# How to select a good mutual fund scheme with low risk?

Lot of perplexity remains in investors mind when it comes to selecting a good mutual fund scheme to invest. Most investors look at the performance of the funds in terms of simple returns of the fund generated in the past. Whereas, analysts and experts talk about funds performance in terms of ratios such as Expense ratio, Sharpe ratio and Treynor ratio in common. In this blog, let us examine the two important ratios – Sharpe ratio and Treynor ratio.

Understanding these two ratios is vital in selecting a mutual fund scheme for investment. The fact sheet of equity mutual fund will disclose the Sharpe ratio and Treynor ratio of the fund as part of the fund analytics section. Both the Sharpe ratio and Treynor ratio measures the performance of the fund in relation to the risk involved in earning the returns on an investment. We will see in detail what these ratios mean, how it is different from each other, when to apply and how it can be interpreted to arrive at an investment decision. Sharpe Ratio

Sharpe ratio is developed by William F.Sharpe. It helps to study the risk-adjusted performance – excess returns of a scheme (over a risk-free rate) divided by standard deviation of the scheme’s returns over a period of time. Standard deviation is a measure of risk. Risk-adjusted returns imply the returns that you are earning for every unit of risk taken. The formula of Sharpe ratio is as follows:

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

In simple terms, the return of the fund is the return that the fund manager earns in absolute terms. Whereas, the risk-free return is what you would have earned without any risk as in case of a bank FD or a government treasury bond. So, obviously, it is good to measure the returns in excess of the risk-free rate. Standard deviation measures risk and therefore measures excess returns per unit of total risk. This total risk includes the impact of systematic factors and of unsystematic factors. Systematic risks are inflation, interest rates, government policy etc which apply to the entire economy and therefore systematically impact all stocks. Unsystematic risks are the ones specific to the company or industry.

As standard deviation is a measure of risk, the higher the standard deviation lower will be the Sharpe ratio.

Treynor Ratio

Treynor ratio is developed by Jack L.Treynor. This ratio is slightly different from the Sharpe ratio. Treynor ratio is calculated in terms of market risk, with the beta as the denominator. The formula of Treynor ratio is as follow:

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

Beta is a measure of systematic risk of the portfolio and calculates the relation to the Nifty or Sensex. A portfolio with a Beta > 1 is considered aggressive while a portfolio with a Beta < 1 is considered defensive. The market index (Nifty or Sensex) has a Beta of 1, by default.

Illustration

 ABSL Frontline Equity Fund – Direct HDFC Top 100 Fund – Direct 1 – year returns 8.46% 8.58% Risk free rate 7.50% 7.50% Beta of the fund 0.93 1.18 Standard deviation 13.32% 16.97%

When applying Sharpe ratio, the returns are

Returns of ABSL Frontline Equity Fund = +(8.46% – 7.5%) = 0.96% / 13.32 = 7.21%

Returns of HDFC Top 100 Fund = +(8.58% – 7.5%) = 1.08% / 16.97 = 6.36%

When applying Treynor ratio, the returns are

Returns of ABSL Frontline Equity Fund = +(8.46% – 7.5%) = 0.96% / 0.93= 103.23%

Returns of HDFC Top 100 Fund = +(8.58% – 7.5%) = 1.08% / 1.18 = 91.53%

In the above example, if we compare just with the simple returns, we would pick HDFC Top 100 Fund, as it has given a return of 8.58% that is more than 8.46% of ABSL Frontline Equity Fund. But, when you compare in terms of Beta of the fund or standard deviation of the fund, then ABSL Frontline Equity Fund fares well as the risk-adjusted returns is more in ABSL Frontline Equity Fund than in HDFC Top 100 Fund. Here comes the benefits of analyzing the funds performance on the basis of the fund’s risk-adjusted returns.

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

The only difference between the Sharpe ratio and Treynor ratio is the denominator used to calculate these ratios. Sharpe ratio used standard deviation and Treynor rator used a beta. Standard deviation measures the total risk and Treynor ratio measures the market risk or systematic risk.

Sharpe ratio can be applied when the portfolio of the fund is not properly diversified and Treynor ratio can be applied when the portfolio of the fund is well diversified. However, these ratios should be compared between the schemes under the same category.

Conclusion

Analyzing the Sharpe ratio and Treynor ratio is an important step in arriving at an investment decision with regard to mutual fund schemes. However, among the two, Sharpe ratio is widely used in India as it seems to be more pragmatic in Indian conditions. 