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 xkeven 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. The asymmetry of bubble innovations results in observed excess returns that tend to be positive while the bubble continues, causing autocorrelation and longer runs of positive excess return than expected from a temporally independent series. For illustrative purposes, assume that pt+ is unimodal and symmetrically distributed with mean zero. From Equation (8), the probability of a negative innovation, Af+i = Probfo+i < 0], is