The Treynor ratio (also called the Treynor measure or reward-to-volatility ratio) measures the excess return per unit of systematic risk (beta). It was developed by Jack Treynor.
Formula: > Treynor Ratio = (Portfolio Return − Risk-free Rate) ÷ Beta
Interpretation: - Higher Treynor ratio = better risk-adjusted performance per unit of market risk. - Most appropriate when comparing fully diversified portfolios (where unsystematic risk has been eliminated).
Example: - Portfolio return: 14% - Risk-free rate: 4% - Beta: 1.2 - Treynor ratio = (14% − 4%) ÷ 1.2 = 8.33%
Treynor vs. Sharpe: - Use Sharpe when comparing portfolios that are NOT fully diversified (total risk matters). - Use Treynor when comparing portfolios that ARE fully diversified (only systematic risk matters). - Both will give the same ranking for perfectly diversified portfolios.
Comparison example:
| Portfolio | Return | Risk-free | Beta | Std Dev | Treynor | Sharpe | |---|---|---|---|---|---|---| | A | 14% | 4% | 1.2 | 18% | 8.33 | 0.56 | | B | 11% | 4% | 0.7 | 9% | 10.0 | 0.78 |
Portfolio B wins on both Treynor and Sharpe — better risk-adjusted performance with lower risk.
> Exam tip: Treynor = beta in denominator. Sharpe = standard deviation in denominator. If the portfolio is fully diversified (only systematic risk), use Treynor. If not fully diversified (some unsystematic risk remains), use Sharpe.