# Treynor Ratio

The Treynor ratio, also called the reward-to-volatility ratio, it measures portfolio performance by calculating the excess return per unit of risk. Excess return is the return above what a risk-free investment would earn.
Treynor Ratio
18-June-2024

The Treynor ratio, also known as the reward-to-volatility ratio, assesses how much additional return a portfolio generates per unit of risk undertaken. Here, "excess return" indicates the return above what could be earned in a risk-free investment. For instance, consider Portfolio Manager A who achieves an 8% portfolio return in a year when the risk-free rate is 5%, with a portfolio beta of 1.5. In comparison, Portfolio Manager B achieves a 7% portfolio return with a beta of 0.8 during the same period.

Before you decide to invest your hard-earned money in any stock, mutual fund or market-linked asset, you need to assess the true risk-reward proposition it offers. The Treynor ratio is one of the many metrics that can help you with this assessment. It is named after American economist Jack Treynor, who developed this ratio and was renowned for co-creating the Capital Asset Pricing Model (CAPM).

Let us see what the meaning of the Treynor ratio is and how you can calculate it.

## Treynor ratio definition

The Treynor ratio is a measure of the risk-adjusted returns earned from an asset per unit of systematic risk it brings. For this reason, it is also called the reward-to-volatility ratio. The systematic risk of an asset is represented by its beta.

The risk-adjusted return, on the other hand, is simply the excess return that an asset offers beyond the risk-free rate. While there is technically no risk-free investment, the rate of returns offered by Treasury Bills (T-bills) is commonly considered to be the risk-free rate for calculating the Treynor ratio.

## Key takeaways

• The Treynor ratio, named after economist Jack Treynor, measures the risk-adjusted returns of an asset per unit of systematic risk (beta).
• It helps investors evaluate how much excess return an investment generates relative to its risk level.
• To calculate the Treynor ratio, subtract the risk-free rate of return from the asset's return and divide by its beta.
• This formula provides a quantitative measure to assess investment performance adjusted for risk.
• Investors use the Treynor ratio to compare the risk-adjusted returns of different assets or portfolios.
• Unlike the Treynor ratio, the Sharpe ratio considers total risk (standard deviation) rather than just systematic risk (beta), providing a broader assessment of risk-adjusted returns.

## How the Treynor ratio works

In essence, the Treynor ratio aims to gauge how effectively an investment compensates investors for assuming investment risk. This ratio hinges on the portfolio's beta, which indicates how sensitive the portfolio's returns are to market movements and serves as a measure of risk.

The underlying principle of this ratio is that investors should receive compensation for the inherent risk of the portfolio, which cannot be eliminated through diversification efforts.

## The formula for the Treynor ratio andhow to calculate it

The process of calculating the Treynor ratio in a mutual fund scheme or any other asset is easy as long as you have the required inputs. Check out the formula to compute this ratio:

 Treynor Ratio = (Rp — Rf) ÷ βp

Here, Rp represents the returns from the asset or portfolio, Rf represents the risk-free rate of returns and βp indicates the beta value of the portfolio or asset. The beta measures the volatility in an asset’s price relative to the broad market as a whole. In other words, it tells you about the systematic risk in the asset.

Let us discuss an example of how to calculate the Treynor ratio and interpret it. Say an asset has the following characteristics:

• Annual rate of returns = 20%
• Risk-free rate of returns = 7%
• The beta of the asset = 1.8

A beta of 1.8 means the asset is 80% more volatile than the overall market, which indicates a fairly high level of risk. Substituting these values in the formula for the ratio, we have the following:

Treynor ratio:

= (20% — 7%) ÷ 1.8

= 13% ­÷ 1.8

= 7.22%

## Interpreting the Treynor ratio

The Treynor ratio effectively tells you the true returns you can expect from an asset after factoring in its systematic risk. In the example discussed above, although the returns from the asset may appear to be 20% at first glance, the Treynor ratio shows you that the risk-adjusted returns dwindle to 7.22%.

The thumb rule to interpret the ratio is simply that the higher it is, the better.

## Uses of the Treynor ratio

The Treynor ratio in mutual funds and other assets can be extremely useful for making investment decisions. One of the most common uses of this ratio is to help investors evaluate the risk-adjusted returns of an asset — and use that information to decide if it is worth investing in the same. Additionally, you can also use the Treynor ratio to compare the risk-adjusted returns of different assets in the same category.

