Risk-Adjusted Performance Using Sharpe Ratio

In the field of portfolio management, investors often seek to measure the performance of their investment portfolios. One important aspect of this performance measurement is understanding how returns relate to the level of risk taken. A common way to evaluate risk-adjusted performance is through the Sharpe Ratio, which compares the excess return of the portfolio over the risk-free rate relative to the portfolio's standard deviation.

Consider the following scenario: An investor has two portfolios, Portfolio X and Portfolio Y. Portfolio X has an expected return of 10% and a standard deviation of 15%. Portfolio Y has an expected return of 8% and a standard deviation of 10%. Based on the Sharpe Ratio, which portfolio demonstrates better risk-adjusted performance?