Risk and returns go hand in hand. Take a higher risk, and you stand a better chance to get higher returns.

But how much higher returns should you get for taking a higher risk? Conversely, how much risk should you take for getting a targeted higher return?

If you invest in a fixed deposit, the 10 per cent return you will get (as interest) is assured. So the risk -- which is nothing but the probability that you might lose some or all of the money you invested -- in this case is practically zero.

Since FDs still have some risk associated with them, a better benchmark for risk-free security would be Government of India Securities, G-Secs.

G-Secs are nothing but papers representing a loan taken by the government. Since it is the government which is taking the loan, there is a sovereign guarantee that your capital will be returned after the loan matures.

As G-Secs assure no loss of capital (no risk at all), the returns on them will also be the lowest, as compared to similar loans taken by corporates or anybody else for that matter.

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If you decide to forego the safety of these options and want to go for riskier investments, it will be because your only objective will be to make more money by way of higher returns.

Therein lies the question -- how much excess return should you expect for the higher risk you assume? Basically, what you would like to know is: what is the extra return you get per unit of extra risk you take?

This is where the Sharpe's Ratio comes into picture.

What does this ratio do?

It shows you how much return your investment is making per unit of risk you have assumed.

How is that calculated?

It is a ratio. Since it is the measure of return per unit of risk, the numerator is the return and the denominator is the risk.

Now, remember, you are getting a minimum return through G-Secs, so the excess return that your investment is generating is what matters to us. What you need to do is find out what the annual return from your investment is, and deduct the risk free rate of return from that. This is the extra return that your investment has generated.

Assuming your G-Sec return is five per cent and FD return is 10 per cent, then the excess return generated by taking some risks (in FDs) will be five per cent. The return from FDs, less the return from G-Secs, is the extra return generated in this case.

This is also the risk you have taken.

What is risk?

It is the probability of you losing your investment capital.

How do you find that?

Calculate the average annual returns on your investment and find out the Standard Deviation. The SD shows how wildly your investment returns are swinging away from the mean (average).

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The lesser the swing, the lesser the probability of you losing your capital.

The next thing you need to do is just to divide the excess return by the SD and you get the Sharpe Ratio.

The higher the ratio, the better; it implies that your investment is generating higher return for the risk assumed.

Process and formula

Calculate annual investment return -- R_I

Calculate portfolio SD -- X

Find annual risk free return -- R_F

S = (R_I � R_F)/ X

Example

*Risk Free Return (R_F) assumed @ 7.5 per cent, that is, return from G-Secs

Look at the above table. The schemes are arranged in the ascending order of their annual returns. Now, if you were to look at the SDs of these schemes, you will see that even these are increasing with the annual returns. But what is happening to the Sharpe's Ratio?

In case of S1 and S2, the absolute returns are similar (8 per cent), but the SD of S2 is higher than S1. Why would anyone like to invest in a scheme where the risk is high, but the returns are similar to what some other scheme is generating? That is what the Sharpe's Ratio is pointing out.

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Look at the Sharpe's Ratio for S3 and S4; both are the same. That means even though S4's SD is far higher than that of S3, the returns S4 is generating are commensurate with the extra risk.

So, if you have to choose between S1 and S2, it would be better to choose S1; between S3 and S4, the investor would be better off investing in S4 as the returns are higher in absolute terms.

Drawbacks of Sharpe's Ratio

These returns we used are historical. This is of hardly any relevance. If your investment decision is to be based upon Sharpe's Ratio, you need to use expected returns from the scheme and also the expected risk-free returns.

Another drawback, a very peculiar one, is what if the Sharpe's Ratio is negative? There is no consensus on this; the debate is still on.

This ratio equates volatility to risk. However, any volatility, which is above the average returns, is not unfavourable.

Typically, investors would want huge swings above the average returns and no or very low swings below the mean. That is it is only the downside risk which is harmful. This ratio makes no distinction between upside and downside volatility.

The Sharpe Ratio equates volatility to risk.

But volatility means swings above as well as below the mean. Since risk in this case is the probability of losing capital, any swing above the mean return would be profitable. Similarly, any swing below the average returns is capable of eroding capital.

Usage

Most mutual fund research websites and publications give Sharpe's Ratio for schemes. Comparing the ratio for similar schemes and choosing the scheme with higher Sharpe's Ratio can increasen your chances of making more returns for every unit of risk you take.

The author runs a Nagpur-based finance advisory Money Bee Investments. He can be reached at moneybee.finplan@gmail.com.

Disclaimer

Mutual Fund investments are subject to market risk. Please read the offer document carefully before investing. This article is for information purposes only.