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Mean-Variance-Skewness Portfolio Performance Gauging: A General Shortage Function and Dual Approach

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Author Info

  • Walter Briec

    ()
    (University of Perpignan, 52 Avenue Villeneuve, F-66000 Perpignan, France)

  • Kristiaan Kerstens

    ()
    (CNRS-LEM (UMR 8179), IESEG School of Management, 3 Rue de la Digue, F-59000 Lille, France)

  • Octave Jokung

    ()
    (EDHEC Business School, 58 Rue du Port, F-59046 Lille, France)

Abstract

This paper proposes a nonparametric efficiency measurement approach for the static portfolio selection problem in mean-variance-skewness space. A shortage function is defined that looks for possible increases in return and skewness and decreases in variance. Global optimality is guaranteed for the resulting optimal portfolios. We also establish a link to a proper indirect mean-variance-skewness utility function. For computational reasons, the optimal portfolios resulting from this dual approach are only locally optimal. This framework permits to differentiate between portfolio efficiency and allocative efficiency, and a convexity efficiency component related to the difference between the primal, nonconvex approach and the dual, convex approach. Furthermore, in principle, information can be retrieved about the revealed risk aversion and prudence of investors. An empirical section on a small sample of assets serves as an illustration.

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File URL: http://dx.doi.org/10.1287/mnsc.1060.0596
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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 53 (2007)
Issue (Month): 1 (January)
Pages: 135-149

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Handle: RePEc:inm:ormnsc:v:53:y:2007:i:1:p:135-149

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Keywords: shortage function; efficient frontier; mean-variance-skewness portfolios; risk aversion; prudence;

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  1. Markowitz, Harry M., 1990. "Foundations of Portfolio Theory," Nobel Prize in Economics documents 1990-1, Nobel Prize Committee.
  2. Sun, Qian & Yan, Yuxing, 2003. "Skewness persistence with optimal portfolio selection," Journal of Banking & Finance, Elsevier, vol. 27(6), pages 1111-1121, June.
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  4. N. J. Jobst & M. D. Horniman & C. A. Lucas & G. Mitra, 2001. "Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 489-501.
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  7. Lien, Gudbrand, 2002. "Non-parametric estimation of decision makers' risk aversion," Agricultural Economics, Blackwell, vol. 27(1), pages 75-83, May.
  8. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
  9. William F. Sharpe, 1965. "Mutual Fund Performance," The Journal of Business, University of Chicago Press, vol. 39, pages 119.
  10. Deaton, Angus, 1979. "The Distance Function in Consumer Behaviour with Applications to Index Numbers and Optimal Taxation," Review of Economic Studies, Wiley Blackwell, vol. 46(3), pages 391-405, July.
  11. Simkowitz, Michael A. & Beedles, William L., 1978. "Diversification in a Three-Moment World," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(05), pages 927-941, December.
  12. Simar, L. & Wilson, P.W., 1998. "A General Methodology for Bootstrapping in Nonparametric Frontier Models," Papers 9811, Catholique de Louvain - Institut de statistique.
  13. 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.
  14. Chunhachinda, Pornchai & Dandapani, Krishnan & Hamid, Shahid & Prakash, Arun J., 1997. "Portfolio selection and skewness: Evidence from international stock markets," Journal of Banking & Finance, Elsevier, vol. 21(2), pages 143-167, February.
  15. Scott, Robert C & Horvath, Philip A, 1980. " On the Direction of Preference for Moments of Higher Order Than the Variance," Journal of Finance, American Finance Association, vol. 35(4), pages 915-19, September.
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