Research On Investment Portfolio Risk Based On Copula Methods

Risk measure of portfolio has been very popular in the research field on financial risk management in recent years.The risk measure model is also one of the research interests of domestic and international financial scholars.VaR(Value at Risk)is used to measure the maximum possible loss of financial assets at a confidence level during a certain period of time.The meaning of VaR is very clear to measure financial risk.It has been used to measure risk by more and more financing institutions because it is rigorous and generally applicable.With the research development on VaR,it has become one of the most popular methods to build a risk measure model based on it.Based on the research on VaR,this paper proposes a t-Copula-GARCH-t model to measure the risk of portfolio.Chapter 1 introduces the relevant research,the outline and the conclusions.Chapter 2 is the theory of VaR,including the definition,basic principles and algorithm etc.In addition,it introduces Copula theory,including definition,important theorem,the common Copula functions and parameter estimation etc.Chapter 3 studies the marginal distribution of portfolio.According to the characters of financial time series,this chapter presents conditional heteroscedasticity models.Then based on the characters of heavy-tail distribution,it proposes a GARCH model,uses it to simulate the distributions,discusses the methods on calculation and test and calculates the VaR of Small and Medium-sized Enterprise Board(SMEB)and Growth Enterprise Market(GEM)indexes.Chapter 4 focuses on the correlationship of portfolio,including the correlationship theory of Copula function.In the empirical research,it proposes a model by selecting the most appropriate Copula function,which describes the correlationship between the assets of portfolio.Then it discusses the parameters estimation and statistical test of the models.Chapter 5 proposes a multi-objective portfolio model based on maximum entropy principle.In this chapter,the first part is the model and algorithm based on the maximum entropy principle.The second one is the empirical research about the portfolio of SMEB and GEM indexes,in which the model is proposed and the weights of the assets are calculated.Chapter 6 summarizes the details about building a risk measure model of portfolio based on the previous chapters.Using the portfolio of SMEB and GEM indexes as example,t-Copula-GARCH-t model is proposed based on the characters of the portfolio and the Copula function selected in previous chapter.Then using the weights given by the multi-objective portfolio model in Chapter 5,the VaR of the portfolio is simulated by Monte Carlo method.Finally,VaR of different methods and models are compared.The results show VaR given by tCopula-GARCH-t model and Monte Carlo method is the most effective for this portfolio.In addition,we can drive the conclusion that this portfolio is risk diversification according to compare the VaR of portfolio with that of the two independent indexes.Furthermore,it proves the validity of t-Copula-GARCH-t model for the risk of portfolio.This paper makes some improvements on risk measure model.Firstly,based on the characters of marginal distribution and joint distribution of portfolio,we choose some appropriate distributions.One is using a GARCH-t model to simulate the marginal distribution of portfolio according to the characters from statistical test of data.It is with high peaks and heavy tails so it can reflect the characters of investments tail risk better.Then we prove the t-Copula function is more suitable to the correlationship between investment portfolio random variables.And the empirical results show that the model is more reliable to portfolio risk measure.Secondly,the investment proportions are determined by the multi-objective investment portfolio model,which eliminates the subjective randomness and makes the results more reasonable.Thirdly,using SMEB and GEM indexes as the empirical examples,it extends the empirical research field and provides some theoretical foundation and suggestions for the investment portfolio risk analysis on SMEB and GEM.Apparently,the research on t-Copula-GARCH-t model,methods and results can provide some theoretical foundation and investments suggestions for investors and institutions of financial risk management.Therefore,it is significant to the research on theoretical and practical fields.