The CFA recognizes 3 general classifications of multifactor models. Macroeconomic factor models, fundamental factor models and statistical factor models. The CAPM itself is a single-factor model which describes return as a factor of the return on the market portfolio.

Macroeconomic factor modelsassume that asset returns are explained by unexpected realized values in macroeconomic risk factors like GDP, interest rates, and inflation. Factor surprises are defined as the difference between the realized value of the factor and its consensus predicted value

Fundamental factor models assume asset returns are explained by multiple firm-specific factors (e.g., P/E ratio, market cap, leverage ratio, and earnings growth rate).

Statistical factor models use statistical methods to explain asset returns. Two primary types of statistical factor models are used: factor analysis and principal component models. In factor analysis, factors are portfolios that explain covariance in asset returns. In principal component models, factors are portfolios that explain the variance in asset returns. The major weakness is that the statistical factors do not lend themselves well to economic interpretation. Therefore, statistical factors are mystery factors.

The key differences between the macroeconomic factor model and the fundamental factor model can be summarized as follows:

- The
standardized sensitivities in the fundamental factor model (b
_{i1}and b_{i2}) are calculated directly from the attribute (e.g., P/E) data—they are not estimated. This contrasts with the macroeconomic factor model, in which the sensitivities are regression slope estimates. - The
macroeconomic factors (F
_{GDP}and F_{QS}) are surprises in the macroeconomic variables (e.g., inflation shock and interest rate shock). In contrast, the fundamental factors (F_{P/E}and F_{SIZE}) are rates of return associated with each factor and are estimated using multiple regression. - The intercept in the macroeconomic factor model equals the stock’s expected return (based on market consensus expectations of the macro factors) from an equilibrium pricing model like the APT. In contrast, the intercept of a fundamental factor model with standardized sensitivities has no economic interpretation.