# Treynor Ratio: Definition, Calculation & Other Details

10 min read • Published 28 October 2022
Written by Anshul Gupta

Before choosing a mutual fund , investors must  assess their risk-taking capacity to determine  if the investment is suitable. Besides this, there are several factors that people need to evaluate, such as a fund’s historical performance, costs, investment objectives, fund manager’s expertise, etc.

Several mutual fund ratios help  us assess a particular fund’s risk levels and return potential. The Treynor ratio is one such important ratio that people can check to evaluate the performances of their shortlisted mutual funds.

## What Is the Treynor Ratio?

This mutual fund ratio is also referred to as ‘reward to volatility ratio’. It measures the additional returns that a group of securities or a particular financial asset earns for every extra unit of risk that has been taken.

Mutual fund investments are always associated with risks, and the Treynor ratio is one such risk assessment formula that assists us. Let us look at the important types of risks that the Treynor ratio takes into account:

• Market risk

It is the overall risk of the entire market falling due to unavoidable macroeconomic factors. Generally, investors tend to follow the direction of the market. As a result, market risk can also be defined as the tendency of security prices to move together in the same market direction. For example, the share prices of established companies fall when the overall market falls.

Mutual fund investments are also subject to market fluctuations. For instance, the value of investments may rise when the market falls and vice versa. The Treynor ratio places every investment on a risk-free level, i.e. it adjusts investments with respect to their market volatility and associated risks before comparing their performances.

It is named after Jack Treynor, a famous American economist, who considered William Sharpe’s work while developing this mutual fund ratio. So while it is similar to the Sharpe ratio, there are differences as well, the chief among them being that the Treynor ratio uses the beta value in the denominator.

To elaborate further, the Treynor ratio uses a fund’s beta value as a measurement of risk. Potential investors can assess the risks associated with a scheme by comparing a fund’s beta value to market volatility.

We will explore the differences between these two mutual fund ratios later. First, let us analyse how the Treynor ratio works.

## How Does the Treynor Ratio Work?

The Treynor ratio is a measure of a mutual fund’s risk-adjusted performance using the beta of its portfolio. It measures a fund’s systematic risks, unlike the Sharpe ratio, which uses standard deviation to calculate risk-adjusted returns. In other words, the Treynor ratio measures extra returns a fund has generated over the returns of a risk-free investment against additional risks it has taken.

The beta value of a mutual fund plays a vital  role in Treynor ratio calculation. It helps understand how volatile an investment is concerning  its current position in the stock market.

Let’s understand how beta value affects the mutual fund:

• Beta value has a baseline of 1 for mutual funds. So, if a mutual fund has a higher beta value, it indicates that it is more volatile than its benchmark index.
• In contrast, a fund with a few volatile stocks may have a beta value of less than 1.

When the beta value is greater than one, it indicates that the mutual fund is more volatile than its underlying benchmark. Such funds would rise higher than the market when the latter rises. In addition, they fall lower when the market spirals down.

If it is less than one, it indicates that the fund is less volatile than its benchmark. In other words, the fund shares a low correlation with the market. So, for example, if the market rises by 9%, the fund’s returns will rise by a value less than 9%.

However, if the beta value of a fund is equal to 1, its returns are aligned with the benchmark returns. In other words, it shares a perfect correlation with the market.

A negative beta value indicates that the mutual fund shares a negative correlation with the market. In other words, if the market rises by 5%, the fund will fall by 5% and vice versa. For example, Gold generally has a negative beta value. This is because it does not move in the same direction as the stock market.

It is important to remember that stocks with a high beta value are more prone to market fluctuations when compared to those with a lower beta value. So, when potential investors decide to make an average comparison of beta values, it will not provide an accurate result. Moreover, as a fund’s beta is calculated using its historical returns, it cannot accurately predict its future returns.

This is where the importance of the Treynor ratio lies, as it allows people to compare investments that do not share anything in common by evaluating their returns based on per unit of risks. For example, investors can compare the performances of a stock portfolio and a corporate bond portfolio on a risk-adjusted basis.

