Treynor Ratio and Jensen’s Alpha Calculator
Measure return above the risk-free rate per unit of beta, calculate the CAPM expected return and compare actual performance with Jensen’s alpha.
Risk-adjusted performance results
| Measure | Result | Meaning |
|---|
Treynor ratio formula
The Treynor ratio, also called the Treynor measure or reward-to-volatility ratio, divides portfolio return above a risk-free rate by portfolio beta:
Treynor ratio = (portfolio return − risk-free rate) ÷ portfolio beta
The calculator converts percentage inputs to decimals before applying the formula. A result of 0.066667 is also 6.6667 percentage points of excess return per unit of beta.
Jensen’s alpha and CAPM formulas
Jensen’s alpha compares actual portfolio return with the return predicted by the Capital Asset Pricing Model (CAPM):
CAPM expected return = risk-free rate + beta × (market return − risk-free rate)
Jensen’s alpha = portfolio return − CAPM expected return
A positive alpha means the portfolio beat the CAPM estimate for the selected period; a negative alpha means it fell short. This is a historical comparison, not proof of manager skill or a forecast.
Verified examples
| Inputs | Treynor ratio | CAPM return | Jensen’s alpha |
|---|---|---|---|
| Portfolio 12%; risk-free 4%; beta 1.20; market 10% | 0.066667 (6.6667% per beta) | 11.20% | +0.80 percentage point |
| Portfolio 6%; risk-free 3%; beta 0.80; market 8% | 0.037500 (3.7500% per beta) | 7.00% | −1.00 percentage point |
| Portfolio −2%; risk-free 2%; beta 1.50; market −5% | −0.026667 (−2.6667% per beta) | −8.50% | +6.50 percentage points |
How to interpret the results
A higher Treynor ratio indicates more excess return per unit of systematic market risk under the inputs used. Compare portfolios only when beta, returns and the risk-free rate use the same benchmark, period, currency and estimation convention. A negative beta reverses the ratio’s sign and can make a simple “higher is better” comparison misleading.
Jensen’s alpha answers a different question: whether actual return exceeded the CAPM estimate. A portfolio can have a positive Treynor ratio but negative alpha because the two measures use different reference points.
Limits and assumptions
- Portfolio, market and risk-free returns may range from −100% through 1,000%, with up to six decimal places.
- Beta may range from −10 through 10, with up to six decimal places, but cannot equal zero. When beta is zero, the Treynor ratio is undefined.
- All rates must cover the same period. The tool does not annualize monthly, quarterly or daily data.
- Beta must be estimated against the same market benchmark whose return is entered. Changing the benchmark, sample window or return interval can change beta and both results.
- CAPM assumes a linear beta relationship and a suitable risk-free asset. It does not capture all risks, fees, taxes, leverage changes, nonlinear exposures or estimation error.
- Negative beta values are mathematically accepted but require careful interpretation. A near-zero beta can create an extremely large Treynor ratio.
- Results are educational estimates, not investment advice or a performance forecast.
Enter returns as percentages, not decimals. For example, enter 12 for 12%, not 0.12.
Frequently asked questions
Is the Treynor ratio a percentage?
The standard decimal result is excess return divided by beta. Because the numerator is a return, it can also be expressed as a percentage per unit of beta. This calculator shows both formats.
What is a good Treynor ratio?
There is no universal cutoff. It is most useful for comparing portfolios calculated with the same period, benchmark, risk-free rate and beta method. A positive value means return exceeded the risk-free rate when beta is positive.
How is Treynor different from Sharpe?
Treynor divides excess return by beta, which represents systematic market risk. Sharpe divides excess return by total volatility. Treynor is generally more meaningful for diversified portfolios where asset-specific risk is limited.
Can Jensen’s alpha be positive during a market loss?
Yes. If CAPM predicts an even lower return, the portfolio can lose money and still have positive alpha for the selected period.
Related calculators
- Portfolio Beta Calculator — calculate weighted beta from individual holdings.
- Sharpe Ratio Calculator — compare excess return with total and downside volatility.
- ROI Calculator — calculate total and annualized investment return.
- WACC Calculator — estimate cost of equity with CAPM and combine financing costs.