We suggest that fat-tail variations can cause both short-term momentum and long-term reversal simultaneously, in both the time series and cross-sectional returns of securities. The fat-tail of the distribution is known to explain many anomalies in the financial market, but not momentum. To support our argument, we adopt widely accepted models in the literature, which generate reversal only, and revise a single assumption: Each random variable follows a non-normal stable distribution rather than a normal distribution. This single difference generates additional short-term return momentum. This finding shows that 1) investor irrationality is not essential to generate both phenomena, and 2) we must be cautious not to overuse normal distributions in the models.