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Testing Sharpe ratio: luck or skill ?

Benhamou, Éric; Saltiel, David; Guez, Beatrice; Paris, Nicolas (2020), Testing Sharpe ratio: luck or skill ?. https://basepub.dauphine.fr/handle/123456789/21203

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Article-Testing Sharpe Ratio.pdf (806.1Kb)
Type
Document de travail / Working paper
Lien vers un document non conservé dans cette base
https://hal.archives-ouvertes.fr/hal-02886500
Date
2020
Titre de la collection
Preprint Lamsade
Ville d’édition
Paris
Métadonnées
Afficher la notice complète
Auteur(s)
Benhamou, Éric
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Saltiel, David
Université du Littoral Côte d'Opale [ULCO]
Guez, Beatrice
Paris, Nicolas cc
Centre de Recherche en Informatique de Lens [CRIL]
Résumé (EN)
Sharpe ratio (sometimes also referred to as information ratio) is widely used in asset management to compare and benchmark funds and asset managers. It computes the ratio of the (excess) net return over the strategy standard deviation. However, the elements to compute the Sharpe ratio, namely, the expected returns and the volatilities are unknown numbers and need to be estimated statistically. This means that the Sharpe ratio used by funds is likely to be error prone because of statistical estimation errors. In this paper, we provide various tests to measure the quality of the Sharpe ratios. By quality, we are aiming at measuring whether a manager was indeed lucky of skillful. The test assesses this through the statistical significance of the Sharpe ratio. We not only look at the traditional Sharpe ratio but also compute a modified Sharpe insensitive to used Capital. We provide various statistical tests that can be used to precisely quantify the fact that the Sharpe is statistically significant. We illustrate in particular the number of trades for a given Sharpe level that provides statistical significance as well as the impact of auto-correlation by providing reference tables that provides the minimum required Sharpe ratio for a given time period and correlation. We also provide for a Sharpe ratio of 0.5, 1.0, 1.5 and 2.0 the skill percentage given the auto-correlation level.
Mots-clés
Sharpe ratio; Student distribution; compounding effect on Sharpe; Wald test; T-test; Chi square test
JEL
C12 - Hypothesis Testing: General
G11 - Portfolio Choice; Investment Decisions

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