# What is the Treynor Ratio?

Osmand Vitez

The Treynor ratio is a statistical tool individuals can use to measure the performance of their investment portfolios. The purpose of the Treynor ratio is to calculate the return of a financial portfolio that has no diversifiable risk. Another feature of this ratio is the use of systematic risk, which is defined as the inherent risk found in the entire investment market. The developer of the ratio is Jack L. Treynor, an American investment professional. He attended Harvard University as a mathematics major and helped to create the capital asset pricing model. The Treynor ratio is a statistical tool individuals can use to measure the performance of their investment portfolios.

The Treynor ratio uses three different figures in its calculation: a portfolio’s average rate of return, average return for a risk-free investment, and the beta of the portfolio. While the first two pieces are pretty basic, beta is a somewhat unique and complex investment theory. In short, the beta is a number specific to each stock that indicates the return of a stock against the financial market. In investment theory, the stock market has a beta of 1.0; stocks with a beta over 1.0 move more than the market while a beta of less than 1.0 indicates a stock will move less than the entire market. For example, assume a stock has a beta of 2.0. When the entire market rises 5 percent, the stock will rise 10 percent. The reverse is also true, where the stock will fall twice as much when the market decreases.

To calculate the Treynor ratio, assume the following: a stock portfolio has a three-year average return of 15 percent, the three-year average of a risk-free investment is 5 percent, and the portfolio has a 1.5 total beta. The risk-free investment in this ratio is usually a government’s treasury bonds, assuming the government is stable and economic conditions are relatively favorable. While other investments may be considered risk-free, treasury bonds are usually the most common investment. The formula for the Treynor ratio is portfolio return less the risk-free investment return divided by the portfolio beta. Using the figures above, the portfolio’s Treynor ratio is 9.0 (15 – 5 / 1.5). The higher the ratio result, the better the performance of the portfolio.

This ratio can provide a good historical indicator when measuring a portfolio’s performance. Like all investment measurement tools, however, the formula is only as good as the information in the formula. Additionally, using beta leaves out the total risk — or standard deviation — of the portfolio. While these figures are important, the benefit of using beta is that it is readily available on most financial websites, allowing users to quickly calculate the formula.

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