Find the coefficient of variation for each of the two samples, then compare the variation.

1. Career development
2. How To Calculate Coefficient of Variation (With Examples)

By Lauren Oliver

Updated May 12, 2022 | Published April 14, 2020

Updated May 12, 2022

Published April 14, 2020

Lauren Oliver, B.Ed. is a 10-year veteran educator with experience teaching secondary mathematics, including personal finance and economics.

A coefficient of variation is a statistical metric that can help professionals record changes in data over time. This metric can also be an effective method for calculating financial risk and reward for investment activities. You can calculate the coefficient of variation using a simple formula.

In this article, we discuss what a coefficient of variation is and how to calculate it, with several examples of how this statistical measurement applies to various investment scenarios.

Key takeaways:

• A coefficient of variation is an effective metric for quickly evaluating the relative dispersion of the data points around a sample mean.

• Financial analysts and investors may often evaluate the coefficient of variation to analyze risk and volatility respective to anticipated investment returns.

• A lower ratio between the standard deviation and the mean can indicate a higher return factor, whereas a higher ratio can indicate a lower return factor.

 

A coefficient of variation (CV) measures data point dispersion around a mean. Representing the standard deviation to the mean makes CV a valuable resource in comparing variations from one data series to another. It shows how much data varies in a sample in comparison to the mean of the population.

When you evaluate the CV, you can represent the value with a percentage, where a lower percentage can indicate a lower CV and a higher percentage can mean a higher CV. In financial and investment analysis where volatility and risk can influence potential returns, a lower CV means a lower risk-to-return ratio, indicating a better trade-off between the potential returns and the inherent risk of a particular investment instrument.

Related: Definitive Guide to Understanding Descriptive Statistics

What is the formula for the coefficient of variation?

The CV formula uses the standard deviation and the mean of your sample data to calculate a ratio to represent the dispersion of your values around the mean. In statistical analysis, the basic formula for calculating the coefficient of variation is:

CV = standard deviation / sample mean x 100

When applying the formula to business applications—like financial calculations—many professionals simplify the CV formula so it's relevant to financial measures like investment returns, capital gains, risk and investment volatility. Therefore, many analysts may also use the following formula to calculate the CV in terms of financial risk and reward:

CV = volatility / projected return x 100

Related: Return on Investment (ROI): Definition and Calculation

Using the coefficient of variation

You can use the CV to determine a risk-to-return ratio and whether the reward is greater than the risk of the investment. The CV can also sometimes result in an inaccurate or unusable value. For instance, calculating a negative value or zero can indicate your ratio measurement inaccurately represents your coefficient. Finding the coefficient of variation within data doesn't solely relate to the industries of business and finance.

For example, biologists and researchers often use it in their observations to calculate repeatability within their data results. Educators may also apply the CV to compare teaching methodologies, discovering what leads to higher grade point averages. Meteorologists use it to measure temporal precipitation variability. There is some debate, however, on the accuracy of CV within these situations. With a wide range of variables and conditions comes an increased chance of inaccuracy.

Related: A Guide to Statistics for Business

How to calculate the coefficient of variation

To calculate the coefficient of variation, follow the steps below using the aforementioned formula: 

1. Determine volatility

To find volatility or standard deviation, subtract the mean price for the period from each price point. To convert the difference into variance, square, sum and average the answer. The square root of the variance becomes a viable percentage for volatility.

2. Determine expected return

To find the expected return, multiply potential outcomes or returns by their chances of occurring. The sum of all collected answers becomes the expected return. At this point, both figures are ready for the formula.

3. Divide

With both volatility and expected return figures calculated, divide them by each other. Most answers come in the form of decimals. You can also convert the CV to a percentage.

4. Multiply by 100

To convert to a percentage, multiply decimals by 100. Doing so moves the decimal place by two numerals, creating either a whole number or decimal percentage. The final answer is the coefficient of variation.

Related: How To Calculate the Coefficient of Determination

How to calculate a coefficient of variation in a spreadsheet

Some businesses and individuals use spreadsheets to record large amounts of data over long periods of time. They choose spreadsheets not only to keep up with the sheer amount of collected data, but to easily calculate the coefficient of variation within their data. Spreadsheets can record the calculations alongside the data and continue to as you add more data. You can calculate the coefficient of variation with the help of a spreadsheet using the following three steps:

1. Use the standard deviation function for the data set

Spreadsheet processors should have a specified function for standard deviation. For the calculation to work, the data set needs this function. In many common spreadsheet programs, the command =STDEVP is what you can enter to calculate the standard deviation. Enter the formula into a blank cell next to the related data set you're evaluating. 

2. Calculate the mean

Calculating the mean in spreadsheets requires specific formulas. For example, in most spreadsheet applications, you can use =AVERAGE to apply the program function. When entering the mean command, place it in a cell next to the related data set to see it more easily.

3. Divide the standard deviation by the mean

Divide the cells containing the standard deviation and mean values. For example, to divide a standard deviation in cell A3 and a mean value in cell A5, you can use the function =A3/A5 in a blank cell to calculate the quotient and display the coefficient of variation.

Some spreadsheet processors can calculate the coefficient of variation using the command =STDEV.P, which eliminates the need for multiple steps. Depending on the program, you can simply enter the command into a blank cell and designate the data range you want to calculate. The CV then appears in the selected cell.

Related: How To Use Excel To Calculate Standard Deviation (With Example)

Example calculation

To make an informed decision between stocks and bonds, Jamila applies the coefficient of variation formula to determine the risk-to-return value for both investment instruments. She first evaluates the stock investment, which has a volatility of 5% and a projected return of 13%. Using these values in the formula Jamila finds:

• CV = standard deviation / sample mean x 100 =

• CV = volatility / projected return x 100 =

• CV = (0.05) / (0.13) x 100 = 0.38 x 100 = 38%

To calculate the coefficient of variation in the bond for comparison, Jamila divides a volatility of 3% by a projected return of 15%. Using the formula, she evaluates:

• CV = standard deviation / sample mean x 100 =

• CV = volatility / projected return x 100 =

• CV = (0.03) / (0.15) x 100 = 0.2 = 20%

Jamila compares the bond and stock investments and finds that the bond investment CV of 20% indicates a lower risk-to-return ratio than the stock's potential CV of 38%. Now that Jamila understands which investment instrument presents the lowest risk-to-return ratio, she can choose the most suitable option to meet her financial goals.