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The opportunity cost of mean–variance choice under estimation risk


  • Simaan, Yusif


Mean–variance portfolio choice is often criticized as sub-optimal in the more general expected utility framework. It is argued that the expected utility framework takes into consideration higher moments ignored by mean variance analysis. A body of research suggests that mean–variance choice, though arguably sub-optimal, provides very close-to-expected utility maximizing portfolios and their expected utilities, basing its evaluation on in-sample analysis where mean–variance choice is sub-optimal by definition. In order to clarify this existing research, this study provides a framework that allows comparing in-sample and out-of-sample performance of the mean variance portfolios against expected utility maximizing portfolios. Our in-sample results confirm the results of earlier studies. On the other hand, our out-of-sample results show that the expected utility model performs worse. The out-of-sample inferiority of the expected utility model is more pronounced for preferences and constraints under which in-sample mean variance approximations are weakest. We argue that, in addition to its elegance and simplicity, the mean–variance model extracts more information from sample data because it uses the covariance matrix of returns. The expected utility model may reach its optimal solution without using information from the covariance matrix.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:234:y:2014:i:2:p:382-391 DOI: 10.1016/j.ejor.2013.01.025

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    References listed on IDEAS

    1. 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.
    2. 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.
    3. Yusif Simaan, 1993. "Portfolio Selection and Asset Pricing---Three-Parameter Framework," Management Science, INFORMS, vol. 39(5), pages 568-577, May.
    4. 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.
    5. 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.
    6. Arditti, Fred D & Levy, Haim, 1975. "Portfolio Efficiency Analysis in Three Moments: The Multiperiod Case," Journal of Finance, American Finance Association, vol. 30(3), pages 797-809, June.
    7. Hanoch, Giora & Levy, Haim, 1970. "Efficient Portfolio Selection with Quadratic and Cubic Utility," The Journal of Business, University of Chicago Press, vol. 43(2), pages 181-189, April.
    8. Yusif Simaan, 1993. "What is the Opportunity Cost of Mean-Variance Investment Strategies?," Management Science, INFORMS, vol. 39(5), pages 578-587, May.
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    Cited by:

    1. repec:eee:ejores:v:266:y:2018:i:1:p:371-390 is not listed on IDEAS
    2. Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2018. "Estimation of the global minimum variance portfolio in high dimensions," European Journal of Operational Research, Elsevier, vol. 266(1), pages 371-390.
    3. Levy, Haim & Simaan, Yusif, 2016. "More possessions, more worry," European Journal of Operational Research, Elsevier, vol. 255(3), pages 893-902.
    4. David Stefanovits & Urs Schubiger & Mario V. Wüthrich, 2014. "Model Risk in Portfolio Optimization," Risks, MDPI, Open Access Journal, vol. 2(3), pages 1-34, August.


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