What Is the Coefficient of Variation (CV)?
The coefficient of variation (CV) is a statistical measure of the dispersion of data points in a data series around the mean. The coefficient of variation represents the ratio of the standard deviation to the mean, and it is a useful statistic for comparing the degree of variation from one data series to another, even if the means are drastically different from one another.
Key Takeaways
- The coefficient of variation (CV) is a statistical measure of the relative dispersion of data points in a data series around the mean.
- It represents the ratio of the standard deviation to the mean.
- The CV is useful for comparing the degree of variation from one data series to another, even if the means are drastically different from one another.
- In finance, the coefficient of variation allows investors to determine how much volatility, or risk, is assumed in comparison to the amount of return expected from investments.
- The lower the ratio of the standard deviation to mean return, the better the risk-return tradeoff.
Matt hew Collins
Understanding the Coefficient of Variation (CV)
The coefficient of variation shows the extent of variability of data in a sample in relation to the mean of the population.
In finance, the coefficient of variation allows investors to determine how much volatility, or risk, is assumed in comparison to the amount of return expected from investments. Ideally, if the coefficient of variation formula should result in a lower ratio of the standard deviation to mean return, then the better the risk-return tradeoff.
They’re most often used to analyze dispersion around the mean, but quartile, quintile, or decile CVs can also be used to understand variation around the median or 10th percentile, for example. The coefficient of variation formula or calculation can be used to determine the deviation between the historical mean price and the current price performance of a stock, commodity, or bond, relative to other assets.
Coefficient of Variation (CV) Formula
Below is the formula for how to calculate the coefficient of variation:
( CV = \frac{σ}{μ} )
where:
(σ) = standard deviation (μ) = mean
To calculate the CV for a sample, the formula is:
( CV = \frac{s}{x̄} * 100 )
where:
(s) = sample standard deviation (x̄) = mean for the sample
Multiplying the coefficient by 100 is an optional step to get a percentage rather than a decimal.
Coefficient of Variation (CV) in Excel
The coefficient of variation formula can be performed in Excel by first using the standard deviation function for a data set. Next, calculate the mean by using the Excel function provided. Since the coefficient of variation is the standard deviation divided by the mean, divide the cell containing the standard deviation by the cell containing the mean.
Coefficient of Variation (CV) vs. Standard Deviation
The standard deviation is a statistic that measures the dispersion of a data set relative to its mean. It is used to determine the spread of values in a single data set rather than to compare different units.
When we want to compare two or more data sets, the coefficient of variation is used. The CV is the ratio of the standard deviation to the mean. And because it’s independent of the unit in which the measurement was taken, it can be used to compare data sets with different units or widely different means.
In short, the standard deviation measures how far the average value lies from the mean, whereas the coefficient of variation measures the ratio of the standard deviation to the mean.
Advantages and Disadvantages of the Coefficient of Variation (CV)
Advantages
The coefficient of variation can be useful when comparing data sets with different units or widely different means.
That includes when the risk/reward ratio is used to select investments. For example, an investor who is risk-averse may want to consider assets with a historically low degree of volatility relative to the return, in relation to the overall market or its industry. Conversely, risk-seeking investors may look to invest in assets with a historically high degree of volatility.
Disadvantages
When the mean value is close to zero, the CV becomes very sensitive to small changes in the mean. Using the example above, a notable flaw would be if the expected return in the denominator is negative or zero. In this case, the coefficient of variation could be misleading.
If the expected return in the denominator of the coefficient of variation formula is negative or zero, then the result could be misleading.
How Can the Coefficient of Variation (CV) Be Used?
The coefficient of variation is used in many different fields, including chemistry, engineering, physics, economics, and neuroscience.
Other than helping when using the risk/reward ratio to select investments, it is used by economists to measure economic inequality. Outside of finance, it is commonly applied to audit the precision of a particular process and arrive at a perfect balance.
Example of Coefficient of Variation (CV) for Selecting Investments
For example, consider a risk-averse investor who wishes to invest in an exchange-traded fund (ETF), which is a basket of securities that tracks a broad market index. The investor selects the SPDR S&P 500 ETF (SPY), the Invesco QQQ ETF (QQQ), and the iShares Russell 2000 ETF (IWM). Then, the investor analyzes the ETFs’ returns and volatility over the past 15 years and assumes that the ETFs could have similar returns to their long-term averages.
For illustrative purposes, the following 15-year historical information is used for the investor’s decision:
- If the SPDR S&P 500 ETF has an average annual return of 5.47% and a standard deviation of 14.68%, the SPY’s coefficient of variation is 2.68.
- If the Invesco QQQ ETF has an average annual return of 6.88% and a standard deviation of 21.31%, the QQQ’s coefficient of variation is 3.10.
- If the iShares Russell 2000 ETF has an average annual return of 7.16% and a standard deviation of 19.46%, the IWM’s coefficient of variation is 2.72.
Based on the approximate figures, the investor could invest in either the SPDR S&P 500 ETF or the iShares Russell 2000 ETF, since the risk/reward ratios are approximately the same and indicate a better risk-return tradeoff than the Invesco QQQ ETF.
What Does the Coefficient of Variation Tell Us?
The coefficient of variation (CV) indicates the size of a standard deviation in relation to its mean. The higher the coefficient of variation, the greater the dispersion level around the mean.
What Is Considered a Good Coefficient of Variation?
That depends on what you’re looking at and comparing. No set value can be considered universally “good.” However, generally speaking, it is often the case that a lower coefficient of variation is more desirable, as that would suggest a lower spread of data values relative to the mean.
How Do I Calculate the Coefficient of Variation?
To calculate the coefficient of variation, first find the mean, then the sum of squares, and then work out the standard deviation. With that information at hand, it is possible to calculate the coefficient of variation by dividing the standard deviation by the mean.
The Bottom Line
The coefficient of variation is a simple way to compare the degree of variation from one data series to another. It can be applied to pretty much anything, including the process of picking suitable investments.
Generally speaking, a high CV indicates that the group is more variable, whereas a low value would suggest the opposite.
Related Terms: Standard Deviation, Risk-Return Tradeoff, Variability, Volatility, Mean.
References
- JoVE. “JoVE Core Statistics; Chapter 4, Measures of Variation; 4.7: Coefficient of Variation”.
- Penn State, Eberly College of Science. “STAT 500: Applied Statistics; 1.5.3—Measures of Variability”.
- UCLA, Advanced Research Computing: Statistical Methods and Data Analytics. “FAQ: What Is the Coefficient of Variation?”
