What Is the Coefficient of Variation (CV)?

What Is the Coefficient of Variation (CV)?

Let me explain the coefficient of variation to you directly: it's the ratio of the standard deviation to the expected return, and I use it as a statistic to compare the degree of variation between different data series. You can express it as a decimal or a percentage. The CV formula specifically measures the deviation between the historical mean price and the current price performance of a financial asset, such as stocks or bonds, relative to other investments.

Key Takeaways

Understand this: the standard deviation shows how far the average value is from the mean, while the coefficient of variation gives you the ratio of the standard deviation to the mean. I apply the CV to compare two or more data sets. Remember, the lower the CV, the better the risk-return tradeoff.

Understanding the Coefficient of Variation (CV)

The coefficient of variation reveals the extent of variability in a sample's data relative to the population's mean. In finance, I use it to help you determine how much volatility or risk you're assuming compared to the expected return from investments. A lower coefficient of variation means a better risk-return tradeoff. You'll see CVs most often for analyzing dispersion around the mean, but they can also apply to quartiles, quintiles, or deciles to understand variation around the median or 10th percentile, for instance.

It's important to note that the CV formula determines 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

Here's the formula you need for calculating the coefficient of variation: CV = σ / μ, where σ is the standard deviation and μ is the mean. For a sample, it's CV = s / x̄ * 100, where s is the sample standard deviation and x̄ is the mean for the population. Multiplying by 100 is optional if you want a percentage instead of a decimal.

CV in Excel

You can perform the coefficient of variation formula in Excel easily. First, use the standard deviation function for your data set. Then, calculate the mean with the Excel function. Divide the cell with the standard deviation by the cell with the mean to get the CV.

Coefficient of Variation (CV) vs. Standard Deviation

The standard deviation measures the dispersion of a data set relative to its mean, focusing on the spread within a single data set rather than comparisons. When you need to compare two or more data sets, turn to the coefficient of variation, which is the ratio of the standard deviation to the mean. Since it's independent of the unit of measurement, CV lets you compare data sets with different units or widely different means. In essence, standard deviation tells you how far the average value is from the mean, while CV gives the ratio of standard deviation to the mean.

Advantages and Disadvantages of the CV

One advantage is that the coefficient of variation works well for comparing data sets with different units or very different means, including when you're using the risk/reward ratio to select investments. For instance, if you're a risk-averse investor, you might consider assets with historically low volatility relative to their return compared to the market or industry. On the other hand, risk-seeking investors could look for assets with high volatility.

A disadvantage comes when the mean value is close to zero, making the CV very sensitive to small changes in the mean. If the expected return in the denominator is negative or zero, the CV can be misleading.

How Can the CV Be Used?

You'll find the coefficient of variation applied in fields like chemistry, engineering, physics, economics, and neuroscience. Beyond helping with risk/reward ratios for investments, economists use it to measure economic inequality. Outside finance, it's common for auditing the precision of processes to achieve a perfect balance.

Example: CV for Selecting Investments

Consider this example: suppose you're a risk-averse investor looking to invest in an ETF that tracks a broad market index. You might evaluate the SPDR S&P 500 ETF (SPY), the Invesco QQQ ETF (QQQ), and the iShares Russell 2000 ETF (IWM). Analyzing their returns and volatility over the past 15 years, assuming similar future returns to their long-term averages, here's what you get.

For SPY, with an average annual return of 5.47% and standard deviation of 14.68%, the CV is 2.68. For QQQ, with 6.88% return and 21.31% standard deviation, the CV is 3.10. For IWM, with 7.16% return and 19.46% standard deviation, the CV is 2.72. Based on these figures, you could choose SPY or IWM, as their risk/reward ratios are similar and better than QQQ's.

What Does the Coefficient of Variation Tell Us?

The CV indicates the size of the standard deviation relative to the mean. A higher CV means greater dispersion around the mean.

What Is Considered a Good Coefficient of Variation?

It depends on what you're comparing. There's no universal 'good' value, but generally, a lower CV is more desirable, indicating a lower spread of data relative to the mean.

How Do I Calculate the Coefficient of Variation?

To calculate it, first find the mean, then the sum of squares, and work out the standard deviation. Then divide the standard deviation by the mean.

The Bottom Line

The coefficient of variation provides a simple way to compare variation between data series, applicable in contexts like selecting investments. A high CV shows more variability, while a low value suggests the opposite. Overall, a lower CV points to a more favorable risk-to-reward ratio.