What is Treynor Ratio?
The Treynor Ratio measures risk-adjusted return per unit of systematic risk (beta), unlike the Sharpe Ratio which uses total risk (standard deviation). It answers: "How much excess return did the fund generate for each unit of market risk taken?"
Formula
Where:
Rfund = Annualized fund return (CAGR)
Rf = Risk-free rate (configurable, default 5%)
Beta = Fund's beta relative to the selected benchmark
Example
Treynor Ratio Calculation
Fund return = 15% annualized, Risk-free rate = 5%, Beta = 1.2
Treynor = (15% − 5%) / 1.2 = 10% / 1.2 = 8.33
Compare with another fund: 12% return, Beta = 0.8
Treynor = (12% − 5%) / 0.8 = 7% / 0.8 = 8.75
The second fund has a higher Treynor despite lower absolute return - it earned more per unit of market risk.
How to Interpret
- Higher is better - more excess return per unit of systematic risk.
- Unlike Sharpe (which divides by total risk/std dev), Treynor divides by systematic risk (beta only).
- Most useful when comparing funds within a diversified portfolio, where unsystematic risk is diversified away and only beta matters.
- If two funds have similar Sharpe but different Treynor, the one with higher Treynor is adding more value per unit of market exposure.
Important Notes
- Undefined when beta = 0 (no market sensitivity). These cases are shown as N/A.
- Negative beta produces a negative denominator - interpret with caution.
- Uses the same configurable risk-free rate (Rf) as Sharpe and Sortino (default 5%).
- Depends on the benchmark choice - changing the benchmark changes beta, which changes Treynor.
- Less meaningful for funds with low R² (beta is unreliable when the benchmark explains little of the fund's variance).
Related metrics
More Advanced Risk methodology from the MFPRO analytics tool: