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Fama-French + momentum. The model that revealed momentum was a free factor anyone could replicate.
Carhart 4-factor model is Mark Carhart's 1997 extension of Fama-French 3-factor, adding momentum (UMD = up-minus-down) as a fourth factor alongside market, size (SMB), and value (HML). After fitting Carhart 4-factor, the residual alpha is much smaller for most active managers — much apparent skill was actually momentum exposure that anyone could replicate.
Rp − Rf = α + βMKT·MKT + βSMB·SMB + βHML·HML + βUMD·UMD + εRp − Rf = α + βMKT·MKT + βSMB·SMB + βHML·HML + βUMD·UMD + εCarhart added UMD because Fama-French 3-factor left a "momentum puzzle" — winners from the past year tend to outperform losers, and this pattern was not captured by market/size/value. Adding momentum eliminated most of the residual.
Momentum is the most robust empirical factor in finance — it works in almost every asset class, in almost every country, in almost every century studied. Carhart's contribution was making it explicit: most "growth fund" alpha was just systematic exposure to momentum.
A momentum-tilted growth fund earned 16% in a year. After Fama-French 3-factor, alpha looks like +2%. Add Carhart momentum factor (UMD returned +6% with the fund's βUMD=0.4 = 2.4% explained): Carhart alpha = +2% − 2.4% = −0.4%. The "skill" was momentum exposure.
Statistically significant positive Carhart 4-factor alpha is even rarer than positive Fama-French alpha. Anything sustained above +1.5% over a decade is exceptional.
Returns from buying the prior-year winners and shorting the prior-year losers (UMD = up-minus-down).
It is widely used in academic research but less in industry, because momentum is harder to disentangle from "growth" in retail funds. Most analyses now use Fama-French 5-factor instead.
Yes — alongside Fama-French 3 and 5-factor for comprehensive style decomposition.
Different factors capture different phenomena. Carhart UMD captures price momentum; Fama-French 5-factor RMW/CMA capture fundamental quality.
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