How to Use Capm?

In a world where non-linearity and randomness are the norm, the capital asset pricing model (CAPM) is widely accepted despite it being a linear model, and this is probably due to the simplicity of the model and its pre-computer age birth (see equation below). A well recognized and utilized metric in finance is beta (β), which is the slope in the linear CAPM. To derive β one simply plots the returns (capital gains plus dividend yields) of an individual stock (y-axis) against the returns of a well diversified portfolio of stocks ( x-axis), with the resulting slope being called β. Thus β represents the risk associated with an individual stock, as it is compared to a well diversified portfolio, and since the market portfolio theoretically only contains market risk, a β above (below) one reflects the degree of company-specific risk of the individual stock that should be diversified away as it is added to the market portfolio.

Finance literature is riddled with support for β, as well as doubt surrounding its validity, but why do these mixed reviews exist?, probably because it is nearly impossible to prove or refute the model when the very data being used for this purpose is extracted from within the impure and intertwined marketplace. Recent efforts have been made to go beyond β via multiple linear regression models, with two such examples being: (1) the arbitrage pricing theory (APT), and (2) the more widely accepted Famma French model. The impetus behind these models is the desire to bridge the linear CAPM model into the realm of multiple linear factors instead of a single factor, β. And both of these models are definitely a step in the right directions since non-linearity can be captured via their curvilinear regression (multiple linear regression). This post will not expand further on curvilinear regression, but a future post to this blog will address this topic in great detail.
If we step back though and examine the CAPM and its application, we would