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Evaluating Portfolio Policies: A Duality Approach

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  • Martin B. Haugh
  • Leonid Kogan
  • Jiang Wang

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.

Suggested Citation

  • Martin B. Haugh & Leonid Kogan & Jiang Wang, 2003. "Evaluating Portfolio Policies: A Duality Approach," NBER Working Papers 9861, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:9861
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    Cited by:

    1. Michele Longo & Alessandra Mainini, 2017. "Welfare effects of information and rationality in portfolio decisions under parameter uncertainty," Papers 1709.04387, arXiv.org.
    2. Hong, Yi & Jin, Xing, 2018. "Semi-analytical solutions for dynamic portfolio choice in jump-diffusion models and the optimal bond-stock mix," European Journal of Operational Research, Elsevier, vol. 265(1), pages 389-398.
    3. Kasper Larsen & Oleksii Mostovyi & Gordan Žitković, 2018. "An expansion in the model space in the context of utility maximization," Finance and Stochastics, Springer, vol. 22(2), pages 297-326, April.
    4. Castañeda, Pablo & Reus, Lorenzo, 2019. "Suboptimal investment behavior and welfare costs: A simulation based approach," Finance Research Letters, Elsevier, vol. 30(C), pages 170-180.
    5. Kasper Larsen & Oleksii Mostovyi & Gordan v{Z}itkovi'c, 2014. "An expansion in the model space in the context of utility maximization," Papers 1410.0946, arXiv.org, revised Aug 2016.
    6. Paolo Guasoni & Gu Wang, 2020. "Consumption in incomplete markets," Finance and Stochastics, Springer, vol. 24(2), pages 383-422, April.
    7. Kamma, Thijs & Pelsser, Antoon, 2022. "Near-optimal asset allocation in financial markets with trading constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 766-781.
    8. Thijs Kamma & Antoon Pelsser, 2019. "Near-Optimal Dynamic Asset Allocation in Financial Markets with Trading Constraints," Papers 1906.12317, arXiv.org, revised Oct 2019.

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    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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