# Coefficient of Variation (CV)

## 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 addresses the ratio of the standard deviation to the mean, and it is a valuable statistic for contrasting the degree of variation starting with one data series then onto the next, even on the off chance that the means are definitely not quite the same as each other.

## Figuring out the Coefficient of Variation

The coefficient of variation shows the degree of variability of data in a sample corresponding 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. In a perfect world, in the event that the coefficient of variation formula ought to bring about a lower ratio of the standard deviation to mean return, then, at that point, the better the risk-return compromise. Note that assuming the expected return in the denominator is negative or zero, the coefficient of variation could misdirect.

The coefficient of variation is useful while utilizing the risk/reward ratio to choose investments. For instance, an investor who is risk-opposed might need to consider assets with a historically low degree of volatility relative to the return, comparable to the overall market or its industry. On the other hand, risk-seeking investors might hope to invest in assets with a historically high degree of volatility.

While most frequently used to investigate dispersion around the mean, quartile, quintile, or decile CVs can likewise be utilized to grasp variation around the median or 10th percentile, for instance.

The coefficient of variation formula or calculation can be utilized to determine the deviation between the historical mean price and the current price performance of a stock, commodity, or bond, relative to different assets.

## Coefficient of Variation Formula

Below is the formula for how to work out the coefficient of variation:

$\begin &\text = \frac { \sigma }{ \mu } \ &\textbf \ &\sigma = \text \ &\mu = \text \ \end$

Kindly note that assuming the expected return in the denominator of the coefficient of variation formula is negative or zero, the outcome could misdirect.

### Coefficient of Variation in Excel

The coefficient of variation formula can be acted in Excel by first involving the standard deviation function for a data set. Next, work out the mean utilizing the Excel function gave. Since the coefficient of variation is the standard deviation separated by the mean, partition the cell containing the standard deviation by the cell containing the mean.

## Illustration of Coefficient of Variation for Selecting Investments

For instance, consider a risk-loath investor who wishes to invest in a exchange-traded fund (ETF), which is a basket of securities that tracks a broad market index. The investor chooses the SPDR S&P 500 ETF, Invesco QQQ ETF, and the iShares Russell 2000 ETF. Then, they dissect the ETFs' returns and volatility throughout recent years and accepts the ETFs could have comparative returns to their long-term averages.

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

- In the event that the SPDR S&P 500 ETF has an average annual return of 5.47% and a standard deviation of 14.68%, the SPDR S&P 500 ETF's coefficient of variation is 2.68.
- On the off chance that the Invesco QQQ ETF has an average annual return of 6.88% and a standard deviation of 21.31%, the QQQ's coefficient of variation is 3.10.
- In the event that the iShares Russell 2000 ETF has an average annual return of 7.16% and a standard deviation of 19.46%, the IWM's coefficient of variation is 2.72.

In view of the estimated 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 roughly something similar and show a better risk-return compromise than the Invesco QQQ ETF.

## Highlights

- The lower the ratio of the standard deviation to mean return, the better risk-return compromise.
- The coefficient of variation (CV) is a statistical measure of the relative 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.