基于均值-CVaR投资组合优化模型实证分析

基于均值-CVaR投资组合优化模型实证分析重庆大学硕士学位论文（专业学位)学生姓名：邓天石指导教师：刘琼荪教授学位类别：应用统计硕士重庆大学数学与统计学院二O一四年四月TheempiricalanalysisbasedontheMean-CVaRportfoliooptimizationmodelAThesisSubmittedtoChongqingUniversityinPartialFulfillmentoftheRequirementfortheProfessionalDegreeByDengTianshiSupervisedbyProf.LiuQiongsunSpecialty:MasterofApplidStatisticsCollegeofMathematicsandStatisticsofChongqingUniversity,Chongqing,China.April,2014重庆大学硕士学位论文中文摘要I摘要投资组合理论研究的是如何进行投资决策，将资金按一定比例分配到不同的风险资产上，在获取一定收益的同时又达到分散风险的目的。理性的投资者以追求期望效用最大化为目标，在可承受风险水平下获取最大收益或预期收益目标。风险与收益是息息相关、密不可分的。均值-方差模型(简称MV模型)是投资组合理论的基础，其他形式的投资组合模型大多以它为基础拓展而得。均值-方差模型以资产收益率的均值来反映投资收益，以收益率的方差来描述风险。VaR和CVaR方法是近些年被广泛使用的风险测量方法。本文将CVaR方法与均值-方差模型相结合，构建了均值-CVaR模型，以CVaR代替方差刻画了收益率时间序列的尾部风险的大小，并通过线性规划求解方法，计算出最优的投资组合权重。本文还将均值-CVaR模型运用到国内的证券市场，实证分析结果表明均值-CVaR模型不仅对国内的证券市场适用，而且可有效地描述和分散投资组合的潜在风险。本文的选题具有一定的理论意义和实用价值。均值-CVaR模型既可以帮助投资者实现资产的最优合理配置，还可以对投资风险进行测量，并通过选择不同的置信水平来控制风险，得到不同的投资组合有效前沿。本文采用历史模拟法，将均值-CVaR模型运用到我国证券市场，进行投资组合优化的实证分析，并通过一定时期对模型效果的观察，验证了该模型在中国证券市场的适用性。关键词：投资组合，VaR，CVaR，均值-CVaR模型，有效前沿重庆大学硕士学位论文英文摘要IIABSTRACTThePortfoliotheoryisastudyofhowtomakeaninvestmentdecisiontoallocateassets.Thetargetofaportfolioistoobtainsomebenefitsandspreadriskatthesametime.Rationalinvestorsexpectmaximumutility.Theywanttomakethereturnoftheportfoliomaximizedinatolerantrisklevelortomaketheriskoftheportfoliominimizedinagiventargetofreturn.Riskandreturniscloselyrelated.TheMean-VariancemodelwhichisusuallycalledMVmodelforshortisthebasisofthePortfoliotheory.MostmodelsaboutinvestmentportfolioarethusextendedbytheMVmodel.IntheMVmodel,meanofreturnonassetsisusedtoreflecttheinvestmentprofitandvariancetodescriberisk.butMVmodelisunabletodeterminethesizeofrisk.TheVaRandCVaRmethodsarebothriskmeasurementmethodswhichhadbeenrecognizedandwidelyusedinrecentyears.Withtheadventofthesemethods,anewmodelisbuilt,whichiscalledMean-CVaRmodelthatisbetterthanMVmodelintermsofriskmetrics.IntheMean-CVaRmodel,conditionalvalueatriskisusedtodescribetailriskinsteadofvariance.Bythemethodforsolvinglinearprograme,theoptimalprotfolioweightswillbecalculatedfinally.Inthispaper,theMean-CVaRmodelisusedinthedomesticsecuritiesmarket.TheempiricalanalysisshowsthattheMean-CVaRmodelissuitableforthedomesticsecuritiesmarket.Andthemodelcaneffectivelydescribeandpotentialriskofportfoliodiversification.Thepaperhasacertaintheoreticalsignificanceandpracticalvalue.Mean-CVaRmodelcanhelpinvestorsachievetheoptimalassetallocationandalsobeusedforthemeasurementofinvestmentrisk.Byselectingdifferentconfidencelevelstocontroltherisk,differentportfolioefficientfrontiercanbecompeted.Withhistoricalsimulationmethodused,theMean-CVaRmodelisusedtothestockmarketinChinatocouducttheempiricalanalysisofportfoliooptimization.Andafteraperiodofobservationoftheeffectofmodel,theapplicabilityofthemodelinChinasecuritiesmarketisbeverified.Keywords:portfolio,VaR,CVar,Mean-CVaRmodel,efficientfrontier重庆大学硕士学位论文目录III目录中文摘要..........................................................................................................................................I英文摘要........................................................................................................................................II1绪论.........................................................................................................................................11.1研究背景及意义...................................................................................................................11.2国内外现状...........................................................................................................................21.2.1现代投资组合理论概述............................................................................................21.2.2VaR的研究概况.........................................................................................................31.2.3CVaR方法概述...........................................................................................................41.3研究内容、方法及结构框架...............................................................................................52投资组合理论基础...........................................................................................................72.1投资组合管理理论...............................................................................................................72.1.1投资组合管理的基本过程........................................................................................72.1.2投资组合策略............................................................................................................82.2Markowitz均值-方差模型...................................................................................................82.2.1基本假设....................................................................................................................82.2.2模型理论....................................................................................................................83VaR及CVaR风险度量方法...................................................................................113.1VaR方法............................................