# What Is the Treynor Ratio?

by Angel One
The Treynor ratio is an effective metric used to evaluate the excess returns you earn for every additional unit of risk. It is a crucial part of fundamental analysis and used to evaluate mutual funds.

Fundamental analysis is an essential exercise for medium-term and long-term investors in the stock market. It involves evaluating an investment’s intrinsic value and checking if the rewards justify the risks. To weigh the risks and rewards against one another, you can rely on various ratios and metrics. One of the most popular ratios in this category is the Treynor ratio

If you are a beginner to long-term investing, you may not be aware of what the Treynor ratio is and why it is significant. Worry not, because in this article, we’ll delve into the finer details of the Treynor ratio, how to calculate it and how you can use it to make smart investment choices.

## What Is the Treynor Ratio?

The Treynor ratio is a performance indicator that measures the excess return an investment or portfolio generates for every unit of risk taken on by that asset or portfolio. The ratio is thus named because it was developed by American economist Jack Treynor, who played a pivotal role in developing the Capital Asset Pricing Model (CAPM)

The Treynor ratio is also known as the reward-to-volatility ratio because it tells you how you are rewarded for the systematic risk you take on in your portfolio. To measure this, the Treynor ratio compares the following two metrics:

• The excess return from an asset or portfolio
• The systematic risk of the asset or portfolio

Here, the excess return is the additional return you gain over and above the risk-free rate of returns. Although there is practically no risk-free investment, the rate of returns from treasury bills is considered the theoretical risk-free rate. As for the systematic risk, it is measured by the beta of the asset or portfolio, as the case may be.

Now that we’ve discussed what the Treynor ratio is and looked at the key metrics it compares, let’s move on to see how you can calculate it.

## How Is the Treynor Ratio Calculated?

To calculate the Treynor ratio, you simply need to divide the excess returns from an asset or portfolio by its systematic risk or beta. Putting this together, we get the following Treynor ratio formula:

Treynor Ratio = (Rp — Rf) ÷ βp

Where:

Rp is the rate of returns from the portfolio or asset

Rf is the risk-free rate of returns

Βp is the beta of the portfolio i.e. the level of volatility of the security compared to the market as a whole.

To calculate the Treynor ratio using the above formula, you only need to input the required values. Let’s look at an example to understand how the Treynor ratio is calculated. Consider the following details for a mutual fund:

• Rate of returns per annum: 16%
• Risk-free rate of returns per annum: 5%
• The beta of the mutual fund: 1.4

A beta of 1.4 means that this mutual fund is 1.4 times or 40% more volatile than the market. Using the Treynor ratio formula, we can calculate the metric thus:

Treynor ratio = (16% — 5%) ÷ 1.4

This gives us a Treynor ratio of 7.86% or 0.0786.

## How To Interpret the Treynor Ratio?

Once you calculate the Treynor ratio, you need to understand how to interpret it. Only then can you use this metric in your decision-making process. So, let’s continue with the above example itself and see how you can interpret the ratio obtained.

The hypothetical mutual fund we discussed has a Treynor ratio of 7.86%. This is essentially the risk-adjusted returns from the fund. Although its overall returns may be 16%, its true returns when compared with the risk taken are only 7.86%.

This number can be interpreted on an individual basis, or you can use the ratio to compare multiple investments or securities. Let’s delve into the details of how you can use the Treynor ratio to your advantage to obtain more clarity about your investments and portfolio.

## How Is the Treynor Ratio Useful?

The Treynor ratio is a powerful tool for evaluating and comparing investments for your portfolio. It also helps you evaluate your portfolio at large. Here’s how the ratio can be useful in different ways.

• ### Evaluating the Risk-Adjusted Performance

The main use of the Treynor ratio is to assess the risk-adjusted returns from an investment. If the returns earned do not justify the risk exposure, the security or asset may not be a suitable addition to your portfolio. Additionally, understanding the risk-adjusted performance will also help you understand the true returns from any security. So, you can set your expectations accordingly and align your financial goals to match up to the adjusted returns.

