Sharpe Ratio: Risk-Adjusted Performance.pdf

Carl Bacon, Chairman of StatPro, discusses risk-adjusted performance measures, starting with the Sharpe ratio. The Sharpe ratio, a reward-to-variability measure, divides the portfolio's excess return by its standard deviation. It ranks portfolios based on the steepness of the line from the risk-free rate to the portfolio's return and risk, with a higher Sharpe ratio indicating better risk-adjusted performance. However, it's not a risk-adjusted return measure and doesn't facilitate easy comparison of relative performance.

To address this, the Modigliani-Adler (M2) statistic is introduced. M2 calculates the return a portfolio would need to achieve to have the same Sharpe ratio as another portfolio but with the benchmark's risk level. This provides a genuine risk-adjusted return for comparing portfolios with different risk levels.

Other risk-adjusted measures include:
- Treynor Ratio: Similar to Sharpe, but uses systematic risk (beta) instead of total risk.
- Appraisal Ratio: Uses Jensen's alpha (systematic risk-adjusted excess return) divided by specific risk.
- Information Ratio: Compares excess return to tracking error (standard deviation of excess return).

Each measure serves a unique purpose, and understanding their differences is crucial for comprehensive risk-adjusted performance analysis.