Where does beta collide?

The slope from regressing an asset's returns on the returns of the whole market: it measures how much the asset moves with market-wide swings, the part of risk that cannot be diversified away. A beta of one moves with the market, above one amplifies it, and below one dampens it. Sharpe's 1964 Capital asset prices set out the pricing model in which this coefficient, not an asset's total variability, determines its expected return. The referent here is a measured number describing co-movement with a market, and it has nothing to do with a probability of error in a test, a comparison of species between places, or a stage in releasing a program.[1]

Unit

A dimensionless slope of asset return on market return

Recovery means

Not applicable

Measured by

Estimated by regressing an asset's excess returns on the market's excess returns over a return history

The probability of failing to reject a null hypothesis when it is in fact false: the chance a test misses a real effect, so that one minus this quantity is the test's power. Neyman and Pearson's 1933 On the problem of the most efficient tests of statistical hypotheses formalised the two kinds of error a test can make and named this the error of the second kind. The referent is a probability attached to a decision rule, tied to sample size and effect size, and it is unrelated to a market slope, a count of how species differ between places, or a pre-release version of a program.[2]

Unit

A probability between 0 and 1 for a given test and alternative

Recovery means

Not applicable

Measured by

Computed from the test, the true effect, the variance, and the sample size, or estimated by simulation

The extent to which the mix of species changes from one place to another across a landscape or an environmental gradient: high beta diversity means neighbouring sites share few species, low beta diversity means they share many. Whittaker's 1960 Vegetation of the Siskiyou Mountains introduced this measure alongside local (alpha) and regional (gamma) diversity to describe how communities turn over in space. The referent is a property of variation among sites, computed from species lists, and it is not a financial slope, an error probability, or a step in shipping software.[3]

Unit

A ratio or distance summarising species change between sites

Recovery means

Not applicable

Measured by

Derived from species presence or abundance across sites, as gamma over mean alpha or by pairwise dissimilarity indices