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
TypeDocument de travail / Working paper
Lien vers un document non conservé dans cette basehttps://hal.archives-ouvertes.fr/hal-02886500
Titre de la collectionPreprint Lamsade
MétadonnéesAfficher la notice complète
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
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-clésSharpe ratio; Student distribution; compounding effect on Sharpe; Wald test; T-test; Chi square test
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