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^{1}^{2}Meaning of the Coefficient of Variation

Coefficient of Variation is a statistical tool to analyze risk per unit of return of an investment. The standard deviation of returns from an investment option is to be divided by the mean annual return of that option, to arrive at the coefficient of variation. In the world of finance, this tool helps an investor to determine which investment option to choose. This decision will be following his risk-return trade-off.

An investment option with a high coefficient of variation is riskier. Therefore, a risk-averse investor will want to choose an option with a low coefficient of variation. They will want to invest in assets whose returns are not volatile and close to the mean annual return. On the other hand, an investor who wants higher returns may opt for assets with a high degree of volatility. He will go for an option with a higher risk and a higher coefficient of variation.

## Calculation of coefficient of variation

The method of calculation is:

The standard deviation of an investment/ Mean return of the investment.

Standard deviation is a statistical tool to determine the volatility of an asset. The return of the assets remains more volatile, where the standard deviation is higher.

Mean return is the average of the gains of an investment option over several periods. In case the mean return is not available for any investment option, its expected rate of return can be used to arrive at the coefficient of variation.

## Example

Let us consider the case of a rational investor, who is risk-averse and at the same time, wants decent returns on his investment. He is looking to invest in either stock A of a blue-chip company or gold. Both are safe investment options. Here stock A has a mean annual return of 9% p.a. and a standard deviation of 13.5%, whereas gold has a mean annual return of 7% and a standard deviation of 11%.

If the investor looks at just the returns, stock A is the better choice as the performance is higher. But he needs to check for the coefficient of variation for both the cases. It will take into account the risk factor, as well.

In the case of stock A- Standard deviation of stock A/ Mean annual return of stock A

15.5/9= 1.72

In the case of Gold- Standard deviation of gold/ Mean annual return of gold

11/7= 1.57

Therefore it is safer to invest in gold than stock A as the coefficient of variation is lesser for gold. It means that there is a lesser chance of volatility in returns from investing in gold.

## Limitations of the coefficient of variation

This statistical tool has a few limitations as well.

### Unreliable in volatile situations –

The returns from an investment option might have varied significantly from the mean over the last few periods or years. It can be due to unfavourable economic conditions or some other uncontrollable factors. The situation may have improved in favour of the investment option and can be an excellent return opportunity in the present times.

The standard deviation will be high for the stock when calculated, and hence, the coefficient of variation will be high too. If an investor solely relies on this figure for making his investment decision, he might not go for this option. Hence, he may miss out on an opportunity to get high returns.

### Misleading in case of negative values or zero-

This statistical measure may be misleading or incorrect if the mean annual returns from an investment option are negative or zero.

## Conclusion

The coefficient of variation is an essential statistical measure to protect a rational investor from volatile investment options. It can also help in predicting returns from any investment as it takes into account data from several periods.

It is not solely based on risk and returns data from just one single period or instance. Hence, it helps in making wise and correct investment decisions and to achieve a proper balance between risk and returns. It is for these reasons that portfolio managers and analysts widely use this statistical tool in their reports and analysis. However, as explained earlier, this also needs to be considered in conjunction with other similar indicators for a better view.