Evaluating Portfolio Policies: A Duality Approach

Authors:
Martin B. Haugh;Leonid Kogan;Jiang Wang
Affiliations:
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
Venue:
Operations Research
Year:
2006

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Abstract

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.