The coefficient of variation (COV) is a measure of relative event dispersion that's equal to the ratio between the standard deviation and the mean. While it is most commonly used to compare relative risk, the COV may be applied to any type of quantitative likelihood or probability distribution. And in a different mathematical context, COV is calculated as the ratio between root mean squared error and the mean of a separate dependent variable. Although this type of COV analysis is used less frequently, it can go a long way in determining if a model is an apt fit for a specific task.

### Key Takeaways

- In statistical analysis, the coefficient of variation (COV) measures relative event dispersion.
- The COV is equal to the ratio between the standard deviation and the mean. Although COV is most commonly used in comparing relative risk, it may be applied to many types of probability distribution.
- The COV isn't practical if there's a strong presence of both positive and negative values in the sample population.
- The COV metric is best used when nearly all of the data points share the same plus-minus sign.

## Applications of the Coefficient of Variation

When used to evaluate investment risk, COV can be interpreted similarly to the standard deviation in modern portfolio theory (MPT). But the COV is arguably a better overall indicator of relative risk when it's used to compare different securities. For example, suppose two different stocks offer different returns, with each exhibiting a different standard deviation. Specifically, let's assume Stock A has an expected return of 15% with a standard deviation of 10%, while Stock B has an expected return of 10% coupled with a 5% standard deviation. In this scenario, the COV for Stock A is 0.67 (10%/15%), while the COV for Stock B is 0.5 (5%/10%). Simply put: the data suggests that Stock B is a superior investment from a risk-based perspective.

## Advantages of the Coefficient of Variation

The COV's chief advantage is its applicability to any given quantifiable data, thus paving the way for a comparative analysis between two unrelated entities. This quality separates COV from a standard deviation analysis, which cannot facilitate a meaningful comparison between two independent variables.

As a measure of risk, the COV measures volatility in the prices of stocks and other securities, letting analysts contrast the risks associated with different potential investments. This helps financial advisors construct diversified portfolios in an effort to dampen the risk of a single investment tanking a client's net worth.

Several other terms are synonymous with COV, including the variation coefficient, unitized risk, and relative standard deviation.

## The Zero Disadvantage

Suppose the mean of a sample population is zero. In other words, the sums of all values above and below zero equal one other. Under this circumstance, the formula for COV is useless because it would effectively place a zero in the denominator. Hence, any strong presence of both positive and negative values in the sample population becomes problematic for COV analysis. Contrarily, the COV metric thrives when nearly all of the data points share the same plus-minus sign.