Distinct from the Sharpe ratio — Treynor divides excess return by beta (market risk) rather than total volatility, better suited for one holding within an already-diversified portfolio.
How it works
Portfolio return minus the risk-free rate, divided by beta, gives the Treynor ratio.
What this does not include
Treynor only accounts for systematic (market) risk — for an undiversified portfolio still carrying significant unsystematic risk, the Sharpe ratio (which uses total volatility) gives a more complete risk-adjusted picture.
How to use this calculator
- Enter portfolio return, the risk-free rate, and portfolio beta.
A worked example
A portfolio returning 12%, risk-free rate 3%, beta 1.2: Treynor ratio = (12 − 3) ÷ 1.2 = 7.5.
What the variables mean
| Variable | Meaning |
|---|---|
| Portfolio return | Actual return achieved |
| Risk-free rate | Return available from a virtually risk-free investment, like short-term government bonds |
| Beta | The portfolio’s volatility relative to the overall market |
Edge cases worth knowing
Unlike the Sharpe ratio, this divides by beta (market risk) rather than total volatility. It measures return per unit of market risk specifically, which matters most for portfolios that are part of a larger, diversified whole.
A beta of zero makes the ratio undefined — a portfolio with no market sensitivity has nothing to divide the excess return by using this particular measure.
Frequently asked questions
When should Treynor be used instead of Sharpe?
Treynor is most appropriate for evaluating one holding as part of a larger, already-diversified portfolio, where unsystematic risk is assumed diversified away; Sharpe is more appropriate for a standalone, undiversified investment.
What does a negative Treynor ratio mean?
The portfolio underperformed the risk-free rate — a negative result regardless of the beta value used.
Why can’t beta be zero in this calculator?
A zero beta means no measured correlation to market movements at all, making the ratio mathematically undefined — there’s no market risk to divide by.
