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Treynor Ratio

A Risk-Adjusted Return Ratio

What is the Treynor Ratio?

The Treynor Ratio is a portfolio performance measure that adjusts for systematic risk. In contrast to the Sharpe Ratio, which adjusts return with the standard deviation of the portfolio, the Treynor Ratio uses the Portfolio Beta; which is a measure of systematic risk.

The two ratios are concerned with both the risk and return performance of a portfolio and are a quotient of return divided by risk. The Treynor Ratio got its name from Jack Treynor, who was an American economist known as one of the Inventors of the Capital Asset Pricing Model.

Treynor Ratio

Treynor Ratio Formula

From the formula below, you can see that the ratio is concerned with both the return of the portfolio and its systematic risk. From a purely mathematical perspective, the formula represents the amount of excess return from the risk-free rate per unit of systematic risk. Like the Sharpe Ratio, it is also a Return/Risk Ratio.

Treynor Ratio Formula

 

The Treynor Ratio measures portfolio performance and is part of the Capital Asset Pricing Model. To read more about how to calculate Beta, click here.

 

Treynor Ratio Example

Suppose you are comparing two portfolios, an Equity Portfolio and a Fixed Income Portfolio. You’ve done extensive research on both portfolios and can’t decide which one is a better investment. You decide to use the Treynor Ratio to help you select which portfolio would be a more suitable investment.

The Equity Portfolio’s total return is 7%, and the Fixed Income Portfolio’s total return is 5%. As a proxy for the risk-free rate, we use the return on U.S Treasury Bills, which was 2%. Now assume that the Beta of the Equity Portfolio is 1.25, and the Fixed Income Portfolio’s Beta is 0.7. From the following information, we compute the Treynor Ratio of each portfolio.

Treynor Ratio Example

From the result above, we see that the Treynor Ratio of the Equity Portfolio is slightly higher – thus, we can deduce that it is a more suitable portfolio to invest in. One thing to remember is that Treynor Ratio values are based on past performance, and may not translate into actual future performance. As a financial analyst, it is important to not rely on only one ratio for your investment decision.

 

When using the Treynor Ratio, keep in mind:

  • For negative values of Beta, the Ratio does not give meaningful values.
  • When comparing two portfolios, the Ratio does not extract the economic significance on the difference of the values, as they are ordinal. For example, a Treynor Ratio of 0.5 is better than one of 0.25, but not necessarily twice as good.
  • The numerator is the excess return to the risk-free rate, and the denominator is the Beta of the portfolio, or, in other words, a measure of systematic risk of a portfolio.

 

More Resources

CFI offers the Financial Modeling & Valuation Analyst (FMVA)™ certification program for those looking to take their careers to the next level. To keep learning and advancing your career, the following resources will be helpful:

  • Capital Asset Pricing Model (CAPM)
  • Internal Rate of Return (IRR)
  • Treasury Bills (T-Bills)
  • Financial Modeling Guide

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