What are the three types of multifactor models and how do they differ?

Multifactor models explain asset returns using multiple systematic risk factors. The three types differ in how the factors are identified and measured.

1. Macroeconomic Factor Models

Factors are observable macroeconomic variables. Asset returns are regressed against surprise changes in these macro factors.

Rᵢ = αᵢ + βᵢ₁ × F_GDP + βᵢ₂ × F_Inflation + βᵢ₃ × F_TermSpread + εᵢ

Example factors: GDP growth surprise, inflation surprise, oil price change, term spread change, credit spread change

Advantage: Economically interpretable — you know exactly what drives returns.

Disadvantage: Factor selection is subjective; may miss important risk dimensions.

2. Fundamental Factor Models

Factors are company-specific attributes. Returns are explained by cross-sectional characteristics like size, value, momentum, and leverage.

Rᵢ = αᵢ + βᵢ₁ × Size + βᵢ₂ × Book/Market + βᵢ₃ × Momentum + εᵢ

Here, the betas are known (company characteristics), and the factor returns are estimated via cross-sectional regression.

Example: The Fama-French three-factor model uses market, size (SMB), and value (HML). The Carhart four-factor model adds momentum (UMD).

Advantage: Directly tied to investable portfolio characteristics.

Disadvantage: May not capture all systematic risk; factors can be correlated.

3. Statistical Factor Models

Factors are extracted from return data using statistical techniques like Principal Component Analysis (PCA). No economic interpretation is imposed.

Advantage: Captures the maximum variance in the data; no subjective factor selection.

Disadvantage: Factors have no economic meaning — "Factor 1" might be a blend of market, size, and momentum that's hard to interpret.

Practical Example

Pinnacle Quant Fund uses all three:

• Macro model for top-down allocation (how exposed are we to inflation surprises?)
• Fundamental model for stock selection (overweight cheap, high-momentum stocks)
• Statistical model for risk management (what are the principal components driving portfolio variance?)

For the FRM exam, understand the construction differences, be able to identify each type from a description, and know that the APT is most closely related to macroeconomic factor models. Explore our FRM valuation course for deeper factor analysis content.