ANDCAPITALALLOCATIONTORISKYASSETS风险厌恶程课件

RISKAVERSIONANDCAPITALALLOCATIONTORISKYASSETS6-1Lecture3HafizHoqueRISKAVERSIONANDCAPITALALLO6-2AllocationtoRiskyAssetsInvestorswillavoidriskunlessthereisareward.Theutilitymodelgivestheoptimalallocationbetweenariskyportfolioandarisk-freeasset.HafizHoque6-2AllocationtoRiskyAssetsI6-3RiskandRiskAversionSpeculationTakingconsiderableriskforacommensurategainPartieshaveheterogeneousexpectationsHafizHoque6-3RiskandRiskAversionSpecu6-4RiskandRiskAversionGambleBetorwageronanuncertainoutcomeforenjoymentPartiesassignthesameprobabilitiestothepossibleoutcomesHafizHoque6-4RiskandRiskAversionGambl6-5RiskAversionandUtilityValuesInvestorsarewillingtoconsider:risk-freeassetsspeculativepositionswithpositiveriskpremiumsPortfolioattractivenessincreaseswithexpectedreturnanddecreaseswithrisk.Whathappenswhenreturnincreaseswithrisk?HafizHoque6-5RiskAversionandUtilityV6-6Table6.1AvailableRiskyPortfolios(Risk-freeRate=5%)Eachportfolioreceivesautilityscoretoassesstheinvestor’srisk/returntradeoffHafizHoque6-6Table6.1AvailableRiskyP6-7UtilityFunctionU=utilityE(r)=expectedreturnontheassetorportfolioA=coefficientofriskaversions2=varianceofreturns½=ascalingfactor

HafizHoque6-7UtilityFunctionU=utility6-8Table6.2UtilityScoresofAlternativePortfoliosforInvestorswithVaryingDegreeofRiskAversionHafizHoque6-8Table6.2UtilityScoresof6-9Mean-Variance(M-V)CriterionPortfolioAdominatesportfolioBif:AndHafizHoque6-9Mean-Variance(M-V)Criteri6-10EstimatingRiskAversionUsequestionnairesObserveindividuals’decisionswhenconfrontedwithriskObservehowmuchpeoplearewillingtopaytoavoidriskHafizHoque6-10EstimatingRiskAversionUs6-11CapitalAllocationAcrossRiskyandRisk-FreePortfoliosAssetAllocation:Isaveryimportantpartofportfolioconstruction.Referstothechoiceamongbroadassetclasses.ControllingRisk:Simplestway:Manipulatethefractionoftheportfolioinvestedinrisk-freeassetsversustheportioninvestedintheriskyassetsHafizHoque6-11CapitalAllocationAcross6-12BasicAssetAllocationTotalMarketValue$300,000Risk-freemoneymarketfund$90,000Equities$113,400Bonds(long-term)$96,600Totalriskassets$210,000HafizHoque6-12BasicAssetAllocationTota6-13BasicAssetAllocationLety=weightoftheriskyportfolio,P,inthe

completeportfolio;(1-y)=weightofrisk-freeassets:HafizHoque6-13BasicAssetAllocationLet6-14TheRisk-FreeAssetOnlythegovernmentcanissuedefault-freebonds.Risk-freeinrealtermsonlyifpriceindexedandmaturityequaltoinvestor’sholdingperiod.T-billsviewedas“the”risk-freeassetMoneymarketfundsalsoconsideredrisk-freeinpracticeHafizHoque6-14TheRisk-FreeAssetOnlyth6-15Figure6.3SpreadBetween3-Month

CDandT-billRatesHafizHoque6-15Figure6.3SpreadBetween6-16It’spossibletocreateacompleteportfoliobysplittinginvestmentfundsbetweensafeandriskyassets.Lety=portionallocatedtotheriskyportfolio,P(1-y)=portiontobeinvestedinrisk-freeasset,F.PortfoliosofOneRiskyAssetandaRisk-FreeAssetHafizHoque6-16It’spossibletocreatea6-17ExampleUsingChapter6.4Numbersrf=7%rf=0%E(rp)=15%p=22%y=%inp(1-y)=%inrfHafizHoque6-17ExampleUsingChapter6.46-18Example(Ctd.)Theexpectedreturnonthecompleteportfolioistherisk-freerateplustheweightofPtimestheriskpremiumofPHafizHoque6-18Example(Ctd.)Theexpected6-19Example(Ctd.)TheriskofthecompleteportfolioistheweightofPtimestheriskofP:HafizHoque6-19Example(Ctd.)HafizHoque6-20Example(Ctd.)Rearrangeandsubstitutey=sC/sP:HafizHoque6-20Example(Ctd.)Rearrangean6-21Figure6.4TheInvestment

