# Treynor Ratio

The Treynor ratio, also commonly known as the reward-to-volatility ratio, is a measure that quantifies return per unit of risk. It is similar to the Sharpe and Sortino ratios.

The metric is defined as the excess return of a portfolio divided by the portfolio’s beta:

Treynor Ratio = (Return of portfolio – Risk-free rate) / Portfolio beta

The risk-free rate is considered the return of a financial asset that bears no risk. This is generally considered a short-term safe bond, such as a United States Treasury bill.

The portfolio beta is a measure of its volatility, which is used as a proxy for overall risk – specifically risk that cannot be diversified. A beta of one indicates volatility on par with the broader market, usually an equity index. A beta of 0.5 means half the volatility of the market. Portfolios with twice the volatility of the market would be given a beta of 2.

A higher Treynor ratio is considered superior to a lower reading.

Treynor ratios can be used in both an ex-ante and ex-post sense. The ex-ante form of the ratio uses expected values for all variables, while the ex-post variation uses realized values.

The example below uses the ex-post version, though it can be adapted in the ex-ante form is these were presented as expected values.

## Example

If the annualized return of a portfolio is 10%, the risk-free rate is 2%, and its beta is 1.25, its Treynor ratio would be equal to:

Treynor Ratio = (.10 – .02) / 1.25 = .064

The Treynor ratio of the US equity market, on the basis of long-run returns of about 7% and the risk-free rate of 3%, and a beta of 1 (by definition), this gives:

Treynor Ratio = (.07 – .03) / 1 = .04