What do the Sharpe ratio and M^2 both indicate?

The Sharpe ratio and M^2 (M-squared) both assess the performance of an investment relative to its risk, providing a comprehensive measure of investment skill. The Sharpe ratio measures the excess return per unit of risk, calculated as the difference between the portfolio return and the risk-free rate, divided by the portfolio's standard deviation. It allows investors to understand how well the return compensates for the risk taken; higher values indicate better risk-adjusted performance.

M^2, on the other hand, extends the concept of the Sharpe ratio by converting the risk-adjusted performance into a percentage measure, effectively allowing for a comparison of the portfolio's performance to a benchmark. In essence, M^2 calculates the returns of a portfolio adjusted for risk, thus making it easier to see if the investor has outperformed a benchmark after adjusting for risk.

Both metrics are specifically designed to evaluate investment skill by considering how returns relate to the risk undertaken, making them valuable tools for investors looking to gauge the effectiveness of their investment strategies. Hence, they converge on the same assessment of investment skill, providing insights into how well an investor can navigate risk to achieve higher returns.