The Fama-French three-factor model, introduced in Fama and French (1993), augments the CAPM with two additional factors to capture the size and value effects documented in Fama and French (1992).
Model specification
Factor definitions
- RM-RF (market): value-weight return on all CRSP stocks minus the one-month T-bill rate. Average: 0.43%/month (t=1.76).
- SMB (Small Minus Big): average return on three small portfolios minus three big portfolios, from independent 2x3 sorts on size and BE/ME. Average: 0.27%/month (t=1.73). Designed to be free of ME influence.
- HML (High Minus Low): average return on two high-BE/ME portfolios minus two low-BE/ME portfolios. Average: 0.40%/month (t=2.91). Designed to be free of size influence.
- SMB-HML correlation: -0.08 (near orthogonal).
Bond-market extension
The original paper also includes two bond-market factors:
- TERM: long-term government bond return minus T-bill rate (term premium)
- DEF: long-term corporate bond return minus government bond return (default premium)
Stock returns share variation with bond factors, but the three stock-market factors subsume TERM and DEF for all equities except low-grade corporates.
Empirical performance
The three factors produce R-squared values above 0.93 for the 25 size/BE/ME portfolios, with intercepts close to zero. The model is rejected by the GRS F-test primarily because of the lowest-BE/ME quintile (growth stocks), where the smallest firms have returns too high and the largest too low.
Construction methodology
Portfolios are formed annually at end of June using NYSE breakpoints:
- Size: NYSE median market cap
- BE/ME: NYSE 30th and 70th percentiles
This creates six portfolios (2 size x 3 BE/ME) from which SMB and HML are derived.
Theoretical interpretation
Fama and French interpret SMB and HML as proxies for undiversifiable risk factors tied to economic fundamentals: high-BE/ME firms have persistently low earnings and small firms suffer prolonged earnings depressions. The factors may proxy for sensitivity to business cycle risk.
Limitations
- Does not capture momentum (added in the Carhart model)
- Does not capture profitability or investment effects (addressed by the five-factor model)
- Anomalies related to profitability, issuance, and accruals remain unexplained
Legacy
The FF3 model became the dominant benchmark for asset pricing research for over two decades. Its methodology (time-series regressions, 2x3 portfolio sorts, GRS tests) set the standard for all subsequent factor model tests.