ANDCAPITALALLOCATIONTORISKYASSETS风险厌恶程.ppt

RISKAVERSIONANDCAPITALALLOCATIONTORISKYASSETS,6-1,Lecture3,HafizHoque,6-2,AllocationtoRiskyAssets,Investorswillavoidriskunlessthereisareward.Theutilitymodelgivestheoptimalallocationbetweenariskyportfolioandarisk-freeasset.,HafizHoque,6-3,RiskandRiskAversion,SpeculationTakingconsiderableriskforacommensurategainPartieshaveheterogeneousexpectations,HafizHoque,6-4,RiskandRiskAversion,GambleBetorwageronanuncertainoutcomeforenjoymentPartiesassignthesameprobabilitiestothepossibleoutcomes,HafizHoque,6-5,RiskAversionandUtilityValues,Investorsarewillingtoconsider:risk-freeassetsspeculativepositionswithpositiveriskpremiumsPortfolioattractivenessincreaseswithexpectedreturnanddecreaseswithrisk.Whathappenswhenreturnincreaseswithrisk?,HafizHoque,6-6,Table6.1AvailableRiskyPortfolios(Risk-freeRate=5%),Eachportfolioreceivesautilityscoretoassesstheinvestorsrisk/returntradeoff,HafizHoque,6-7,UtilityFunction,U=utilityE(r)=expectedreturnontheassetorportfolioA=coefficientofriskaversions2=varianceofreturns=ascalingfactor,HafizHoque,6-8,Table6.2UtilityScoresofAlternativePortfoliosforInvestorswithVaryingDegreeofRiskAversion,HafizHoque,6-9,Mean-Variance(M-V)Criterion,PortfolioAdominatesportfolioBif:And,HafizHoque,6-10,EstimatingRiskAversion,UsequestionnairesObserveindividualsdecisionswhenconfrontedwithriskObservehowmuchpeoplearewillingtopaytoavoidrisk,HafizHoque,6-11,CapitalAllocationAcrossRiskyandRisk-FreePortfolios,AssetAllocation:,Isaveryimportantpartofportfolioconstruction.Referstothechoiceamongbroadassetclasses.,ControllingRisk:,Simplestway:Manipulatethefractionoftheportfolioinvestedinrisk-freeassetsversustheportioninvestedintheriskyassets,HafizHoque,6-12,BasicAssetAllocation,HafizHoque,6-13,BasicAssetAllocation,Lety=weightoftheriskyportfolio,P,inthecompleteportfolio;(1-y)=weightofrisk-freeassets:,HafizHoque,6-14,TheRisk-FreeAsset,Onlythegovernmentcanissuedefault-freebonds.Risk-freeinrealtermsonlyifpriceindexedandmaturityequaltoinvestorsholdingperiod.T-billsviewedas“the”risk-freeassetMoneymarketfundsalsoconsideredrisk-freeinpractice,HafizHoque,6-15,Figure6.3SpreadBetween3-MonthCDandT-billRates,HafizHoque,6-16,Itspossibletocreateacompleteportfoliobysplittinginvestmentfundsbetweensafeandriskyassets.Lety=portionallocatedtotheriskyportfolio,P(1-y)=portiontobeinvestedinrisk-freeasset,F.,PortfoliosofOneRiskyAssetandaRisk-FreeAsset,HafizHoque,6-17,ExampleUsingChapter6.4Numbers,HafizHoque,6-18,Example(Ctd.),Theexpectedreturnonthecompleteportfolioistherisk-freerateplustheweightofPtimestheriskpremiumofP,HafizHoque,6-19,Example(Ctd.),TheriskofthecompleteportfolioistheweightofPtimestheriskofP:,HafizHoque,6-20,Example(Ctd.),Rearrangeandsubstitutey=sC/sP:,HafizHoque,6-21,Figure6.4TheInvestmentOpportunitySet,HafizHoque,6-22,Lendatrf=7%andborrowatrf=9%Lendingrangeslope=8/22=0.36Borrowingrangeslope=6/22=0.27CALkinksatP,CapitalAllocationLinewithLeverage,HafizHoque,6-23,Figure6.5TheOpportunitySetwithDifferentialBorrowingandLendingRates,HafizHoque,6-24,RiskToleranceandAssetAllocation,Theinvestormustchooseoneoptimalportfolio,C,fromthesetoffeasiblechoicesExpectedreturnofthecompleteportfolio:Variance:,HafizHoque,6-25,Table6.4UtilityLevelsforVariousPositionsinRiskyAssets(y)foranInvestorwithRiskAversionA=4,HafizHoque,6-26,Figure6.6UtilityasaFunctionofAllocationtotheRiskyAsset,y,HafizHoque,6-27,Table6.5SpreadsheetCalculationsofIndifferenceCurves,HafizHoque,6-28,Figure6.7IndifferenceCurvesforU=.05andU=.09withA=2andA=4,HafizHoque,6-29,Figure6.8FindingtheOptimalCompletePortfolioUsingIndifferenceCurves,HafizHoque,6-30,Table6.6ExpectedReturnsonFourIndifferenceCurvesandtheCAL,HafizHoque,6-31,PassiveStrategies:TheCapitalMarketLine,ThepassivestrategyavoidsanydirectorindirectsecurityanalysisSupplyanddemandforcesmaymakesuchastrategyareasonablechoiceformanyinvestors,HafizHoque,6-32,PassiveStrategies:TheCapitalMarketLine,Anaturalcandidateforapassivelyheldriskyassetwouldbeawell-diversifiedportfolioofcommonstockssuchastheS&P500.Thecapitalmarketline(CML)isthecapitalallocationlineformedfrom1-monthT-billsandabroadindexofcommonstocks(e.g.theS&P500).,HafizHoque,6-33,PassiveStrategies:TheCapitalMarketLine,TheCMLisgivenbyastrategythatinvolvesinvestmentintwopassiveportfolios:virtuallyrisk-freeshort-termT-bills(oramoneymarketfund)afundofcommonstocksthatmimicsabroadm