About the Equivalence of Optimal Sharpe Ratio and Loss-Minimizing Portfolios

This article explores the relationship between the Sharpe ratio and the probability of losses. When asset returns are normally distributed, the optimal Sharpe ratio portfolio is the one that minimizes the probability of losses. In practice, however, asset returns are rarely normally distributed. Therefore, there are fundamental differences between optimal Sharpe ratio portfolios and loss-minimizing ones. The author proves this in both a theoretical setting, with a simple model, as well as in an empirical setting, using stock, bond, and commodity indexes to build multiasset portfolios. Interestingly, in the empirical examples, the loss-minimizing portfolio outperforms the optimal Sharpe one.