Last Updated on 17 November, 2020 by Samuelsson

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 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 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 that 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 that of the broad market.
• When the beta value is negative, the portfolio has no correlation with the market benchmark, so the value of the Treynor Ratio will not make any sense.

## The Significance of Treynor Ratio

As a measure of the risk-adjustment performance based on systematic risk, the Treynor Ratio shows how much return an investment in a particular market, such as a mutual fund, an ETF, or a portfolio of stocks, earned per unit risk taken by the investment over that period.

What this means is that you don’t use it for a portfolio of securities from different asset classes as there would be no benchmark to compute the beta. Using the equity market benchmark to compute the beta for such a portfolio could lead to a beta value of zero or a negative beta value, both of which would render the Treynor Ratio meaningless. A negative Treynor ratio indicates that the investment has performed worse than a risk-free instrument.

However, the ratio can be used to compare two separate portfolios in different asset classes, such as a portfolio of stocks and a portfolio of commodities. In this case, each portfolio’s beta is computed by comparing its returns to its market index, and the Treynor Ratio (which is the excess return per unit risk) of both portfolios can then be compared.

A higher Treynor Ratio is preferable, as it shows that the portfolio is a more suitable investment on a risk-adjusted basis. Since beta is a measure of the systematic risk, which cannot be reduced by diversifying within the same market, the Treynor Ratio tries to show how well the investment compensates the investor for taking the risk. Of course, an investor deserves a return for taking a risk, and the Treynor Ratio can tell him/her how much return the investment has earned per unit risk.

But you should note that the returns here are of the past, which may not indicate future performance. So, you shouldn’t rely on this one ratio alone for your investment decisions.

## How to use the Treynor Ratio

Being a risk-adjusted measure of historical performance, the Treynor Ratio can be used in many different ways in financial analysis. Here are some of them:

### Compare different funds – What is a good Treynor ratio?

One of the common uses of the Treynor Ratio is to compare the returns from different funds to know the one that earns more return compared to the amount of risk inherent in it. A fund may seem to be making more returns, but at the same time, the returns may be subject to significantly more volatility than the one that appears to be making a lower return.

Until you adjust the returns for risk, you won’t know the one that has been more efficient on per risk basis. For example, take a look at the table below:

 Fund A Fund B Fund C Beta 2.5 2.0 0.9 Returns 20% 18% 10% Risk-free rate (U.S. Treasury) 2% 2% 2% Treynor Ratio = (Portfolio return – risk-free rate)/Beta (0.20-0.02)/2.5   = 0.072 (0.18-0.02)/2.0   = 0.080 (0.10-0.02)/0.9   = 0.089

From the table above, Fund C has the least volatile returns as indicated by the lowest beta value. In fact, it is less volatile than the market benchmark is normally given a beta value of 1. But it turned out to offer the best return per unit risk taken as shown by the Treynor Ratio.

### Compare the risk-adjusted return of a stock portfolio to that of the equity market benchmark

You can use the Treynor Ratio to compare the return of your stock portfolio or a stock-based mutual fund to that of the equity market benchmark. For example, let’s say that your stock portfolio returned 21% in the past year and had a beta of 2.4, while the S&P 500 Index Fund returned 10% during the same period. We take the yield of the U.S Treasury Bills to be 2%.

Your portfolio’s Treynor Ratio = (0.19-0.02)/2.4 = 0.071

S&P 500 Index Fund’s Treynor Ratio = (0.10-0.02)/1.0 = 0.08

So, the market index yielded a better risk-adjusted return during that period. Note that the S&P 500 is given a beta value of 1 because it is a broad market index.

### Compare investments in different asset classes

Another use of the Treynor Ratio is to compare the return of investments in different asset classes since it gives the excess return per unit risk inherent in the investment. Let’s look at an example:

Assuming a portfolio of commodities has a beta value of 1.8 and earned 15% in the past year while a portfolio of stocks with a beta of 2.5 earned 22% during the same period, their Treynor ratios can be compared as follows. Here, we still take the U.S. Treasury Bill yield as 2%.

Treynor Ratio for the Commodity Portfolio = (0.15-0.02)/1.8 = 0.072

Treynor Ratio for the Stock Portfolio = (0.22-0.02)/2.5 = 0.080

Hence, on a risk-adjusted basis, the stock portfolio performed better.

## The drawbacks of the Treynor Ratio

The major drawback of the Treynor Ratio is that it uses historical returns, which may not be indicative of future performance. Another concern is that the market benchmark used to measure the beta must be appropriate for the fund you are analyzing as that can determine the accuracy of the measurement.

For instance, it would not be appropriate to use the Dow 30 Index to measure the beta of a mutual fund whose portfolio consists of small-cap companies.

## The difference between Treynor Ratio and Sharpe Ratio

Both the Treynor Ratio and Sharpe Ratio measure the performance of an investment per unit risk, but they do it differently. While the Treynor Ratio uses the portfolio’s beta, which is the degree of volatility in the portfolio relative to the whole market, as a measure for risk, Sharpe Ratio uses the standard deviation of the portfolio’s returns. Another difference is that Treynor Ratio uses historical returns only, while the Sharpe ratio can use either expected returns or actual returns. 