Sorting two assets portfolios by copula-based Squared Maximum Sharpe Ratio

The Sharpe ratio is one the most commonly used tools to evaluate the performance of investment strategies. A related measure that is widely used in testing the arbitrage pricing theory is the squared Sharpe ratio. In this paper, we consider the squared maximum Sharpe ratio (SMSR) of a two assets portfolio, as a single value that summarizes the joint performance of a bivariate random vector of returns of assets. We propose a copula-based approach to deal with the problem of estimating the SMSR. Considering the SMSR as a bivariate Sharpe ratio, which is a function of the marginal Sharpe ratios and the correlation coefficient of the asset’s returns, can help in choosing the components of a two assets portfolio.The application of the proposed estimator is shown by a real data analysis.