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Mean-Variance Approximations to Expected Logarithmic Utility

Author

Listed:
  • Lawrence B. Pulley

    (Brandeis University, Waltham, Massachusetts)

Abstract

In this paper, we investigate how closely functions of means and variances can approximate Von Neumann-Morgenstern expected utility modeled as a logarithmic utility-of-wealth function. Using historical security return data, we computed portfolios maximizing expected logarithmic utility and compared them to those maximizing appropriate mean-variance formulations. In all cases the approximations were very good, and in many cases the optimal portfolios were virtually identical. We conclude that the mean-variance model can serve as a useful surrogate to at least one popular alternative investment strategy.

Suggested Citation

  • Lawrence B. Pulley, 1983. "Mean-Variance Approximations to Expected Logarithmic Utility," Operations Research, INFORMS, vol. 31(4), pages 685-696, August.
    • Handle: RePEc:inm:oropre:v:31:y:1983:i:4:p:685-696
    DOI: 10.1287/opre.31.4.685
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    Cited by:

    1. Monica Billio & Bertrand Maillet & Loriana Pelizzon, 2022. "A meta-measure of performance related to both investors and investments characteristics," Annals of Operations Research, Springer, vol. 313(2), pages 1405-1447, June.
    2. Kassimatis, Konstantinos, 2021. "Mean-variance versus utility maximization revisited: The case of constant relative risk aversion," International Review of Financial Analysis, Elsevier, vol. 78(C).
    3. Frank Schuhmacher & Hendrik Kohrs & Benjamin R. Auer, 2021. "Justifying Mean-Variance Portfolio Selection when Asset Returns Are Skewed," Management Science, INFORMS, vol. 67(12), pages 7812-7824, December.
    4. Petsakos, Athanasios & Rozakis, Stelios, 2015. "Calibration of agricultural risk programming models," European Journal of Operational Research, Elsevier, vol. 242(2), pages 536-545.
    5. Harry Markowitz & Joseph Blasi & Douglas Kruse, 2010. "Employee stock ownership and diversification," Annals of Operations Research, Springer, vol. 176(1), pages 95-107, April.
    6. Gregor Dorfleitner & Mai Nguyen, 2017. "A new approach for optimizing responsible investments dependently on the initial wealth," Journal of Asset Management, Palgrave Macmillan, vol. 18(2), pages 81-98, March.
    7. Boehl, Gregor & Fischer, Thomas, 2017. "Capital Taxation and Investment: Matching 100 Years of Wealth Inequality Dynamics," Working Papers 2017:8, Lund University, Department of Economics.
    8. Appelbaum, Elie & Melatos, Mark, 2024. "Preferential trade agreements as insurance," Journal of International Money and Finance, Elsevier, vol. 148(C).
    9. Joseph R. Blasi & Douglas L. Kruse & Harry M. Markowitz, 2010. "Risk and Lack of Diversification under Employee Ownership and Shared Capitalism," NBER Chapters, in: Shared Capitalism at Work: Employee Ownership, Profit and Gain Sharing, and Broad-based Stock Options, pages 105-136, National Bureau of Economic Research, Inc.
    10. Appelbaum, Elie, 2021. "Implicit Trade in Risk and Risk Aversion," MPRA Paper 113000, University Library of Munich, Germany.
    11. Böhl, Gregor & Fischer, Thomas, 2017. "Can taxation predict US top-wealth share dynamics?," IMFS Working Paper Series 118, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    12. Zhuang, Hejun & Popkowski Leszczyc, Peter T.L., 2022. "Optimal seller strategy in overlapping auctions," Journal of Retailing and Consumer Services, Elsevier, vol. 65(C).
    13. Fahrenwaldt, Matthias A. & Sun, Chaofan, 2020. "Expected utility approximation and portfolio optimisation," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 301-314.
    14. Petsakos, Athanasios & Rozakis, Stelios, 2011. "Integrating risk and uncertainty in PMP models," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 114762, European Association of Agricultural Economists.
    15. Harry M. Markowitz, 2002. "Efficient Portfolios, Sparse Matrices, and Entities: A Retrospective," Operations Research, INFORMS, vol. 50(1), pages 154-160, February.

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