Do share trading volumes conform to Benford’s law?

Manipulation in the stock market is a serious risk to the stability and integrity of financial markets. The daily volume of shares traded in the stock market is a natural process, as a result of which the number of shares traded on a daily basis is a naturally occurring phenomenon. Naturally occurring digits normally follow Benford’s law. The law states that the frequency of getting a smaller digit (1, 2, 3, …) as a leading digit of a number in a dataset is greater than that of a larger digit (9, 8, 7, …). To detect manipulation in the naturally occurring numbers, Benford’s law is widely used. It is a convenient method while dealing with a bulk quantity of data. In this paper, we used Benford’s law to study the probability of any manipulation in the daily volume of shares traded. The study sample has been collected from the financial service sector companies listed on the Bombay Stock Exchange of India. The study uses a total of 24,760 data points (2,476 data points in each company’s dataset) from April 2013 to March 2023 to analyze the daily volume of shares traded by the top 10 companies shorted by market capitalization. The study aims to assess the conformity of leading-digit distributions in the share’s daily trade volume to the logarithmic patterns predicted by Benford’s law. We applied the chi-square test to determine the statistical significance of the observed distribution by comparing it with the expected outcome based on Benford’s law. Out of 10 selected companies in this study, eight companies trade the volume of shares following Benford’s law, and the remaining two accept the null hypothesis. Deviations from the estimated outcome may indicate irregularities, anomalies, or intentional manipulations in the reported daily trade volume of shares.