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Testing Sharpe ratio: luck or skill?

Author

Listed:
  • Eric Benhamou

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • David Saltiel

    (LISIC - Laboratoire d'Informatique Signal et Image de la Côte d'Opale - ULCO - Université du Littoral Côte d'Opale)

  • Beatrice Guez
  • Nicolas Paris

    (CRIL - Centre de Recherche en Informatique de Lens - UA - Université d'Artois - CNRS - Centre National de la Recherche Scientifique)

Abstract

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. JEL classification: C12, G11.

Suggested Citation

  • Eric Benhamou & David Saltiel & Beatrice Guez & Nicolas Paris, 2020. "Testing Sharpe ratio: luck or skill?," Working Papers hal-02886500, HAL.
    • Handle: RePEc:hal:wpaper:hal-02886500
    Note: View the original document on HAL open archive server: https://hal.science/hal-02886500
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    Cited by:

    1. Eric Benhamou & David Saltiel & Serge Tabachnik & Sui Kai Wong & François Chareyron, 2021. "Distinguish the indistinguishable: a Deep Reinforcement Learning approach for volatility targeting models," Working Papers hal-03202431, HAL.
    2. Eric Benhamou & David Saltiel & Serge Tabachnik & Sui Kai Wong & Franc{c}ois Chareyron, 2021. "Adaptive learning for financial markets mixing model-based and model-free RL for volatility targeting," Papers 2104.10483, arXiv.org, revised Apr 2021.
    3. Eric Benhamou & Beatrice Guez, 2021. "Computation of the marginal contribution of Sharpe ratio and other performance ratios," Working Papers hal-03189299, HAL.
    4. Parley Ruogu Yang & Ryan Lucas, 2021. "DMS, AE, DAA: methods and applications of adaptive time series model selection, ensemble, and financial evaluation," Papers 2110.11156, arXiv.org, revised Jul 2022.
    5. Eric Benhamou, 2021. "Distribution and statistics of the Sharpe Ratio," Working Papers hal-03207169, HAL.

    More about this item

    Keywords

    Sharpe ratio; Student distribution; compounding effect on Sharpe; Wald test; T-test; Chi square test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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