Endogenous Events and Long-Run Returns

We analyze event abnormal returns when returns predict events. In fixed samples, we show that the expected abnormal return is negative and becomes more negative as the holding period increases. Asymptotically, abnormal returns converge to zero provided that the process of the number of events is stationary. Nonstationarity in the process of the number of events is needed to generate a large negative bias. We present theory and simulations for the specific case of a lognormal model to characterize the magnitude of the small-sample bias. We illustrate the theory by analyzing long-term returns after initial public offerings (IPOs) and seasoned equity offerings (SEOs)