## How to Calculate Treynor Ratio?

Given below is the formula for calculating the Treynor ratio of mutual funds:

Treynor ratio = (Rp – Rf) / B

Here, Rp = Return on the portfolio

Rf = Risk-free rate (often the returns from Treasury Bills)

B = Beta, Shows the sensitivity of any portfolio as compared to its the market index

An Example of Treynor Ratio

Let us use an example to understand the Treynor ratio better. The table given below provides the beta value and returns percentage for three schemes:

To calculate the Treynor ratio, we also need the risk-free rate of these three investments. Suppose the risk-free rate of all three funds  is 5%.

Now, let us proceed to calculate the Treynor ratio for all three schemes:

Treynor ratio for mutual fund A = (10% – 5%) / 1.05 = 0.05

Treynor ratio for mutual fund B = (12% – 5%) / 0.8 = 0.09

Treynor ratio for mutual fund C = (20% – 5%) / 2.2= 0.07

From the above calculations, we understand that mutual fund B has the highest Treynor ratio of the three schemes. This is because with a better return %, it also has a low beta compared to the other schemes.

We can conclude that mutual fund B has the best performance. On the other hand, mutual fund C has the second-best performance, while mutual fund A has the lowest performance.

Now, let us look at the raw data of the performances of these schemes. Considering the return percentage of the schemes, mutual fund C has the best performance with a return percentage of 20% and mutual fund B is second-best.

However, the Treynor ratio of these mutual funds presents a different picture altogether. The primary reason behind this difference is that while calculating the Treynor ratio, we consider the overall market risks of a fund’s portfolio.

## Benefits of the Treynor Ratio

The benefits  of using the Treynor ratio for mutual fund investments:

• The Treynor ratio helps in assessing and analysing each Mutual Fund in the portfolio
• It also helps in making a better informed investment decision when you have to choose amongst multiple funds.
• With Treynor ratio, you can calculate risk adjusted returns of various funds and compare them in order to optimise your portfolio.

## Limitations of Treynor Ratio

Although the Treynor ratio is a helpful metric for analysing the performances of various mutual funds, investors need to be aware that it also suffers from certain limitations. The following are some of its significant  limitations:

• Treynor ratio is dependent on past performances of securities. In addition, it also considers any unusually volatile market behaviour from the past.
• As Treynor ratio relies on historical performance of a scheme, it disregards the fact that markets may perform differently, and investments may generate better returns in the future. In other words, knowledge of historical returns is not enough for mutual fund analysis, as portfolios are subject to change.
• It also does not consider that large-cap and small-cap funds might exhibit different levels of volatility. This is especially problematic because the beta value of a fund is considered for calculating the Treynor ratio  Hence, it might be difficult to compare two funds with entirely different investment objectives.
• There is no clear data with respect to how high a Treynor ratio should be. It is entirely subjective. Investors must use the Treynor ratio in conjunction with other ratios like sharpe ratio, standard deviation, etc to make  a better investment decision.

For example, suppose a mutual fund has a beta of 2 and has generated an average return of around 13% in the past. It may not continue to perform in the same way in the future. Returns will increase or decrease based on macroeconomic factors.

## What Are the Differences between Treynor Ratio and Sharpe Ratio?

The table below illustrates the differences between these two important mutual fund ratios:

## Final Word

Many people need help to balance their return expectations with their risk appetites.  That is where the different mutual fund ratios, such as alpha, beta, standard deviation, Sharpe ratio and Treynor ratio, become essential tools for shortlisting investments. Financial experts recommend using the Treynor ratio as it shows the additional returns a fund generates for every extra unit of risk it takes.

### Does the Treynor ratio use standard deviation?

No, the Treynor ratio doesn’t use standard deviation. Treynor Ratio uses beta in the denominator. Beta is a mutual fund ratio that evaluates the systematic risk present in a mutual fund. Unlike the Treynor ratio, the Sharpe ratio uses standard deviation as its denominator.

### When to apply the  Sharpe and when to apply the Treynor ratio?

Investors can use the Sharpe ratio to evaluate a fund when its portfolio is not well diversified. On the other hand, the Treynor ratio can be used when a scheme’s portfolio is well diversified.

### What are market risks?

The continuous change in the market affects the mutual fund’s performance which is seen during market volatility.   Possibility  of loss due to such fluctuations in the market is referred to as market risk.

IIT Roorkee Alumnus and CFA with experience of structuring debt products worth more than 15000Cr for institutional and retail investors.

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