Treynor Ratio: How To Calculate it, Significance, and What Is Good? – (Example & Formula)

The Treynor Ratio, which is sometimes referred to as the reward-to-volatility ratio, was named after Jack Treynor, an American economist who developed it, who also happens to be one of the inventors of the Capital Asset Pricing Model (CAPM). But what is the Treynor Ratio about and how is it calculated?

Treynor Ratio is the excess return earned per unit of risk taken by a portfolio. It is a performance metric that measures the return a portfolio generates in excess of the risk-free rate and divides that by the systematic risk. As a measure of the risk-adjusted return of a financial portfolio, Treynor Ratio can be used to compare the performance of investments in different asset classes.

In this post, you will learn the following:

  • What the Treynor Ratio is
  • How it is calculated
  • The significance of the ratio
  • Examples of its uses
  • The limitations
  • The difference between the ratio and Sharpe Ratio

What is the Treynor Ratio?

Also known as the reward-to-volatility ratio, the Treynor ratio is a performance metric for determining how much excess return was generated for each unit of risk taken on by a portfolio. The Treynor reward to volatility model, named after Jack L. Treynor, is a measurement of the returns earned in excess of that which could have been earned from a risk-free investment.

The Treynor Ratio is a portfolio performance measure that adjusts for systematic – “undiversifiable” – risk. In contrast to the Sharpe Ratio, which adjusts returns with the standard deviation of the portfolio’s returns, the Treynor Ratio is a measure of returns earned in excess of the risk-free return at a given level of market risk. It highlights the risk-adjusted return based on the portfolio’s beta.

A security’s or portfolio’s beta is a measurement of the volatility of returns relative to the overall market. It shows how sensitive the portfolio’s returns are to movements in the market. A portfolio with a higher beta has a bigger return potential, but it also has a bigger risk. So, beta is a measure of systemic risk, which is the risk in a portfolio that cannot be offset by diversification within the same market. Beta is an integral part of the Capital Asset Pricing Model (CAPM).

In the stock market, the broad market index, such as the S&P 500, is given a beta of 1. A beta of more than 1 means that the asset or portfolio is more volatile than the market, while a beta of less than 1 but greater than zero indicates a less volatile asset. When the beta is zero, the asset is not correlated to the market, and when it is less than zero, the asset is negatively correlated to the market. By measuring the excess returns of a portfolio per unit systemic risk taken, the Treynor Ratio is a measurement of efficiency, utilizing the relationship between risk and returns.

How to calculate Treynor Ratio

The Treynor Ratio, sometimes called the reward to volatility ratio, is a risk assessment formula that measures the volatility in the market to calculate the value of the excess return per unit risk taken in a portfolio. It is a metric widely used in finance for calculations based on returns earned by a firm.

Unlike the Sharpe Ratio which uses the standard deviation of returns as the denominator, here, the denominator is the beta of the portfolio — which measures the volatility in the portfolio relative to that of the general market — while the numerator is the difference between the average returns from the portfolio and the average returns from a risk-free asset, which can be termed as the excess returns. Let’s learn the calculation; the Treynor Ratio formula is given as:

T = (rp – rf)/βp

Where:

T = Treynor Ratio

Rp = Portfolio’s return

rf = risk-free rate

βp = the beta of the portfolio, which measures the sensitivity of the portfolio’s returns to the movement of the market benchmark.

The Treynor ratio shows the risk-adjusted performance of the fund, so it uses actual returns rather than expected returns. When calculating it, these are the steps to follow:

  1. Subtract the risk-free rate of return (usually the returns of the short-term U.S. Treasury Bills) from the actual return generated by the portfolio over the past year to get the excess return from the portfolio
  2. Compute the portfolio beta by comparing its weekly returns to that of the market benchmark
  3. Divide the portfolio’s excess return with the portfolio’s beta

Is the Treynor Ratio graded?

The Treynor Ratio is not graded, but there are a few things you need to know about it:

  • The bigger the Treynor Ratio, the better, but the magnitude of the difference between two ratios is not indicated in the values since they are ordinal. Hence, while a ratio of 0.8 is greater than one of 0.4, it does not mean that the former is twice as good as the latter.
  • The denominator is the beta of the portfolio, which is a measure of its systematic risk relative to