Mean-Variance Analysis in Post-Retirement Planning

Abstract

In this study we analyze the variability and average level ofspending in retirement under two strategies: the popular “4% rule” and what we will term the self-funded variableannuity strategy (SVA strategy). The 4% rule stipulates thateach year a retiree should spend 4% of her initial wealthat retirement; the value of spending grows with the rateof inflation. Under the SVA strategy, each year the retireedetermines her spending level as equivalent to the incomeshe could theoretically obtain by purchasing an annuity(but without actually purchasing one). The 4% rule entailslower average spending and little variability, while theSVA strategy entails higher average spending and highervariability.

The SVA strategy is based on a theoretical foundationof expected utility maximization. We demonstrate howa retiree can make an informed decision about allocatingamong stocks, bonds, and annuities, and whether to combinethe 4% spending rule with the SVA strategy to achievehigher average spending. In particular, if future returns turnout to be lower than historical returns, as many experts predict,combining the 4% rule and SVA strategy may achievespending of more than 4% of initial wealth on average whilereducing the failure rate to less than 10%. We also considerhow mortality might affect a mixed strategy that combinesa purchased annuity with the SVA strategy.