The Cost and Duration of Cash-Balance Pension Plans

Controversy about the fairness of early transitions from traditional defined-benefit plans to cash-balance plans may have overshadowed 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. For example, given the yield curve from November 15, 1999, 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. The effective duration of a cash-balance liability also varies dramatically according to various crediting rates; the effective duration is typically positive but much shorter than the expected time until retirement or other payment and, depending on the choice of crediting rate, can vary by a factor of five or so. These findings are useful for comparing the costs of plans, for comparing how various groups are treated in a plan conversion, or for evaluating the riskiness of any mismatch between assets and liabilities for various funding alternatives. Cash-balance pension plans have become popular since first introduced by Bank of America in 1984. An employee's “cash balance” is the lump-sum accrued pension benefit that depends on both “pay-related credits” linked to salary or wages and “interest-related credits” linked to a market rate. The market rate is a constant-maturity U.S. Treasury bond or bill yield or discount or the U.S. Consumer Price Index. The interest-related credit is at a rate equal to the market rate or the market rate plus a fixed premium.Controversy about the fairness of early transitions from traditional defined-benefit plans to cash-balance plans may have overshadowed the subtleties of funding a cash-balance pension liability. We analyze the market-value cost (i.e., the present value at appropriate market interest rates) of a liability at a fixed maturity represented by $1.00 of cash balance today. This cost, projecting only future interest-related credits and no pay-related credits, is the appropriate present value of the final payoff. The cost is the fair-market-value analog of the projected benefit obligation in a traditional defined-benefit plan.For a cash-balance liability, an increase in interest rates affects value through two channels: increases in the growth rate of the liability over time and increases in the rate at which the terminal value is discounted. Because these two channels have opposite impacts on the value and only the second channel influences the value of a traditional defined-benefit plan, the effective duration of a cash-balance liability is much lower than the effective duration of a comparable traditional defined-benefit liability. Furthermore, the extent to which future crediting rates are expected to increase following an interest rate increase depends critically on the time to maturity of the crediting asset. For example, the increase in projected future 10-year bond yields over the next 10 years following an upward shift in the term structure of interest rates is greater than the expected increase in the projected future 30-year bond yields over the same 10 years.Using the Vasicek model of interest rates with parameters consistent with historical observed yield curves, we show that a 20-year liability credited at the 1-year Treasury rate has an effective duration of 0.4 years. The duration of a 20-year liability credited at the 30-year par Treasury yield has an effective duration of about 4.5 years. The effective duration of a cash-balance plan increases as the maturity of the crediting asset increases and is much less than the duration of a 20-year traditional defined-benefit liability.The cost of funding a cash-balance liability depends on the slope of the term structure of interest rates, the maturity of the crediting asset, and any margin. Although any mismatch between cost and cash balance is most pronounced when yield curves are very steep or inverted, a significant discrepancy can occur even when the yield curve is relatively flat. Using a “benchmark” Treasury yield curve from November 15, 1999, we compute the market-value cost of a cash-balance liability maturing in 20 years and crediting at the 30-year par Treasury yield to be $0.92 per dollar of cash balance. The $0.08 discount to the $1.00 cash balance means that the cost of funding the liability is 41 basis points a year less than the 20-year rate. The market-value cost of this liability is $0.97 per dollar of cash balance if it credits at the 10-year yield or $1.18 per dollar of cash balance if it credits at the 1-year rate plus the U.S. Internal Revenue Service guideline margin. Interestingly, nonzero IRS guideline margins tend to dominate the other effects and make cash-balance liabilities expensive to fund.