### What Is the Coefficient of Variation (CV)?

The coefficient of variation (CV) is a statistical measure of the dispersion of data points in a data series around the mean. The coefficient of variation represents the ratio of the standard deviation to the mean, and it is a useful statistic for comparing the degree of variation from one data series to another, even if the means are drastically different from one another.

### Understanding the Coefficient of Variation

The coefficient of variation shows the extent of variability of data in a sample in relation to the mean of the population. In finance, the coefficient of variation allows investors to determine how much volatility, or risk, is assumed in comparison to the amount of return expected from investments. Ideally, the coefficient of variation formula should result in a lower ratio of the standard deviation to mean return, meaning the better risk-return trade-off. Note that if the expected return in the denominator is negative or zero, the coefficient of variation could be misleading.

The coefficient of variation is helpful when using the risk/reward ratio to select investments. For example, an investor who is risk-averse may want to consider assets with a historically low degree of volatility and a high degree of return, in relation to the overall market or its industry. Conversely, risk-seeking investors may look to invest in assets with a historically high degree of volatility.

While most often used to analyze dispersion around the mean, quartile, quintile, or decile CVs can also be used to understand variation around the median or 10th percentile, for example.

The coefficient of variation formula or calculation can be used to determine the variance between the historical mean price and the current price performance of a stock, commodity, or bond.

### Key Takeaways

- The coefficient of variation (CV) is a statistical measure of the dispersion of data points in a data series around the mean.
- In finance, the coefficient of variation allows investors to determine how much volatility, or risk, is assumed in comparison to the amount of return expected from investments.
- The lower the ratio of the standard deviation to mean return, the better risk-return trade-off.

### Coefficient of Variation Formula

Below is the formula for how to calculate the coefficient of variation:

$\begin{aligned} &\text{CV} = \frac { \sigma }{ \mu } \\ &\textbf{where:} \\ &\sigma = \text{standard deviation} \\ &\mu = \text{mean} \\ \end{aligned}$

Please note that if the expected return in the denominator of the coefficient of variation formula is negative or zero, the result could be misleading.

#### Coefficient of Variation in Excel

The coefficient of variation formula can be performed in Excel by first using the standard deviation function for a data set. Next, calculate the mean using the Excel function provided. Since the coefficient of variation is the standard deviation divided by the mean, divide the cell containing the standard deviation by the cell containing the mean.

#### Coefficient Of Variation (CV)

### Example of Coefficient of Variation for Selecting Investments

For example, consider a risk-averse investor who wishes to invest in an exchange-traded fund (ETF), which is a basket of securities that tracks a broad market index. The investor selects the SPDR S&P 500 ETF, Invesco QQQ ETF, and the iShares Russell 2000 ETF. Then, he analyzes the ETFs' returns and volatility over the past 15 years and assumes the ETFs could have similar returns to their long-term averages.

For illustrative purposes, the following 15-year historical information is used for the investor's decision:

- SPDR S&P 500 ETF has an average annual return of 5.47% and a standard deviation of 14.68%. SPDR S&P 500 ETF's coefficient of variation is 2.68.
- Invesco QQQ ETF has an average annual return of 6.88% and a standard deviation of 21.31%. QQQ's coefficient of variation is 3.09.
- iShares Russell 2000 ETF has an average annual return of 7.16% and a standard deviation of 19.46%. IWM's coefficient of variation is 2.72.

Based on the approximate figures, the investor could invest in either the SPDR S&P 500 ETF or the iShares Russell 2000 ETF, since the risk/reward ratios are comparatively the same and indicate a better risk-return trade-off than the Invesco QQQ ETF.