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

Published online by Cambridge University Press:  06 April 2009

Jessica A. Wachter
Jessica A. Wachter
Affiliation:
NYU, Stern School of Business, Department of Finance, 44 West 4th St., Suite 9–190, New York, NY 10012, jwachter@stern.nyu.edu.
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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.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 37 , Issue 1 , March 2002 , pp. 63 - 91
Copyright
Copyright © School of Business Administration, University of Washington 2002

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