Market Consistent Valuation of Cash Balance Liabilities

MarketConsistentValuationofCashBalance Liabilities M R Hardy, D Saunders & X Zhu Statistics and Actuarial Science, University of Waterloo. April 26, 2013 Abstract Cash balance (CB) pension benefits are accumulated at guaranteed crediting rates, usually based on interest rates on government securities. Viewed as a financial liability, the benefit is a form of interest rate derivative, which can be valued using financial models and theory. In this paper, we consider the value using the Hull White interest rate model, and explore the risks associated with different crediting rate choices. The results indicate that the CB liability is rather larger than emerges from traditional actuarial methods, and, further, that the most popular choices for crediting rates are also the most risky, from

a perspective of volatility in the liability value. 1 Introduction Cash Balance (CB) pension plans play a highly significant role in US employer-sponsored pension provision. According to the US Department of Labor Employee Benefits Security Administration (EBSA, 2012), in 2010 there were over 12 million participants in Cash Balance pension plans, representing around 9% of the total number of participants in any employer sponsored plan. The Cash Balance design started to become popular in the US during the late 1990’s, when several large employers shifted their final salary DB plans to Cash Balance plans. The attraction of Cash Balance plans for employers is very similar to the attraction of De- fined Contribution plans (DC). Both ostensibly involve the payment of employer/employee 1 contributions into a fund for each member; the fund accumulates over time to create a lump sum benefit at the member’s retirement. The benefit may be annuitized, but the rates for conversion are determined at retirement. The difference between the CB plan and the DC plan is that the DC contributions are invested in assets, and the interest on the assets is passed back to the employee. In the CB plan, the interest earned on the employee’s account is fixed in advance, either in absolute terms, or in terms of a market rate applying at each crediting date. So, for example, the employer may specify that all member accounts will earn 6% per year until retirement, or that the interest rate applied at each year end will be the published yield on 5-year government bonds, with an additional margin of, say, 0.25%. This specification of the crediting rate results in a benefit that is classified under US regulation as a Defined Benefit plan, not a Defined Contribution plan. This regulatory situation has been a motivating factor in some transitions from traditional DB to Cash Balance, as the requirements for changing from one type of DB plan to another are much less onerous in many cases, than switching from DB to DC, with apparently similar benefits to the employer. Much has been written about Cash Balance plans, in the financial and accounting literature, and in actuarial notes and monographs. In the 1990s and early 2000s, the literature focussed on the impact on employers and plan members of the decision to move from traditional DB to CB. Kopp and Sher (1998) compared the benefits from traditional DB...

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