The Likelihood of Small Cap Premium Distributions

In 1981, Rolf W. Banz published “The Relationship Between Return and Market Value of Common Stocks,” concluding that the common stocks of smaller firms outperformed the common stocks of larger firms on a risk-adjusted basis. Recent studies argue that the small cap premium Banz reported was an anomaly that has been arbitraged away since its publication. The present paper applies Bayesian inference principles to hypotheses concerning the probability distribution of the monthly small cap premium before and after the publication of Banz's paper. We find no evidence that Bayesians should shift their beliefs about the mean of the small cap premium in the value and neutral segments of the market. The likelihood-maximizing means of the monthly small cap premium in these segments remain in the range from 0.20% to 0.30% in the post-Banz period. On the other hand, there is evidence that the likelihood-maximizing monthly mean in the growth segment fell from 0.10% in the pre-Banz period to -0.35% in the post-Banz period