Sharpe Ratio vs Treynor Ratio: Difference Between Sharpe Ratio and Treynor Ratio

Expected returns and risks are the two primary dimensions around which the performance of any investment avenue is analysed. While some investors focus more on the return side, others look at the risk factor involved first. Particularly for mutual funds, the technical analysis requires you to dive deeper into the performance factsheet that includes information disclosed returns for different periods - since inception, last five years, last ten years, etc. This is where you would find metrics like the Sharpe ratio, and Treynor ratio, among many others.

What are these ratios and how can they be used to evaluate mutual fund performance? Let's take you through the detailed Sharpe ratio vs Treynor ratio comparison.

What is Sharpe Ratio?

Let's set the context for this ratio first -

Mutual fund investment performance is usually analysed in terms of whether the scheme has beaten the benchmark or index. For example, suppose the Nifty Fifty Index delivers a 15% return in a specific year while your mutual fund earns 17% in the same period. In that case, the fund has outperformed the underlying index by 200 basis points. While this approach to mutual fund analysis is quite easy to understand, it mainly considers the returns, not the risk.

Look at it from some other angle -

If the fund manager earns a 2% additional return, as in the example above, by taking thrice as much risk as the Nifty Fifty, then the outcome is not as great as it would seem otherwise. This is where the concept of risk-adjusted returns comes up, measured with the help of the Sharpe ratio.

Sharp ratio is a metric that calculates the returns delivered by a mutual fund scheme over the risk-free return. The difference is then divided by the standard deviation of the portfolio. As a measure of relative performance, this ratio helps investors in comparing various mutual fund schemes.

Sharpe ratio is calculated using the following formula:

Sharpe ratio = (Expected or Actual return on investment - risk-free return) / Standard deviation

You should also know that:

• The Sharpe ratio was first developed in the year 1966 by William Sharpe.
• Generally, the higher the ratio value, the more attractive the scheme seems to investors.
• The purpose of analysing this ratio is to determine whether you are selecting the right fund in exchange for accepting the risk involved as compared to selecting risk-free investment options.

Let's move to the other side of the Sharpe ratio vs Treynor ratio comparison.

What is Treynor Ratio?

The Treynor ratio was developed around the same period as the Sharpe ratio and is named after the U.S. economist Jack Treynor. The main difference between Sharpe and Treynor ratios is that both measure portfolio performance against distinct benchmarks. Unlike the Sharpe ratio, which measures the return of a portfolio against the return rate for a risk-free investment, the Treynor ratio substitutes beta in place of standard deviation in the same formula.

Here, beta is the systematic risk measure and determines how much the portfolio correlates with the benchmark. In other words, beta can also be defined as the return rate as per the overall performance of the market.

You should also know that:

• A portfolio with a beta greater than 1 is considered an aggressive one. On the other hand, defensive portfolios have a beta of less than one.
• The market index always has a beta equal to 1.

Consider this example for a better understanding -

Suppose a standard market index gives a 12% return, including beta, while the investment portfolio shows a 14% return. In that case, the Treynor ratio only encompasses the extra 2% return generated over and above the market performance. You can use this ratio to check whether your investment portfolio is expected to outperform the average gains in the market.

Sharpe Ratio vs Treynor Ratio Comparison

1. Primary Difference

As said above, the difference between the Sharpe ratio and Treynor ratio is that the former has standard deviation as the denominator in its​ formula, while the latter includes beta in place of the deviation. Using standard deviation helps in measuring the overall risk related to the portfolio. On the other hand, beta allows you to measure systematic risks like interest rates, inflation, and government policy amendments. What's more important to understand here is that unsystematic risks specific to an industry or company cannot be ignored.

You can use the Sharpe ratio as a measure of a portfolio that is not well-diversified. On the other hand, the Treynor ratio is a better alternative for well-diversified portfolios. Particularly for mid-cap and small-cap mutual funds without a credible index for benchmarking, the Sharpe ratio may be a better option to measure risk-adjusted returns.

1. Limitation

The primary drawback of using the Sharpe ratio is that investments without normal distribution of returns (For example - hedge funds) accentuate it. Many such investments involve dynamic trading that can lead to sudden changes in returns.

Treynor ratio, on the other hand, may seem disadvantageous because of its backwards-looking nature. The beta used in its calculation relies on a specific benchmark. Many investments may not perform ahead as they did in the past.

Both Sharpe and Treynor ratios can be used to rank mutual fund schemes. The more you know about the differences between the two, the better it will be for you to decide when to use which ratio. Whichever way you go, remember that the final returns you will receive depend on the type of mutual fund you select and the related risk exposure.