In investment theory, risk and reward are two sides of the same coin. The return from a given investment should not be seen in isolation but only in the context of the risk profile. But most investors fall prey to one of two human emotions and overlook either of variable.

Greed and fear are strong emotions. The greedy investor focuses only on rewards and ignores the risk. The fearful investor worries so much about the potential loss of capital that the potential reward is overlooked. The relationship between risk and reward is easy to understand. The more risky the investment profile, the higher the potential rewards should be.

In circumstances where the risk can be quantified, we can quantify the required returns. For example, what are the chances of the Nifty gaining 10 per cent or more in a given month? It has happened 11 times in the past 120 months so it’s roughly 9 per cent or 1/11. Is it worth taking an option position? Only if the payoff is larger than 1100 per cent because that return:risk equation will yield a positive return if our 1/11 ‘strike rate’ is maintained. (With an option position held till settlement we stand to lose 100 per cent of premium)

A long Nifty call 5 per cent from money will cost around 1 per cent and thus yield a maximum of 4 per cent on a 10 per cent move. This is 400 per cent return — impressive but not good enough, even though we will make some money every time that the market moves more than +5 per cent. In general, to take an investment that has 1 in ‘n’ chances of success, we need a return that is greater than n*100 per cent.

In any risk-reward calculation, we have to take a benchmark of risk-free return. This should be realistic and transparent. Commonly used risk-free benchmarks include bank fixed deposit rates and government securities yields. Of these, the bank FD rates make more sense for individual since G-Sec and T-Bill yields are not directly available. You can finetune for post-tax returns because different instruments have different tax-profiles. For example, a high-income investor pays roughly one-third income tax on FD returns and zero tax for equity-fund returns or direct equity investments. But it’s simpler to directly compare pre-tax returns. Right now, one-year bank FD rates are around 7.5-8 per cent pre-tax.

Once we have a benchmark risk-free rate, we can apply one of the most useful ratios for comparing risk and reward equations across different instruments with different profiles. This is called the Sharpe Ratio (SR) and it is commonly used by financial analysts.

SR is simple. First calculate the average return for the given instrument. Then calculate the Standard Deviation (SD) — this is zero for the risk-free benchmark and it will be low for a low-risk instrument. Essentially SD is a measure of variability of return and we are using it as a proxy for judging risk.

Then subtract the benchmark rate from the average rate of return — this is the risk premium or the excess return that you hope to get by investing in a risky instrument. Divide the risk premium by the SD. This gives the SR. The higher the SR, the better the risk-reward equation.

The SR is a single number. It allows you to compare instruments with very different risk profiles. It can throw up surprising insights. Sometimes you discover a very high risk instrument has a high SR because it gives extraordinary returns. Sometimes you discover that a high return instrument carries unacceptably risk and the SR is low.

Let’s see how the SR works. The Nifty for example, has an annual average return of around 17.5 per cent over the past 10 years. It has an SD of about 38. With a benchmark risk-free return of 7.5 per cent, the risk premium is 10 per cent and the SR is about 0.26. We can further refine any selection of equity funds by using SR. Let’s look for funds that offer SR higher than 0.26.

Taking a look at a population of 194 equity-diversified funds with a 3-year track record, we discover that while as many as 40 delivered average returns as high as the Nifty or higher. But the risk levels were mostly unacceptable. Only four funds beat the Nifty’s SR while also delivering higher returns. This is certainly a surprising insight.

The Sharpe Ratio is very versatile. It is easy to calculate and it can be used across a range of instruments. It is a very convenient way to link the associated concepts of risk-reward. Bear it in mind next time you are looking at investing.