The Fama-French five-factor model, introduced in Fama and French (2015), adds profitability and investment factors to the three-factor model, motivated by the dividend discount model.
Model specification
Factors
| Factor | Name | Long | Short | Avg return |
|---|---|---|---|---|
| RM-RF | Market | All stocks | T-bills | — |
| SMB | Small Minus Big | Small stocks | Big stocks | 0.29%/mo |
| HML | High Minus Low | High B/M | Low B/M | 0.37%/mo |
| RMW | Robust Minus Weak | High OP | Low OP | 0.25%/mo |
| CMA | Conservative Minus Aggressive | Low invest | High invest | 0.33%/mo |
All factors are statistically significant (t>2.3). Constructed using independent 2x3 sorts on size and each characteristic, with NYSE breakpoints.
Theoretical motivation
The dividend discount model implies that expected stock returns depend on three variables:
- Book-to-market (higher B/M implies higher expected returns)
- Expected profitability (higher earnings imply higher expected returns)
- Expected investment (higher growth in book equity implies lower expected returns)
B/M alone is a noisy proxy because market prices also respond to forecasts of earnings and investment.
Performance
The five-factor model captures 71-94% of cross-sectional variance in expected returns on portfolios formed on size, B/M, profitability, and investment. It substantially outperforms the three-factor model, reducing average absolute intercepts by 2-8 bps/month.
Results are robust across three factor construction methods (2x3, 2x2, 2x2x2x2 sorts).
The HML redundancy result
When HML is regressed on the other four factors, its intercept is essentially zero (-0.04%/month, t=-0.47). The average HML return is fully absorbed by HML’s exposures to RMW and CMA. A four-factor model dropping HML performs identically to the five-factor model.
The authors caution this may be sample-specific (U.S., 1963-2013).
Main weakness
The model fails for small stocks whose returns behave like those of firms that invest aggressively despite low profitability. These portfolios produce large negative intercepts (-0.47%/month, t=-5.89), sufficient for model rejection. Large stocks with similar characteristics do not pose this problem. The pattern appears across multiple sorts, suggesting a common underlying issue.
Dissecting anomalies (Fama and French 2016)
Fama and French (2016) test the five-factor model against anomalies not specifically targeted by it: beta, net share issues, volatility, accruals, and momentum. The sample covers July 1963 to December 2014. Key findings:
What FF5 absorbs. Positive exposures to RMW and CMA capture the high average returns associated with low beta, share repurchases, and low volatility. Returns on low-beta and low-volatility stocks behave like those of profitable firms that invest conservatively. Conversely, negative RMW and CMA slopes explain the low average returns of high-beta, large-share-issuing, and high-volatility stocks, whose returns behave like those of unprofitable firms that invest aggressively. The repurchase anomaly effectively disappears in the five-factor model.
- For Size-beta portfolios, average absolute intercepts drop from 0.106% (three-factor) to 0.072% (five-factor). Intercept dispersion is about 30% as large as the dispersion of average returns.
- For Size-residual variance portfolios, the three-factor model produces intercepts of +0.34%/mo (low RVar microcaps) to -1.23%/mo (high RVar microcaps). The five-factor model shrinks these, though extreme intercepts remain for small high-volatility stocks (-0.85%/mo for microcaps, -0.46%/mo for the second size quintile).
- For net share issues, repurchase portfolio intercepts fall from 0.11-0.24%/mo (three-factor) to at most 0.10%/mo (five-factor, t=1.73).
What FF5 does not absorb. The model fails for momentum: regression intercepts are about as dispersed as the average returns themselves (A|a|/A|d|=0.83). Adding a momentum factor (MOM) improves performance but leaves nontrivial unexplained momentum returns among small stocks. Accruals also pose problems: the five-factor model does worse than the three-factor model for accrual-sorted portfolios because microcaps have negative RMW slopes without the predicted low average returns.
Common lethal pattern. The portfolios that cause the most serious problems across all anomaly sorts share the same trait identified in Fama and French (2015): small stocks whose returns behave like those of relatively unprofitable firms that invest aggressively (negative RMW and CMA slopes).
Comparison with the q-factor model
The Hou, Xue, and Zhang (2015) q-factor model offers a competing four-factor specification with the same core insights (investment and profitability matter) but different construction and theoretical grounding. The q-factor investment factor correlates 0.69 with HML, and the ROE factor correlates 0.50 with UMD. In head-to-head tests across ~80 anomalies, the q-factor model produces smaller average alphas (0.20%/mo vs. 0.33% for Carhart and 0.55% for FF3) and captures momentum through its quarterly ROE factor, a key advantage over FF5.
What it does not include
The model omits momentum, which Fama and French view as lacking theoretical motivation from rational asset pricing. Momentum and liquidity factors add nothing for non-momentum-sorted portfolios.