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A Cross-Sectional Performance Measure for Portfolio Management

Author

Listed:
  • Monica Billio

    () (Università Ca' Foscari of Venice - Department of Economics)

  • Ludovic Calès

    () (Università Ca' Foscari of Venice - Department of Economics, CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne)

  • Dominique Guegan

    () (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne, PSE - Paris School of Economics)

Abstract

Sharpe-like ratios have been traditionally used to measure the performances of portfolio managers. However, they are known to suffer major drawbacks. Among them, two are intricate : (1) they are relative to a peer's performance and (2) the best score is generally assumed to correspond to a "good" portfolio allocation, with no guarantee on the goodness of this allocation. Last but no least (3) these measures suffer significant estimation errors leading to the inability to distinguish two managers' performances. In this paper, we propose a cross-sectional measure of portfolio performance dealing with these three issues. First, we define the score of a portfolio over a single period as the percentage of investable portfolios outperformed by this portfolio. This score quantifies the goodness of the allocation remedying drawbacks (1) and (2). The new information brought by the cross-sectionality of this score is then discussed through applications. Secondly, we build a performance index, as the average cross-section score over successive periods, whose estimation partially answers drawback (3). In order to assess its informativeness and using empirical data, we compare its forecasts with those of the Sharpe and Sortino ratios. The results show that our measure is the most robust and informative. It validates the utility of such cross-sectional performance measure.

Suggested Citation

  • Monica Billio & Ludovic Calès & Dominique Guegan, 2010. "A Cross-Sectional Performance Measure for Portfolio Management," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00523466, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00523466
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    References listed on IDEAS

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    1. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
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    Keywords

    Performance measure; portfolio management; relative-value strategy; large portfolios; absolute return strategy; multivariate statistics; Generalized hyperbolic Distribution.; Mesure de performance; gestion de portefeuilles; Sharpe ratio; Sortino ratio; distribution hyperbolique généralisée; statistiques d'ordre.;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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