What Is Dispersion?

Dispersion is a statistical term that describes the size of the distribution of values expected for a particular variable. Dispersion can be measured by several different statistics, such as range, variance, and standard deviation. In finance and investing, dispersion usually refers to the range of possible returns on an investment, but it can also be used to measure the risk inherent in a particular security 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.

Key Takeaways

  • Dispersion refers to the range of potential outcomes of investments based on historical volatility or returns.
  • Dispersion can be measured using alpha and beta, which measure risk-adjusted returns and returns relative to a benchmark index, respectively.
  • Generally speaking, the higher the dispersion, the riskier an investment is, and vice versa.

Understanding Dispersion

InvestorsĀ have thousands of potential securities to invest in and many factors to consider in choosing where to invest. One factor high on their list of considerations is the risk profile of the investment. Dispersion is one of many statistical measures to give perspective. Most securities will have fact sheets or prospectuses that can be readily found on the internet, under the name of the ETF or mutual fund that list some of these statistics. Individual stocks can be found on Morningstar and similar stock rating companies.

The dispersion of return on an asset shows the volatility and risk associated with holding that asset. The more variable the return on an asset, the more risky or volatile it is. For example an asset whose historical return in any given year ranges from +10% to -10% is more volatile because its returns are more widely dispersed than an asset whose historical return ranges from +3% to -3%.

The primary risk measurement statistic, beta, measures the dispersion of a security's return relative to a particular benchmark or market index, most frequently the U.S. S&P 500 index. A beta measure of 1.0 indicates the investment moves in unison with the benchmark. A beta greater than 1.0 indicates the security is likely to outperform the market as a whole: e.g., a stock with a beta of 1.3 could be expected to outperform the market by 1.3 times (e.g., market up 10%, beta stock of 1.3 up 13%). However, there is no guarantee that a security with a 1.3 beta will outperform the market if it goes up. The flip side is that if the market goes down, that security will similarly likely go down more than the market.

A beta of less than 1.0 signifies a less dispersed return relative to the overall market. For example, a security with a beta of 0.87 will likely trail the overall market: e.g., if the market is up 10%, then the investment with the lower beta would be expected to be up only 8.7%.

Alpha is a statistic that measures a portfolio's risk-adjusted returns, that is, how much more or less did the investment return relative to the index or beta. A return higher than the beta indicates a positive alpha, usually attributed to the success of the portfolio manager or model. A negative alpha indicates the lack of success of the portfolio manager in beating the beta, or more broadly, the market.