A Dynamic-Programming Approach to Multiperiod Asset Allocation

Abstract

Academicians and practitioners recently have focused a great deal of attention on the issue of retirement asset allocation. However, research on the academic side typically has assumed a static allocation of a fixed amount over the investor's lifetime, while the advice on the practitioner side has been largely ad hoc in nature. Moreover, both academics and practitioners often fail to link allocations to the individual's attitude toward risk. This paper uses several performance measures that incorporate the individual's aversion to risk and finds the allocations in the year before retirement that maximize the expected value of those performance measures. It then uses a dynamic programming procedure to “roll back” one year at a time to determine optimal allocations for previous years as well. We find that the traditional advice that young investors should invest more heavily in equity (with a gradual shift to more debt as they near retirement) indeed is correct, and in fact the optimal equity allocation is even higher than commonly suggested. Deviations of the growth in an individual's income from a long-term national average did not seem to significantly affect the optimal allocations. The optimal allocations, however, vary widely as a function of (1) investor attitudes toward risk and (2) accumulated savings to date. These results suggest greater care should be taken to assess and incorporate these factors into the asset-allocation decision.