FIN-01-055

Portfolio and Consumption Decisions under Mean-Revering Returns: An Exact Solution for Complete Markets

November 2001

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 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 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, 44th West 4th Street, New York, NY 10012
Telephone: (212) 998-0799
Fax: 212) 995-4233
Email: jwachter@stern.nyu.edu
Homepage:http://www.stern.nyu.edu/~jwachter/

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