Income Drawdown Schemes for a Defined-Contribution Pension Plan

In retirement a pensioner must often decide how much money to withdraw from a pension fund, how to invest the remaining funds, and whether to purchase an annuity. These decisions are addressed here by introducing a number of income drawdown schemes, which are relevant to a defined-contribution personal pension plan. Rather than assume that drawdown is at a constant rate fixed at retirement, we describe pension schemes which maintain the expected level of the pension fund over the drawdown period, whilst investing the fund in a portfolio of a risky and riskless asset. Since the pensioner takes on investment risk, we find the optimal asset allocation which minimises the expected loss of the pensioner as measured by the performance of the pension fund against a benchmark. Two benchmarks are considered: a risk-free investment and the price of an annuity. If income drawdown is proportional to the fund performance then the optimal fund performance has positive drift. The fair-value drawdown rate is defined so that the fund performance is a martingale under the objective measure. Annuitisation should occur if the expected fair-value drawdown rate falls below the annuity rate available at retirement. Since the pensioner takes on investment risk, the annuitisation age depends on the risk preferences of the individual. As an illustration, the annuitisation age is calculated for a Gompertz mortality distribution function and a power law loss function