In this article, we will discuss a type of relative measure of dispersion commonly famous as the Coefficient of Variation. This measure is available by taking out the ratio of the standard deviation to the mean. The answer is quantified in percentage as it represents a dimensionless quantity. The principal use of the Coefficient of Variation is the comparison of the dispersion of the data between distinguishable series of data. In contrast to standard deviation, this statistical formula is a straightforward and quick tool that helps in the comparison of different data series.
Abbreviated as CV, it is also a viable financial instrument for gauging investment selection. To understand the usage of coefficient of variation from a financial perspective, we will highlight the risk-to-reward ratio. The volatility in the risk-to-reward ratio represents the risk involved in investments, whereas the mean indicates the underlying rewards.
Before investing in any security, it is thoughtful for investors to seek those securities that provide low volatility but high returns(security with a lower coefficient of variation). When the average expected return is below zero, the low coefficient value is not substantial.
The Formula
The standard formula to calculate coefficient of variation is as follows;
CV= (standard deviation%mean) x 100
If taken in terms of finance, the formula will be determined as;
CV= (Volatility % expected return) x100
How to use the formula?
When the analysts feel the need of comparing results from two different surveys with different values, they employ the coefficient of variation formula. Also denoted as relative standard deviation (RSD), statisticians call it a definitive measure of the dispersal of a probability distribution or frequency distribution. If the result shows a lower value then it can be deduced that the data has less variability and high stability. Following are the steps to derive the coefficient of variation value;
Step#1 Select the sample set.
Step#2 Estimate the value of standard deviation and mean.
Step#3 Now apply the CV calculation formula using those values.
Here are a few examples that will help clear the concept.
Example A: Factory B has hired 5000 workers and pays $2500 as wages in total for the month whereas factory C has hired 6000 workers and pays $2500 as wages in total for the month. The standard deviation for both factories is 9 and 10 respectively. Now employing the CV formula, we will find out which factory has greater variability in individual wages.
For Factory B:
CV = (σ/μ) × 100, μ≠0
CV = (9/2500) × 100
Now CV = 0.36%
For Factory C:
CV = (σ/μ) × 100
Now CV = (10/2500) × 100
CV = 0.4%
Thus, factory C has greater variability than factory B in individual wages.
Uses of Coefficient of Variation
Most of the time, people get confused between the use of a CV and standard deviation. Here is the catch- standard deviation can be used if there is a need to compare two data sets having similar values. CV can be utilized when there is a need to compare two data sets having different units. To be more precise, CV is a relative measure whereas standard deviation is an absolute measure of dispersion. CV combines multiple data sets but standard deviation consumes only a single set. Here are a few areas where the CV formula is preferred over other statistical tools;
1. The finance industry: We have already talked about the financial application of CV in the above section. This formula helps investors in estimating the most optimal risk-to-reward ratio.
2. To calculate the consistency of data: The analysts may know that a smaller coefficient of variation confirms the consistent distribution of data than one with a larger CV.
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