Will you select an equity fund that gave 13% returns or a similar fund that gives 15% returns? The answer is quite obvious. Now add an additional data point and say that the 13% returns come with 10% risk (standard deviation) and the 15% returns come with 40% risk (standard deviation), what is your choice? Is it worthwhile taking on 4 times the risk for 2% extra returns? The answer would obviously be that it is not justified. That is where risk-adjusted returns come in handy. Risk adjusted returns imply the returns that you earn for every unit of risk taken.

If you look at the monthly factsheet of any equity mutual fund, it will disclose the Sharpe ratio and sometimes the Treynor ratio of the fund as part of the fund analytics section. What exactly are these ratios and how should investors interpret these ratios? Let us look at both these measures separately and see how they apply to live portfolios.

Understanding the Sharpe ratio

The general performance metrics of a mutual fund is all about outperformance. If the Nifty index has earned 16% returns last year and the fund has earned 18% last year then it is a 200 basis points outperformance. This is very simple and appeals to every investor. But then this measure only looks at the returns and not the risk. If your fund manager has earned 2% additional return by taking on twice as much as risk as the Nifty then there is no big achievement in that. That is where Sharpe Ratio comes in.

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

The return of the fund is the return that the 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 or ideally a government bond. Obviously, your measure is going to start only beyond the risk free rate. Standard deviation measures risk as volatility and therefore measures excess returns per unit of total risk. This total risk includes the impact of systematic factors and of unsystematic factors.

Now, let us understand the Treynor ratio

The Treynor Ratio is a slight modification of the Sharp Ratio. It also is a measure of excess returns per unit of risk. While the numerator remains the same in case of Sharpe and Treynor (Rm – Rf) what changes is the denominator. Treynor ratio uses the Beta as the denominator, instead of the standard deviation. 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.

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

Let us understand Sharpe and Treynor with an example…

Fund A

Details

Fund B

Details

1-Year Returns

21%

1-Year Returns

18%

Risk Free Rate

9%

Risk Free Rate

9%

Beta of the Fund

1.8

Beta of the Fund

1.1

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 has earned higher returns 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 which help you get a better hang of returns per unit of risk.

When to apply Sharpe and when to apply Treynor?

The difference between Sharpe and Treynor is that Sharpe uses standard deviation while Treynor uses the Beta. 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 and therefore systematically impact all stocks.

Sharpe makes a lot of sense when the portfolio is not properly diversified while Treynor is better 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? But in reality Sharpe is used more frequently and more extensively.

Why is Sharpe more popular in India? Mid-cap funds do not have a representative index to benchmark against. Also, they are too heterogeneous to enable benchmarking with an index. Treynor may be a better measure on paper but it is Shape that is more pragmatic, at least in the Indian conditions. That is why, if you open the fact sheet of an equity fund, you find a greater focus on Sharpe than on Treynor. Focus has to be on adjusting returns for risk!

Will you select an equity fund that gave 13% returns or a similar fund that gives 15% returns? The answer is quite obvious. Now add an additional data point and say that the 13% returns come with 10% risk (standard deviation) and the 15% returns come with 40% risk (standard deviation), what is your choice? Is it worthwhile taking on 4 times the risk for 2% extra returns? The answer would obviously be that it is not justified. That is where risk-adjusted returns come in handy. Risk adjusted returns imply the returns that you earn for every unit of risk taken.

If you look at the monthly factsheet of any equity mutual fund, it will disclose the Sharpe ratio and sometimes the Treynor ratio of the fund as part of the fund analytics section. What exactly are these ratios and how should investors interpret these ratios? Let us look at both these measures separately and see how they apply to live portfolios.

Understanding the Sharpe ratioThe general performance metrics of a mutual fund is all about outperformance. If the Nifty index has earned 16% returns last year and the fund has earned 18% last year then it is a 200 basis points outperformance. This is very simple and appeals to every investor. But then this measure only looks at the returns and not the risk. If your fund manager has earned 2% additional return by taking on twice as much as risk as the Nifty then there is no big achievement in that. That is where Sharpe Ratio comes in.

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

The return of the fund is the return that the 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 or ideally a government bond. Obviously, your measure is going to start only beyond the risk free rate. Standard deviation measures risk as volatility and therefore measures excess returns per unit of total risk. This total risk includes the impact of systematic factors and of unsystematic factors.

Now, let us understand the Treynor ratioThe Treynor Ratio is a slight modification of the Sharp Ratio. It also is a measure of excess returns per unit of risk. While the numerator remains the same in case of Sharpe and Treynor (Rm – Rf) what changes is the denominator. Treynor ratio uses the Beta as the denominator, instead of the standard deviation. 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.

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

Let us understand Sharpe and Treynor with an example…

Fund ADetailsFund BDetails1-Year Returns

21%

1-Year Returns

18%

Risk Free Rate

9%

Risk Free Rate

9%

Beta of the Fund

1.8

Beta of the Fund

1.1

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 has earned higher returns 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 which help you get a better hang of returns per unit of risk.

When to apply Sharpe and when to apply Treynor?The difference between Sharpe and Treynor is that Sharpe uses standard deviation while Treynor uses the Beta. 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 and therefore systematically impact all stocks.

Sharpe makes a lot of sense when the portfolio is not properly diversified while Treynor is better 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? But in reality Sharpe is used more frequently and more extensively.

Why is Sharpe more popular in India? Mid-cap funds do not have a representative index to benchmark against. Also, they are too heterogeneous to enable benchmarking with an index. Treynor may be a better measure on paper but it is Shape that is more pragmatic, at least in the Indian conditions. That is why, if you open the fact sheet of an equity fund, you find a greater focus on Sharpe than on Treynor. Focus has to be on adjusting returns for risk!