Research On Portfolio Optimization Based On Period Value At Risk

The establishment of the socialist market economy system has brought the market economy system of our country to maturity,which has greatly improved the disposable income of residents.At the same time,due to China’s opening up,international capital began to flow into China.Therefore,the single investment model dominated by savings in the past has begun to waver,and financial investments such as stocks and futures have begun to enter people’s attention.However,the rapid development of finance is also a double-edged sword,which drives the rapid development of the economy and increases the systemic risk of the market.Therefore,the measurement of risk becomes very important.PVaR(Period Value at Risk)is a new method proposed in recent years to measure market risk in the future.This paper is mainly to further expand the method of using PVaR to measure market risk.According to the market risk characteristics in a period of time,we will further characterize the market risk under normal and abnormal conditions.The specific research contents are as follows:First of all,we summarize the relevant theories of modern portfolio and risk measurement through reading and combing a large number of documents.On the basis of that,further research was conducted on the use of PVaR to measure market risk.Secondly,the calculation method of solving PVaR based on historical simulation method is proposed.We first give a historical simulation method to simulate stock price,and use PVaR calculated by this method as the objective function to establish the corresponding portfolio model,and then the portfolio model with PVaR as the objective function by Monte Carlo simulation method and the portfolio model with VaR(Value at Risk)as the objective function calculated by historical simulation method are established respectively.In order to facilitate the solution,the above model is linearized.Finally,CPLEX is applied to solve the three models under different confidence levels for simulation experiments,and the experimental results are analyzed from two dimensions.The results show the validity of using historical simulation method to calculate PVaR,which provides a broader theoretical basis for investors in different investment scenarios.Finally,we propose a method to measure abnormal market risk using CPVaR(Conditional Period Value at Risk).We first give the mathematical expression of CPVaR and the specific calculation process by describing the market risk under the abnormal conditions.Then,the consistency of PVaR is analyzed.It is found that it is not a consistent risk measurement method,and the Coherent Axiom of CPVaR is verified by mathematical derivation.Furthermore,we have separately established portfolio model with the objective function of minimizing CPVaR and portfolio model with the objective function of Minimizing CVaR(Conditional Value at Risk).In the end,these models are solved by CPLEX.The results show that using CPVaR as the risk measurement method of financial market,it measures the risk that the financial market may encounter in a period of time in the future under abnormal conditions,which further explains the practical significance of the existence of CPVaR.