# 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

## Advantages and Disadvantages of the Treynor Ratio

The Treynor ratio’s value is limited to its comparison against other Treynor ratios. That is, it does not numerically describe the value added. It only has meaning in the context of its use as a ranking metric.

Portfolio beta as a determinant of risk is flawed. Volatility is not the equivalent of risk, though it can often be used as a convenient proxy. For portfolios with large upside potential but capped downside, such as portfolio long options, downside volatility risk will be low but upside volatility risk will be high. This is positive, because it can mean potential for capturing more gains. Beta will not accurately reflect this because it weights both upside and downside volatility equally. A better measure in this case might be the Sortino ratio.

Moreover, beta makes the assumption that the portfolios considered are not exposed to idiosyncratic risk. The risk associated is rather assumed to be systematic, or exclusively related to market risk. This is obviously frequently not the case, as portfolios that deviate from the indices they’re being compared to have risks pertaining to the idiosyncratic investment choices they make.

The main advantage to the Treynor ratio is that it provides a simple calculation to gauge the overall reward to risk profile of a given portfolio.