# Coefficient Of Variation - CV

## What is a '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. It is calculated as follows:

## BREAKING DOWN 'Coefficient Of Variation - CV'

In the investing world, the coefficient of variation allows you to determine how much volatility, or risk, you are assuming in comparison to the amount of return you can expect from your investment. In simple language, the lower the ratio of standard deviation to mean return, the better your risk-return tradeoff. Note that if the expected return in the denominator of the calculation is negative or zero, the coefficient of variation could be misleading.

## Coefficient of Variation for Selecting Investments

The coefficient of variation could help investors select investments based on the risk/reward ratio and their profiles. For example, an investor who is risk-averse may want to consider assets that have historically had a 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 that have had a high degree of volatility.

For example, assume a risk-averse investor wishes to invest in an exchange traded fund (ETF) that tracks a broad market index. The investor narrowed the ETFs down to the SPDR S&P 500 ETF, PowerShares QQQ ETF, and the iShares Russell 2000 ETF. The investor analyzes the ETFs' returns and volatility over the past 15 years, and the investors assumes the ETFs could be expected to have similar returns to their long-term averages.

The SPDR S&P 500 ETF has an average annual return of 5.47% and standard deviation of 14.68% over the past 15 years, as of May 31, 2016. Therefore, SPY has a coefficient of variation of 2.68. The PowerShares QQQ ETF has an average annual standard deviation of 21.31% and return of 6.88% over the same period. Consequently, QQQ has a coefficient of variation of 3.09. The iShares Russell 2000 ETF has an average annual return of 7.16% and standard deviation of 19.46%. Therefore, IWM has a coefficient of variation of 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 approximately in line.