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Mean–variance approximations to expected utility

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  • Markowitz, Harry

Abstract

It is often asserted that the application of mean–variance analysis assumes normal (Gaussian) return distributions or quadratic utility functions. This common mistake confuses sufficient versus necessary conditions for the applicability of modern portfolio theory. If one believes (as does the author) that choice should be guided by the expected utility maxim, then the necessary and sufficient condition for the practical use of mean–variance analysis is that a careful choice from a mean–variance efficient frontier will approximately maximize expected utility for a wide variety of concave (risk-averse) utility functions. This paper reviews a half-century of research on mean–variance approximations to expected utility. The many studies in this field have been generally supportive of mean–variance analysis, subject to certain (initially unanticipated) caveats.

Suggested Citation

  • Markowitz, Harry, 2014. "Mean–variance approximations to expected utility," European Journal of Operational Research, Elsevier, vol. 234(2), pages 346-355.
  • Handle: RePEc:eee:ejores:v:234:y:2014:i:2:p:346-355
    DOI: 10.1016/j.ejor.2012.08.023
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    References listed on IDEAS

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    1. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    2. Chamberlain, Gary, 1983. "A characterization of the distributions that imply mean--Variance utility functions," Journal of Economic Theory, Elsevier, vol. 29(1), pages 185-201, February.
    3. Hlawitschka, Walter, 1994. "The Empirical Nature of Taylor-Series Approximations to Expected Utility," American Economic Review, American Economic Association, vol. 84(3), pages 713-719, June.
    4. Loistl, Otto, 1976. "The Erroneous Approximation of Expected Utility by Means of a Taylor's Series Expansion: Analytic and Computational Results," American Economic Review, American Economic Association, vol. 66(5), pages 904-910, December.
    5. Markowitz, Harry M & Usmen, Nilufer, 1996. "The Likelihood of Various Stock Market Return Distributions, Part 1: Principles of Inference," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 207-219, November.
    6. Jean, William H. & Helms, Billy P., 1983. "Geometric Mean Approximations," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(03), pages 287-293, September.
    7. Henry A. Latané & Donald L. Tuttle, 1967. "Criteria For Portfolio Building," Journal of Finance, American Finance Association, vol. 22(3), pages 359-373, September.
    8. Kroll, Yoram & Levy, Haim & Markowitz, Harry M, 1984. " Mean-Variance versus Direct Utility Maximization," Journal of Finance, American Finance Association, vol. 39(1), pages 47-61, March.
    9. Markowitz, Harry M, 1991. " Foundations of Portfolio Theory," Journal of Finance, American Finance Association, vol. 46(2), pages 469-477, June.
    10. Levy, H & Markowtiz, H M, 1979. "Approximating Expected Utility by a Function of Mean and Variance," American Economic Review, American Economic Association, vol. 69(3), pages 308-317, June.
    11. Harry M. Markowitz, 2010. "Portfolio Theory: As I Still See It," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 1-23, December.
    12. Markowitz, Harry M & Usmen, Nilufer, 1996. "The Likelihood of Various Stock Market Return Distributions, Part 2: Empirical Results," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 221-247, November.
    13. Yusif Simaan, 1993. "What is the Opportunity Cost of Mean-Variance Investment Strategies?," Management Science, INFORMS, vol. 39(5), pages 578-587, May.
    14. Grauer, Robert R., 1986. "Normality, Solvency, and Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(03), pages 265-278, September.
    15. Hakansson, Nils H., 1971. "Capital Growth and the Mean-Variance Approach to Portfolio Selection," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 6(01), pages 517-557, January.
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