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Virtually every investment decision in the financial market is preceded by ratio analysis. Interpreting metrics in tandem with objectives is a crucial practice for all market participants. That’s because such ratios offer key insights into different aspects of an investment, primarily how profitable it will be.

These ratios act as critical decision-making tools, providing an understanding of how different portfolios or securities fare. The Treynor ratio belongs to this realm of performance metrics.

## What is the Treynor Ratio?

Jack Treynor, an eminent American economist and one of the founding fathers of the Capital Asset Pricing Model, developed this metric.

It measures the excess returns a financial asset or a group of securities earns for every extra unit of risk assumed by the portfolio. It is also called the reward-to-volatility ratio since it betrays how much an investor is rewarded for the systematic risk undertaken.

This excess return is over and above the gains of a risk-free investment, which is often considered to be Treasury bills. For instance, if Treasury bills have a rate of return of 3% and a portfolio provides a rate of return of 10%, then 7% is the excess gain.

However, such a portfolio has to assume some degree of systematic risk to achieve additional returns. A portfolio’s beta value represents this component in the Treynor ratio.

Beta denotes the degree of change in returns a fund exhibits in response to market volatility. If the beta value of a financial asset or portfolio is high, it is more volatile and vice versa.

## How is the Treynor Ratio Calculated?

This measure gauges the returns from a collection of securities’ above a risk-free rate, adjusted by the beta value.

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Thus, the Treynor Ratio (TR) is calculated based on the following formula –

TR = (Portfolio’s returns – Risk-free return rate) / Beta value of the portfolio

Beta is a crucial factor in the Treynor ratio formula that distinguishes this metric. That is because it represents the systematic risk, which is volatility at a macro level. It’s determined by factors that are not influenced by portfolio diversification.

• Treynor ratio example

XYZ is a mutual fund with a rate of return of 15%. Its beta value is 1.3, meaning it’s 30% more volatile than the market. And the risk-free return rate is 3%.

Thus, XYZ’s Treynor ratio = (15% – 3%) / 1.3

Or, XYZ’s TR = 9.23

It’s a measure of risk-reward. Hence, if one were to invest in XYZ mutual fund, their compensation or reward for assuming one unit of risk will be Rs.9.23.

## How is the Treynor Ratio Useful?

Essentially, a Treynor ratio reveals how well each unit of risk that a collection of securities, mutual funds, or ETFs assumes, pays off. Thus, it isolates the risk-factor and provides investors with a better understanding of the gains they can earn by undertaking the same. It’s somewhat in line with Sharpe ratio, but not entirely similar.

Treynor ratio utilises the component of beta. Thus, it shows how a portfolio’s volatility correlates with that of the index, like Nifty 50 or Sensex. A beta above 1 means a fund is more volatile than the index and vice versa.

Therefore, TR acts as a crucial decision-making tool. Investors can compare different funds to determine which would be ideal to their risk-appetite as well as the one that provides reasonable returns at a particular level of risk. That’s why the Treynor ratio in mutual fund and ETF analysis is widely prevalent.

An example would better illustrate how investors can use TR to make investment decisions.

Raj is comparing between two mutual funds, X and Y. X is an equity fund, while Y is a fixed income fund. The rate of return of X is 12%, and that of Y is 7%. Additionally, Y’s beta is 0.5 and X’s is 1.2. It denotes that X is 20% more volatile, and Y is 50% less volatile than the market.

Let’s assume the risk-free return rate is 2%.

Therefore, X’s Treynor Ratio = (12% – 2%) / 1.2

Or, X’s TR = 8.33

The Treynor ratio of Y = (7% – 2%) / 0.5

Or, Y’s TR = 10

If Raj chose to go by such rates of returns, the obvious choice would have been X. However, this conclusion changes when those two options are compared based on Treynor ratio.

It shows that although X provides higher returns, it does not justify the risk such a fund assumes. Y compensates better for the assumed risk, and thus, is a better choice.

## What are the Limitations of Treynor Ratio?

One of the primary limitations of this metric is that it does not apply when the beta value of a portfolio is negative. Thus, it does not facilitate comparison between funds if one of them holds a negative beta value.

Another limitation of this ratio is its dependence on historical data. Even though a portfolio has fared better compared to another in the past, it’s no assurance that the same trend will repeat in the future.

Moreover, the accuracy of TR depends on whether one applies an appropriate index in its calculation. If one were to use Nifty 50 to determine TR of a portfolio consisting mainly of small and mid-cap stocks, then it would not work. It’s because Nifty 50 represents the top 50 large-cap stocks.

Lastly, this metric does not provide any basis to determine how much better one investment option is from another. If Fund A’s TR is 2.5 and Fund B’s TR is 5, it does not necessarily mean that the latter is two times better than the former.

Thus, like any other metric, investors should use TR along with other ratios to develop a better understanding.

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

The table below demonstrates the differences between these two metrics.

 Basis of distinction Treynor Ratio Sharpe Ratio Definition It measures the risk-adjusted returns of a portfolio based on its beta. It measures the risk-adjusted returns of a portfolio based on the standard deviation of its gains. Nature of risk considered It considers the systematic risk of a portfolio, which a fund manager cannot set off by diversifying. It considers the unsystematic risk of a portfolio, which can be set off by diversification. Suitability It’s more suitable to assess portfolios that are well diversified. It’s more suitable to assess a bevvy of securities that is less diversified.

Investment decisions go hand in hand with ratio analysis. Thus, having a clear understanding of them and applying metrics correctly can facilitate more effective decisions.

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