# Dispersion

## What is 'Dispersion'

Dispersion is a statistical term describing the size of the range of values expected for a particular variable. In finance, dispersion is used in studying the effects of investor and analyst beliefs on securities trading, and in the study of the variability of returns from a particular trading strategy or investment portfolio. It is often interpreted as a measure of the degree of uncertainty, and thus risk, associated with a particular security or investment portfolio.

## BREAKING DOWN 'Dispersion'

For example, the familiar risk measurement, beta, measures the dispersion of a security's returns relative to a particular benchmark or market index. If the dispersion is greater than that of the benchmark, then the instrument is thought to be riskier than the benchmark. If the dispersion is less, then it is thought to be less risky than the benchmark.

A beta measure of 1.0 indicates the investment moves in unison with the benchmark. A beta of 0 signifies no correlation, and a beta less than 0 shows contrary movement to the benchmark. For example, if an investment portfolio has a beta of 1.0 using the S&P 500 as a benchmark, the movement between the portfolio and benchmark is nearly identical. If the S&P 500 is up 10%, so is the portfolio. On a negative beta, if the S&P 500 is up, the portfolio moves in the exact opposite direction, which in this case will move down.

## Standard Deviation

Standard deviation is another commonly used statistic for measuring dispersion. It is a simple way to measure an investment or portfolio's volatility. The lower the standard deviation, the lower the volatility. For example, a biotech stock has a standard deviation of 20.0% with an average return of 10%. An investor should expect the price of the investment to move 20% in either a positive or negative manner away from the average return. In theory, the stock can fluctuate in value from negative 10% to positive 30%. Stocks have the highest standard deviation, with bonds and cash having much lower measures.

## Alpha

Both beta and standard deviation are common measurements used to determine the dispersion of a portfolio but often work independently of each other. Alpha is a statistic that measures a portfolio's risk-adjusted returns. A positive number suggests the portfolio should get a positive return in exchange for the risk level taken. A portfolio taking excessive risk and not getting a sufficient return has an alpha of 0 or less. Alpha is a tool for investors looking to measure the success of a portfolio manager. A portfolio manager with a positive alpha indicates a better return with either the same or less risk than the benchmark.