$	70,721	$	8,070	$	21,914	$	178	$	572,796

Net realized gains in the quarter ended September 30, 2020 were $0.3 million resulting from the call of fixed maturity securities. Net realized losses in the quarter ended September 30, 2019 were immaterial.

Net realized gains in the nine months ended September 30, 2020 were $1.5 million resulting primarily from the sale of fixed maturity securities classified as available-for-sale and from called fixed maturity securities. Net realized losses in the nine months ended September 30, 2019 were immaterial.

During the third quarter of 2020, we recognized through income $0.8 million of net unrealized gains on equity securities held as of September 30, 2020. During the third quarter of 2019, we recognized through income $0.4 million of net unrealized gains on equity securities held as of September 30, 2019.

During the nine months ended September 30, 2020, we recognized through income $2.3 million of net unrealized losses on equity securities held as of September 30, 2020. During the nine months ended September 30, 2019, we recognized through income $3.2 million of net unrealized gains on equity securities held as of September 30, 2019.

Investment income is recognized as it is earned. The discount or premium on fixed maturity securities is amortized using the “constant yield” method. Anticipated prepayments, where applicable, are considered when determining the amortization of premiums or discounts. Realized investment gains and losses are determined using the specific identification method.