Before revision: 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.
After revision: When optimizing the Sharpe ratio over a k-dimensional parameter space the thus obtained 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).