The Mean-VaR Model And Capital Asset Pricing Model Based On The Asymmetric Laplace Distribution

The Asymmetric Laplace Distribution,which is used by many researchers to fit the distribution of the return rate of financial assets and measure the tail risk of financial assets,is suitable to describe the heavy tail and asymmetry characteristics of the distribution.The research in this paper is carried out under the assumption that the financial yield sequence obeys the Asymmetric Laplace Distribution,there are two research objects,one is the mean-VaR model under Asymmetric Laplace Distribution,the mean-VaR model under the Asymmetric Laplace Distribution is established.In theory,we prove that the model is a convex optimization problem.Therefore,the global optimal analytical solution of the model can be easily obtained.Then we get the portfolio frontier whether there is a risk-free asset or not,and prove that the two fund separation is established.Compared with the mean-VaR model under the elliptic distribution,our model considers the asymmetry of the return rate's distribution,while compared with the mean-VaR under the general distribution,our model can obtain a global optimal analytical solution.Finally,we use the SSE50 index and its constituent stocks' data to carry on the empirical analysis,the results show that the actual investment performance of our model is good.And the other is to establish a Capital Asset Pricing Model based on the mean-VaR model under Asymmetric Laplace Distribution,in the theoretical deduction,this paper gets the capital asset pricing formula which is more complicated with the traditional Capital Asset Pricing Model in the form of beta coefficient,and is no longer the traditional ratio of covariance and variance.Finally,using the historical data of Shanghai and Shenzhen stock market to verify two Capital Asset Pricing Models,it is found that the estimated beta coefficients of the two Capital Asset Pricing Models are almost equal.This paper proves that in practice,the characteristics of asymmetry and peak thick tail will have an important influence on risk estimation,but little impact on pricing efficiency.Using VaR to measure the risk of financial assets under ALD is of great practical significance in the financial field,and the mean-VaR model based on ALD can be used for actual investment,as well as for making investment decisions,while enriching the research theory of Capital Asset Pricing Model under ALD.