The Empirical Distribution Of Chinese Stock Market Returns

Financial asset return is a random variable. The description of the financial asset return distribution is a very important part in Financial Economics. When we choose the portfolio, do risk management and option pricing, we must know the distribution of thefinancial asset returns. Many scholars did a lot of theory and empirical research which based on the assumption that financial returns are normally distributed. The results showed that a big part of stock markets returns are not normally distributed in financial market, but have the properties that leptokurtosis, fat-tail, unsymmetrical and so on. Non-normal distribution has many forms, but we do not have a same conclusion which non-normal distribution is more suits for describe financial asset returns. In this paper, we did empirical research on SGT distribution family, EGB distribution family, GP distribution family, GH distribution family and Stable distribution family which based on the data of Chinese stock market returns to find out which empirical distribution is the best one to describe Chinese stock market returns. The main research content is as below:Firstly, we did an analysis on Hu and Shen stock index daily returns, weekly returns and monthly returns. The result shows that Hu and Shen stock index returns are not normally distributed, but display significant leptokurtosis and non-normally.Secondly, according to Hu and Shen daily, weekly and monthly returns data, we used maximum likelihood estimation to estimate the parameter of those 5 kinds of distribution families. The result shows that EGB distribution is the best distribution to describe Chinese stock marke returns. And this result is not same to the International main stock market index daily returns distribution.Thirdly, using ICSS algorithm, we searched 5 change points in Hu and Shen stock market. So we got 6 periods of each market. Then used these 6 periods data to fit 5 kinds of distribution families. The result shows that the fittest distribution of each period is not the same.Fourthly, based on the description of tail distribution concept, used HKKP method to estimate the tail index of Hu and Shen stock market index returns. The conclusion shows the differences of right and left tails.