When genius succeeded: source of momentum anomaly

The title is, of course, a play on the Long Term Capital Management story.

In this case, a genius named Yichuan Lui from MIT has determined how the momentum anomaly is congruent with the 3 Fama-French factors of market, size and value.  Previously, the source of this robust anomaly has not been explained adequately.  In his own words:

a multifactor asset pricing model is capable of explaining a large portion of momentum profits … Two features inherent in factor structures, positive autocorrelation and the leverage effect, allow for the creation of small, positive alphas in factor portfolios where the weights are equal to past returns. Momentum loads selectively on factors depending on their realized returns and magnifies alphas by choosing stocks with highly positive and negative betas in a long-short portfolio.

Other researchers have added a factor to the Fama-French 3 factor model to explain momentum.  Lui shows that momentum can be generated within the existing factor structure:

The factors (size, value and market) are auto-correlated: effectively their historical performance has a degree of persistence, which is the core concept of momentum.  This effect appears weak until 5% of outliers are removed.

Removing around 5% of the most extreme realizations of past factor returns changes the estimates dramatically. Market, SMB and HML now have autocorrelation coefficients of 6.9%, 10.5% and 7.6%, respectively

which would imply a momentum alpha of 0.38% per month.

These numbers agree with data in a previous post showing auto-correlation of 20% for a “small-value” portfolio (see trendline equation in third plot).

Then leverage is applied by selecting stocks with the highest betas, which has the effect of magnifying the factors:


Note how rapidly the loadings on the factors change and values of beta greater than 1 (i.e. leverage).

Overall, a seminal paper describing the origins of the momentum anomaly:



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