Pensionmetrics 2: Stochastic Pension Plan Design during the Distribution Phase1

We consider the choices available to a defined contribution (DC) pension plan member at the time of retirement for conversion of his pension fund into a stream of income in retirement. In particular, we compare the purchase at retirement age from a life office of a conventional life annuity (that is, a bond-based investment) with distribution programmes that involve differing exposures to equities during retirement. The residual fund at the time of the plan member’s death can either be bequested to his estate or, in exchange for the payment of survival credits while alive, reverts to the life office. We find that the best programme depends (unsurprisingly) on the plan member’s attitude to risk, with more risk-averse individuals preferring a greater investment in bonds or, in the limit, a conventional life annuity. For plan members with different degrees of risk aversion, we quantify the cost of holding a sub-optimal portfolio. More surprisingly, we find: • For the central values chosen for the bequest utility function, the plan member will favour an equity-linked annuity over an income drawdown policy. • For a given level of relative risk aversion, the optimal choice of programme is robust with respect to: – the weight attached by the plan member to the provision of a bequest; – differences between life-office mortality experience and the plan member’s subjective assessment of his own mortality prospects. Finally when we allow for a one-off switch from an initial, equity-linked programme into a fixed, level annuity, we find that the optimal switching age is critically dependent on both the plan member’s level of risk aversion and on recent equity performance.