Abstract This paper documents that U.S. equity returns are large and positive during the opening hours of European markets. These returns are pervasive and highly economically and statistically significant. Consistent with models of inventory risk, we demonstrate a strong relationship with order imbalances at the close of the preceding U.S. trading day. Rationalizing unconditionally positive “overnight drift” returns, we uncover an asymmetric reaction to demand shocks: market sell-offs generate robust positive overnight reversals, while reversals following market rallies are much more modest. We argue that demand shock asymmetry can arise in inventory management models with time-varying market maker risk-bearing capacity. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.