A Cross-Sectional Performance Measure for Portfolio Management

Monica Billio, Ludovic Calès and Dominique Guegan ()
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Dominique Guegan: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

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.

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 (search for similar items in EconPapers)
Date: 2010-08
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00523466v1
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Published in 2010

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Related works:
Working Paper: A Cross-Sectional Performance Measure for Portfolio Management (2010)
Working Paper: A Cross-Sectional Performance Measure for Portfolio Management (2010)
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