Which term describes the excess returns of a portfolio compared to the risk taken, often analyzed in portfolio performance?

The correct choice, which identifies the measure that examines excess returns of a portfolio relative to the risk taken, is the Sharpe ratio. The Sharpe ratio calculates the risk-adjusted return of an investment by comparing the excess return—defined as the return above a risk-free rate—to the portfolio's standard deviation, which is a measure of total risk.

This ratio helps investors understand how well the return compensates for the risk taken. A higher Sharpe ratio indicates a more favorable risk-return trade-off when assessing portfolio performance. Thus, it is particularly valuable when comparing different portfolios or asset classes, as it allows an investor to gauge how much additional return they are receiving for each unit of risk endured.

Jensen's alpha is focused on the excess return compared to a benchmark, Treynor ratio measures returns per unit of systematic risk, and M^2 is a measure related to the Sharpe ratio but expresses performance in percentage terms as compared to a benchmark. Each of these also offers insights into portfolio performance but does not directly focus on the risk-adjusted return in the same manner as the Sharpe ratio.