The Carhart four-factor model, introduced in Carhart (1997), extends the Fama-French three-factor model by adding a momentum factor.
Model specification
Factors
- RM-RF, SMB, HML: as in the FF3 model
- UMD (Up Minus Down): return on high prior-return stocks minus low prior-return stocks, based on 12-1 month past returns (following Jegadeesh and Titman 1993)
Context
Carhart (1997) studied mutual fund performance persistence and found that the one-year persistence in fund returns documented by earlier studies is almost entirely explained by the momentum factor. Funds that load heavily on momentum (buying recent winners) appear to have persistent skill, but the persistence disappears once UMD is included. After controlling for all four factors, only the worst-performing funds show persistence (they continue to underperform), while no evidence of genuine stock-picking skill remains.
Significance
The Carhart model became the standard benchmark for:
- Evaluating mutual fund and hedge fund performance (alpha)
- Controlling for known return anomalies in empirical asset pricing
- Attributing portfolio returns to systematic factor exposures
Relationship to other models
The model is sometimes called the “Fama-French-Carhart” model. Fama and French did not include momentum in their own models, arguing it is an empirical regularity without clear theoretical grounding in rational asset pricing. They later addressed profitability and investment effects in the five-factor model rather than adding momentum.
Asness et al. (2014) note the irony that momentum’s return premium (8.3%/year, Sharpe 0.50) exceeds both value (4.7%/year, 0.39) and size (2.9%/year, 0.26).