Maximizing the Out-of-Sample Sharpe Ratio

Maximizing the out-of-sample Sharpe ratio is an important objective for investors. To achieve this, we characterize optimal portfolio combinations maximizing expected out-of-sample Sharpe ratio. When investing in the risk-free asset is allowed and combination coefficients are unconstrained, as in Kan and Zhou (2007), we uncover that combining portfolios to maximize expected out-of-sample utility optimizes expected outof-sample Sharpe ratio as well. However, the two criteria are not equivalent for portfolios fully invested in risky assets, and in this case we show how to adapt the optimal portfolio combination of Kan, Wang, and Zhou (2021) to maximize expected out-of-sample Sharpe ratio. We find that the proposed mean-variance portfolio combinations calibrated to maximize expected out-of-sample Sharpe ratio generally outperform the considered benchmarks. Relative to the minimum-variance portfolio estimated with a nonlinearly shrunk covariance matrix, the annualized out-of-sample Sharpe ratio increases from 0.988 to 1.110 before transaction costs, and from 0.914 to 1.007 net of transaction costs, on average across four typical datasets.