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.
After revision:  Then tied to that result , we also show that the precision matrix of returns can be estimated consistently, even with an increasing number of factors. Benefiting from the consistency of the precision matrix estimate of returns, we show that: (1) the portfolios in high dimensions are mean-variance efficient; (2) maximum out-of-sample Sharpe ratio can be consistently estimated in this large portfolio of assets.