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Geometric Representation of the Mean-Variance-Skewness Portfolio Frontier Based upon the Shortage Function

Author

Listed:
  • Kristiaan Kerstens

    (CNRS-LEM (UMR 8179), IESEG School of Management)

  • Amine Mounir

    (Hogeschool Universiteit Brussel, Brussels, Belgium)

  • Ignace Van de Woestyne

    (Hogeschool Universiteit Brussel, Brussels, Belgium)

Abstract

The literature suggests that investors prefer portfolios based on mean, variance and skewness rather than portfolios based on mean-variance (MV) criteria solely. Furthermore, a small variety of methods have been proposed to determine mean-variance-skewness (MVS) optimal portfolios. Recently, the shortage function has been introduced as a measure of efficiency, allowing to characterize MVS optimalportfolios using non-parametric mathematical programming tools. While tracing the MV portfolio frontier has become trivial, the geometric representation of the MVS frontier is an open challenge. A hitherto unnoticed advantage of the shortage function is that it allows to geometrically represent the MVS portfolio frontier. The purpose of this contribution is to systematically develop geometric representations of the MVS portfolio frontier using the shortage function and related approaches.

Suggested Citation

  • Kristiaan Kerstens & Amine Mounir & Ignace Van de Woestyne, 2008. "Geometric Representation of the Mean-Variance-Skewness Portfolio Frontier Based upon the Shortage Function," Working Papers 2008-ECO-17, IESEG School of Management.
    • Handle: RePEc:ies:wpaper:e200817
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    10. Chang, Tzu-Pu & Hu, Jin-Li & Chou, Ray Yeutien & Sun, Lei, 2012. "The sources of bank productivity growth in China during 2002–2009: A disaggregation view," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 1997-2006.
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    13. Jens J. Krüger, 2021. "Nonparametric portfolio efficiency measurement with higher moments," Empirical Economics, Springer, vol. 61(3), pages 1435-1459, September.
    14. Valeria V. Lakshina, 2019. "Do Portfolio Investors Need To Consider The Asymmetry Of Returns On The Russian Stock Market?," HSE Working papers WP BRP 75/FE/2019, National Research University Higher School of Economics.
    15. Krüger, Jens, 2021. "Nonparametric Portfolio Efficiency Measurement with Higher Moments," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 130825, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
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    20. Emmanuel Jurczenko & Bertrand Maillet & Paul Merlin, 2008. "Efficient Frontier for Robust Higher-order Moment Portfolio Selection," Post-Print halshs-00336475, HAL.
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