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

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Author Info
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)

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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.

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Paper provided by Department of Business Economics, Universitat Autonoma de Barcelona in its series Working Papers with number 200203.

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Date of creation: Apr 2002
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Handle: RePEc:bbe:wpaper:200203

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Related research
Keywords: shortage function; efficient frontier; risk aversion; mean-variance portfolios;

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Léopold Simar, Paul W. Wilson, 2000. "A general methodology for bootstrapping in non-parametric frontier models," Journal of Applied Statistics, Taylor and Francis Journals, vol. 27(6), pages 779-802, August. [Downloadable!] (restricted)
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  2. Forsund, Finn R. & Lovell, C. A. Knox & Schmidt, Peter, 1980. "A survey of frontier production functions and of their relationship to efficiency measurement," Journal of Econometrics, Elsevier, vol. 13(1), pages 5-25, May. [Downloadable!] (restricted)
  3. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July. [Downloadable!] (restricted)
  4. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481. [Downloadable!] (restricted)
  5. Morey, Matthew R. & Morey, Richard C., 1999. "Mutual fund performance appraisals: a multi-horizon perspective with endogenous benchmarking," Omega, Elsevier, vol. 27(2), pages 241-258, April. [Downloadable!] (restricted)
  6. Luenberger, David G, 1996. "Welfare from a Benefit Viewpoint," Economic Theory, Springer, vol. 7(3), pages 445-62, April.
  7. Murthi, B. P. S. & Choi, Yoon K. & Desai, Preyas, 1997. "Efficiency of mutual funds and portfolio performance measurement: A non-parametric approach," European Journal of Operational Research, Elsevier, vol. 98(2), pages 408-418, April. [Downloadable!] (restricted)
  8. David G. Luenberger, 1996. "Welfare from a benefit viewpoint (*)," Economic Theory, Springer, vol. 7(3), pages 445-462.
  9. Gourieroux, C. & Jouneau, F., 1999. "Econometrics of efficient fitted portfolios," Journal of Empirical Finance, Elsevier, vol. 6(1), pages 87-118, January. [Downloadable!] (restricted)
  10. William F. Sharpe, 1965. "Mutual Fund Performance," Journal of Business, University of Chicago Press, vol. 39, pages 119. [Downloadable!]
  11. Pastor, Jose M, 1999. "Efficiency and Risk Management in Spanish Banking: A Method to Decompose Risk," Applied Financial Economics, Taylor and Francis Journals, vol. 9(4), pages 371-84, August. [Downloadable!] (restricted)
  12. Fare, Rolf & Grosskopf, Shawna, 1995. "Nonparametric tests of regularity, Farrell efficiency, and goodness-of-fit," Journal of Econometrics, Elsevier, vol. 69(2), pages 415-425, October. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Silvia Bou, 2003. "Evaluación de fondos de inversión garantizados por medio de portfolio insurance," Working Papers 200308, Department of Business Economics, Universitat Autonoma de Barcelona. [Downloadable!]
  2. Rossano Eusebio & Alex Rialp-Criado, 2002. "Innovación tecnológica y resultado exportador: un análisis empírico aplicado al sector textil-confección español," Working Papers 200204, Department of Business Economics, Universitat Autonoma de Barcelona. [Downloadable!]
  3. Rafel Crespí & Miguel A. García-Cestona & Vicente Salas Fumas, 2002. "Governance Mechanisms in Spanish Financial Intermediaries," Working Papers 200209, Department of Business Economics, Universitat Autonoma de Barcelona. [Downloadable!]
  4. Stephan Hecking, 2003. "A methodology to measure shareholder value orientation and shareholder value creation aimed at providing a research basis to investigate the link between both magnitudes," Working Papers 200301, Department of Business Economics, Universitat Autonoma de Barcelona. [Downloadable!]
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