Second, we study the cross-section of firm-specific persistence of the risk-neutral distribution’s central moments and future stock returns. The risk-neutral probabilities are essentially realworld probabilities tilted toward bad states. Thus, risk-neutral moments might change if the physical distribution changes or if the mapping from real-world to risk-neutral probabilities changes. In the latter case, the moments for all stocks are equally unpredictable. Thus, in the cross-section, higher persistence of the central moments of the risk-neutral distribution should be associated with higher persistence of the physical distribution. Changes in the mapping between the two measures should only yield more noise in our main measure and, thus, make it less likely to detect a significant impact on the cross-section of stock returns.