Noise Fit, Estimation Error and a Sharpe Information Criterion

Abstract

When optimizing the Sharpe ratio over a k-dimensional parameter space the thus obtained in-sample Sharpe ratio tends to be higher than what will be captured out-of-sample. For two reasons: the estimated parameter will be skewed towards the noise in the in-sample data (noise fitting) and, second, the estimated parameter will deviate from the optimal parameter (estimation error). This article derives a simple correction for both. Selecting a model with the highest corrected Sharpe selects the model with the highest expected out-of-sample Sharpe in the same way as selection by Akaike Information Criterion does for the log-likelihood as measure of fit.