Coefficient of Variation (CV): Definition, Formula & Example

KEY TAKEAWAYS

• The coefficient of variation (CV) is a type of statistical measure that’s used to help predict variables. It measures the changes in data points using both inside and outside data sets.
• The coefficient of variation shows and measures the variability in data sets to show the standard deviation to its mean. 
• Having a lower ratio of the standard deviation to mean return often indicates a better trade-off for risk and return. 
• Within the finance industry, the coefficient of variation gives investors valuable information. This can include how much risk or volatility there could be compared to a potential return from an initial investment.

What Is the Coefficient of Variation (CV)?

The coefficient of variation (CV) is an important measurement unit and concept to help predict variables. It’s used with both inside and outside data sets and it can be used in several different contexts. A few of the most common include various types of population studies as well as investments made in the stock market. 

It can commonly be referred to as relative standard deviation, but it uses variability in data sets to show the standard deviation to its mean. The coefficient of variation helps when you want to compare a data series with another to determine the degree of variation. This is still the case even if the comparable means are completely different from each other.

How Does the Coefficient of Variation (CV) Work?

The coefficient of variation works well in a few different ways. The statistical measurement shows the variability of data when comparing data sets when it comes to the mean of the population. In the financial industry, the coefficient of variation provides investors with extra information, such as investment risks or even investment options. 

For example, it can show or help determine the amount of risk or volatility compared to the expected amount of return from an investment. In most cases, if the coefficient of variation formula indicates a lower ratio of the standard deviation to mean return, then the trade-off between risk and return can be better. 

However, with that said, it’s always important to recognize that if the expected return ends up being zero or a negative number, it might not be fully accurate and could be misleading. 

Using the coefficient of variation will be extremely helpful for investors when analyzing the risk and reward ratio for certain investments. For example, investors or analysts might want to find an asset that has a low degree of volatility in its history. And this is relative to the return and is also in relation to the rest of the industry or overall market. 

On the flip side, an investor that’s more risk-seeking might want to find and invest in an asset that has previously had a high degree of volatility. 

Coefficient of Variation Formula

The formula to calculate the coefficient of variation would look like the below:

How to Calculate the Coefficient of Variation 

The good news is that calculating the coefficient of variation can be a fairly simple process as long as you have the relevant information. This includes finding the mean and the standard deviation. It’s worth noting that you should be aware of the denominator. If the expected return is zero or a negative number, it might mean the calculations are misleading or inaccurate. 

Mean

When you’re working with a data set, mean simply refers to the average value. In other words, it’s the most common variable from several observations. It’s important to evaluate the mean because it accounts for all of the different values included in a data set. Ultimately, this makes it easier to identify the midpoint of any research or data. 

It’s worth noting that there can also be a harmonic mean, a geometric mean, and a weighted mean. To calculate the mean, you can use the following formula: 

Standard Variation

Standard variation shares some similarities to variability and dispersion. Yet, when it comes to the coefficient of variation, standard deviation considers the distribution of the values related to its mean. 

After you’re able to find out the data variance, you simply take the square root of the value to determine the standard variation. A high standard deviation often shows, in the case of regular data distributions, that individual numerical values are far away from the mean. 

On the other hand, a lower standard deviation shows that the values are likely to be grouped around the mean. 

Example of Coefficient of Variation 

Let’s say that a risk-averse investor is looking into an exchange-traded fund (ETF) as an investment. An ETF is essentially several securities that are able to track a market index broadly. 

The investor selects three distinct ETFs and then analyzes the returns and volatility that each had over the past 15 years. As well, the investor is able to assume that each ETF has roughly the same returns compared to their long-term averages. 

Analysis would be undertaken based on the 15-year historical information that the investor used to initially make their decision. Using the coefficient of variation calculations, they can determine which ETFs have the best risk and reward ratios. As well, they would be able to see and compare the better trade-off for risk and return between each of the three ETFs being compared. 

This would ultimately provide the investor with actionable information to be able to compare the data sets. From here, they can make a more informed decision about which investment would be the best moving forward. 

Coefficient of Variation Advantages

There are a few advantages that come with using the coefficient of variation. One of the biggest benefits is that it’s unitless. Essentially, this allows a coefficient of variation to be compared against another. Other measures for example, such as root mean squared residuals and standard deviations, cannot be compared in a similar way.

It’s an effective statistical measure that can help protect an investor from a potentially volatile investment. As well, it can help predict investment returns by considering account data from several different periods. 

Coefficient of Variation Disadvantages

There are also some disadvantages worth understanding for the coefficient of variation to be interpreted the way it’s supposed to be. The biggest often comes when the mean of a variable ends up being zero. When this happens, you’re unable to calculate the coefficient of variation. 

Plus, even if there is a scenario where the mean of a variable isn’t zero and there are positive and negative values, the coefficient of variation could be misleading.

Summary

The coefficient of variation is a statistical concept that helps predict certain variables, both inside and outside a data set. It can be used in various contexts and situations, such as population studies and researching investments in the stock market. 

Essentially, it accounts for the relative variability in data sets to determine the size of a standard deviation compared to its mean.