Moving average rates of return and the variability of pension contributions and fund levels for a defined benefit pension scheme

A mathematical model is described which facilitates the comparison of different pension funding methods for a defined benefit pension scheme. Real investment rates of return to the pension fund are assumed to be represented by a moving average model for the corresponding force of interest. Expressions for the moments of the contribution and fund level are then derived. This leads to a discussion of methods of funding which are optimal in the sense of choosing the period for spreading surpluses and deficiencies in order to reduce the variability of both contributions and fund levels. The results are compared with those obtained when the investment returns are independent and identically distributed or autoregressive and, in this sense, the paper is a natural successor to Haberman (1994).