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

31 Pages Posted: 4 Nov 2008

See all articles by Jessica A. Wachter

Jessica A. Wachter

University of Pennsylvania - Finance Department; National Bureau of Economic Research (NBER)

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Date Written: September 2000

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 andof 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 multiplepoints in time.

Suggested Citation

Wachter, Jessica A., Optimal Consumption and Portfolio Allocation Under Mean-Reverting Returns: An Exact Solution for Complete Markets (September 2000). NYU Working Paper No. FIN-00-027, Available at SSRN: https://ssrn.com/abstract=1295231

Jessica A. Wachter (Contact Author)

University of Pennsylvania - Finance Department ( email )

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