On the control of defined-benefit pension plans

Abstract

Conventionally, contribution rates for defined-benefit pension plans have been set with reference to funding levels without making allowance for current market interest rates: for example, on one-year bonds where rates of return on fund assets are not independent from one year to the next. We consider how to make use of market information to reduce contribution rate volatility. The purpose of this paper is to provide a model for determining an appropriate contribution rate for defined benefit pension plans under a model where interest rates are stochastic and rates of return are random.We extend previous work in two ways. First, we introduce a model for short-term interest rates, which can be used to help control contribution-rate volatility. Second, we model three assets rather than the usual one (cash, bonds and equities) to allow comparison of different asset strategies. We develop formulae for unconditional means and variances. We then discuss how variability can be controlled most efficiently by setting contribution rates with reference to current funding levels and interest rates.