A measure of how variations in the return on a particular share correlate with variations in the return on a market index. The beta coefficient is used as a summary of the riskiness of an asset. If r_it is the return on asset i from time t − 1 to time t, and r_It is the return on the market index, β‎_i is calculated by finding the best fit to

so the beta of asset i is defined by ${\beta }_i=\frac{{\sigma }_{iI}}{{\sigma }_I^2},$ where ${\sigma }_I^2$ is the variance of the return on the index representative of the market and σ‎_iI is the covariance between the return on asset i and the return on the index. In the special case of the Capital Asset Pricing Model the index I is the market portfolio. Beta is used as a measure of risk because the variance of return for asset i is

where ${\sigma }_{{\epsilon }_i}^2$ is the part of the variance unexplained by the index. β‎_i < 0 means that r_i moves opposite to the market on average; a zero or low value of β‎_i means that the asset has mainly idiosyncratic risk, independent of overall market movements; a positive value of β‎_i means that r_i moves on average with the market.