Deviations from the CAPM
If the CAPM held, then discussion of various investment strategies related to (for example) style analysis, low volatility, sector rotation, momentum, and reversal, would be moot academic exercises. But the empirical evidence against CAPM is overwhelming with the tests, themselves, giving rise to a host of alternative portfolio strategies that are regarded as anomalies because they should not work in the equilibrium state described by CAPM.
The central questions are why the CAPM fails as a pricing relationship and what we learn about the relationships between risk and returns from these tests. The elegance of the CAPM model lies in the linear relationship between the expected return on any security and its covariance (beta) with the market rate of return, that is, the familiar relationship given by:
The asset's beta is determined by its covariance with the market return as a ratio to the market variance, that is, . The CAPM takes the empirical form given by:
Expected returns are replaced by observed returns and appended with the pricing error term, εi, representing the firm's (asset's) specific risk. Specific risk is, of course, diversifiable but otherwise ...