What Is the Coefficient of Variation (CV)?

The coefficient of variation represents the ratio of the 澳洲幸运5开奖号码历史查询:standard deviation to the expected return. It is a useful statistic for comparing the degree of variation from one data series to another. It can be expressed as a decimal 🌄oꦬr a percentage.

The CV formula measures the deviation between the historical mean ♍price and the cu𓂃rrent price performance of a financial asset, like stocks or bonds, relative to other investments.

Understanding the Coefficient of Variation (CV)

The coefficient of variation shows the extent of 澳洲幸运5开奖号码历史查询:variability of data in a sample relative to the mean of the population. In finance, the coefficient of variation allows investors to determine how much 澳洲幸运5开奖号码历史查询:volatility, or risk, is assume🦩d in comparison to the amount of return expe⭕cted from investments.

The lower the coefficient of variation, the better the 澳洲幸运5开奖号码历史查询:risk-return tradeoff.CVs are most often used to analyze dispe📖rsion around the mean, but quartile, quintile, or decile CVs can also be used to under🎉stand variation around the median or 10th percentile, for example.

Coefficient of Variation (CV) Formula

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

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

澳洲幸运5开奖号码历史查询:To calculate the 🐲CV for a sample, the 𒐪formula is:

$CV = s/x * 100$CV=s/x∗100
where:
s = sample
x̄ = mean for the population

CV in Excel

The coeffiꦺcient of variation formula can be performed in Excel by first 🐭using the standard deviation function for a data set. Next, calculate the mean by 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 o🍬f Variation (CV) vs. Standard Deviation

The standard deviation is a statistic that measures th꧅e dispersion of a data set relative to its mean. It is used to determine the spread of values in a single data set rather than to compare different units.

When we want to compare two or more data sets, the coefficient of variation is used. The CV is the ratio of the standard deviation to the mean. And because it’s ind🧔ependent of the unit in which the measurement was taken, it can be used to compare data sets with different units or widely different means.

In short, the standard deviation measures how far the average value lies from the mean, whereas the coefficient of variation measures the ratio of the standard deviation to the mean.

Advantages and Disadvantages of the CV

Advantages

The coefficient of variation can be useful when comparing data sets with different units or very different means.

That includes when the risk/reward ratio is used to select investments. For example, a risk-averse investor may want to conꦚsider assets with a historically low degree of volatility relative to the return, to the overall market or its industry. Conversely, risk-seeking investors may look to invest in assets with a historically high degree of vol👍atility.

Disadvantages

When the mean value is close to zero, the CV becomes very sensitive to small changes in the mean. Using the example above, a notable flaw would be if the expected return in the denominator is negative or zero. In this case, the coefficient of variation could be misleading.

How Can the CV Be Used?

The coefficient of♛ variation is used in many different fields, including chemistry, engi𒊎neering, physics, economics, and neuroscience.

Other than helping when using the risk/reward ratio to select investments, it is used by economists to measure economic inequality. Outside of finance, it is commonly applied to audit the precision of a particular process and arri𝓰ve at a perfect balance.

Example: CV for Selecting Investments

For example, consider a risk-averse investor who wishes to invest in an 澳洲幸运5开奖号码历史查询: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 (SPY), the Invesco QQQ ETF (QQQ), and the iShares Russell 2000 ETF (IWM). Then, the investor analyzes the ETFs’ returns and volatility over the past 15 years and a♍ssumes that the ETFs could have similar returns to their long-term averages.

For illustrative purposes, the following 15-year historical infor൩mation is used for the investor’s decision:

• If the SPDR S&P 500 ETF has an average annual return of 5.47% and a standard deviation of 14.68%, the SPY’s coefficient of variation is 2.68.
• If 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.
• If 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.

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 the sam🌊e and indicate a better risk-return tradeoff than the Invesco QQQ ETF.

The Bottom Line

The coefficient of variation is a simple way to compare the degree of variation from one data♊ series to another. It can be applied to several contexts, including the process of picking suitable investments.

A high CV indicates that the group is more variable, whereas a low value would suggest the opposite. Generally, a lower CV suggests a more favor♑able risk-to-rewar𝓀d ratio.