Abstract
We derive (1) an unbiased estimator for the out-of-sample Sharpe ratio when the in-sample Sharpe ratio is obtained by optimizing over a $k$-dimensional parameter space. The estimator corrects the in-sample Sharpe ratio for both: noise fit and estimation error. We then show (2) how to use the corrected Sharpe ratio as model selection criterion analogous to the Akaike Information Criterion (AIC). Selecting a model with the highest corrected 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.
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