Two Stage Decumulation Strategies for DC Plan Investors: 'A Goal Properly Set Is Halfway Reached'

Abstract

Optimal stochastic control methods are used to examine decumulation strategies for a defined contribution (DC) plan retiree. An initial investment horizon of fifteen years is considered, since the retiree will attain this age with high probability. The objective function reward measure is the expected sum of the withdrawals. The objective function tail risk measure is the expected linear shortfall with respect to a desired lower bound for wealth at fifteen years. The lower bound wealth level is the amount which is required to fund a lifelong annuity fifteen years after retirement, which generates the required minimum cash flows. This ameliorates longevity risk. The controls are the withdrawal amount each year, and the asset allocation strategy. Maximum and minimum withdrawal amounts are specified. Specifying a short initial decumulation horizon, results in the optimal strategy achieving: (i) median withdrawals at the maximum rate within 2-3 years of retirement (ii) terminal wealth larger than the desired lower bound at fifteen years, with greater than $90\%$ probability and (iii) median terminal wealth at fifteen years considerably larger than the desired lower bound. The controls are computed using a parametric model of historical stock and bond returns, and then tested in bootstrap resampled simulations using historical data. At the fifteen year investment horizon, the retiree has the option of (i) continuing to self-manage the decumulation policy or (ii) purchasing an annuity.