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.
After revision: 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 thus obtained in-sample Sharpe ratio tends to be higher than what will be captured out-of-sample.