ANDCAPITALALLOCATIONTORISKYASSETS风险厌恶程.ppt

RISKAVERSIONANDCAPITALALLOCATIONTORISKYASSETS,Lecture3,AllocationtoRiskyAssets,Investorswillavoidriskunlessthereisareward.Theutilitymodelgivestheoptimalallocationbetweenariskyportfolioandarisk-freeasset.,RiskandRiskAversion,SpeculationTakingconsiderableriskforacommensurategainPartieshaveheterogeneousexpectations,RiskandRiskAversion,GambleBetorwageronanuncertainoutcomeforenjoymentPartiesassignthesameprobabilitiestothepossibleoutcomes,RiskAversionandUtilityValues,Investorsarewillingtoconsider:risk-freeassetsspeculativepositionswithpositiveriskpremiumsPortfolioattractivenessincreaseswithexpectedreturnanddecreaseswithrisk.Whathappenswhenreturnincreaseswithrisk?,Table6.1AvailableRiskyPortfolios(Risk-freeRate=5%),Eachportfolioreceivesautilityscoretoassesstheinvestorsrisk/returntradeoff,UtilityFunction,U=utilityE(r)=expectedreturnontheassetorportfolioA=coefficientofriskaversions2=varianceofreturns=ascalingfactor,Table6.2UtilityScoresofAlternativePortfoliosforInvestorswithVaryingDegreeofRiskAversion,Mean-Variance(M-V)Criterion,PortfolioAdominatesportfolioBif:And,EstimatingRiskAversion,UsequestionnairesObserveindividualsdecisionswhenconfrontedwithriskObservehowmuchpeoplearewillingtopaytoavoidrisk,CapitalAllocationAcrossRiskyandRisk-FreePortfolios,AssetAllocation:,Isaveryimportantpartofportfolioconstruction.Referstothechoiceamongbroadassetclasses.,ControllingRisk:,Simplestway:Manipulatethefractionoftheportfolioinvestedinrisk-freeassetsversustheportioninvestedintheriskyassets,BasicAssetAllocation,BasicAssetAllocation,Lety=weightoftheriskyportfolio,P,inthecompleteportfolio;(1-y)=weightofrisk-freeassets:,TheRisk-FreeAsset,Onlythegovernmentcanissuedefault-freebonds.Risk-freeinrealtermsonlyifpriceindexedandmaturityequaltoinvestorsholdingperiod.T-billsviewedas“the”risk-freeassetMoneymarketfundsalsoconsideredrisk-freeinpractice,Figure6.3SpreadBetween3-MonthCDandT-billRates,Itspossibletocreateacompleteportfoliobysplittinginvestmentfundsbetweensafeandriskyassets.Lety=portionallocatedtotheriskyportfolio,P(1-y)=portiontobeinvestedinrisk-freeasset,F.,PortfoliosofOneRiskyAssetandaRisk-FreeAsset,ExampleUsingChapter6.4Numbers,Example(Ctd.),Theexpectedreturnonthecompleteportfolioistherisk-freerateplustheweightofPtimestheriskpremiumofP,Example(Ctd.),TheriskofthecompleteportfolioistheweightofPtimestheriskofP:,Example(Ctd.),Rearrangeandsubstitutey=sC/sP:,Figure6.4TheInvestmentOpportunitySet,Lendatrf=7%andborrowatrf=9%Lendingrangeslope=8/22=0.36Borrowingrangeslope=6/22=0.27CALkinksatP,CapitalAllocationLinewithLeverage,Figure6.5TheOpportunitySetwithDifferentialBorrowingandLendingRates,RiskToleranceandAssetAllocation,Theinvestormustchooseoneoptimalportfolio,C,fromthesetoffeasiblechoicesExpectedreturnofthecompleteportfolio:Variance:,Table6.4UtilityLevelsforVariousPositionsinRiskyAssets(y)foranInvestorwithRiskAversionA=4,Figure6.6UtilityasaFunctionofAllocationtotheRiskyAsset,y,Table6.5SpreadsheetCalculationsofIndifferenceCurves,Figure6.7IndifferenceCurvesforU=.05andU=.09withA=2andA=4,Figure6.8FindingtheOptimalCompletePortfolioUsingIndifferenceCurves,Table6.6ExpectedReturnsonFourIndifferenceCurvesandtheCAL,PassiveStrategies:TheCapitalMarketLine,ThepassivestrategyavoidsanydirectorindirectsecurityanalysisSupplyanddemandforcesmaymakesuchastrategyareasonablechoiceformanyinvestors,PassiveStrategies:TheCapitalMarketLine,Anaturalcandidateforapassivelyheldriskyassetwouldbeawell-diversifiedportfolioofcommonstockssuchastheS&P500.Thecapitalmarketline(CML)isthecapitalallocationlineformedfrom1-monthT-billsandabroadindexofcommonstocks(e.g.theS&P500).,PassiveStrategies:TheCapitalMarketLine,TheCMLisgivenbyastrategythatinvolvesinvestmentintwopassiveportfolios:virtuallyrisk-freeshort-termT-bills(oramoneymarketfund)afundofcommonstocksthatmimicsabroad