Employee Benefit Plans

a)The Company maintains defined contribution plans for employees of its U.S. insurance operations in accordance with Section 401(k) of the U.S. Internal Revenue Code of 1986. Employees of the Company's Markel Ventures subsidiaries are provided post-retirement benefits under separate plans. The Company also provides various defined contribution plans for employees of its international insurance and other operations, which are in line with local market terms and conditions of employment. Expenses relating to the Company's defined contribution plans were $41.8 million, $36.7 million and $30.1 million in 2018, 2017 and 2016, respectively.

b)The Terra Nova Pension Plan is a defined benefit plan which covers certain employees in the Company's international insurance operations who meet the eligibility conditions set out in the plan. The plan has been closed to new participants since 2001. The cost of providing pensions for employees is charged to earnings over the average working life of employees according to actuarial recommendations. Final benefits are based on the employee's years of credited service and the higher of pensionable compensation received in the calendar year preceding retirement or the best average pensionable compensation received in any three consecutive years in the ten years preceding retirement. Employees have not accrued benefits for future service in the Terra Nova Pension Plan since April 2012. The Company uses December 31 as the measurement date for the Terra Nova Pension Plan.

The following table summarizes the funded status of the Terra Nova Pension Plan and the amounts recognized on the accompanying consolidated balance sheets of the Company.



	Years Ended December 31,
(dollars in thousands)	2018			2017
Change in projected benefit obligation:
Projected benefit obligation at beginning of period	$	199,117		$	178,618
Interest cost	4,815			5,016
Benefits paid	(8,045		)	(5,644		)
Actuarial gain (loss)	(15,853		)	4,985
Effect of foreign currency rate changes	(8,537		)	16,142
Projected benefit obligation at end of year	$	171,497		$	199,117
Change in plan assets:
Fair value of plan assets at beginning of period	$	206,570		$	175,644
Actual gain (loss) on plan assets	(5,683		)	16,902
Employer contributions	3,368			3,393
Benefits paid	(8,045		)	(5,644		)
Effect of foreign currency rate changes	(9,246		)	16,275
Fair value of plan assets at end of year	$	186,964		$	206,570
Funded status of the plan	$	15,467		$	7,453
Net actuarial pension loss	$	74,604		$	77,567

Net actuarial pension loss is recognized as a component of accumulated other comprehensive income, net of taxes. The asset for pension benefits, also referred to as the funded status of the plan, at December 31, 2018 and 2017 was included in other assets on the consolidated balance sheets.

The following table presents the changes in plan assets and projected benefit obligation recognized in accumulated other comprehensive income.



	Years Ended December 31,
(dollars in thousands)	2018			2017			2016
Net actuarial gain (loss)	$	—		$	3,728		$	(25,243	)
Amortization of net actuarial loss	2,963			3,815			1,951
Tax benefit (expense)	(622		)	(1,284		)	4,192
Total other comprehensive income (loss)	$	2,341		$	6,259		$	(19,100	)

The following table summarizes the components of net periodic benefit income (loss) and the weighted average assumptions for the Terra Nova Pension Plan.



	Years Ended December 31,
(dollars in thousands)	2018			2017			2016
Components of net periodic benefit income (loss):
Interest cost	$	4,815		$	5,016		$	6,113
Expected return on plan assets	(8,782		)	(8,189		)	(9,124		)
Amortization of net actuarial pension loss	2,963			3,815			1,951
Net periodic benefit income (loss)	$	(1,004	)	$	642		$	(1,060	)
Weighted average assumptions as of December 31:
Discount rate	3.0		%	2.6		%	2.7		%
Expected return on plan assets	4.5		%	4.5		%	4.5		%
Rate of compensation increase	3.0		%	3.0		%	3.0		%

The projected benefit obligation and the net periodic benefit income (loss) are determined by independent actuaries using assumptions provided by the Company. In determining the discount rate, the Company uses the current yield on high-quality, fixed maturity investments that have maturities corresponding to the anticipated timing of estimated defined benefit payments. The expected return on plan assets is estimated based upon the anticipated average yield on plan assets using asset return assumptions for each asset class, and the cross-correlations between the asset classes, over a specified projection horizon. The rate of compensation increase is based upon historical experience and management's expectation of future compensation.

Management's discount rate and rate of compensation increase assumptions at December 31, 2018 were used to calculate the Company's projected benefit obligation. Management's discount rate, expected return on plan assets and rate of compensation increase assumptions at December 31, 2017 were used to calculate the net periodic benefit income for 2018. The Company estimates that net periodic benefit cost in 2019 will include an expense of $2.7 million resulting from the amortization of the net actuarial pension loss included as a component of accumulated other comprehensive loss at December 31, 2018.

The fair values of each of the plan's assets are measured using quoted prices in active markets for identical assets, which represent Level 1 inputs within the fair value hierarchy established in ASC 820. The following table summarizes the fair value of plan assets as of December 31, 2018 and 2017.



	December 31,
(dollars in thousands)	2018		2017
Plan assets:
Fixed maturity index funds	$	102,047	$	110,936
Equity security index funds	84,909		95,452
Cash and cash equivalents	8		182
Total	$	186,964	$	206,570

The Company's target asset allocation for the plan is 47% equity securities and 53% fixed maturities. At December 31, 2018, the actual allocation of assets in the plan was 45% equity securities and 55% fixed maturities. At December 31, 2017, the actual allocation of assets in the plan was 46% equity securities and 54% fixed maturities.

Investments are managed by a third party investment manager. Equity securities are invested in an index fund where 30% is indexed to U.K. equities and 70% is indexed to other markets. Assets are also invested in a mutual fund with a diversified global portfolio of equities, investment grade debt, property and cash. The primary objective of investing in these funds is to earn rates of return that are consistently in excess of inflation. Investing in equity securities, historically, has provided rates of return that are higher than investments in fixed maturities. Fixed maturity investments are allocated between five mutual funds; two index funds that include U.K. government securities, one index fund that includes securities issued by other foreign governments, one mutual fund that includes investment grade corporate bonds from the U.K. and foreign markets and one index fund that includes U.K. corporate securities. The assets in these funds are invested to meet the Company's obligations for current pensioners and those individuals nearing retirement. The plan does not invest in the Company's common shares.

At December 31, 2018 and 2017, the fair value of plan assets exceeded the plan's accumulated benefit obligation of $168.1 million and $195.1 million, respectively. The Company expects to make plan contributions of $3.4 million in 2019.

The benefits expected to be paid in each year from 2019 to 2023 are $3.8 million, $3.8 million, $3.9 million, $4.0 million and $4.1 million, respectively. The aggregate benefits expected to be paid in the five years from 2024 to 2028 are $22.0 million. The expected benefits to be paid are based on the same assumptions used to measure the Company's projected benefit obligation at December 31, 2018.