Chap006风险厌恶与风险资产的配置课件

CHAPTER6RiskAversionandCapitalAllocationtoRiskyAssets风险厌恶与风险资产的配置CHAPTER6RiskAversionandCap6-2AllocationtoRiskyAssets

风险资产的配置Investorswillavoidriskunlessthereisareward.投资者是风险趋避的除非风险会产生收益Theutilitymodelgivestheoptimalallocationbetweenariskyportfolioandarisk-freeasset.效用模型认为最优的资产配置是风险组合和无风险资产的一个最优搭配6-2AllocationtoRiskyAssets

6-3RiskandRiskAversion

风险与风险趋避Speculation投机Takingconsiderableriskforacommensurategain考虑风险补偿Partieshaveheterogeneousexpectations参与者有不同的期望，会对较高赢面的结果下较大的赌注，否则宁愿不做6-3RiskandRiskAversion

风险与风6-4RiskandRiskAversion

风险与风险趋避Gamble赌博Betorwageronanuncertainoutcomeforenjoyment享受为不确定性结果的下注Partiesassignthesameprobabilitiestothepossibleoutcomes参与者对不同概率的结果下同样的赌注，为享受不确定性下的结果6-4RiskandRiskAversion

风险与风6-5RiskAversionandUtilityValues

风险厌恶与效用价值Investorsarewillingtoconsider:risk-freeassets无风险资产speculativepositionswithpositiveriskpremiums正值风险溢价的投机Portfolioattractivenessincreaseswithexpectedreturnanddecreaseswithrisk.收益越高风险越低组合就越吸引投资者Whathappenswhenreturnincreaseswithrisk?如果风险与收益同步上升？6-5RiskAversionandUtilityV6-6Table6.1AvailableRiskyPortfolios(Risk-freeRate=5%)可供选择的风险组合Eachportfolioreceivesautilityscoretoassesstheinvestor’srisk/returntradeoff效用分数就是用一个函数来对投资者获得的风险与收益进行打分排序，选择最好的组合6-6Table6.1AvailableRiskyP6-7UtilityFunction效用方程U=utility效用E(r)=expectedreturnontheassetorportfolio期望收益A=coefficientofriskaversion风险趋避系数s2=varianceofreturns方差，或者风险½=ascalingfactor尺度调节因子

6-7UtilityFunction效用方程U=uti6-8Table6.2UtilityScoresofAlternativePortfoliosforInvestorswithVaryingDegreeofRiskAversion

几种投资组合对不同风险厌恶水平投资者的效用6-8Table6.2UtilityScoresof6-9Mean-Variance(M-V)Criterion

均值方差准则PortfolioAdominatesportfolioBif:And6-9Mean-Variance(M-V)Criteri6-10EstimatingRiskAversion

估计风险厌恶水平Usequestionnaires调查问卷Observeindividuals’decisionswhenconfrontedwithrisk观察面对风险时的个人决策选择Observehowmuchpeoplearewillingtopaytoavoidrisk观察人们是否愿意付钱来避免风险6-10EstimatingRiskAversion

估6-11CapitalAllocationAcrossRiskyandRisk-FreePortfolios风险资产与无风险资产组合的资本配置AssetAllocation:Isaveryimportantpartofportfolioconstruction.构建投资组合时非常重要的步骤Referstothechoiceamongbroadassetclasses.是指大类资产的偏好，如股票、债券、货币市场证券或者其他资产ControllingRisk:Simplestway:Manipulatethefractionoftheportfolioinvestedinrisk-freeassetsversustheportioninvestedintheriskyassets最简单的方法就是觉得多少份额投资于无风险资产，多少在风险资产上6-11CapitalAllocationAcross6-12BasicAssetAllocation基本资产配置TotalMarketValue$300,000Risk-freemoneymarketfund$90,000Equities$113,400Bonds(long-term)$96,600Totalriskassets$210,0006-12BasicAssetAllocation基本资产6-13BasicAssetAllocation基本资产配置Lety=weightoftheriskyportfolio,P,inthe

completeportfolio;(1-y)=weightofrisk-freeassets:6-13BasicAssetAllocation基本资产6-14TheRisk-FreeAsset无风险资产Onlythegovernmentcanissuedefault-freebonds.只有政府才能发行近似的无违约风险资产（俄罗斯除外）Risk-freeinrealtermsonlyifpriceindexedandmaturityequaltoinvestor’sholdingperiod.投资期限等于持有期时才能看做无风险（没有逼债&清偿风险）T-billsviewedas“the”risk-freeasset美国短期国库券被看做是风险最低的资产Moneymarketfundsalsoconsideredrisk-freeinpractice货币市场基金在实践中也是无风险6-14TheRisk-FreeAsset无风险资产On6-15Figure6.3SpreadBetween3-Month

