# What is Dispersion?

## What is Dispersion?

dispersion, in wave motion, any phenomenon associated with the propagation of individual waves at speeds that depend on their wavelengths. Ocean waves, for example, move at speeds proportional to the square root of their wavelengths; these speeds vary from a few feet per second for ripples to hundreds of miles per hour for tsunamis.

A wave of light has a speed in a transparent medium that varies inversely with the index of refraction (a measure of the angle by which the direction of a wave is changed as it moves from one medium into another).

Any transparent medium—e.g., a glass prism—will cause an incident parallel beam of light to fan out according to the refractive index of the glass for each of the component wavelengths, or colours. Dispersion is sometimes called the separation of light into colours, an effect more properly called angular dispersion.

## Measuring Dispersion

### Beta

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 experience moves greater than the market as a whole—a stock with a beta of 1.3 could be expected to experience moves that are 1.3x the market, meaning if the market is up 10%, the beta stock of 1.3 climbs 13%. The flip side is that, if the market goes down, that security will likely go down more than the market, although there are no guarantees of the magnitude of the moves.

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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—if the market is up 10%, then the investment with the lower beta would be expected to rise only 8.7%.

### Alpha

Alpha is a statistic that measures a portfolio’s risk-adjusted returns—that is, how much, more or less, the investment returned 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, on the other hand, indicates the lack of success of the portfolio manager in beating the beta or, more broadly, the market.