Is factor momentum greater than stock momentum?

Is factor momentum greater than stock momentum? Yes, but only at short lags. In this paper we investigate the relationship between factor momentum and stock momentum. Using a sample of 72 factors documented in the literature, we first replicate earlier findings stating that factor momentum exists and works both directionally and cross-sectionally. We then ask if factor momentum is spanned by stock momentum. A simple spanning test reveals that after controlling for stock momentum and factor exposure, statistically significant Sharpe ratios only belong to implementations that include the last month of returns. Hence, factor momentum differs from stock momentum for one reason only: at the one-month horizon, stock returns mean-revert, while factor returns exhibit momentum. We conclude this study with a simple theoretical model that captures these forces: first, there is stock-level mean reversion at short lags and momentum at longer lags; second, there is stock and factor momentum at all lags; and third, there is natural comovement between the profit and loss of stock and factor momentums at all horizons.