Noise Fit, Estimation Error and a Sharpe Information Criterion

TL;DR

This paper introduces an unbiased estimator for the out-of-sample Sharpe ratio that corrects for noise fit and estimation error, and proposes a model selection criterion similar to AIC based on this adjusted ratio.

Contribution

It derives a bias-adjusted estimator for the Sharpe ratio and develops a model selection method analogous to AIC using this estimator.

Findings

Unbiased estimator effectively corrects for bias in in-sample Sharpe ratio.

Adjusted Sharpe ratio serves as a reliable model selection criterion.

Method improves out-of-sample performance prediction.

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 measure of fit.