Stock Market Behavior and Diversity

Abstract

In this chapter we study the diversity of the distribution of capital in an equity market. Heuristically speaking, a market is “diverse” if the capital is spread among a reasonably large number of stocks. We show that the excess growth rate of the market is related to the diversity of the capital distribution, and we use this relationship to study the long-term behavior of market diversity under the hypothesis that all the stocks have the same growth rate. It might seem that in such a market, diversity would naturally be maintained, but we shall see that this is not so, and in fact, such markets have a tendency to concentrate capital into single stocks. Dividend payments are a natural means to maintain market diversity, and we investigate the structure of this mechanism. Finally, we propose market entropy as a measure of market diversity, and study a derived portfolio called the entropy-weighted portfolio.