Pensionmetrics: Stochastic Pension Plan Design During the Distribution Phase

We consider the choices available to a pension plan member at the time of retirement for conversion of his personal or defined contribution (DC) pension fund into a stream of income in retirement. In particular, we compare the purchase at retirement age of a conventional life annuity (that is, a bond-based investment) against a variety of programmes that involve differing exposures to equities during retirement. To make the comparison, we use stochastic modelling to evaluate the expected discounted utility associated with each programme as viewed by a policyholder on retirement. The simulation results demonstrate that the best programme depends (unsurprisingly) on the policyholder’s attitude to risk: if he is highly risk averse, the appropriate programme is a conventional life annuity; on the other hand, if he is more risk loving, the best programme involves a mixture of bonds and equities, with the optimal mix depending on the policyholder’s degree of risk aversion. We quantify the cost of holding a sub-optimal portfolio. More surprisingly, we find that: • The best programme pays a mortality bonus to the policyholder in return for which the residual fund reverts to the pension provider on the policyholder’s death. The best programme is therefore an annuity programme rather than an income drawdown programme that leaves a bequest to the policyholder’s survivors. • There are no investors for whom the best programme involves a derivativebased hedge to provide downside protection. • For a given level of relative risk aversion, the optimal choice of programme is robust relative to: the weight attached by the policyholder to the provision of a bequest; differences between life-office mortality rates and an individual’s assessment of his own mortality rates; the choice of utility function.