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Geometric representation of the mean-variance-skewness portfolio frontier based upon the shortage function

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  • Kerstens, Kristiaan

    () (IESEG School of Management, Lille, France)

  • Mounier, Amine

    () (Hogeschool-Universiteit Brussel (HUB), Belgium)

  • Van de Woestyne, Ignace

    () (Hogeschool-Universiteit Brussel (HUB), 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 meanvariance-skewness (MVS) optimal portfolios. Recently, the shortage function has been introduced as a measure of efficiency, allowing to characterize MVS optimal portfolios 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

  • Kerstens, Kristiaan & Mounier, Amine & Van de Woestyne, Ignace, 2008. "Geometric representation of the mean-variance-skewness portfolio frontier based upon the shortage function," Working Papers 2008/61, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
  • Handle: RePEc:hub:wpecon:200861
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    References listed on IDEAS

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    Cited by:

    1. Constantin Zopounidis & Michael Doumpos, 2013. "Multicriteria decision systems for financial problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 241-261, July.
    2. Briec, Walter & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2013. "Portfolio selection with skewness: A comparison of methods and a generalized one fund result," European Journal of Operational Research, Elsevier, vol. 230(2), pages 412-421.
    3. Sahoo, Biresh K. & Luptacik, Mikulas & Mahlberg, Bernhard, 2011. "Alternative measures of environmental technology structure in DEA: An application," European Journal of Operational Research, Elsevier, vol. 215(3), pages 750-762, December.
    4. repec:eee:jomega:v:76:y:2018:i:c:p:28-37 is not listed on IDEAS
    5. Harris, Richard D.F. & Stoja, Evarist & Tan, Linzhi, 2017. "The dynamic Black–Litterman approach to asset allocation," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1085-1096.
    6. K. Saranya & P. Prasanna, 2014. "Portfolio Selection and Optimization with Higher Moments: Evidence from the Indian Stock Market," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(2), pages 133-149, May.
    7. Nalpas, Nicolas & Simar, Léopold & Vanhems, Anne, 2016. "Portfolio Selection in a Multi-Input Multi-Output Setting: a Simple Monte-Carlo-FDH Algorithm," TSE Working Papers 16-648, Toulouse School of Economics (TSE).
    8. 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.
    9. Brandouy, Olivier & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2009. "Exploring Bi-Criteria versus Multi-Dimensional Lower Partial Moment Portfolio Models," Working Papers 2009/29, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    10. Lord Mensah, 2016. "Asset Allocation Brewed Accross African Stock Markets," Proceedings of Economics and Finance Conferences 3205757, International Institute of Social and Economic Sciences.
    11. Brandouy, Olivier & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2015. "Frontier-based vs. traditional mutual fund ratings: A first backtesting analysis," European Journal of Operational Research, Elsevier, vol. 242(1), pages 332-342.
    12. Aparicio, Juan & Mahlberg, Bernhard & Pastor, Jesus T. & Sahoo, Biresh K., 2014. "Decomposing technical inefficiency using the principle of least action," European Journal of Operational Research, Elsevier, vol. 239(3), pages 776-785.
    13. Branda, Martin, 2015. "Diversification-consistent data envelopment analysis based on directional-distance measures," Omega, Elsevier, vol. 52(C), pages 65-76.
    14. Briec, Walter & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2011. "Portfolio Selection with Skewness: A Comparison and a Generalized Two Fund Separation Result," Working Papers 2011/09, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    15. Goh, Joel Weiqiang & Lim, Kian Guan & Sim, Melvyn & Zhang, Weina, 2012. "Portfolio value-at-risk optimization for asymmetrically distributed asset returns," European Journal of Operational Research, Elsevier, vol. 221(2), pages 397-406.

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