CDandT-billRates（3个月大额存单与短期国库券的收益差的历史数据）6-15Figure6.3SpreadBetween6-16It’spossibletocreateacompleteportfoliobysplittinginvestmentfundsbetweensafeandriskyassets.将投资资金分配到安全和风险的资产中就可以创造一个完整的组合（意味着调整份额就可以复制其他任何组合）Lety=portionallocatedtotheriskyportfolio,P(1-y)=portiontobeinvestedinrisk-freeasset,F.PortfoliosofOneRiskyAssetandaRisk-FreeAsset单一风险资产与无风险资产的投资组合6-16It’spossibletocreatea6-17rf=7%

rf=0%E(rp)=15%

p=22%y=%inp(1-y)=%inrfExampleUsingChapter6.4Numbers

案例6-17rf=7%rf=0%E(rp)=15%6-18Example(Ctd.)期望收益Theexpectedreturnonthecompleteportfolioistherisk-freerateplustheweightofPtimestheriskpremiumofP该组合的期望收益等于无风险资产的收益乘以它的份额再加上风险资产的收益乘以它的份额6-18Example(Ctd.)期望收益Theexpe6-19Example(Ctd.)期望的风险TheriskofthecompleteportfolioistheweightofPtimestheriskofP:期望的风险就是风险资产的风险乘以它的份额6-19Example(Ctd.)期望的风险6-20Example(Ctd.)期望的风险收益Rearrangeandsubstitutey=sC/sP:6-20Example(Ctd.)期望的风险收益Rearr6-21Figure6.4TheInvestment

OpportunitySet投资集合6-21Figure6.4TheInvestment6-22Lendatrf=7%andborrowatrf=9%Lendingrangeslope=8/22=0.36Borrowingrangeslope=6/22=0.27CALkinksatP在借贷利率发生变化的一点发生歪曲连接CapitalAllocationLinewithLeverage

资本配置线与杠杆6-22Lendatrf=7%andborrowa6-23Figure6.5TheOpportunitySetwithDifferentialBorrowingandLendingRates投资集合（借贷利率不同）6-23Figure6.5TheOpportunity6-24RiskToleranceandAssetAllocation

风险容忍度与资产配置Theinvestormustchooseoneoptimalportfolio,C,fromthesetoffeasiblechoices投资者必须从可选集中择出最优Expectedreturnofthecompleteportfolio:Variance:6-24RiskToleranceandAssetA6-25Table6.4UtilityLevelsforVariousPositionsinRiskyAssets(y)foranInvestorwithRiskAversionA=4

风险厌恶系数4时投资不同风险资产的效用水平6-25Table6.4UtilityLevelsf6-26Figure6.6UtilityasaFunctionofAllocationtotheRiskyAsset,y效用值作为风险资产比例y的函数6-26Figure6.6UtilityasaFu6-27Table6.5SpreadsheetCalculationsofIndifferenceCurves无差异曲线的计算6-27Table6.5SpreadsheetCalc6-28Figure6.7IndifferenceCurvesfor

U=.05andU=.09withA=2andA=4

风险厌恶系数为2、4时效用水平为0.05、0.09的无差异曲线

6-28Figure6.7IndifferenceCu6-29Figure6.8FindingtheOptimalCompletePortfolioUsingIndifferenceCurves使用无差异寻找最优投资组合6-29Figure6.8FindingtheOpt6-30Table6.6ExpectedReturnsonFourIndifferenceCurvesandtheCAL四条无差异曲线和资本配置线对不同风险的期望收益6-30Table6.6ExpectedReturns6-31PassiveStrategies:TheCapitalMarketLine

被动策略：资本市场线Thepassivestrategyavoidsanydirectorindirectsecurityanalysis被动策略中投资者避免任何直接或者间接的证券分析Supplyanddemandforcesmaymakesuchastrategyareasonablechoiceformanyinvestors供给和需求的力量将使得这类策略对很多投资者来说是可行的6-31PassiveStrategies:TheCa6-32Anaturalcandidateforapassivelyheldriskyassetwouldbeawell-diversifiedportfolioofcommonstockssuchastheS&P500.被动投资策略中的一个合适的投资品是分散得很好的投资组合比如标普500Thecapitalmarketline(CML)isthecapitalallocationlineformedfrom1-monthT-billsandabroadindexofcommonstocks(e.g.theS&P500).资本配置线就是1月短期国库券和股票价值指数的搭配PassiveStrategies:TheCapitalMarketL