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CHAPTER4RiskAversionandCapitalAllocationtoRiskyAssets
6-2AllocationtoRiskyAssetsInvestorswillavoidriskunlessthereisareward.Theutilitymodelgivestheoptimalallocationbetweenariskyportfolioandarisk-freeasset.
6-3RiskandRiskAversionSpeculationTakingconsiderableriskforacommensurategainPartieshaveheterogeneousexpectations
6-4RiskandRiskAversionGambleBetorwageronanuncertainoutcomeforenjoymentPartiesassignthesameprobabilitiestothepossibleoutcomes
6-5RiskAversionandUtilityValuesInvestorsarewillingtoconsider:risk-freeassetsspeculativepositionswithpositiveriskpremiumsPortfolioattractivenessincreaseswithexpectedreturnanddecreaseswithrisk.Whathappenswhenreturnincreaseswithrisk?
6-6Table4.1AvailableRiskyPortfolios(Risk-freeRate=5%)Eachportfolioreceivesautilityscoretoassesstheinvestor’srisk/returntradeoff
6-7UtilityFunctionU=utilityE(r)=expectedreturnontheassetorportfolioA=coefficientofriskaversions2=varianceofreturns½=ascalingfactor
6-8Table4.2UtilityScoresofAlternativePortfoliosforInvestorswithVaryingDegreeofRiskAversion
6-9Mean-Variance(M-V)CriterionPortfolioAdominatesportfolioBif:And
6-10EstimatingRiskAversionUsequestionnairesObserveindividuals’decisionswhenconfrontedwithriskObservehowmuchpeoplearewillingtopaytoavoidrisk
6-11CapitalAllocationAcrossRiskyandRisk-FreePortfoliosAssetAllocation:Isaveryimportantpartofportfolioconstruction.Referstothechoiceamongbroadassetclasses.ControllingRisk:Simplestway:Manipulatethefractionoftheportfolioinvestedinrisk-freeassetsversustheportioninvestedintheriskyassets
6-12BasicAssetAllocationTotalMarketValue$300,000Risk-freemoneymarketfund$90,000Equities$113,400Bonds(long-term)$96,600Totalriskassets$210,000
6-13BasicAssetAllocationLety=weightoftheriskyportfolio,P,inthecompleteportfolio;(1-y)=weightofrisk-freeassets:
6-14TheRisk-FreeAssetOnlythegovernmentcanissuedefault-freebonds.Risk-freeinrealtermsonlyifpriceindexedandmaturityequaltoinvestor’sholdingperiod.T-billsviewedas“the”risk-freeassetMoneymarketfundsalsoconsideredrisk-freeinpractice
6-15Figure4.3SpreadBetween3-MonthCDandT-billRates
6-16It’spossibletocreateacompleteportfoliobysplittinginvestmentfundsbetweensafeandriskyassets.Lety=portionallocatedtotheriskyportfolio,P(1-y)=portiontobeinvestedinrisk-freeasset,F.PortfoliosofOneRiskyAssetandaRisk-FreeAsset
6-17rf=7%rf=0%E(rp)=15%p=22%y=%inp(1-y)=%inrfExampleUsingChapter4.4Numbers
6-18Example(Ctd.)Theexpectedreturnonthecompleteportfolioistherisk-freerateplustheweightofPtimestheriskpremiumofP
6-19Example(Ctd.)TheriskofthecompleteportfolioistheweightofPtimestheriskofP:
6-20Example(Ctd.)Rearrangeandsubstitutey=sC/sP:
6-21Figure4.4TheInvestmentOpportunitySet
6-22Lendatrf=7%andborrowatrf=9%Lendingrangeslope=8/22=0.36Borrowingrangeslope=6/22=0.27CALkinksatPCapitalAllocationLinewithLeverage
6-23Figure4.5TheOpportunitySetwithDifferentialBorrowingandLendingRates
6-24RiskToleranceandAssetAllocationTheinvestormustchooseoneoptimalportfolio,C,fromthesetoffeasiblechoicesExpectedreturnofthecompleteportfolio:Variance:
6-25Table4.4UtilityLevelsforVariousPositionsinRiskyAssets(y)foranInvestorwithRiskAversionA=4
6-26Figure4.6UtilityasaFunctionofAllocationtotheRiskyAsset,y
6-27Table4.5SpreadsheetCalculationsofIndifferenceCurves
6-28Figure4.7IndifferenceCurvesforU=.05andU=.09withA=2andA=4
6-29Figure4.8FindingtheOptimalCompletePortfolioUsingIndifferenceCurves
6-30Table4.6ExpectedReturnsonFourIndifferenceCurvesandtheCAL
6-31PassiveStrategies:TheCapitalMarketLineThepassivestrategyavoidsanydirectorindirectsecurityanalysisSupplyanddemandforcesmaymakesuchastrategyareasonablechoiceformanyinvestors
6-32PassiveStrategies:TheCapitalMarketLineAnaturalcandidateforapassivelyheldriskyassetwouldbeawell-diversifiedportfolioofcommonstockssuchastheS&P500.Thecapitalmarketline(CML)isthecapitalallocationlineformedfrom1-monthT-billsandabroadindexofcommonstocks(e.g.theS&P500).
6-33PassiveStrategies:TheCapitalMarketLineTheCMLisgivenbyastrategythatinvolvesinvestmentintwopassiveportfolios:virtuallyrisk-freeshort-termT-bills(oramoneymarketfund)afundofcommonstocksthatmimicsabroadmarketindex.
6-34PassiveStrategies:TheCapitalMarketLineFrom1926to2009,thepassiveriskyportfolioofferedanaverageriskpremiumof7.9%withastandarddeviationof20.8%,resultinginareward-to-volatilityratioof.38.