The 4 percent Strategy Revisited: A Pre-Commitment Optimal Mean-Variance Approach to Wealth Management

Abstract

In contrast to single-period mean-variance portfolio allocation, optimal multi-period mean-variance allocation can be modified slightly to be effectively a down-side risk measure. With this in mind, we consider optimal multi-period mean-variance portfolio allocation in the presence of periodic withdrawals. The investment portfolio can be allocated between a risk-free investment and a risky asset. The risky asset is assumed to follow a jump diffusion process. We consider two wealth management applications, namely optimal de-accumulation rates for a defined contribution pension plan, and sustainable withdrawal rates for an endowment. Compared with a constant proportions strategy, the optimal mean-variance policy achieves the same expected wealth at the end of the investment horizon, while significantly reducing the standard deviation and probability of shortfall.

Keywords: multi-period mean-variance optimal, endowment, pension de-accumulation