Regression

The Characteristic Regression Line (CRL) is a graphic representation of the market model. The characteristic line is used to measure statistically the undiversifiable risk and diversifiable risk of individual assets and portfolios. The characteristic regression line of an asset explains the asset’s systematic variability of returns in terms of market forces that affect all assets simultaneously. The portion of total risk not explained by characteristic line is called unsystematic risk. It is expressed as.

Where:

kj = expected or required rate of return on security j

km= return on market portfolio

ßj= the slope of the average regression relationship

[Non-diversifiable risk of asset or portfolio j / Risk of market portfolio] [Cov (kjkm) / Var (km)]

aj= intercept of the fitted line indicating the return of security or portfolio when the market return is zero.