Optimal Consumption and Portfolio Allocation under Mean-Reverting Returns: An Exact Solution for Complete Markets

Abstract

This paper solves, in closed form, the optimal portfolio choice problem for an investor with utility over consumption under mean-reverting re- turns. Previous solutions either require approximations, numerical methods, or the assumption that the investor does not consume over his life time. This paper breaks the impasse by assuming that markets are complete. The solution leads to a new understanding of hedging demand and of the behavior of the approximate log-linear solution. The portfolio allocation takes the form of a weighted average and is shown to be analogous to duration for coupon bonds. Through this analogy, the notion of invest- ment horizon is extended to that of an investor who consumes at multiple points in time.