The Likelihood of Small Cap Premium Distributions
28 Pages Posted: 13 Nov 2013 Last revised: 18 Dec 2020
Date Written: Novmber 1, 2020
Abstract
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. Since that time, studies have argued 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 parameters of the monthly US 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 or the volatility of the small cap premium in the value and neutral segments of the US equity market. The likelihood-maximizing means of the monthly small cap premium in these segments remain in the range from 0.14% to 0.20% in the post-Banz period, similar to their range in the pre-Banz period (0.14% to 0.24%).
On the other hand, there is evidence that the likelihood-maximizing monthly mean in the growth segment fell from a range of 0.10% to 0.12% in the pre-Banz period to -0.36% to -0.38% in the post-Banz period.
Keywords: Bayesian Inference, Small Cap Premium, Likelihood
Suggested Citation: Suggested Citation