Treynor Index

What Is the Treynor Index?

The Treynor Index measures the risk-adjusted performance of an investment portfolio by analyzing a portfolio's excess return per unit of risk. In the case of the Treynor Index, excess return refers to the return earned above the return that could have been earned in a risk-free investment. (Although this is a theoretical speculation because there are no true risk-free investments.)

For the Treynor Index, the measure of market risk used is beta, which is a measure of overall market risk or systematic risk. Beta measures the tendency of a portfolio's return to change in response to changes in return for the overall market. The higher the Treynor Index, the greater the excess return being generated by the portfolio per each unit of overall market risk.

The Treynor Index is also known as the Treynor Ratio or the reward-to-volatility ratio.

Formula and Calculation of the Treynor Index

The formula for the Treynor Index/Ratio is:

Treynor Ratio = PR − RFR PB where: PR = Portfolio return RFR = Risk free rate \begin{aligned}&\text{Treynor Ratio}=\frac{\text{PR}-\text{RFR}}{\text{PB}}\\&\textbf{where:}\\&\text{PR}=\text{Portfolio return}\\&\text{RFR}=\text{Risk free rate}\\&\text{PB}=\text{Portfolio beta}\end{aligned} Treynor Ratio=PBPR−RFRwhere:PR=Portfolio returnRFR=Risk free rate

What the Treynor Index Can Tell You

The Traynor Index indicates how much return an investment, such as a portfolio of stocks, a mutual fund, or exchange-traded fund, earned for the amount of risk the investment assumed. A higher Treynor Index means a portfolio is a more suitable investment. The index is a performance metric that essentially expresses how many units of reward an investor is given for each unit of volatility they experience.

Like the Sharpe ratio — which uses standard deviation rather than beta as the risk measure — the fundamental premise behind the Treynor Index is that investment performance has to be adjusted for risk in order to convey an accurate picture of performance. The Traynor Index was developed by economist Jack Treynor, an American economist who was also one of the inventors of the Capital Asset Pricing Model (CAPM).

While a higher Treynor Index may indicate a suitable investment, it's important for investors to keep in mind that one ratio should not be the only factor relied upon for investing decisions. More importantly, since the Treynor Index is based on historical data, the information it provides does not necessarily indicate future performance.

Example of the Treynor Index

For example, assume Portfolio Manager A achieves a portfolio return of 8% in a given year, when the risk-free rate of return is 5%; the portfolio had a beta of 1.5. In the same year, Portfolio Manager B achieved a portfolio return of 7%, with a portfolio beta of 0.8.

The Treynor Index is therefore 2.0 for Portfolio Manager A, and 2.5 for Portfolio Manager B. While Portfolio Manager A exceeded Portfolio Manager B's performance by a percentage point, Portfolio Manager B actually had the better performance on a risk-adjusted basis.