JOB MARKET PAPER The Momentum Gap and Return Predictability∗

Momentum strategies have historically delivered high Sharpe ratios and large positive alphas. However, returns to these strategies also display significant time-variation that is not very well understood. I show that expected momentum returns vary negatively and monotonically with the formation period return difference between past winners and losers, which I term the momentum gap. A one standard deviation increase in the momentum gap predicts a 1.29 percent decrease in the monthly momentum return after controlling for existing predictors. The momentum gap remains a significant predictor in out-of-sample tests. Conditional momentum strategies using the momentum gap yield substantially higher Sharpe ratios and lower skewness than the unconditional strategy. These findings are less consistent with the notion that past return proxies for the loading on a priced risk factor. I find evidence to support the alternative hypothesis that momentum is a mispricing phenomenon and that the momentum gap measures momentum arbitrage activity. ∗I would especially like to thank my advisors: Will Goetzmann (chair), Nick Barberis, Andrew Metrick, and Jake Thomas. I would also like to thank Sriya Anbil, Brad Barber, Hui Chen, James Choi, Sean Hundtofte, Peter Kelly, Charles Lee, Stefan Lewellen, Alan Moreira, Tyler Muir, Marina Niessner, Terry Odean, Scott Richardson, Geert Rouwenhorst, Clemens Sialm, Matt Spiegel, Jeff Wurgler, Lei Xie, Hongjun Yan, Frank Zhang, as well as seminar participants at Yale University. I gratefully acknowledge financial support of the Whitebox Advisors Doctoral Fellowship. All remaining errors are my own. Click here for the most recent version of this paper. †Ph.D. Candidate, Financial Economics. Yale School of Management, 135 Prospect Street, New Haven, CT 06520-8200. (415) 623-0776.