Why add a momentum factor to Fama-French?

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AcadiFi · Accepted Answer

Carhart (1997) added momentum (UMD, Up Minus Down, also called MOM or WML) because Fama-French three-factor regressions left a significant positive alpha on past-winner portfolios and negative alpha on past losers. Jegadeesh and Titman (1993) had documented that stocks with the highest returns over the prior 12 months (excluding the most recent month to avoid reversal) tended to outperform over the next 3-12 months.

UMD is constructed monthly as the return on top-30% past winners minus bottom-30% past losers, equal weighted within size groups. The average monthly premium in US data 1927-2020 was roughly 0.70% with high volatility and occasional crashes (notably 2009).

The full Carhart model: R_i - R_f = α + β_mkt × MKTRF + β_SMB × SMB + β_HML × HML + β_UMD × UMD + ε.

Example: Polestar Quant Fund shows β_UMD = 0.42 across 10 years. The momentum loading alone contributes 0.42 × 0.70% × 12 = 3.53% per year to expected return. Failing to include UMD would have shown a false positive alpha of about that magnitude.

Carhart originally used it to show mutual fund 'winners' were just riding momentum, not skilled. Today UMD is a standard control in hedge fund factor-benchmark regressions.

Why add a momentum factor to Fama-French?

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