## Drawbacks of the Treynor ratio

The Treynor ratio is extremely useful, but it also has certain limitations that you must be aware of. Firstly, this ratio is not helpful if the beta of an asset is negative because it makes any comparison meaningless. Additionally, the Treynor ratio depends heavily on historical data, which is not a guarantee of future performance or returns.

Another drawback is that the Treynor ratio is only effective as a decision-making tool if the right benchmark is used to compute the beta. For instance, if you use the Sensex as a benchmark for a portfolio mostly consisting of small-cap stocks alone, the exercise will be futile.

Lastly, the Treynor ratio does not have any specific scale or benchmark to facilitate in-depth comparisons. While you know that an asset or a portfolio with a higher ratio is better, you cannot assess how much better it is than an asset with a lower ratio.

## Treynor ratio vs Sharpe ratio: How do they differ

The key difference between the Treynor ratio and the Sharpe ratio is the nature of the risks they account for. The Treynor ratio takes the systematic risk (or beta) into account, while the Sharpe ratio factors in the standard deviation or the absolute risk of an asset.

## Conclusion

The Treynor ratio is only one of the many metrics that can be used to assess the feasibility of an investment option. To make an informed and well-rounded decision, ensure that you account for its limitations and compare mutual funds of stocks with their peers. This way, you can get a clear picture of the risks and potential returns from an investment option and evaluate if it aligns with your goals.

Once you know which type of funds you want to invest in, you can simply do it through the Bajaj Finserv Mutual Fund Platform. Investing through this platform is also easy and hassle-free, and you can choose to make a lump sum or SIP investment in the funds of your choice.

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What is the Treynor ratio in mutual funds?

The Treynor ratio in mutual funds is a measure of the risk-adjusted returns. It calculates the excess returns you earn per unit of systematic risk taken, over and above the risk-free rate.

How can I calculate the Treynor ratio?

To calculate the Treynor ratio, first find the difference between the asset or portfolio’s returns and the risk-free rate of returns. Then, divide this difference by the asset’s beta to find the Treynor ratio.

Which is better: A high Treynor ratio or a low one?

Yes, a high Treynor ratio is generally considered to be better because it means you earn more risk-adjusted returns for the risk taken by investing in a given asset.

What does a negative Treynor ratio indicate?

A negative Treynor ratio may occur either because the beta is negative (in which case the ratio is not meaningful) or because the asset’s returns are less than the risk-free rate (in which case it is a poor investment).

What value of the Treynor ratio is considered good for investors?

There is no specific range of the Treynor ratio values that may be good or bad. However, a higher Treynor ratio is preferable, while a negative Treynor ratio means the investment may be unsuitable.

What is the Treynor formula?

The Treynor formula calculates the Treynor ratio, which measures the risk-adjusted return of an investment relative to its systematic risk (beta). It is expressed as: Treynor Ratio = (Rp — Rf) ÷ βp, where Rp is the portfolio return, Rf is the risk-free rate, and βp is the portfolio beta.

Is Treynor ratio same as Sharpe ratio?

No, the Treynor ratio differs from the Sharpe ratio. While both assess risk-adjusted returns, the Treynor ratio considers only systematic risk (beta), whereas the Sharpe ratio incorporates total risk (standard deviation).

What is the Treynor ratio also known as?

The Treynor ratio is also known as the reward-to-volatility ratio because it measures how much excess return an investment generates per unit of systematic risk (volatility).

What is a good value for Treynor ratio?

A higher Treynor ratio indicates better risk-adjusted returns. Generally, a ratio above 1 is considered good, but the interpretation depends on the investor's risk tolerance and the comparison with similar investments.

What is CAPM and Treynor ratio?

CAPM (Capital Asset Pricing Model) is a financial model that uses the Treynor ratio to estimate the expected return of an asset based on its beta and the risk-free rate. The Treynor ratio within CAPM helps investors assess whether an asset's returns adequately compensate for its systematic risk.

What is the Treynor and Sortino ratio?

The Treynor ratio measures risk-adjusted returns relative to systematic risk (beta), whereas the Sortino ratio evaluates risk-adjusted returns based on downside risk or volatility below a specific threshold. Both ratios provide different perspectives on how investments perform relative to the risks they carry.

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Bajaj Finance Limited (“BFL”) is an NBFC offering loans, deposits and third-party wealth management products.

The information contained in this article is for general informational purposes only and does not constitute any financial advice. The content herein has been prepared by BFL on the basis of publicly available information, internal sources and other third-party sources believed to be reliable. However, BFL cannot guarantee the accuracy of such information, assure its completeness, or warrant such information will not be changed.

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