  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 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 which include the last
month of returns. We conclude this study with a simple theoretical model that
captures these forces: (1) there is stock-level mean reversion at short lags
and momentum at longer lags, (2) there is stock and factor momentum at all lags
and (3) there is natural comovement between the PNLs of stock and factor
momentums at all horizons.
