Risk-Adjusted Performance Analysis using Sharpe and Treynor Ratios

XYZ Asset Management has recently conducted an in-depth performance evaluation of its diversified equity portfolio, which recorded a return of 12% over the last year. The portfolio's standard deviation of returns was found to be 15%, while the benchmark index delivered a return of 10% with a standard deviation of 12%.

In addition to the traditional measures of performance, the firm's head of portfolio management is particularly interested in assessing risk-adjusted performance using the Sharpe Ratio and the Treynor Ratio. The risk-free rate during this period was 3%.

Your task is to calculate both the Sharpe Ratio and Treynor Ratio for the portfolio and the benchmark index. After obtaining these metrics, provide a detailed analysis of what these ratios imply about the performance of the XYZ Asset Management portfolio compared to the benchmark. Discuss the relevance of these ratios in the context of modern portfolio theory and their limitations in assessing performance.