Comparative Analysis On Tail Behavior Of Stock Returns Distribution

Return of financial assets is a very important concept in finance. The possibility of correct description of return distribution is related to the correctness of portfolio choice, the effectiveness of risk management. The stock market return is usually assumed that obeys normal distribution, in the classical econometrics model description of stock price. Many well-known financial economists made a lot of theoretical and empirical analysis on the classic assumption, results showed that the overwhelming majority of financial market yield of the stock market is not subject to normal distribution, whereas peak, fat tail, asymmetrical characteristics. This paper based on the theories of finance, mainly on the statistical distribution of normal distribution, t distribution, extreme value distribution, generalized extreme value distribution, logistic distribution. Paint the density their graphs and compared with the return of SZZS, calculated the size of the tail, come to the result that logistic distribution is the best fitting for the return, but for the tail only, GEV is the best.This paper is divided into four chapters. Chapter 1 gave a brief introduction of the background and the significance of the issue. In recent years the frequent occurrence of the financial crisis showed the emergence of extreme financial risk was not so little as described before. Financial investment is the fundamental objective of the investment income. Investment income is always associated with risks. Therefore, how to detect abnormal market trend, guard against and defuse financial risks is an extremely urgent need to solve the problems. The study of fat financial data for founding abnormal market to control extreme risk is of great significance. Chapter 2 introduces previous research of the fat tail distribution, talking about the origin of thick tail distribution, giving a brief introduction about foreign and domestic research of the fat tail distribution of in time order. Since Mandelbrot and Fama began the pioneering study, the distribution of stock returns in the financial sector was gradually taken seriously. Some Chinese scholars preliminary discussed return, peak, fat tail and long-term memory of fluctuations of Chinese financial market, but there were methods and models using limitations in the process of quantitative analysis. We can carry out the next phase of research better by Understanding the predecessors'research progress of fat tail distribution.Chapter 3 introduces the theoretical models of the return of stock distribution. In the modern financial theory, the return of capital distribution function is a very important concept. The return of stock market is usually assumed that obeys normal distribution in the classical econometric model. Many well-known financial economists made a lot of theoretical and empirical research on the classic assumption. Concluded that it is difficult to determine the return distribution, but it is certainly not subject to normal. We start with normal distribution, focused on the normal distribution, t distribution, logistic distribution, extreme value distribution and generalized extreme value distribution by making use of sample data to estimate model parameters. Then we draw the density graph of them and compared with the return of szzs, and got the conclusion that return of stock doesn't obey normal distribution, having a fat tail. logistic distribution is the best fit, the next is normal Extreme value distribution and generalized extreme value distribution are biased obviously and the thickness of the tail is different, the effect is not fit good, the effect of t-distribution fitting worst. In this chapter we also introduced a number of additional characterization fat tail distribution: mixed distribution, generalized error distribution, generalized Pareto distribution, the Cauchy distribution and stable distribution. Some of these distributions of the data required something that sample data not available, but they also describe fat tail distribution well, so we explain them.Chapter 4 is the empirical test of statistical distribution. In this chapter we must come to the conclusion that which distribution fits szzs best, as well as which one fits its tail best. First of all we gave a brief analysis to szzs data. Then we draw the probability density distribution into a map so you can see clearly which probability distribution is the best fit. we can see that logistic distribution fit the szzs distribution best. However, the tail effect of fitting can't be seen, so we need to calculate the size of the tail. We believe that in the given interval, two distributions which have the same tail size have the same risks.We calculated the distribution of the left tail that in the interval [-0.1,0.035], generalized extreme value distribution left tail is closed to the szzs distribution left tail, followed by the normal distribution, logistic distribution, extreme value distribution is the worst, overestimated the risk. Therefore, we come to the conclusion: in the samples of szzs on January 2, 1997 to 2008 January 2, left tail of generalized value distribution fit the szzs distribution best.Through these models'comparative analysis, we got the following conclusions: logistic distribution fits szzs distribution best, but for the tail, generalized extreme value distribution is the best fit. Generally speaking, this article quite comprehensive researched existing securities returns ratio's fat tail distributions, carried on the detailed description to these distributions, and made empirical study to several typical distributions, This article selects the data which is very new, moreover sample size is also unusual big, containing enough information. We studied the tail in a new aspect and the conclusion also has the suitable degree reliability. Through the research, we further discovered the theoretical and the practical actual significance of the reach on fat tail. And it is helpful for people to manage risk.