The Application Research Of CVaR Portfolio Model Based On Sparse Opimization

Portfolio theory is an important part of modern financial theory.In the financial market,investment portfolio management is one of the main concerns of investors or investment institutions: how to put a certain amount of funds through the rational allocation of investment in a variety of different securities to maximize revenue.The more the number of securities included in the portfolio,the lower the risk of the portfolio.However,too many securities will lead to the larger amount of the transaction cost when wet construct the trading positions.In addition,if most of the funds will be invested in individual securities,it will lead to non systematic risk can not be effectively decentralized.Besides,in reality we are in a frictional financial market.In the market there are a variety of implicit constraints,these factors include a wide range of transaction costs,the entire transaction,the base constraint,tax and so on,ignoring these factors may lead to ineffective investment portfolio.When portfolio decision variable is too much,the optimal solution of the model in portfolio optimization process is easy to produce too small weight,resulting in a number of non zero weight optimal portfolio is very much,but also there are some problems of excessive weight.Based on this,this paper firstly gives the portfolio theory,risk theory and literature review on sparse optimization theory,and then introduces the definition of Va R,the theory of risk measurement method,and the advantages of Va R,defects and coherent risk measure theory,which leads and expounds the concept and idea of CVa R,the superiority of CVa R introduced and proposed the traditional Mean-CVa R model,this paper according to the defects of the traditional Mean-CVa R model of the proposed Mean-CVa R model Mean-CVa R model with transaction cost and cardinality constrained.Then,this paper focuses on establishing the Mean-CVa R portfolio optimization model based on sparse optimization,combined with historical data of China's securities market,selected 533 stocks data of 489 trading days from January 2,2014 to December 31,2015,the CSI 300 and CSI 500 plate in the empirical analysis of the.In this paper,the traditional Mean-CVa R model,L2 norm regularization model,L1+L2 norm regularization model,L0+L2 norm regularization model,L0+L1+L2norm regularization model respectively,the empirical analysis and comparative analysis,Draw the following conclusions:(1)L2 norm regularization can reduce some power in the portfolio weight,so as to achieve the non system risk is more diversified purpose.However,the effect of L2 norm is not ideal in reducing the number of non-zero weight in the model.(2)L1 norm regularization can make the model sparse.However,we find that the sparsity of L1 norm regularization is not easy to grasp.(3)the L0 norm can make the model more sparse.(4)L0+L1+L2 norm regularization model in addition to the advantages above model,also can naturally consider the transaction cost in the process of investment factors,in addition to taking into account the cardinality constraints in the process of investment.At the same time,the model is more realistic.