Round Numbers and Security Returns

We document consistent differences in daily stock returns related to round numbers. In particular, we examine returns following previous day closing prices that are just above or just below round number benchmarks. We find, for both one-digit, two-digit and three-digit levels, that returns following closing prices just above a round number benchmark are significantly higher than returns following prices just below a round number benchmark. For example, at the one-digit level we find that returns following "9-ending" prices, which are just below a round number, such as $25.49, are significantly lower than returns following "1-ending" prices such as $25.51, just above the round number. Our results hold when controlling for bid/ask bounce, and are robust for a wide collection of subsamples based on year, firm size, trading volume and exchange. While the magnitude of the return difference varies depending on the type of round number examined, or the particular subsample used, the magnitude generally amounts to between 5 and 20 basis points per day (roughly 15% to 75% annualized). These results are equally strong across subsamples based on institutional ownership. We explore alternate explanations for the pattern.