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Single Period Markowitz Portfolio Selection, Performance Gauging and Duality: A Variation on Luenberger’s Shortage Function

Author

Listed:
  • Walter Briec

    (JEREM, Université de Perpignan)

  • Kristiaan Kerstens

    (CNRS-LABORES (URA 362), Université Catholique de Lille,)

  • Jean Baptiste Lesourd

    (GREQAM, Centre de la Vieille Charité)

Abstract

Markowitz portfolio theory (1952) has induced research into the efficiency of portfolio management. This paper studies existing nonparametric efficiency measurement approaches for single period portfolio selection from a theoretical perspective and generalises currently used efficiency measures into the full mean-variance space. Therefore, we introduce the efficiency improvement possibility function (a variation on the shortage function), study its axiomatic properties in the context of Markowitz efficient frontier, and establish a link to the indirect mean-variance utility function. This framework allows distinguishing between portfolio efficiency and allocative efficiency. Furthermore, it permits retrieving information about the revealed risk aversion of investors. The efficiency improvement possibility function thus provides a more general framework for gauging the efficiency of portfolio management using nonparametric frontier envelopment methods based on quadratic optimisation.

Suggested Citation

  • Walter Briec & Kristiaan Kerstens & Jean Baptiste Lesourd, 2002. "Single Period Markowitz Portfolio Selection, Performance Gauging and Duality: A Variation on Luenberger’s Shortage Function," Working Papers 200203, Departament Empresa, Universitat Autònoma de Barcelona.
    • Handle: RePEc:bbe:wpaper:200203
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    File URL: http://selene.uab.es/dep-economia-empresa/documents/02-3.pdf
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    Citations

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    Cited by:

    1. Kerstens, Kristiaan & Mounir, Amine & de Woestyne, Ignace Van, 2011. "Non-parametric frontier estimates of mutual fund performance using C- and L-moments: Some specification tests," Journal of Banking & Finance, Elsevier, vol. 35(5), pages 1190-1201, May.
    2. Kerstens, Kristiaan & Mounir, Amine & Van de Woestyne, Ignace, 2010. "Benchmarking Mean-Variance Portfolios. Using a Shortage Function: The Choice of Direction Vector," Working Papers 2010/01, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    3. Olivier Massol & Albert Banal-Estañol, 2011. "Export diversification and resource-based industrialization : the case of natural gas," Working Papers hal-01031565, HAL.
    4. 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.
    5. 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.

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