Letter to the Editor—The Distribution of Stock Price Differences: Gaussian After All?

Abstract

In this paper the distribution of stock price differences is studied. Starting from Bachelier's hypothesis regarding the independence of stock price changes a model based on price differences taken across transactions, rather than differences obtained across time periods, is investigated. Using this model the distributions of price changes for a sample of 10 stocks were studied. In contrast to the fat tailed, excessively peaked distributions obtained by differencing across time periods, the distributions obtained by differencing across transactions did not have an excessive number of extreme events, although the center classes continued to be overcrowded. As the number of transactions over which the price differences were taken increased from 1 to n where n is equal to the largest number of transactions over which the price has remained unchanged, the distribution of the ΔP's approached the normal distribution. Thus we conclude that stock price changes are not independent across single transactions, and that stock prices should be differenced across blocks of transactions, rather than time intervals.