Universal power-law response of the financial stock price to trading behavior: discussion based on a complete survey

In the financial markets, various quantities exhibit power-law behavior. In particular, the impulse response relationships between traders' stock selling (buying) behavior and the price changes as the market's response is known to exhibit robust power-law behavior: I(Q)∝ Q^δ. This relationship is called the power-law price impact. Interestingly, various empirical studies on the power-law price impact report that the power-law exponent δ typically takes one-half without depending on asset class, market, or traders. Therefore, some researchers state that δ=1/2 belongs to the universal class (universal hypothesis). On the other hand, there are some theories predicting that the power-law exponent δ is dependent on the microscopic parameters, and δ=1/2 is observed by chance (nonuniversal hypothesis). Because of lack of empirical survey, mutually confronting hypotheses are co-existing even though either should be rejected. In this presentation, we present the results of the empirical test for those hypotheses based on a complete survey: investigate all the trader's price impact across all the stocks listed in the Tokyo Stock Exchange. Finally, we discuss whether δ=1/2 belongs to the universal class by comparing them with the result of numerical simulation.