Coefficient Of Variation: A Better Metric To Compare Volatility

Includes: BA, CVS, FLO, IPG, LB, MSFT, TU
by: Steve Bennett

The Standard Deviation is the basic metric to measure volatility.

However, the Standard Deviation is an absolute measurement, not a relative measurement.

To compare the volatility of two or more data sets, the Coefficient of Variation should be used.

According to Modern Portfolio Theory, investment risk is defined by - and measured by - volatility. MPT posits that all investors are rational and operate with perfect knowledge in a perfectly efficient marketplace. Such investors will not accept a known level of risk/volatility unless they receive a return that precisely rewards them for that risk. This means that all securities sell at a market price that is always equal to fair or intrinsic value.

I do not personally subscribe to MPT because I find it very difficult to accept the twin concepts of constant rational investment behavior and instant perfect market knowledge. However, that does not mean that I am indifferent to price volatility. No matter what your definition or conception of market risk may be, no one likes to see their returns jumping around all over the place.

The concept of Beta is well known as a measure of price volatility. A Beta value of 1.00 implies that the company's stock price moves in line with the overall market, while a Beta above 1.00 implies a level of volatility above the market and a Beta below 1.00 implies the opposite.

But volatility is also important to consider when analyzing metrics other than price. For example, I look at total returns for each of the past ten years when evaluating a company. I measure volatility by calculating the Standard Deviation (STDEV) of these ten values.

STDEV is a metric that is fundamental to statistical analysis. STDEV measures the variation of sample values around the average (mean) of the sample. The higher the STDEV, the higher the level of volatility around the mean.

It is important to realize that STDEV is an absolute measure of volatility for a specific data set. It cannot be compared apples-to-apples with other data sets. This can be understood by considering the first two hypothetical data sets below (Company A and Company B):

YEAR 1 2.3% 4.6% 7.4%
YEAR 2 4.6% 100.0 9.2% 100.0 4.7% 36.5
YEAR 3 1.9% -58.7 3.8% -58.7 2.7% -42.6
YEAR 4 7.7% 305.3 15.4% 305.3 8.2% 203.7
YEAR 5 4.3% -44.2 8.6% -44.2 7.5% -8.5
YEAR 6 5.0% 16.3 10.0% 16.3 5.5% -26.7
STDEV: 2.09% 4.19% 2.09%
AVE: 4.3% 8.6% 6.0%
COV: 0.49 0.49 0.35

It can be seen that the total return sample values for Company B are exactly twice the values of Company A. So the STDEV of Company B is exactly twice the value of Company A. If we were to assess volatility simply by comparing the STDEV numbers, we would conclude that Company B was twice as volatile as Company A.

But this is clearly not the case. In terms of the percentage changes between yearly values, the two data sets are exactly equal. So investors should be indifferent between these two companies - there is no difference in terms of their relative volatility.

This is where we need to introduce the coefficient of variation (COV). COV is a relative measure of volatility that lets us compare two data sets on an apples-to-apples basis. It does this by relating the STDEV of a data set to the average of that data set, as follows:

Coefficient of Variation = Standard Deviation / Average

Looking at the example above, we can see that both the Standard Deviation and the Average of sample values for Company B are twice as large as Company A. Applying the equation above, we see that the Coefficient of Variation is the same for both companies. There is no relative difference in volatility.

COV is also useful in demonstrating a corollary condition. Two data sets can have the same STDEV, but because their means are different, they will have different relative levels of volatility. This can be seen above by comparing Company A to a new Company C.

Here the STDEV values of both companies are identical, so it would be easy to assume that there is no difference in volatility. But the COV confirms what we can detect simply by looking at the percentage changes - Company C is relatively less volatile than Company A.

Let's take a look at some actual companies to see how we can apply the concept of COV.

Boeing (NYSE:BA) Flowers Foods (NYSE:FLO) Interpublic Group of Companies (NYSE:IPG) L Brands (NYSE:LB) TELUS (NYSE:TU) Microsoft (NASDAQ:MSFT) CVS Health (NYSE:CVS)
YEAR 1 10.7% -4.2% 3.1% 15.3% 20.3% 14.7% 3.0%
YEAR 2 14.0% 14.9% 14.4% 43.8% -19.7% 22.2% 36.1%
YEAR 3 -2.6% -8.4% 19.5% 34.0% 8.6% 27.2% 49.9%
YEAR 4 83.7% 41.0% 63.3% 29.0% 9.8% 43.7% 20.2%
YEAR 5 5.1% 25.9% 15.7% 43.7% 26.2% 6.1% 18.7%
YEAR 6 15.0% 8.8% -6.1% 83.6% 28.1% -4.6% 9.0%
STDEV 31.4% 18.6% 24.0% 23.2% 17.6% 16.9% 17.4%
AVE 21.0% 13.0% 18.3% 41.6% 12.2% 18.2% 22.8%
COV 1.49 1.43 1.31 0.55 1.44 0.93 0.76

Looking at the first two columns, we can see that Boeing and Flowers Foods have very different Standard Deviations. It would be easy to assume that Boeing was far more volatile. However, because the average of Boeing sample data is much higher than that of Flowers Foods, the COV shows us that on a relative basis there is very little difference in volatility.

The next two columns show that The Interpublic Group of Companies has a very similar STDEV to that of L Brands. However, their average values are very far apart, so that LB is in fact far less volatile than IPG.

The last three columns show that TELUS, Microsoft, and CVS have STDEV values that are quite close together. But because of differences in average values, their COV scores vary quite dramatically.

Unlike STDEV, COV is unitless and should be used instead of STDEV to compare data sets that have different units or different sample averages.

Caution: As the value of the mean approaches zero, the value of COV will become extremely sensitive to changes in the mean.

Sources: "What is the Coefficient of Variation?"

Wikipedia / Coefficient of Variation

Disclosure: I am/we are long BA, FLO, IPG, TU, MSFT.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.