Research On The Application Of Fuzzy Portfolio Based On Factor Volatility Model

The research of portfolio has been the main concerns for many researchers and investors.In the process of practical investment,investors’ decision are affected random objective factors,because different investors have different requirement for risk preferences and returns,there are some fuzzy uncertainty in financial decision making.Portfolio research used to be mean-variance model based on Markowitz’s portfolio,but traditional model cannot describe the fuzzy nature of financial markets.With the application of fuzzy number and fuzzy portfolio theories,scholars began to study the fuzzy portfolio problem through using related fuzzy theories to describe financial markets and fuzzy uncertainty of financial decisions.This paper will combine the fuzzy set theory,fuzzy probability theory and the optimization method to study the fuzzy portfolio based on factor volatility model,and construct fuzzy investment portfolio based on factor GARCH model,factor GJR-GARCH model and EGARCH model.In this paper,the main work and innovation are introduced as follows:(1)Construct the fuzzy portfolio based on the factor volatility model and test the validity of the model by empirical analysis.It is precisely because of the impact of investors in the market decision-making is not only random uncertainty,fuzzy uncertainty will affect investment decisions directly.Therefore,based on the fuzzy possibility theory,this paper presents a fuzzy portfolio analysis based on factor volatility.First of all,the risk rate of return is fuzzied,and the trapezoidal fuzzy number is built.Based on the concept of fuzzy possibility theory,the covariance matrix of fuzzy risk benefit is constructed.Because the dimension of the matrix is too large,there will be a computing disaster.In this paper,the principal component analysis and APT pricing theory are used to reduce the dimension of the fuzzy risk return matrix,and the principal component factor is considered in GARCH model.(2)The fuzzy portfolio based on factor GJR-GARCH model is constructed,which takes into account the impact of different non-linear shocks on the risk return in the market.Financial time series has not been able to be expressed only through the linear model,because the linear model cannot describe and deal with market fluctuations and shocks to the time series,while in the actual investment process,market fluctuation and information ha asymmetric shock to time series.Through the GJR-GARCH model,we can describe the impact of positive and negative shocks on the risk return,so we propose a fuzzy portfolio based on factor GJR-GARCH model in the following chapters.(3)The fuzzy portfolio based on factor EGARCH model is constructed.On the basis of the above analysis,we consider the real financial time series,and the distribution of the risk asset return is not a normal distribution.In the real financial investment environment,the distribution of the risk return shows the phenomenon of the distribution of the skew and kurtosis.Taking into account the characteristics of the distribution of risk characteristics,we introduce the fuzzy EGARCH model based on fuzzy portfolio research.First of all,the EGARCH model is introduced,and the EGARCH model not only explains the impact of different shocks on the risk return,but also uses the model to solve the skew and kurtosis distribution of risk return.In this paper,the EGARCH model is introduced and the fuzzy portfolio based on factor EGARCH model is proposed and empirical analysis is carried out to test the model.The main content of this paper is to illustrate the application of the fuzzy GARCH model based on fuzzy portfolio,the main method is to verify the validity of the model through model construction and test of real data.