OpportunitySetHafizHoque6-21Figure6.4TheInvestment6-22Lendatrf=7%andborrowatrf=9%Lendingrangeslope=8/22=0.36Borrowingrangeslope=6/22=0.27CALkinksatPCapitalAllocationLinewithLeverageHafizHoque6-22Lendatrf=7%andborrowa6-23Figure6.5TheOpportunitySetwithDifferentialBorrowingandLendingRatesHafizHoque6-23Figure6.5TheOpportunity6-24RiskToleranceandAssetAllocationTheinvestormustchooseoneoptimalportfolio,C,fromthesetoffeasiblechoicesExpectedreturnofthecompleteportfolio:Variance:HafizHoque6-24RiskToleranceandAssetA6-25Table6.4UtilityLevelsforVariousPositionsinRiskyAssets(y)foranInvestorwithRiskAversionA=4HafizHoque6-25Table6.4UtilityLevelsf6-26Figure6.6UtilityasaFunctionofAllocationtotheRiskyAsset,yHafizHoque6-26Figure6.6UtilityasaFu6-27Table6.5SpreadsheetCalculationsofIndifferenceCurvesHafizHoque6-27Table6.5SpreadsheetCalc6-28Figure6.7IndifferenceCurvesfor

U=.05andU=.09withA=2andA=4HafizHoque6-28Figure6.7IndifferenceCu6-29Figure6.8FindingtheOptimalCompletePortfolioUsingIndifferenceCurvesHafizHoque6-29Figure6.8FindingtheOpt6-30Table6.6ExpectedReturnsonFourIndifferenceCurvesandtheCALHafizHoque6-30Table6.6ExpectedReturns6-31PassiveStrategies:

TheCapitalMarketLineThepassivestrategyavoidsanydirectorindirectsecurityanalysisSupplyanddemandforcesmaymakesuchastrategyareasonablechoiceformanyinvestorsHafizHoque6-31PassiveStrategies:

TheC6-32PassiveStrategies:

TheCapitalMarketLineAnaturalcandidateforapassivelyheldriskyassetwouldbeawell-diversifiedportfolioofcommonstockssuchastheS&P500.Thecapitalmarketline(CML)isthecapitalallocationlineformedfrom1-monthT-billsandabroadindexofcommonstocks(e.g.theS&P500).HafizHoque6-32PassiveStrategies:

The6-33PassiveStrategies:

TheCapitalMarketLineTheCMLisgivenbyastrategythatinvolvesinvestmentintwopassiveportfolios:

virtuallyrisk-freeshort-termT-bills(oramoneymarketfund)afundofcommonstocksthatmimicsabroadmarketindex.HafizHoque6-33PassiveStrategies:

The6-34PassiveStrategies:

TheCapitalMarketLineFrom1926to2009,thepassiveriskyportfolioofferedanaverageriskpremiumof7.9%withastandarddeviationof20.8%,resultinginareward-to-volatilityratioof.38.HafizHoque6-34PassiveStrategies:

The演讲完毕，谢谢观看！演讲完毕，谢谢观看！RISKAVERSIONANDCAPITALALLOCATIONTORISKYASSETS6-36Lecture3HafizHoqueRISKAVERSIONANDCAPITALALLO6-37AllocationtoRiskyAssetsInvestorswillavoidriskunlessthereisareward.Theutilitymodelgivestheoptimalallocationbetweenariskyportfolioandarisk-freeasset.HafizHoque6-2AllocationtoRiskyAssetsI6-38RiskandRiskAversionSpeculationTakingconsiderableriskforacommensurategainPartieshaveheterogeneousexpectationsHafizHoque6-3RiskandRiskAversionSpecu6-39RiskandRiskAversionGambleBetorwageronanuncertainoutcomeforenjoymentPartiesassignthesameprobabilitiestothepossibleoutcomesHafizHoque6-4RiskandRiskAversionGambl6-40RiskAversionandUtilityValuesInvestorsarewillingtoconsider:risk-freeassetsspeculativepositionswithpositiveriskpremiumsPortfolioattractivenessincreaseswithexpectedreturnanddecreaseswithrisk.Whathappenswhenreturnincreaseswithrisk?HafizHoque6-5RiskAversionandUtilityV6-41Table6.1AvailableRiskyPortfolios(Risk-freeRate=5%)Eachportfolioreceivesautilityscoretoassesstheinvestor’srisk/returntradeoffHafizHoque6-6Table6.1AvailableRiskyP6-42UtilityFunctionU=utilityE(r)=expectedreturnontheassetorportfolioA=coefficientofriskaversions2=varianceofreturns½=ascalingfactor

