Risk Measures for Defined Contribution (DC) Pension Plan Decumulation

Optimal decumulation of a Defined Contribution (DC) pension plan can be viewed as a problem in optimal stochastic control, which requires specification of an objective function, a combination of reward and risk. An intuitive specification of reward is the sum of withdrawals over the retirement period. This article investigates three tail risk measures for running out of savings in a DC plan decumulation strategy, which includes (i) expected shortfall, (ii) linear shortfall, and (iii) probability of shortfall. From the perspective of all optimal solutions, we establish that, under suitable regularity assumptions, the set of optimal controls corresponding to all expected reward expected shortfall Pareto efficient frontier curves is identical to the set of optimal controls associated with all expected reward and linear shortfall Pareto efficient frontier curves. To better understand the impact of a chosen risk measure, we compare its optimal controls across all three combinations of risk measures and reward performance criteria, while fixing the values of the risk aversion and wealth/probability level parameters at reasonable levels. This comparison reveals a clear preference for the linear shortfall risk measure, which yields more desirable optimal strategies. From a practical point of view, we show that allowing variable withdrawals has a large effect on reducing risk, compared to dynamic asset allocation.