Before revision:  Then tied to that result , we also show that the maximum out-of-sample Sharpe ratio can be consistently estimated in this large portfolio of assets. Furthermore, we provide convergence rates and see thatthe number of assets slow down the convergence up to a logarithmic factor .
After revision:  Then tied to that result , we also show that the maximum out-of-sample Sharpe ratio estimator is consistent and the number of assets slow down the convergence up to a logarithmic factor .