What this calculator does
The Treynor ratio divides excess return by beta rather than by total volatility. It asks how well a portfolio was rewarded for the market risk it carried, on the assumption that everything else has been diversified away.
That assumption is what separates it from the Sharpe ratio. The same 8.00 per cent excess return scores 13.33 at a beta of 0.6 and 4.44 at a beta of 1.8, because the low-beta portfolio achieved it with far less exposure to the market.
The formula
Subtract the risk-free rate from the portfolio return, then divide by beta. The result is excess return per unit of systematic risk, expressed in percentage points.
| Term | Meaning |
|---|---|
| Beta | Sensitivity to market movements. A beta of 1 moves with the market. |
| Systematic risk | Market risk that cannot be diversified away, which is what beta measures. |
| Treynor ratio | Excess return per unit of beta, in percentage points rather than as a pure number. |
The inputs explained
| Field | What to enter |
|---|---|
| Portfolio (or asset) return (%) | The portfolio return over the period, as a percentage. |
| Risk-free rate (%) | The risk-free rate over the same period. |
| Portfolio beta | The portfolio beta against its benchmark. |
When to use it
Evaluating a fund within a portfolio
Where a fund is one holding among many, its market risk matters more than its total volatility.
Comparing managers against a benchmark
Treynor puts high-beta and low-beta managers on a common footing.
Checking whether leverage added value
Leverage raises both return and beta, so it should leave the ratio roughly unchanged.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does beta change the score?
The same excess return at four levels of market exposure.
Questions
How does this differ from the Sharpe ratio?
Only in the denominator. Sharpe divides by total volatility, Treynor by beta. Treynor is the right measure when the portfolio is one part of a diversified whole; Sharpe is right when it is the entire investment.
Why is the number not between 0 and 1?
Because the numerator is in percentage points while beta is a pure number, so the result is also in percentage points. A Treynor ratio of 8 means eight points of excess return per unit of beta.
What if beta is near zero?
The ratio becomes very large or undefined, and it stops being meaningful. A market-neutral strategy has little systematic risk by design, so a beta-based measure is the wrong tool for it.
Does it rely on CAPM being correct?
To an extent, yes. It assumes beta is the relevant risk measure and that unsystematic risk has been diversified away. Both are CAPM assumptions, and both are debated.
For the total-volatility version, see the Sharpe ratio calculator. For return above what beta alone would predict, see the Jensen's alpha calculator.