This paper studies the out-of-sample Sharpe ratio of an unconstrained portfolio that combines the global minimum-variance with a hedge portfolio. Furthermore, we investigate how this ratio behaves as the number of risky assets and observations approaches infinity while maintaining a constant ratio. Under these conditions, it becomes possible to simultaneously account for estimation risk and achieve analytical tractability when optimizing the out-of-sample Sharpe ratio. This analysis also provides valuable insights to enhance out-of-sample performance in the finite case by introducing additional deterministic factors to the portfolio components.