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Evaluating Portfolio Policies: A Duality Approach

Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027
Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142
Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142, and CCFR and NBER
mh2078{at}columbia.edu
lkogan{at}mit.edu
wangj{at}mit.edu

The performance of a given portfolio policy can in principle be evaluated by comparing its expected utility with that of the optimal policy. Unfortunately, the optimal policy is usually not computable, in which case a direct comparison is impossible. In this paper, we solve this problem by using the given portfolio policy to construct an upper bound on the unknown maximum expected utility. This construction is based on a dual formulation of the portfolio optimization problem. When the upper bound is close to the expected utility achieved by the given portfolio policy, the potential utility loss of this policy is guaranteed to be small. Our algorithm can be used to evaluate portfolio policies in models with incomplete markets and position constraints. We illustrate our methodology by analyzing the static and myopic policies in markets with return predictability and constraints on short sales and borrowing.

Subject classifications: finance; portfolio; optimal control; applications.
History: Received July 2003; revision received September 2004; accepted March 2005.