Before 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 estimator corrects the in-sample Sharpe ratio for both : noise fit and estimation error.
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 , 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.