RISK AVERSION AND CAPITAL ALLOCATION TO RISKY ASSETS风险厌恶程度与风险资产的分配课件

RISKAVERSIONANDCAPITALALLOCATIONTORISKYASSETS6-1Lecture3HafizHoque6-2AllocationtoRiskyAssetsInvestorswillavoidriskunlessthereisareward.Theutilitymodelgivestheoptimalallocationbetweenariskyportfolioandarisk-freeasset.HafizHoque6-3RiskandRiskAversionSpeculationTakingconsiderableriskforacommensurategainPartieshaveheterogeneousexpectationsHafizHoque6-4RiskandRiskAversionGambleBetorwageronanuncertainoutcomeforenjoymentPartiesassignthesameprobabilitiestothepossibleoutcomesHafizHoque6-5RiskAversionandUtilityValuesInvestorsarewillingtoconsider:risk-freeassetsspeculativepositionswithpositiveriskpremiumsPortfolioattractivenessincreaseswithexpectedreturnanddecreaseswithrisk.Whathappenswhenreturnincreaseswithrisk?HafizHoque6-6Table6.1AvailableRiskyPortfolios(Risk-freeRate=5%)Eachportfolioreceivesautilityscoretoassesstheinvestor’srisk/returntradeoffHafizHoque6-7UtilityFunctionU=utilityE(r)=expectedreturnontheassetorportfolioA=coefficientofriskaversions2=varianceofreturns½=ascalingfactor

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

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

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

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

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

TheCapitalMarketLineThepassivestrategyavoidsanydirectorindirectsecurityanalysisSupplyanddemandforcesmaymakesuchastrategyareasonablechoiceformanyinvestorsHafizHoque6-32PassiveStrategies:

TheCapitalMarketLineAnaturalcandidateforapassivelyheldriskyassetwouldbeawell-diversifiedportfolioofcommonstockssuchastheS&P500.Thecapitalmarketline(CML)isthecapitalallocationlineformedfrom1-monthT-billsandabroadindexofcommonstocks(e.g.theS&P500).HafizHoque6-33PassiveStrategies:

TheCapitalMarketLineTheCMLisgivenbyastrategythatinvolvesinvestmentintwopassiveportfolios:

virtuallyrisk-freeshort-termT-bills(oramoneymarketfund)afundofcommonstocksthatmim