Persistent Patterns in Stock Returns, Stock Volumes, and Accounting Data in the U.S. Capital Markets

Abstract

Benford’s Law gives the expected frequencies of the digits in tabulated data. The expected frequencies show a large bias toward the low digits. An analysis of the Center for Research in Security Prices (CRSP) data shows that the daily returns have a near-perfect fit to Benford’s Law. The daily volumes also have a close fit to Benford’s Law but there are deviations due to round lot trading and the fact that some of the data are rounded to the nearest hundred. An analysis of Compustat data also shows a close fit to Benford’s Law with some explainable deviations. The expected returns and the abnormal returns used in event studies over an extended period showed that these numbers also conformed to Benford’s Law. Recent studies have divided a population into subsets and then tested the subsets for conformity to Benford’s Law. The conclusions are that the subsets with the weakest fit to Benford were fraudulent. The problems with this approach are discussed, and these include statistical considerations, issues with using Compustat data, other plausible explanations for a lack of conformity, and the fact that there is no clear link between a change in the leading digit of a number and the materiality of the dollar value of the change.