On the Network Effect in the Stock Market, The N^3/2 Power Law, and Optimal Volatility Equilibrium

This working paper is an excerpt on the recent finding of the network effect in the stock market. Specifically I summarize the three-half power law which states that the total value of the stock market is proportional to the three-half power of the number of stocks in the market. This power law is based on several intuitive assumptions on a many-body stochastic system, which will be described in this paper. The hypothesis of the optimal volatility equilibrium is introduced as a pillar leading to the power law, which states that such system must adjust itself around a level of optimal volatility in order to survive as a viable market. The connections to Fernholz's diversity index and Clark's lognormal subordinated process are discussed. This hypothesis also indicates that investing in a large market doesn't guarantee the benefit of diversification as prescribed in modern portfolio theory. The tail risk is omnipresent in the financial market