• ### Comparing Different Investments

With the Treynor ratio, it also becomes easier to compare different investments and securities. The higher the Treynor ratio is, the better the risk-adjusted performance of an asset or investment will be. This will make it easier for you to choose between different stocks or mutual funds for your portfolio. That said, keep in mind that the ratio is best used to compare securities or investments with similar risk profiles.

• ### Portfolio Optimisation

The Treynor ratio also helps with overall portfolio optimisation. Portfolio managers can select assets with high risk-adjusted returns to optimise the risk-reward ratio of the portfolios they manage. You can also use the ratio to optimise your own asset portfolio and diversify it with assets whose returns justify the risks they carry. This effectively helps tip the balance of risks and rewards in the favour of the latter.

## What Are the Limitations of the Treynor Ratio?

For all its upsides, the Treynor ratio also has a few limitations that you should be aware of. This way, you can use the ratio along with other indicators and evaluation metrics to get a comprehensive overview of the investments or assets you wish to add to your portfolio. The limitations include the following:

• ### Dependence on Historical Data

To calculate the Treynor ratio, you need to rely on historical data. This is limiting because investments may not perform in a similar manner in the future. So, if a portfolio or security has a good risk-adjusted return rate based on the Treynor ratio, there is no guarantee that this will be repeated in the future.

• ### Not Meaningful for Assets with Negative Beta

The ratio may not be very meaningful because it is based on the Capital Asset Pricing Model, which assumes a positive linear relationship between the expected returns and the beta (or systematic risk). So, the Treynor ratio is not very meaningful for assets with a negative beta or a negative correlation with the market volatility.

• ### No Way to Quantify the Comparison

While you can use the Treynor ratio to compare the risk-adjusted performance of different assets, it is not possible to measure how much better one asset is than another. This makes it difficult to assess the marginal advantage that one asset or security offers over another. However, you can still compare different investment options effectively.

## What Is the Difference between Treynor Ratio and Sharpe Ratio?

The Sharpe ratio and the Treynor ratio are both used to analyse and compare stocks, securities or portfolios. However, they are quite different in many respects, as summarised in the table below:

 Particulars Treynor Ratio Sharpe Ratio Meaning This ratio measures the risk-adjusted returns based on the beta This ratio measures the risk-adjusted returns based on the standard deviation Risk Metric Used Portfolio or asset beta Standard deviation of the asset or portfolio Nature of Risk Measured Measures the systematic risk Measures both systematic and unsystematic risk Best Used For To evaluate an investment’s performance relative to its systematic risk To assess an investment’s performance in relation to its total risk

## Conclusion

This article gives you a clear idea of what the Treynor ratio is and how it is useful. That said, it is advisable to use this ratio alongside other metrics like the Sharpe ratio and Sortino ratio among others. This will help you evaluate your investments or your portfolio more comprehensively so that you can make informed and well-rounded investment decisions.

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## FAQs

### What does the Treynor ratio tell me about an investment?

The Treynor ratio tells you how well an investment or a portfolio performs relative to the systematic risk it’s exposed to. It essentially helps you assess if the returns you earn from an investment justify the risk it carries. A higher Treynor ratio indicates better risk-adjusted performance.

### Why is the risk-free rate used in calculating the Treynor ratio?

The risk-free rate is crucial to calculate the Treynor ratio because it represents the minimum returns you can expect from the investment — when you take on no risk whatsoever. By subtracting the risk-free rate from the total portfolio/investment risk, the ratio tells you how much of the returns can be attributed to the systematic risk taken.

### Is a high Treynor ratio good?

Yes, a high Treynor ratio is favourable because it indicates that your investment or portfolio has generated high returns for each unit of systematic risk. This justifies the risk exposure because the investment or portfolio has performed well in relation to the market.

### Can I use the Treynor ratio to compare two or more investments?

Yes, the Treynor ratio is useful if you want to compare the risk-adjusted performance of two or more investments. They may be stocks, bonds, mutual funds, and even whole portfolios with different assets.

### What does the portfolio beta represent in the formula for the Treynor ratio?

The portfolio beta used in the Treynor ratio formula indicates how sensitive the investment or portfolio is to market movements. It represents the systematic risk or the risk inherent in the market or the segment to which an asset belongs.