As required by the efficient markets condition, the expected value of the total price innovation is zero. However, the probability of a positive innovation or abnormal return can be greater than 1r2 even if the fundamental innovations are symmetric around zero. This is due to the inherent skewness of the bubble innovations. If the bubble continues, its innovation is positive and small relative to an infrequent but large negative innovation if the bubble bursts. In addition to the skewness, the bubble process in Eq. 5 results in total price innovations that are explosive. The Ž . growth rate of the bubble factor increases each period the bubble survives to compensate investors for the potential crash of a progressively larger bubble. While it survives, the explosive bubble factor becomes a more dominant component in total price innovations, causing higher and higher observed returns leading up to the crash.