# Zipf's law for share price and company fundamentals

## TL;DR

This paper demonstrates that share prices and key financial indicators of companies worldwide follow Zipf's law, suggesting a fundamental power-law distribution underlying corporate valuation.

## Contribution

It provides empirical evidence that share prices and financial indicators follow Zipf's law and links this to the distribution of corporate fundamentals.

## Key findings

- Share price distribution follows Zipf's law with exponent 1
- Financial indicators' distributions also follow Zipf's law with exponent 1
- Share price can be explained by company fundamentals following Zipf's law

## Abstract

We statistically investigate the distribution of share price and the distributions of three common financial indicators using data from approximately 8,000 companies publicly listed worldwide for the period 2004-2013. We find that the distribution of share price follows Zipf's law; that is, it can be approximated by a power law distribution with exponent equal to 1. An examination of the distributions of dividends per share, cash flow per share, and book value per share - three financial indicators that can be assumed to influence corporate value (i.e. share price) - shows that these distributions can also be approximated by a power law distribution with power-law exponent equal to 1. We estimate a panel regression model in which share price is the dependent variable and the three financial indicators are explanatory variables. The two-way fixed effects model that was selected as the best model has quite high power for explaining the actual data. From these results, we can surmise that the reason why share price follows Zipf's law is that corporate value, i.e. company fundamentals, follows Zipf's law.