Noise fit, estimation error and a Sharpe information criterion

Dirk Paulsen and Jakob Söhl

Quantitative Finance, 2020, vol. 20, issue 6, 1027-1043

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.

Date: 2020
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DOI: 10.1080/14697688.2020.1718746

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