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A Cross-Sectional Score for the Relative Performance of an Allocation

Author

Listed:
  • Dominique Guegan

    (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 des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Ludovic Calès

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, University of Ca’ Foscari [Venice, Italy])

  • Monica Billio

    (University of Ca’ Foscari [Venice, Italy])

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

  • Dominique Guegan & Ludovic Calès & Monica Billio, 2011. "A Cross-Sectional Score for the Relative Performance of an Allocation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00646070, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00646070
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    Cited by:

    1. Apostolos Chalkis & Emmanouil Christoforou & Ioannis Z. Emiris & Theodore Dalamagas, 2020. "Modeling asset allocation strategies and a new portfolio performance score," Papers 2012.05088, arXiv.org, revised Sep 2021.
    2. Ludovic Cales & Apostolos Chalkis & Ioannis Z. Emiris & Vissarion Fisikopoulos, 2018. "Practical volume computation of structured convex bodies, and an application to modeling portfolio dependencies and financial crises," Papers 1803.05861, arXiv.org.
    3. Monica Billio & Ludovic Calès & Dominique Guegan, 2012. "Cross-Sectional Analysis through Rank-based Dynamic," Documents de travail du Centre d'Economie de la Sorbonne 12036, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    4. Monica Billio & Ludovic Calès & Dominique Guegan, 2012. "Cross-Sectional Analysis through Rank-based Dynamic Portfolios," Post-Print halshs-00707430, HAL.
    5. Apostolos Chalkis & Emmanouil Christoforou & Ioannis Z. Emiris & Theodore Dalamagas, 2021. "Modeling asset allocations and a new portfolio performance score," Digital Finance, Springer, vol. 3(3), pages 333-371, December.
    6. Cyril Bachelard & Apostolos Chalkis & Vissarion Fisikopoulos & Elias Tsigaridas, 2024. "Randomized Control in Performance Analysis and Empirical Asset Pricing," Papers 2403.00009, arXiv.org.

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