What is 'Coefficient of Variation (CV)'
A coefficient of variation (CV) is a statistical measure of the dispersion of data points in a data series around the mean. It is calculated as follows: (standard deviation) / (expected value). 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.
BREAKING DOWN 'Coefficient of Variation (CV)'
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 standard deviation to mean return, the better riskreturn tradeoff. Note that if the expected return in the denominator is negative or zero, the coefficient of variation could be misleading.
Coefficient of Variation for Selecting Investments
The coefficient of variation is helpful when using the risk/reward ratio to select investments. For example, an investor who is riskaverse 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, riskseeking investors may look to invest in assets with a historically high degree of volatility.
For example, consider a riskaverse investor who wishes to invest in an exchangetraded fund (ETF) that tracks a broad market index. The investor selects the SPDR S&P 500 ETF, PowerShares 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 longterm averages.
For illustrative purposes, the following 15year 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%.Â SPDR S&P 500 ETF's coefficient of variation is 2.68.
 PowerShares 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 riskreturn tradeoff than the PowerShares QQQ ETF.

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