Power laws in market capitalization during the Dot-com and Shanghai bubble periods
The distributions of market capitalization across stocks listed in the NASDAQ and Shanghai stock exchanges have power law tails. The power law exponents associated with these distributions fluctuate around one, but show a substantial decline during the dot-com bubble in 1997-2000 and the Shanghai bubble in 2007. In this paper, we show that the observed decline in the power law exponents is closely related to the deviation of the market values of stocks from their fundamental values. Specifically, we regress market capitalization of individual stocks on financial variables, such as sales, profits, and asset sizes, using the entire sample period (1990 to 2015) in order to identify variables with substantial contributions to fluctuations in fundamentals. Based on the regression results for stocks in listed in the NASDAQ, we argue that the fundamental value of a company is well captured by the value of its net asset, therefore a price book-value ratio (PBR) is a good measure of the deviation from fundamentals. We show that the PBR distribution across stocks listed in the NASDAQ has a much heavier upper tail in 1997 than in the other years, suggesting that stock prices deviate from fundamentals for a limited number of stocks constituting the tail part of the PBR distribution. However, we fail to obtain a similar result for Shanghai stocks.