Explain and contrast the three kinds of factor model: macroeconomic, fundamental, and statistical

Macroeconomic factor models use surprises in economic variables, such as unexpected GDP growth or inflation, as factors; each asset's sensitivities are estimated by time-series regression of its returns on those surprises. A return is then expected return plus each sensitivity times its factor surprise plus an asset-specific error. Fundamental factor models use company attributes such as value, size, momentum or industry: sensitivities are standardised attribute values, and factor returns are estimated each period by cross-sectional regression. Statistical models extract factors from return covariances, fitting the data well but without clear economic meaning. The trap is using the level of a macro variable rather than its surprise, or reversing which quantities are observed and which estimated in each model.