IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v234y2014i2p346-355.html
   My bibliography  Save this article

Mean–variance approximations to expected utility

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.sciencedirect.com/science/article/pii/S0377221712006467
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2012.08.023?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Jean, William H. & Helms, Billy P., 1983. "Geometric Mean Approximations," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(3), pages 287-293, September.
    5. 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.
    6. 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.
    7. Yusif Simaan, 1993. "What is the Opportunity Cost of Mean-Variance Investment Strategies?," Management Science, INFORMS, vol. 39(5), pages 578-587, May.
    8. 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(1), pages 517-557, January.
    9. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    10. 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.
    11. Henry A. Latané & Donald L. Tuttle, 1967. "Criteria For Portfolio Building," Journal of Finance, American Finance Association, vol. 22(3), pages 359-373, September.
    12. 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.
    13. Markowitz, Harry M, 1991. "Foundations of Portfolio Theory," Journal of Finance, American Finance Association, vol. 46(2), pages 469-477, June.
    14. 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.
    15. Young, William E. & Trent, Robert H., 1969. "Geometric Mean Approximations of Individual Security and Portfolio Performance*," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 4(2), pages 179-199, June.
    16. Grauer, Robert R., 1986. "Normality, Solvency, and Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(3), pages 265-278, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Emmanuel Jurczenko & Bertrand Maillet & Paul Merlin, 2008. "Efficient Frontier for Robust Higher-order Moment Portfolio Selection," Post-Print halshs-00336475, HAL.
    2. Haim Levy, 2010. "The CAPM is Alive and Well: A Review and Synthesis," European Financial Management, European Financial Management Association, vol. 16(1), pages 43-71, January.
    3. Sonntag, Dominik, 2018. "Die Theorie der fairen geometrischen Rendite [The Theory of Fair Geometric Returns]," MPRA Paper 87082, University Library of Munich, Germany.
    4. Simaan, Majeed & Simaan, Yusif & Tang, Yi, 2018. "Estimation error in mean returns and the mean-variance efficient frontier," International Review of Economics & Finance, Elsevier, vol. 56(C), pages 109-124.
    5. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    6. George Samartzis & Nikitas Pittis, 2022. "On The Equivalence Of The Mean Variance Criterion And Stochastic Dominance Criteria," Papers 2211.01240, arXiv.org.
    7. Diamond, Harvey & Gelles, Gregory, 1999. "Gaussian approximation of expected utility," Economics Letters, Elsevier, vol. 64(3), pages 301-307, September.
    8. 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).
    9. Simaan, Yusif, 2014. "The opportunity cost of mean–variance choice under estimation risk," European Journal of Operational Research, Elsevier, vol. 234(2), pages 382-391.
    10. Briec, Walter & Kerstens, Kristiaan, 2010. "Portfolio selection in multidimensional general and partial moment space," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 636-656, April.
    11. 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.
    12. Alessandra Carleo & Francesco Cesarone & Andrea Gheno & Jacopo Maria Ricci, 2017. "Approximating exact expected utility via portfolio efficient frontiers," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 115-143, November.
    13. Fatma Lajeri-Chaherli, 2016. "On The Concavity And Quasiconcavity Properties Of ( Σ , Μ ) Utility Functions," Bulletin of Economic Research, Wiley Blackwell, vol. 68(3), pages 287-296, April.
    14. Harry Markowitz & Joseph Blasi & Douglas Kruse, 2010. "Employee stock ownership and diversification," Annals of Operations Research, Springer, vol. 176(1), pages 95-107, April.
    15. Eric Jondeau & Michael Rockinger, 2005. "Conditional Asset Allocation under Non-Normality: How Costly is the Mean-Variance Criterion?," FAME Research Paper Series rp132, International Center for Financial Asset Management and Engineering.
    16. 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.
    17. Haim Levy, 2017. "What is the Economic Cost of the Investment Home Bias?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 49(5), pages 897-929, August.
    18. António Alberto Santos & Ana Margarida Monteiro & Rui Pascoal, 2014. "Portfolio Choice under Parameter Uncertainty: Bayesian Analysis and Robust Optimization Comparison," GEMF Working Papers 2014-25, GEMF, Faculty of Economics, University of Coimbra.
    19. Levy, Haim & Simaan, Yusif, 2016. "More possessions, more worry," European Journal of Operational Research, Elsevier, vol. 255(3), pages 893-902.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:234:y:2014:i:2:p:346-355. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.