Power-Law Distribution & Stock Markets

Basing their investigation on the hypothesis that trades made within large populations cause major fluctuations in the stock market investigators found, with the use of power laws, that they were able to closely analyze the fluctuations in stock prices, number of trades, and the size of the trades that occur. Interestingly, they found that the exponents  used to represent various types of markets were similar for all of those varying markets, even for those markets that are in other countries. Two of the many equations used in there investigation were to be applied to the US stock. However, they decided to use equations (2) and (3) for the Paris Bourse, the French stock exchange, and lead it them to some interesting conclusions.

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Initially they applied these equations to the evaluation of 35 million transactions within the 30 biggest stocks in the Paris Bourse between the years 1994 and 1999. They learned that the power laws that were specifically for the US stock market also held for a foreign market. It also showed that equations (2) and (3) could be Universal.

Additionally, they showed that the power laws used in the financial data came about when the trading was conducted in an optimal manner. They also demonstrated the relationship between fluctuations in prices and the number of trades performed.

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The graph above demonstrates the collective distributions of the returns from 1,000 of the largest countries between the period 1994-1995. You can see that this bared a slight resemblance to the graph for the power-law distribution of Web-page links, as it is linear and downward sloping.

Gabaix, Xavier, et al. “A theory of power-law distributions in financial market fluctuations.” Nature 423.6937 (2003): 267+. General OneFile. Web. 21 Apr. 2016.

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