A Critical Evaluation of the Significance of Round Numbers in European Equity Markets in Light of the Predictions from Benford’s Law

In this study, we test the hypothesis that psychological barriers exist in 5 European Equity Market indices [ATX, CAC, DAX, FTSE, SMI]. We employ both a traditional methodology that assumes a uniform distribution of M-Values and a modified approach that accounts for the fact that the digits of stock prices may be distributed in accordance with Benford’s law. In addition, we test the validity of the various assumptions employed in these tests using a Monte Carlo Simulation and Kuiper’s Modified Kolmogorov-Smirnov Goodness of Fit Test. We find evidence for barriers in 1 index [SMI] at the 1000 level under the assumption of uniformity but no significant evidence of barriers at the 100 level or at the 1000 level in the remaining indices. We also find evidence that substantiates the criticism of the use of the uniformity assumption for tests at the 1000 level in favour of a distribution consistent with Benford’s Law. However, we do not reach a different conclusion on the presence of psychological barriers when tests are performed without the implicit use of that uniformity assumption. In addition, we find possible evidence of price clustering around round numbers at the 1000 level in 2 indices [CAC, DAX] even after adjusting for the expected concentration within the region due to Benford-specific effects.