• Statistics ,
• 05 May

The coefficient of variation measures the variability around the mean using a ratio. Ratios are great because they are unit-less. In this way they are similar to Vertical Analysis of Financial statements. This means that you can take two totally different means and standard deviation sets and compare in a meaningful way because you are looking at relative proportions keeping it apples to apples. Essentially you are taking the standard deviation and dividing it by the mean.

Let’s look at an example

Let’s say we work at a liquor bottling plant and we have 2 sizes of bottles, Pints (473ml) and Fifths (750ml) and you are in charge in making sure that the correct amount of liquor is getting into each bottle . You take some samples of each size and find out that the sample mean of the pints is 470ml with a standard deviation of 8ml and the sample mean for the fifths is 747ml with a standard deviation of 10ml.

Pints                                     Fifths

CV = 100 * 8/471                   CV = 100 * 10/747

1.70                                        1.34

So at first glance Fifths appeared to have a greater standard deviation, yet the Coefficient of Variation tells us that is actually less than Pints! This means that the smaller container has more variation than the larger one.

Selecting Investments

We can also use this to help investors make decisions based on risk vs reward ratios. You do this by dividing the standard deviation of returns by the average annual return amount. This way you can find common ground to compare investments even if the means are drastically different. It helps with understanding risk as you interpret the model fit. Typically high CV ratio equates to high risk, in which you would expect a higher return for the increased risk.

If you have a negative or zero as your expected mean (return) CV’s may not be comparable.