Optimal Consumption and Portfolio Allocation under Mean-Reverting Returns: An Exact Solution
for Complete Markets
September 26, 2000
Jessica A. Wachter
ABSTRACT
This paper solves, in closed form, the optimal portfolio choice problem for an investor with utility over consumption under mean-reverting returns. Previous solutions either require approximations, numerical methods, or the assumption that the investor does not consume over his lifetime. This paper breaks the impasse by assuming that markets are complete. The solution leads to a new understanding of hedging demand and the behavior of approximate log-linear solutions. 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 investment horizon is extended to that of an investor who consumes at multiple points in time.
Jessica A. Wachter
Institution: Stern School of Business, New York University
Email: jwachter@stern.nyu.edu
Telephone: (212) 998-0799
Homepage: http://www.stern.nyu.edu/~jwachter/
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