Modeling French Capital Distribution Curves with a Poisson Dirichlet Process

Abstract

This thesis investigates the capital distribution curve of the French stock market from 1990 to 2017. Capital distribution refers to the distribution of firm size as measured by market capitalization. First, the French data is investigated for stability as measured by shape of the capital distribution curve and by volatility. Neither of these metrics indicate stability, and neither shape nor volatility is a satisfactory descriptor of the distribution of firm size. This is a substantial departure from the behavior of the capital distribution curve in the U.S., Europe, and Japan. Thus a stochastic model, the Poisson Dirichlet distribution, is applied to the French curve. Although the model describes the data well, it also does not indicate stability as evidenced by the changing parameter \(\theta\) throughout time. It is concluded that the modern French capital distribution curve is unstable and can be replicated at each time step with the Poisson Dirichlet distribution.