The answer, of course, is that it can't. Hou, Xue, and Zhang's (2014) empirical model does price portfolios sorted on prior year's performance, but for reasons outside of q-theory---it does so by including a fundamental momentum factor, i.e., a factor based on momentum in firm fundamentals. The ROE factor, which does all the work pricing momentum, is constructed by sorting stocks on the most recently announced quarterly earnings, which tend to be high after positive earnings surprises. A post earnings announcement drift factor prices the model's ROE factor, and subsumes the role the ROE factor plays pricing momentum portfolios when both are included as explanatory variables. The HXZ model also only prices portfolios sorted on gross profitability by conflating earnings profitability, which drives the ROE factor's covariance with gross profitability, with post earnings announcement drift, which drives the ROE factor's high average returns. Controlling for fundamental momentum, the HXZ model also loses its power to explain the performance of gross profitability. These facts are inconsistent with a neoclassical interpretation of the empirical model.
