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.