Log-normal Distribution in Market Capitalization of Listed Companies in China

As the second largest economy in the world, the development of Chinas stock market has been of great interest to investors worldwide. By collecting the stock market capitalisation of the listed companies included in Chinas SSE Composite Index from 2003 to 2023, this paper finds that the market capitalisation of these companies shows a log-normal distribution. This work also conducts robustness tests using MSE, R2, PDF images, CDF images, and Q-Q plots, and the preliminary findings remain robust. Further research found that investor sentiment in the market affects the parameters of the log-normal distribution. By constructing market-level investor sentiment indicators using principal component analysis, the paper finds that when investor sentiment in the market is higher, the average market capitalisation of a company will be more prominent, and the gap in market capitalisation between different companies will be more significant. This paper provides a reference value for understanding the current development of Chinas stock market and improving the capital market regulation.