Quantifying financial market dynamics: Scaling law in rank mobility of Chinese stock prices

Rank mobility, which was designed to measure the average variation of relative rank positions with respect to any absolute variable over a given time period, can be used to explore how the memory of stock price ranking orders fades over time. We investigate the variation in rank order of the closing prices of stocks registered at the Shanghai A-share market over a long period of 16 years. And we find that rank mobility increases as a power law with increasing time scale, and eventually converges to a constant level. This power-law relationship can be observed not only over a long period of 16 years but also for each consecutive year, especially their power law exponents are very close. The empirical evidence indicates a fundamental dynamics of Chinese stock price movements.