Lesson 6 of 7 · All lessons in this module
- The risk-free asset, the market portfolio and the CMLVideo lesson
- Lending, borrowing and leveraged portfolios on the CMLVideo lesson
- Systematic and nonsystematic riskVideo lesson
- Return-generating models, the market model and betaVideo lesson
- The CAPM: assumptions, the SML and its limitsVideo lesson
- Sharpe ratio, Treynor ratio, M² and Jensen's alphaVideo lesson
- Applying the CAPM: budgeting, security selection and portfolio buildingVideo lesson
Lesson 6 of 7 · 15 min
Sharpe ratio, Treynor ratio, M² and Jensen's alpha
Risk-adjusted performance divides or adjusts excess return by risk: total risk for the Sharpe ratio and M², systematic risk for the Treynor ratio and Jensen's alpha.
In short
- Performance evaluation has three parts: measurement (return and risk), attribution (sources of performance) and appraisal (skill or luck).
- Sharpe ratio = excess return ÷ σ: the slope of the CAL. Uses total risk; only meaningful when compared with other Sharpe ratios.
- Treynor ratio = excess return ÷ β. Uses systematic risk; needs a positive numerator and positive beta.
- M² = Sharpe ratio × + : the return the portfolio would earn if levered to market risk. M² alpha = M² − . Ranks like Sharpe.
- Jensen's alpha = : the vertical distance from the SML. Its sign alone shows out- or underperformance.
- Not fully diversified (e.g. one manager runs everything): use Sharpe/M². Well diversified: use Treynor/Jensen's alpha.
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