Application Of MCVaR Risk Measurement In Investment Theory

With the development of globalization and liberalization of financial markets,a variety of new investment instruments have continuously poured into the market,making it increas-ingly difficult to measure investment risks.How to choose appropriate risk measures to avoid risks has become a core issue in investment decision theory.Considering that investors' atti-tudes towards risk are not necessarily risk-averse,combining the results of previous research,the MCVaR risk measure with optimism is introduced.Apply MCVaR risk measurement to study the risk of investment portfolio.The first chapter briefly introduces the development of portfolio theory,the research status of risk measurement and the st.ructure of the thesis.The second chapter mainly studies the characteristics of MCVaR risk measurement,and proves that MCVaR satisfies positive homogeneity,subadditivity,monotonicity,and trans-lation invariance;And established the relationship between it and the CVaR risk measure,and proved that MCVaR is a consistent risk measure when the optimistic coefficient and the significant level meet a certain relationship;MCVaR risk metric calculation formulas for normal distribution and kernel density estimation are also given.The third chapter studies the risk optimization of portfolio based on MCVaR risk mea-surement.Kernel density estimation based on MCVaR risk measures,transforming the Mean-CVaR optimal portfolio model into a general linear programming model,A portfolio risk optimization model based on MCVaR kernel density estimation is established,and fi-nally a Newton iterative algorithm is designed to solve the optimization model.An example analysis shows t,hat:given a significant level,when the optimistic coefficient is less than a given significant level,The MCVaR risk metric value of the investment portfolio keeps in-creasing as the optimistic coefficient increases;when the optimistic coefficient is greater than a given significant level,investors will pursue high-risk,high-return investment products.The fourth chapter mainly studies the risk hedging problem based on MCVaR risk measurement.First of all,the risk hedging model of the portfolio is est.ablished under the normal distribution method,and the expression of the optimal hedge ratio is given.Use the least squares algorithm to find the optimal hedge ratio.Secondly,based on the kernel density estimation method,a portfolio risk hedging model is established,and the Newton iterative algorithm given in third Chapter is still used to solve the optimal hedge ratio.Finally,an example analysis shows that when the optimistic coefficient is less than a given significant level,After hedging,When the optimistic coefficient is the same as the significant level,the hedging effect of the kernel density estimation method is better than the normal method The final chapter summarizes the thesis and presents some future research.