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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)

  • Kristiaan Kerstens

    ()
    (CNRS-LEM and IESEG School of Management)

  • Octave Jokung

    (EDHEC Business School, Lille)

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, non-convex 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://my.ieseg.fr/bienvenue/DownloadDoc.asp?Fich=36985728_2005-ECO-5_Briec_Kerstens_Jokung.pdf
File Function: First version, 2005
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Bibliographic Info

Paper provided by IESEG School of Management in its series Working Papers with number 2005-ECO-05.

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Length: 36 pages
Date of creation: Sep 2005
Date of revision:
Publication status: Published in Management Science, January 2007, 53(1), pp. 135-149
Handle: RePEc:ies:wpaper:e200505

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Related research

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

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  1. Sharpe, William F., 1967. "Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(02), pages 76-84, June.
  2. 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.
  3. Samuelson, Paul A., 1967. "General Proof that Diversification Pays," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(01), pages 1-13, March.
  4. Sun, Qian & Yan, Yuxing, 2003. "Skewness persistence with optimal portfolio selection," Journal of Banking & Finance, Elsevier, vol. 27(6), pages 1111-1121, June.
  5. 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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  7. Markowitz, Harry M., 1990. "Foundations of Portfolio Theory," Nobel Prize in Economics documents 1990-1, Nobel Prize Committee.
  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. Eric Jondeau & Michael Rockinger, 2006. "Optimal Portfolio Allocation under Higher Moments," European Financial Management, European Financial Management Association, vol. 12(1), pages 29-55.
  10. William F. Sharpe, 1965. "Mutual Fund Performance," The Journal of Business, University of Chicago Press, vol. 39, pages 119.
  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. 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.
  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. Lien, Gudbrand, 2002. "Non-parametric estimation of decision makers' risk aversion," Agricultural Economics, Blackwell, vol. 27(1), pages 75-83, May.
  15. 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.
  16. Patrick L. Brockett & Yehuda Kahane, 1992. "Risk, Return, Skewness and Preference," Management Science, INFORMS, vol. 38(6), pages 851-866, June.
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