#### What is coefficient of variation?

Investors and analysts are always attempting to evaluate the risk and possible return of various securities in the world of finance. The coefficient of variation is one of the instruments they employ for this (CV). A statistical indicator of predicted return in relation to level of risk taken is the CV. In essence, it informs us of the risk we assume relative to the projected return on investment.

The CV is also known as the “relative standard deviation,” which makes sense since it implies that your expected risk is adjusted based on the expected return. You can easily calculate the CV by dividing the standard deviation of the security by its expected return.

To understand the concept of the CV, it’s helpful to have a basic understanding of standard deviation. Standard deviation is a measure of how much a set of data deviates from the mean (or average). It gives us an idea of the spread of the data – the larger the standard deviation, the more spread out the data points are. In finance, standard deviation is often used as a measure of risk.

Let’s say you are considering two investments: Investment A has an expected return of 10% and a standard deviation of 5%, while Investment B has an expected return of 12% and a standard deviation of 8%. Which investment is riskier?

At first glance, it might seem like Investment B is riskier – after all, it has a higher standard deviation. But the CV tells us a different story. To calculate the CV, we divide the standard deviation by the expected return. For Investment A, the CV is 0.5 (5% ÷ 10%), while for Investment B, the CV is 0.67 (8% ÷ 12%). This means that for every dollar of expected return, Investment B has 33% more risk than Investment A.

In this case, the CV enables us to choose our investment with greater knowledge. Investment A may be preferred if we are risk adverse because it delivers a better return in comparison to the risk. Investment B, on the other hand, might be a better option if we are more risk-averse because it gives a bigger return but also carries a higher level of risk.

The CV is especially useful when comparing investments that have different expected returns. For example, let’s say we are considering two investments: Investment C has an expected return of 8% and a standard deviation of 3%, while Investment D has an expected return of 12% and a standard deviation of 6%. On the surface, Investment D seems like the clear winner – it has a higher expected return and a higher standard deviation. But when we calculate the CV, we get a different story.

For Investment C, the CV is 0.375 (3% ÷ 8%), while for Investment D, the CV is 0.5 (6% ÷ 12%). This tells us that for every dollar of expected return, Investment C has less risk than Investment D. In other words, Investment C offers a better risk-adjusted return.

The CV can also be used to compare the risk and return of different asset classes. For example, let’s say we are considering investing in stocks or bonds. Historically, stocks have offered higher returns but also higher volatility (i.e. risk) than bonds. To compare the two asset classes, we can calculate the CV for each.

According to historical data, the average annual return for U.S. stocks from 1928 to 2020 was 9.7%, with a standard deviation of 20.3%. The CV for stocks is therefore 2.09 (20.3% ÷ 9.7%). On the other hand, the average annual return for U.S. bonds.

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