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Noise fit, estimation error and a Sharpe information criterion

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  • Dirk Paulsen
  • Jakob Söhl

Abstract

When the in-sample Sharpe ratio is obtained by optimizing over a k-dimensional parameter space, it is a biased estimator for what can be expected on unseen data (out-of-sample). We derive (1) an unbiased estimator adjusting for both sources of bias: noise fit and estimation error. We then show (2) how to use the adjusted Sharpe ratio as model selection criterion analogously to the Akaike Information Criterion (AIC). Selecting a model with the highest adjusted Sharpe ratio selects the model with the highest estimated out-of-sample Sharpe ratio in the same way as selection by AIC does for the log-likelihood as a measure of fit.

Suggested Citation

  • Dirk Paulsen & Jakob Söhl, 2020. "Noise fit, estimation error and a Sharpe information criterion," Quantitative Finance, Taylor & Francis Journals, vol. 20(6), pages 1027-1043, June.
    • Handle: RePEc:taf:quantf:v:20:y:2020:i:6:p:1027-1043
    DOI: 10.1080/14697688.2020.1718746
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