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What is Dispersion?
Dispersion is a statistical term that describes the size of the expected distribution of values for a given variable. It can be measured using a variety of statistics, including range, variance, and standard deviation. Dispersion is a term used in finance and investing to describe the range of possible investment returns. It can also be used to assess the level of risk associated with a specific security or investment portfolio.
The degree of uncertainty, and thus risk, associated with a particular security or investment portfolio is often interpreted as dispersion.
Thousands of potential securities are available to investors, and there are numerous factors to consider when deciding where to invest. The risk profile of the investment is one factor high on their list of considerations. Dispersion is one of many statistical measures used to put things in context.
The volatility and risk associated with holding an asset are represented by the dispersion of return on that asset. The riskier or more volatile an asset is, the more variable its return is.
Absolute and relative dispersion are the two types of dispersion. The tools for performing complete enumeration and relative comparison, respectively, are absolute dispersion and relative dispersion. The absolute and relative measures of dispersion are intertwined. The dispersed data are expressed in relative terms or percentages, according to the relative dispersion definition. Because the various series are devoid of a specific unit, they can be compared. A subset of the absolute measure of dispersion is the relative measure of dispersion.
Relative Value of Dispersion
The ratio of a data set’s standard deviation to its arithmetic mean is its relative dispersion, also known as its coefficient of variation. It is, in effect, a measurement of how far an observed variable deviates from its mean value. Because it is a way to determine the risk involved with the holdings in your portfolio, it is a useful measurement in applications such as comparing stocks and other investment vehicles.
Add all of the individual values in your data set together and divide by the total number of values to get the arithmetic mean.
Square the difference between each data point’s individual value and the arithmetic mean
Some Commonly Used Relative Dispersion Measures
The range is the most basic measure of absolute dispersion. This is simply the largest data point subtracted from the smallest. This can be written as R = H – L.
For instance, if a data set included the numbers 4, 5, 8, and 28, the range would be 28 – 4 = 24.
The coefficient of the range is an analogous relative measure of dispersion.
The standard deviation is a more complicated measure of absolute dispersion that can be calculated by squaring the difference between each data point and the mean, summing those squares, dividing by one less than the number of data points, and then taking the square root of that., Finally, the square root is calculated again, and the standard deviation is calculated in your original units of measurement.
Mean Deviation Coefficient
The relative measure is calculated by dividing the absolute measure of variability by the corresponding average.
The coefficient of mean deviation about the mean is equal to
(mean deviation about the mean) divided by the arithmetic mean.
The coefficient of mean deviation about the median is equal to (mean deviation about the median) divided by the median.
(mean deviation about mode)/mode = coefficient of mean deviation about the mode
Standard Deviation Coefficient
The standard deviation coefficient is simply the ratio of a series’ standard deviation to its arithmetic mean.
Standard deviation coefficient=/Mean
(Coefficient of standard deviation)/coefficient of variation=100
Lorenz Curve
The Lorenz curve is a graphic representation of the absolute measure of dispersion. The Lorenz curve graphically depicts the actual curve as well as a line of equal distribution. It shows the difference between the two. The Lorenz Coefficient is the deviation of an actual curve from the line of equal distribution. It has a positive relationship with the Lorenz curve’s distance from the line of equal distribution.
Dispersion Relative Measures
The ratio of the standard deviation to the mean is one example of a relative measure of dispersion. Relative measures of dispersion are always dimensionless, making them ideal for comparing different data sets or experiments with different units. Coefficient of dispersion is another name for them.
Conclusion
The range of possible investment outcomes based on the historical volatility of returns is referred to as dispersion.
The higher the dispersion, the riskier an investment is, and vice versa. Is the state of becoming dispersed or spread, as measured by alpha and beta, which measure risk-adjusted returns and returns relative to a benchmark index, respectively. The extent to which numerical data is likely to vary around an average value is referred to as statistical dispersion.
