Philip H. Dybvig, David T. Brown, and William J. Marshall
Controversy about the fairness of early transitions from traditional defined-benefit plans to cash-balance plans may have over-shadowed the subtleties of funding a cash-balance pension liability. Because crediting rates of cash-balance liabilities float with market rates, the same techniques used to value and hedge floating-rate bonds provide the present-value cost and effective duration of a cash-balance liability. The present-value cost of funding a liability varies dramatically across the menu of IRS-sanctioned crediting alternatives; the present value per \$1.00 of cash balance of funding a liability paying off 30 years from now varies between \$0.90 and \$1.48, given the yield curve from November 15, 1999. The effective duration of a cash-balance liability also varies dramatically across different crediting rates; the effective duration is typically positive but much shorter than the expected time until retirement or other payment and can vary by a factor of five or so depe nding on the choice of crediting rate. These results are useful for comparing the costs of different plans, for comparing how different groups are treated in a plan conversion, or for evaluating the riskiness of any mismatch between assets and liabilities for different funding alternatives.
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