Power Law Distributions for Share Price and Financial Indicators: Analysis at the Regional Level

Abstract

We investigate whether the distribution of share price follows a power law distribution at the regional level, using data from companies publicly listed worldwide. Based on ISO country codes, 7,796 companies are divided into four regions: America, Asia, Europe, and the rest of the world. We find that, at the regional level, the distributions of share price follow a power law distribution and that the power law exponents estimated by region are quite diverse. The power law exponent for Europe is close to that of the world and indicates a Zipf distribution. We also find that the theoretical share price and fundamentals estimated using a panel regression model hold to a power law at the regional level. A panel regression in which share price is the dependent variable and dividends per share, cash flow per share, and book value per share are explanatory variables identifies the two-way fixed effects model as the best model for all regions. The results of this research are consistent with our previous findings that a power law for share price holds at the world level based on panel data for the period 2004–2013 as well as cross-sectional data for these 10 years.