Factor Momentum: Replication & Extension

Key Numbers

Executive Summary

• Factors are autocorrelated. HML and PMU show statistically significant persistence — a factor that performed well over the prior year tends to continue performing well.
• UMD dynamically times other factors. Conditional correlations reveal that UMD's relationship with other factors flips sign depending on recent performance — invisible in unconditional statistics.
• Factor momentum generates significant alpha. Both TSFM and CSFM produce returns unexplained by the five-factor model. CSFM is completely independent of stock-level UMD.
• Momentum concentrates in high-eigenvalue PCs. Consistent with the theoretical prediction that persistent sentiment affects only the most systematic factor combinations.
• Implementation requires scale. With only four factors, the momentum signal is too noisy for reliable long-only rotation. The academic results rely on 20–47 factors.

Factor Construction

Each factor is constructed using the standard Fama-French 2×3 sort methodology. Every month, stocks are independently sorted into two size groups (NYSE median) and three signal groups (NYSE 30th/70th percentiles), producing six value-weighted portfolios. The factor return averages the long-short spread across both size groups.

HML, PMU, and CMA rebalance annually in June (holding July–June). UMD rebalances monthly — momentum is a short-horizon signal that requires frequent refreshing.

Factor Summary Statistics

Testing Factor Autocorrelation

The central empirical claim: factors that performed well over the prior year tend to continue performing well. Each factor is regressed on an indicator for whether its trailing 12-month average return was positive. A positive, significant beta implies the factor exhibits "streaks."

Conditional Returns (Prior-Year Performance)

Unconditional vs. Conditional Correlations with UMD

Unconditional correlations between UMD and other factors are near zero — which is why the Fama-French model treats them as independent. But conditionally, the correlations flip sign: after a good year, momentum goes long value stocks; after a bad year, momentum goes short value. The unconditional correlation masks a strong time-varying relationship, explaining why the FF five-factor model struggles with momentum.

Factor Momentum Strategies

Two strategies that explicitly exploit factor-level autocorrelation: TSFM goes long factors with positive prior-12-month returns and shorts those with negative returns. CSFM goes long the top-2 factors by prior-month return and shorts the bottom-2.

TSFM vs. CSFM Performance

Spanning Tests

A factor momentum strategy is only a genuine anomaly if its returns cannot be explained by known risk factors. Each strategy is regressed on the Fama-French five-factor model, then the six-factor model (adding UMD).

Long-Only Factor Rotation

The strategies above take both long and short positions in factors. In practice, many investors cannot short factors. This section builds a more realistic long-only Factor Momentum Rotation (FMR) strategy and compares it against a passive equal-weight benchmark.

EW vs. FMR Performance

Extension: Principal Component Factor Momentum

Ehsani & Linnainmaa and Arnott et al. show that factor momentum concentrates in the highest-eigenvalue principal components — the systematic directions that explain the most variation in returns. The economic intuition: arbitrageurs can easily correct mispricings in low-eigenvalue directions, so only sentiment-driven mispricings in the most systematic factor combinations persist long enough to generate momentum.

Eigenvalue Distribution (Rolling 5-Year PCA)

Momentum Concentration Test

Conclusion

• Factors are autocorrelated. HML and PMU both show statistically significant persistence, with HML being the strongest (t = 3.33).
• UMD dynamically times other factors. The conditional correlation analysis reveals that UMD's relationship with other factors flips sign depending on their recent performance — positive after good years, negative after bad ones.
• Factor momentum generates significant alpha. Both TSFM and CSFM produce returns unexplained by the five-factor model. Crucially, CSFM is completely independent of stock-level UMD.
• Momentum concentrates in high-eigenvalue PCs. Consistent with the theoretical prediction that persistent sentiment affects only the most systematic factor combinations.
• Implementation requires scale. With only four factors, the momentum signal is too noisy for reliable long-only rotation. The academic results (using 20–47 factors) rely on diversification across many factor bets.