# Dispersion

### What is dispersion?

Dispersion is a statistical term that describes the size of the distribution of expected values ​​for a particular variable. Dispersion can be measured by several different statistics, such as range, variance, and standard deviation. In finance and investment, dispersion generally refers to the range of possible returns from an investment, but it can also be used to measure the risk inherent in a particular securities or investment portfolio. It is often interpreted as a measure of the degree of uncertainty, and therefore of the risk, associated with a particular securities or investment portfolio.

### Key points to remember

• Dispersion refers to the range of potential investment results based on volatility or historical returns.
• Dispersion can be measured using alpha and beta, which measure risk-adjusted returns and returns relative to a benchmark, respectively.
• In general, the higher the dispersion, the more risky an investment is and vice versa.

### Understanding dispersion

Investors have thousands of potential stocks to invest in and many factors to consider when choosing where to invest. A high factor on their list of considerations is the risk profile of the investment. Dispersion is one of the many statistical measures to put into perspective. Most titles will have fact sheets or flyers which can be easily found on the Internet under the name of the ETF or the OPC which lists some of these statistics. Individual stocks can be found on Morningstar and similar rating companies.

The dispersion of the return on an asset shows the volatility and the 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 a given year varies from + 10% to -10% is more volatile because its returns are more widely dispersed than an asset whose historical return varies from + 3% to -3%.

The main risk measurement statistic, beta, measures the dispersion of a security’s return compared to a benchmark index or a particular market index, most often the American S&P 500 index. A beta measure of 1, 0 indicates that the investment moves in unison with the benchmark index. A beta greater than 1.0 indicates that the security is likely to outperform the market as a whole: for example, a security with a beta of 1.3 should outperform the market by 1.3 times (for example, market up 10%, beta stock up 1.3) 13%). However, there is no guarantee that a title with a beta version of 1.3 will outperform the market if it goes up. The flip side is that if the market goes down, this stock will probably go down more than the market.

A beta below 1.0 means a less dispersed return compared to the overall market. For example, a security with a beta of 0.87 will likely follow the broader market: for example, if the market is up 10%, investment with the lower beta should only increase by 8.7%.

Alpha is a statistic that measures the risk-adjusted returns of a portfolio, that is, how much more or less the return on investment compared to the index or beta. A return above beta indicates a positive alpha, generally attributed to the success of the portfolio manager or model. A negative alpha indicates the portfolio manager’s lack of success in beating the beta, or more broadly, the market.