Research On The Applition Of The Risk Diversification Optimization Of Open-end Funds In China Based On Principal Component Analysis

Based on the two statistical concepts of mean and variance,Markowitz put forward the mean-variance portfolio model,making him become the founder of modern portfolio theory and the investment portfolio enter the stage of quantitative research.The purpose of financial investment is to gain higher returns.Nevertheless,higher returns always bring higher risks.Under the financial background,for the securities investment funds holders,the most effective way to resist market risks and obtain stable profits is to build reasonable portfolio and increase the diversification degree of portfolio reasonably.The investment portfolio has a certain correlation between returns,risk and diversification degree,so the investment weight of each constituent share often has an optimal allocation in the portfolio,making the portfolio reach the lowest level of risk under a certain expected return.In order to find this optimal allocation,the first way is to quantify the degree of diversification.The diversification degree of the fund portfolio usually changes with a variety of factors,such as the macroeconomic and the profitability of enterprises,and the change is reflected as a sort of uncertainty.Information entropy can perfectly describe the characteristics and probability distribution of the uncertainty of the diversification degree of fund portfolio.Therefore,this thesis adopts information entropy as the measure index of the uncertainty of the diversification degree of fund portfolio.The investment risk of a security is often caused by many risk factors,and for a security portfolio,its total risk will be expressed by more than one similar risk factors.In this case,there must exist some redundant risk information in the security portfolio and the constituent stocks are are bound to be correlated,which will increase the difficulty of investment decision-making and investors' risk prediction.Therefore,based on the Markowitz portfolio theory,the author firstly analyzes the covariance matrix of the sample fund portfolio with the principal component analysis to eliminate the superimposed effect on the fund risk resulting from redundant information and related risk factors.Secondly,according to the consistency between the uncertainty of information entropy and the uncertainty expressed by portfolio diversification degree,the author adopts information entropy as the measure index of the uncertainty of the diversification degree of fund portfolio and applies the the maximum entropy principle into the decision making of diversification degree,building the Mean-Maximum Entropy Optimization Model.Finally,through applying the Mean-Maximum Entropy Optimization Model into the investment decision of the open-end fund,this thesis empirically analyses the returns and risk characteristics of the sample fund and the optimized fund.The results show that the model has diverted the fund risk,indicating that the portfolio model established in this thesis is effective in real investment and can provide some references for investors' investment decisions.