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, if the coefficient of variation formula should result in a lower ratio of the standard deviation to mean return, then the better the risk-return trade-off. Note that if the expected return in the denominator is negative or zero, the coefficient of variation could be misleading. For example, an investor who is risk-averse may want to consider assets with a historically low degree of volatility relative to the 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 deviation between the historical mean price and the current price performance of a stock, commodity, or bond, relative to other assets.
Below is the formula for how to calculate the coefficient of variation:. 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. 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. 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.
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 year historical information is used for the investor's decision:. Portfolio Management. Risk Management.
Financial Ratios. Tools for Fundamental Analysis. If you want to compare the variability of measurements made in different units, then the coefficient of variability is a valuable metric in this case. However, calculating standard deviation can be helpful when you want to determine the margin of error or volatility in your data sets. One of the significant advantages of the coefficient of variation is that it is unitless, and you can apply it to any given quantifiable observation.
This allows you to compare the degree of variation between two different data sets. Standard deviation gives you a clear idea of the distribution of data in an observation.
It also serves as a shield against the effects of extreme values or outliers in quantifiable observation. Variance is a measure of variability that shows you the degree of spread in your data set using larger units like meters squared. On the other hand, coefficient of variation measures the relative distribution of data points around the mean.
Use variance or variance tests to assess the differences between populations or groups in your research. Meanwhile, coefficient of variation allows you to compare the degree of variability between different data sets. Variance helps you to gain helpful information about a data set for better decision-making. Variance treats all numbers in a set the same, regardless of whether they are positive or negative, which allows you to account for the most minute variability in data sets.
Coefficient of variation helps to measure the degree of consistency and uniformity in the distribution of your data sets. Unlike variance, it doesn't depend on the measurement unit of the original data, which allows you to compare two different distributions. Coefficient of variation is a unitless measure of relative dispersion. The absence of units allows COV to be used to compare variability across mutually exclusive data sets. If the coefficient of variation is greater than 1, it shows relatively high variability in the data sets.
On the flip side, a CV lower than 1 is considered to be low-variance. The coefficient of variation differs based on the composition of data points in your observation. In general, a coefficient of variation between 20—30 is acceptable, while a COV greater than 30 is unacceptable.
If the mean of your data is negative, then the coefficient of variation will be negative. However, this typically means that the coefficient of variation is misleading. Create Research Surveys for Free. Aside from consulting the primary origin or source, data can also be collected through a third party, a process common with secondary data. Ordinal data classification is an integral step towards proper collection and analysis of data.
Therefore, in order to classify data Data cleaning is one of the important processes involved in data analysis, with it being the first step after data collection. It is a very Interval data is quantitative data measured along a scale. By discussing its definition, characteristics etc. Pricing Templates Features Login Sign up. What Is the Coefficient of Variation? Application 2 Coefficient of variation can also be used to measure the viability of new markets before an organization launches a new product, service, or outlet.
Application 3 Researchers use coefficients of variation to compare outcomes of systematic investigations across different populations. Understanding Coefficient of Variation Formula and Related Concepts As you dive deeper into the coefficient of variation, you'd come across several related concepts, including mean, standard deviation, and dispersion.
Dispersion Dispersion or variability accounts for the distribution of numerical values within a statistical function. Absolute Measure of Dispersion Absolute measures of dispersion are used to determine the amount of distribution within a single set of observations. Depending on the purpose of your research and numerical data sets, you can use one or more of these types of absolute measures of dispersion: Range Variance and Standard Deviation Quartiles and Quartile Deviation Mean and Mean Deviation Pros of Using Absolute Measures of Dispersion They are relatively simple to understand and calculate.
Absolute measures of dispersion limit any distortions caused by extreme scores in data sets, especially when you depend on mean deviation. Relative Measure of Dispersion On the other hand, researchers use relative measures of dispersion to compare the distribution of two or more data sets.
They help researchers to control the variability of a phenomenon. Cons of Using Relative Dispersion Methods They can result in misinterpretations and generalizations in data sets. They are liable to yield inappropriate results as there are different methods of calculating the dispersions.
Mean Mean refers to the average value of a data set. Pros of Using Mean in Statistics It provides an objective presentation of the different variables in a data set. It limits the influence of extreme values in large research samples. Cons of Using Mean in Statistics It is sensitive to extreme values in a small data set. Mean is not the most appropriate measure of central tendency for skewed distribution. This reflects the predilection for only assessing outcome in terms of the mean or median , rather than also considering effects on levels of variability.
Even where they are commented on, some workers do not follow accepted conventions on what a 'good' level of repeatability is. Inappropriate or unspecified methods are often used to estimate within subject coefficient of variation. Another problem is that often very little information is given on how the coefficient of variation is estimated, so that its reliability cannot be assessed.
Lastly, we found that some veterinary researchers only estimated intra-assay and inter-assay coefficients of variation after excluding 'outliers', apparently just to bring the coefficient of variation down to acceptable levels. This seems to rather defeat the whole point of assessing variability! Other uses and misuses of the coefficient of variation are many and varied, and we meet some of these in the ecological and wildlife examples.
The coefficient of variation is underused rather than overused as a measure of temporal or spatial variability. Some researchers still use standard deviations for variables where the standard deviation is directly proportional to the mean - instead such variables should be log transformed, or alternatively the coefficient of variation used to describe variability. We have included a few examples of its correct use for these purposes. Krebs discusses the use of the coefficient of variation for measuring temporal variability.
He emphasizes that it is only appropriate when the slope of Taylor's Power Law is equal to 2 i.
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