The link between abnormal numbers and price movements of financial securities: How does Benford’s law predict stock returns?

Abstract

This paper studies the potential effect of deviation from Benford’s law on stock return prediction. Departures from the anticipated pattern can act as early indicators of irregular market behavior or possible fraudulent activities, both of which have the potential to impact future price trends. In this study, the deviation is measured by chi-squared test statistics over the first significant digit. Preliminary results indicate no compliance between daily stock returns data from Euronext Paris and Tunisian stock markets with Benford’s distribution. Then, the impact on the returns is explored via several models: linear regression and smooth transition models with various transition variables. Empirical results show the nonlinear effect of Benford’s law on stock returns prediction. We illustrate that this law can detect and predict abnormal returns generated by fraudulent or abnormal activities in both developed and emerging markets. By using Benford’s Law to analyze leading digits, investors and analysts can effectively identify irregularities and gain valuable insights into market dynamics.