A Copula-based estimator for the Sharpe Ratio of a two-asset portfolio

‎‎‎Performance measures are essential for evaluating portfolio performance in the risk management and fund industries‎, ‎with the Sharpe ratio being a widely adopted risk-adjusted metric‎. ‎This ratio compares the excess expected return to its standard deviation‎, ‎enabling investors to assess the returns of risk-taking activities against risk-free options‎. ‎Its popularity stems from its ease of calculation and straightforward interpretation‎. ‎However‎, ‎the actual Sharpe ratio value is often unavailable and must be estimated empirically based on the assumption of normality of asset returns‎. ‎In practice‎, ‎financial assets typically exhibit non-normal distributions and nonlinear dependencies‎, ‎which can compromise the accuracy of the Sharpe ratio estimation when normality is assumed‎. ‎This paper challenges the normality assumption‎, ‎aiming to enhance the accuracy of Sharpe ratio estimates‎. ‎We investigate the impact of dependency on the Sharpe ratio of a two-asset portfolio using copulas‎. ‎Theoretical findings and extensive simulations demonstrate the effectiveness of the proposed copula-based approach to the classic Sharpe ratio‎.