Study On Financial Risk And Portfolio Selection Based On Fractal Distribution

Classic Capital Market Theory is based on Efficient Market Hypothesis. Efficient Market Theory is the footstone of modern financial theory. However, some phenomenon in the practical financial market cannot be reasonably explained by Efficient Market Theory. The study result of Behavioral Finance shows that it is impossible for investors to make rational unbiased reaction to information in any case.Therefore the long-period dominant position of efficient market in financial market theory seriously weakens.In this context, the paper establishes the risk metric system within the framework of Fractal Theory. This paper further proposes the investment portfolio decision with VaR and CVaR which are based on fractaldistribution as constraints. Specifically, the tasks of this paper are as follows: Firstly,this paper elaborates roundly on the content of Fractal Market Theory, and shows specific studying methods. With yield figures in Shanghai market as samples and through the calculation on Hurst index, fractal dimension and correlation dimension, this paper reveals that China's stock market has obvious fractal features. Therefore the normality hypothesis of the return distribution in efficient market does not fit the actual features, and this implies that the study of further risk metric and investment decisions must be set up on a new theoretic basis.Secondly, this paper introduces the definition of Fractal Distribution, presents the natures of fractal distribution and conducts distributions fitting and testing on the yield distribution in China stock market. The results show that the practical financial market is more complex than efficient market, it has certain fractal characteristics, and its yield series presents a feature of rush thick tail and heteroskedasticity. Compared to traditional normal distribution, fractal distribution can better depict the actual features of financial market.Thirdly, financial assets have obvious non-normal features. The risk measurement method under normal conditions is no longer applicable. This paper introduces the current mainstream VaR method and sums up its advantages and disadvantages. This paper also further puts forward CVaR method, and compares the advantages and disadvantages of both methods through empirical study. In addition, this paper calculates the VaR and CVaR based on normal distribution and fractal distribution respectively under given confidence by stable programme, and then conducts the back testing. Empirical result indicates that VaR and CVaR under fractal distribution can better capture the financial assets risk and well describe the actual features of financial market.Lastly this paper illustrates the portfolio theory in detail, and on the previous study basis it establishes an investment decision model under constraint condition of VaR and CVaR based on fractal distribution, giving the actual calculation example. Thus, from the distribution of yields, this paper puts forward the assumption of fractal distribution. It is on this basis that CVaR and VaR methods for the measure of financial risk under fractal distribution are obtained, and the investment decision model based on the FVaR and FCVaR constraint condition is finally established. A complete investment portfolio system based on fractal theory is established, providing certain theoretical support for the financial market research under the nonlinear framework.