Stock Trading and Stock Returns: Understanding the Distributional Properties of the Numbers—The Evidence from India Nifty Fifty

Abstract

Benford’s law which studied the distributional properties of numbers observed that data patterns follow a certain frequency. The application of the Benford law to accounting numbers was tested by Dan Amiram, Zahn Bozanic, and Ethan Roven (2015), and was proven that accounting numbers follow the same frequency. There are several theories that advocated a strong relationship between accounting numbers and stock returns. Taking this as a base, the study aims to investigate whether Benford’s law, which was proven to be working for accounting numbers, would also work for stock trading and stock returns. The study uses data from National Stock exchange of Nifty Fifty stocks. Initially, data of daily stock returns and daily stock trade for five years from 2012 to 2016 are observed for the theoretical distribution. Later, the daily stock returns and daily trading activity for the results announcement months of April and May covering the five years were observed. It was examined whether data of stock returns and trading activity followed the distribution of Prob (d) = log10 (1+ (1/d)), for d = 1, 2, 3 ….9. Later the frequency pattern of stock returns and trading activity is tested by KS statistic to conclude whether data followed the same frequency as Benford’s law. The Kernel density estimates were also used to confirm the results.