Endogenous Events and Long Run Returns

We analyze event abnormal returns when returns predict events. We show that the expected abnormal return is negative for any fixed sample and this increases with the holding period of returns. However, we prove that if the number of events process is stationary, abnormal returns converge to zero asymptotically. This suggests that non-stationarity in the number of events process is needed to generate a large negative bias. We present simulation and small sample evidence for our results to show that sample size and stationarity property of the event process are important in assessing the magnitude of the small sample bias. We also show that the confidence intervals are larger when events are endogenous, and event returns are correlated, reinforcing the difficulty of inference in event studies