Why Multifactor Pricing Models Are Equivalent to Stochastic Discount Factors
Summary
This article explains the theoretical link between beta pricing models, including the Fama-French three-factor model, and stochastic discount factors (SDFs). It distinguishes absolute pricing, which connects asset values to macroeconomic risks, from relative pricing, which uses already-priced assets to value others. The central claim is that a beta model corresponds to an SDF that is linear in its factors, giving empirical multifactor work a foundation in asset-pricing theory.
The discussion uses Fama and French’s research to illustrate how to evaluate models. A joint GRS test can reject a model even when pricing errors are small for most test portfolios, so statistical rejection should be read alongside the size and pattern of errors and the model’s practical guidance. The article reports that the three-factor model explains many tested portfolios but does not explain momentum. It cautions against choosing factors solely to fit historical data and argues that empirical tests should remain guided by economic theory. The evidence is a historical and conceptual review, not a new test or trading strategy.
Key ideas
- A beta pricing model has an equivalent SDF that is linear in its factors.
- Multifactor models support relative pricing by relating expected returns to factor exposures.
- A joint statistical rejection should be interpreted alongside the magnitude and distribution of pricing errors.
- The Fama-French three-factor model explained many tested portfolios but did not account for momentum.
- Empirical factor research should connect findings to economic theory rather than rely only on historical fit.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.