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: http://www.sciencedirect.com/science/article/pii/S0377221712006467
    Download Restriction: Full text for ScienceDirect subscribers only

    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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rui Pedro Brito & Hélder Sebastião & Pedro Godinho, 2015. "Efficient Skewness/Semivariance Portfolios," GEMF Working Papers 2015-05, GEMF, Faculty of Economics, University of Coimbra.
    2. Robert M'barek & Jesus Barreiro-Hurle & Pierre Boulanger & Arnaldo Caivano & Pavel Ciaian & Hasan Dudu & Maria Espinosa Goded & Thomas Fellmann & Emanuele Ferrari & Sergio Gomez Y Paloma & Celso Gorri, 2017. "Scenar 2030 - Pathways for the European agriculture and food sector beyond 2020," JRC Working Papers JRC108449, Joint Research Centre (Seville site).
    3. repec:pal:assmgt:v:17:y:2016:i:5:d:10.1057_jam.2016.9 is not listed on IDEAS
    4. repec:eee:ejores:v:266:y:2018:i:2:p:761-774 is not listed on IDEAS
    5. Ray, Pritee & Jenamani, Mamata, 2016. "Mean-variance analysis of sourcing decision under disruption risk," European Journal of Operational Research, Elsevier, vol. 250(2), pages 679-689.
    6. John Griffin, 2015. "Risk Premia and Knightian Uncertainty in an Experimental Market Featuring a Long-Lived Asset," Fordham Economics Discussion Paper Series dp2015-01, Fordham University, Department of Economics.
    7. repec:eee:transe:v:109:y:2018:i:c:p:293-310 is not listed on IDEAS
    8. John Griffin, 2015. "Risk Premia and Knightian Uncertainty in an Experimental Market Featuring a Long-Lived Asset," Fordham Economics Discussion Paper Series dp2015-01er:dp2015-01, Fordham University, Department of Economics.
    9. Carol Alexander & Xi Chen, 2014. "Risk-adjusted Valuation of the Real Option to Invest," ICMA Centre Discussion Papers in Finance icma-dp2014-19, Henley Business School, Reading University.
    10. repec:eee:eneeco:v:65:y:2017:i:c:p:64-74 is not listed on IDEAS
    11. Kolm, Petter N. & Tütüncü, Reha & Fabozzi, Frank J., 2014. "60 Years of portfolio optimization: Practical challenges and current trends," European Journal of Operational Research, Elsevier, vol. 234(2), pages 356-371.
    12. Levy, Moshe & Kaplanski, Guy, 2015. "Portfolio selection in a two-regime world," European Journal of Operational Research, Elsevier, vol. 242(2), pages 514-524.
    13. Bodnar, Taras & Mazur, Stepan & Okhrin, Yarema, 2017. "Bayesian estimation of the global minimum variance portfolio," European Journal of Operational Research, Elsevier, vol. 256(1), pages 292-307.
    14. repec:spr:decfin:v:40:y:2017:i:1:d:10.1007_s10203-017-0201-0 is not listed on IDEAS
    15. Legendre, François & Togola, Djibril, 2016. "Explicit solutions to dynamic portfolio choice problems: A continuous-time detour," Economic Modelling, Elsevier, vol. 58(C), pages 627-641.
    16. Bell, Peter N, 2014. "On the optimal use of put options under trade restrictions," MPRA Paper 62155, University Library of Munich, Germany.
    17. repec:eee:ejores:v:261:y:2017:i:2:p:606-612 is not listed on IDEAS
    18. Rooderkerk, Robert P. & van Heerde, Harald J., 2016. "Robust optimization of the 0–1 knapsack problem: Balancing risk and return in assortment optimization," European Journal of Operational Research, Elsevier, vol. 250(3), pages 842-854.
    19. repec:eee:ejores:v:263:y:2017:i:2:p:719-732 is not listed on IDEAS
    20. José Antonio Robles-Zurita, 2015. "Alternation Bias and Sums of Identically Distributed Monetary Lotteries," Working Papers 15.08, Universidad Pablo de Olavide, Department of Economics.
    21. repec:krk:eberjl:v:2:y:2014:i:4:p:85-100 is not listed on IDEAS
    22. repec:spr:annopr:v:254:y:2017:i:1:d:10.1007_s10479-017-2447-x is not listed on IDEAS
    23. repec:gam:jrisks:v:6:y:2018:i:1:p:19-:d:134997 is not listed on IDEAS
    24. Levy, Haim & Simaan, Yusif, 2016. "More possessions, more worry," European Journal of Operational Research, Elsevier, vol. 255(3), pages 893-902.
    25. Jim Y. Jin & Shinji Kobayashi, 2016. "Impact of risk aversion and countervailing tax in oligopoly," Annals of Finance, Springer, vol. 12(3), pages 393-408, December.

    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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/eor .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.