Before revision:  Furthermore, we provide convergence rates and see thatthe number of assets slow down the convergence up to a logarithmic factor . Then, we provide consistency of maximum Sharpe Ratio when the portfolio weights add up to one, and also provide a new formula and an estimate for constrained maximum Sharpe ratio .
After revision:  Furthermore, we provide convergence rates and see thatthe number of assets slow down the convergence up to a logarithmic factor ; (3) the maximum Sharpe ratio estimator is consistent when the portfolio weights add up to one, and also provide a new formula and an estimate for constrained maximum Sharpe ratio .