Noisy information and the size effect in stock returns

Noisy information (i.e., informative signals) can affect the likelihood of observing a size effect in realized stock returns. In a one period model with two firms, the observed firm sizes at date 0 can deviate from the true firm sizes that are revealed at date 1. Noisy information gets embedded in stock prices and can make the true big firm appear to be small and vice versa. Using NYSE size deciles from 1926 to 2011, the ratio of the 90th percentile size breakpoint to the 10th percentile size breakpoint is about 66 on average. If the true big firm in our model is 66 times bigger than the true small firm, there is about a 7.8 % chance that the observed size of the true big firm will be smaller than that of the true small firm. Since the true sizes are revealed at date 1, there is about a 7.8 % chance that the observed small firm migrates to the big category. Conditional on no migration, the observed big firm has the higher equilibrium expected return. However, conditional on migration, the observed small firm has the higher expected return, which is consistent with the empirical results in Fama and French (Financ Anal J 63:48–58, 2007 ). Copyright Springer-Verlag Berlin Heidelberg 2015