Understanding Sharpe versus Treynor in evaluating MF portfolios - Motilal Oswal

# Understanding Sharpe versus Treynor in evaluating MF portfolios

If you open the factsheet of any equity mutual fund, you will find the Sharpe ratio disclosed of the fund under the fund analytics section. Some funds also disclose the Treynor ratio for the particular equity fund. So what exactly are these Sharpe Ratios and Treynor ratios and how can investors interpret these ratios? More importantly, can the Sharpe and Treynor Ratios be used to evaluate fund performance and take a decision with respect to fund selection?

What exactly is the Sharpe Ratio all about?
The normal performance metrics of a mutual fund investments is whether the fund has actually beaten the index or not. So if the Nifty index has earned 16% returns last year and your fund has earned 18% last year then your fund has outperformed the index by 200 basis points. This is a very simple and elegant measure that appeals to every investor. But then this measure only looks at the returns and not the risk. So if your fund manager has earned 2% additional return by taking on twice as much as risk as the Nifty then in risk-adjusted terms the fund manager’s performance is not exactly great. It is this concept of risk-adjusted returns that Sharpe Ratio measures.

Sharpe Ratio = {(Return on the Fund – Risk-Free returns) / Standard deviation of fund returns}

The return of the fund is the return that your fund manager earns in absolute terms. The risk-free return is what you would have earned without any risk as in case of a bank FD. Obviously, your measure is going to start only beyond the risk free rate. Standard deviation measures the risk through volatility and Sharpe therefore measures excess returns per unit of total risk.

Then, what exactly is the Treynor Ratio all about?
The Treynor also is a measure of excess returns earned by the fund manager per unit of risk. The numerator remains the same in case of Sharpe and Treynor (Rm – Rf). What changes is the denominator. While Sharpe ratio uses the standard deviation as the denominator, the Treynor ratio uses the Beta as the denominator. Beta, as we popularly know, is a measure of systematic risk of the portfolio and calculates to what extent the stock or the portfolio correlates with the index. Therefore a portfolio with a Beta > 1 is considered to be an aggressive portfolio whereas a portfolio with a Beta < 1 is considered to be a defensive portfolio. The market index (Nifty or Sensex) will always have a Beta of 1.

Treynor Ratio = {(Return on the Fund – Risk-Free returns) / Beta of the  fund }

Beta is a measure of systematic risk and measures the systematic risk at a macro level that cannot be diversified away by the fund manager. We shall see the significance of this aspect later when we assess how to choose between the Treynor ratio and the Sharpe ratio.

Why return per unit of risk is important?
Both Sharpe and Treynor measure excess return per unit of risk. But first let us see why it is important to measure returns per unit of risk. Let us understand with this example..

Fund ADetailsFund BDetails1-Year returns21%1-Year Returns18%Risk Free Rate9%Risk Free Rate9%Beta of the Fund1.8Beta of the Fund1.1

In the above example if one were to compare Fund A and Fund B purely on the basis of their returns then one can clearly say that Fund A has outperformed Fund B. Fund A has earned 21% in the last one year whereas Fund B has merely earned 18% in the last year. But what this pure return measure misses out is the risk that the fund manager has taken. Let us bridge that gap by calculating the Treynor ratio of both the funds:

Treynor Ratio of Fund A = (21%-9%) / 1.8 = 12% / 1.8 = 6.67

Treynor Ratio of Fund B – (18% - 9% / 1.1 = 9% / 1.1 = 8.18

When the Treynor ratio is calculated it is evident that the manager of Fund B has performed better. Fund manager A may have earned higher return but that has come at the cost of disproportionately higher risk. That is what Treynor helps you to pinpoint. Both Sharpe and Treynor are measures of risk-adjusted returns and the above example illustrates the importance of using these measures to get a better hang of returns per unit of risk.

When to apply Sharpe and when to apply Treynor ratio?
As mentioned earlier, the difference between Sharpe and Treynor is that the former uses the standard deviation as the denominator while the latter uses the Beta as denominator. While standard deviation measures the total risk of the portfolio, the Beta measures the systematic risk. For any business there are unsystematic risks that are specific to the company or industry. Then there are systematic risks like inflation, interest rates, government policy etc which apply to the entire economy. Therefore, Sharpe is a good measure where the portfolio is not properly diversified while Treynor is a better measure where the portfolios are well diversified. Of course, the basic job of a fund manager is to eliminate the unsystematic risk in the portfolio by diversifying and hence only systematic risk must be applicable. So, Treynor must be a more ideal measure for evaluating fund performance.

There is an important counter argument to that. Most mid-cap funds do not have a credible index to benchmark against. Also mid-caps and small caps are too heterogeneous to enable benchmarking with an index. Treynor may be a good measure for large cap-diversified funds but in case of mid-cap, small cap or hybrid portfolios, Sharpe will be a better measure of risk adjusted returns. Either ways, both Sharpe and Treynor offer an important development in understanding returns on your fund  holdings net of risks!

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