HafizHoque6-7UtilityFunctionU=utility6-43Table6.2UtilityScoresofAlternativePortfoliosforInvestorswithVaryingDegreeofRiskAversionHafizHoque6-8Table6.2UtilityScoresof6-44Mean-Variance(M-V)CriterionPortfolioAdominatesportfolioBif:AndHafizHoque6-9Mean-Variance(M-V)Criteri6-45EstimatingRiskAversionUsequestionnairesObserveindividuals’decisionswhenconfrontedwithriskObservehowmuchpeoplearewillingtopaytoavoidriskHafizHoque6-10EstimatingRiskAversionUs6-46CapitalAllocationAcrossRiskyandRisk-FreePortfoliosAssetAllocation:Isaveryimportantpartofportfolioconstruction.Referstothechoiceamongbroadassetclasses.ControllingRisk:Simplestway:Manipulatethefractionoftheportfolioinvestedinrisk-freeassetsversustheportioninvestedintheriskyassetsHafizHoque6-11CapitalAllocationAcross6-47BasicAssetAllocationTotalMarketValue$300,000Risk-freemoneymarketfund$90,000Equities$113,400Bonds(long-term)$96,600Totalriskassets$210,000HafizHoque6-12BasicAssetAllocationTota6-48BasicAssetAllocationLety=weightoftheriskyportfolio,P,inthe

completeportfolio;(1-y)=weightofrisk-freeassets:HafizHoque6-13BasicAssetAllocationLet6-49TheRisk-FreeAssetOnlythegovernmentcanissuedefault-freebonds.Risk-freeinrealtermsonlyifpriceindexedandmaturityequaltoinvestor’sholdingperiod.T-billsviewedas“the”risk-freeassetMoneymarketfundsalsoconsideredrisk-freeinpracticeHafizHoque6-14TheRisk-FreeAssetOnlyth6-50Figure6.3SpreadBetween3-Month

CDandT-billRatesHafizHoque6-15Figure6.3SpreadBetween6-51It’spossibletocreateacompleteportfoliobysplittinginvestmentfundsbetweensafeandriskyassets.Lety=portionallocatedtotheriskyportfolio,P(1-y)=portiontobeinvestedinrisk-freeasset,F.PortfoliosofOneRiskyAssetandaRisk-FreeAssetHafizHoque6-16It’spossibletocreatea6-52ExampleUsingChapter6.4Numbersrf=7%rf=0%E(rp)=15%p=22%y=%inp(1-y)=%inrfHafizHoque6-17ExampleUsingChapter6.46-53Example(Ctd.)Theexpectedreturnonthecompleteportfolioistherisk-freerateplustheweightofPtimestheriskpremiumofPHafizHoque6-18Example(Ctd.)Theexpected6-54Example(Ctd.)TheriskofthecompleteportfolioistheweightofPtimestheriskofP:HafizHoque6-19Example(Ctd.)HafizHoque6-55Example(Ctd.)Rearrangeandsubstitutey=sC/sP:HafizHoque6-20Example(Ctd.)Rearrangean6-56Figure6.4TheInvestment

OpportunitySetHafizHoque6-21Figure6.4TheInvestment6-57Lendatrf=7%andborrowatrf=9%Lendingrangeslope=8/22=0.36Borrowingrangeslope=6/22=0.27CALkinksatPCapitalAllocationLinewithLeverageHafizHoque6-22Lendatrf=7%andborrowa6-58Figure6.5TheOpportunitySetwithDifferentialBorrowingandLendingRatesHafizHoque6-23Figure6.5TheOpportunity6-59RiskToleranceandAssetAllocationTheinvestormustchooseoneoptimalportfolio,C,fromthesetoffeasiblechoicesExpectedreturnofthecompleteportfolio:Variance:HafizHoque6-24RiskToleranceandAssetA6-60Table6.4UtilityLevelsforVariousPositionsinRiskyAssets(y)foranInvestorwithRiskAversionA=4HafizHoque6-25Table6.4UtilityLevelsf6-61Figure6.6UtilityasaFunctionofAllocationtotheRiskyAsset,yHafizHoque6-26Figure6.6UtilityasaFu6-62Table6.5SpreadsheetCalculationsofIndifferenceCurvesHafizHoque6-27Table6.5SpreadsheetCalc6-63Figure6.7IndifferenceCurvesfor

U=.05andU=.09withA=2andA=4HafizHoque6-28Figure6.7IndifferenceCu6-64Figure6.8FindingtheOptimalCompletePortfolioUsingIndifferenceCurvesHafizHoque6-29Figure6.8FindingtheOpt6-65Table