Portfolio Models Based On Interval-Valued VaR And Empirical Analysis

Because of the asymmetry of information and the incompleteness of the market,the price of risk assets shows a more complex form.In order to describe the complexity,randomness and inaccuracy of the financial market,the idea of interval-valued random variable is introduced into the general portfolio model in this paper.Value at risk(VaR)is a financial risk measurement tool that has been developed and widely used recently.This tool is convenient,easy to calculate.It can reflect the risks faced by investors,companies and financial institutions.We use VaR in the mean-variance portfolio model instead of variance to characterize asset risk.It is a natural extension of the classic portfolio model and can comprehensively reflect the risk situation of all aspects of the market.A portfolio is a collection of stocks,bonds,and financial derivatives held by investors or financial institutions to spread risk.In this paper,we consider the risky stocks of the portfolio.Firstly,the return rate of stock is regarded as a random interval.Then we introduce interval-valued VaR to measure the stock risk.Finally,the portfolio selection model based on interval-valued VaR is constructed,which can reflect the risk preference of investors.We also make the empirical analysis based on real data of financial market.Related to empirical analysis,10 stocks come from different markets and stages of development.According to the closing price,the highest price and the lowest price of the stock,we calculate the exact value and the interval value of return rate.Using historical simulation method,the interval-valued VaR is estimated under two ranking methods.Then the optimal solutions of the corresponding portfolio models are calculated and compared.At the same time,the paper explores different cases according to the maximum risk that investors can bear.The results show that the optimal solution of portfolio obtained by different ranking methods is different.Therefore the appropriate ranking method is important to the establishment of portfolio model.Different risk preference has some differences for portfolio selection.In the process of solving the model,we can reasonably allocate the investment share according to the degree of risk preference of investors.The risk of stock is not only related to the industry,but also closely related to the size of the company,national policy,and so on.