A Simple Law for the Distribution of Long-term Profits

Abstract: Gibrat's law offers a remarkably simple description for the distribution of firm sizes. Since its discovery almost a century ago, it has been a principal anchor for understanding growth dynamics. However, it is profit---not size---that is the key determinant of long-term value. Despite decades of research into the empirical regularities governing corporate profits, no simple law akin to Gibrat's or Zipf's has been found for its distribution. This study reports the discovery of such a law, finding that a four-parameter normal log-normal (NLN) mixture distribution very well fits observed data of listed firms' 20-year cumulative profit. Though the NLN law applies across industries, geographies, and time periods, its distributional parameters vary. This variation indicates differences in competitive dynamics and outcomes, especially across industries.