ANDCAPITALALLOCATIONTORISKYASSETS风险厌恶程

RISKAVERSIONANDCAPITALALLOCATIONTORISKYASSETS6-1Lecture3HafizHoque6-2AllocationtoRiskyAssetsInvestorswillavoidriskunlessthereisareward.Theutilitymodelgivestheoptimalallocationbetweenariskyportfolioandarisk-freeasset.HafizHoque6-3RiskandRiskAversionSpeculationTakingconsiderableriskforacommensurategainPartieshaveheterogeneousexpectationsHafizHoque6-4RiskandRiskAversionGambleBetorwageronanuncertainoutcomeforenjoymentPartiesassignthesameprobabilitiestothepossibleoutcomesHafizHoque6-5RiskAversionandUtilityValuesInvestorsarewillingtoconsider:risk-freeassetsspeculativepositionswithpositiveriskpremiumsPortfolioattractivenessincreaseswithexpectedreturnanddecreaseswithrisk.Whathappenswhenreturnincreaseswithrisk?HafizHoque6-6Table6.1AvailableRiskyPortfolios(Risk-freeRate=5%)Eachportfolioreceivesautilityscoretoassesstheinvestor’srisk/returntradeoffHafizHoque6-7UtilityFunctionU=utilityE(r)=expectedreturnontheassetorportfolioA=coefficientofriskaversions2=varianceofreturns½=ascalingfactor21()2UErAsHafizHoque6-8Table6.2UtilityScoresofAlternativePortfoliosforInvestorswithVaryingDegreeofRiskAversionHafizHoque6-9Mean-Variance(M-V)CriterionPortfolioAdominatesportfolioBif:AndBArErEBAssHafizHoque6-10EstimatingRiskAversionUsequestionnairesObserveindividuals’decisionswhenconfrontedwithriskObservehowmuchpeoplearewillingtopaytoavoidriskHafizHoque6-11CapitalAllocationAcrossRiskyandRisk-FreePortfoliosAssetAllocation:Isaveryimportantpartofportfolioconstruction.Referstothechoiceamongbroadassetclasses.ControllingRisk:Simplestway:Manipulatethefractionoftheportfolioinvestedinrisk-freeassetsversustheportioninvestedintheriskyassetsHafizHoque6-12BasicAssetAllocationTotalMarketValue$300,000Risk-freemoneymarketfund$90,000Equities$113,400Bonds(long-term)$96,600Totalriskassets$210,00054.0000,210$400,113$EW46.000,210$600,96$BWHafizHoque6-13BasicAssetAllocationLety=weightoftheriskyportfolio,P,inthecompleteportfolio;(1-y)=weightofrisk-freeassets:7.0000,300$000,210$y3.0000,300$000,90$1y378.000,300$400,113$:E322.000,300$600,96$:BHafizHoque6-14TheRisk-FreeAssetOnlythegovernmentcanissuedefault-freebonds.Risk-freeinrealtermsonlyifpriceindexedandmaturityequaltoinvestor’sholdingperiod.T-billsviewedas“the”risk-freeassetMoneymarketfundsalsoconsideredrisk-freeinpracticeHafizHoque6-15Figure6.3SpreadBetween3-MonthCDandT-billRatesHafizHoque6-16It’spossibletocreateacompleteportfoliobysplittinginvestmentfundsbetweensafeandriskyassets.Lety=portionallocatedtotheriskyportfolio,P(1-y)=portiontobeinvestedinrisk-freeasset,F.PortfoliosofOneRiskyAssetandaRisk-FreeAssetHafizHoque6-17ExampleUsingChapter6.4Numbersrf=7%srf=0%E(rp)=15%sp=22%y=%inp(1-y)=%inrfHafizHoque6-18Example(Ctd.)Theexpectedreturnonthecompleteportfolioistherisk-freerateplustheweightofPtimestheriskpremiumofP()()cfPfErryErr7157yrEcHafizHoque6-19Example(Ctd.)TheriskofthecompleteportfolioistheweightofPtimestheriskofP:yyPC22ssHafizHoque6-20Example(Ctd.)Rearrangeandsubstitutey=sC/sP:CfPPCfCrrErrEsss2287228PfPrrESlopesHafizHoque6-21Figure6.4TheInvestmentOpportunitySetHafizHoque6-22Lendatrf=7%andborrowatrf=9%Lendingrangeslope=8/22=0.36Borrowingrangeslope=6/22=0.27CALkinksatPCapitalAllocationLinewithLeverageHafizHoque6-23Figure6.5TheOpportunitySetwithDifferentialBorrowingandLendingRatesHafizHoque6-24RiskToleranceandAssetAllocationTheinvestormustchooseoneoptimalportfolio,C,fromthesetoffeasiblechoicesExpectedreturnofthecompleteportfolio:Variance:()()cfPfErryErr222CPyssHafizHoque6-25Table6.4UtilityLevelsforVariousPositionsinRiskyAssets(y)foranInvestorwithRiskAversionA=4HafizHoque6-26Figure6.6UtilityasaFunctionofAllocationtotheRiskyAsset,yHafizHoque6-27Table6.5SpreadsheetCalculationsofIndifferenceCurvesHafizHoque6-28Figure6.7IndifferenceCurvesforU=.05andU=.09withA=2andA=4HafizHoque6-29Figure6.8FindingtheOptimalCompletePortfolioUsingIndifferenceCurvesHafizHoque6-30Table6.6ExpectedReturnsonFourIndifferenceCurvesandtheCALHafizHoque6-31PassiveStrategies:TheCapitalMarketLineThepassivestrategyavoidsanydirectorindirectsecurityanalysisSupplyanddemandforcesmaymakesuchastrategyareasonablechoiceformanyinvestorsHafizHoque6-32PassiveStrategies:TheCapitalMarketLineAnaturalcandidateforapassivelyheldriskyassetwouldbeawell-diversifiedportfolioofcommonstockssuchastheS&P500.Thecapitalmarketline(CML)isthecapitalallocationlineformedfrom1-monthT-billsandabroadindexofcommonstocks(e.g.theS&P500).HafizHoque6-33PassiveStrategies:TheCapitalMarketLineTheCMLisgivenbyastrategythatinvolvesinvestmentintwopassiveportfolios:1.virtuallyrisk-freeshort-termT-bills(oramoneymarketfund)2.afundofcommonstocksthatmimicsabroadmarketindex.HafizHoque6-34PassiveStrategies:TheCapitalMarketLineFrom1926to2009,thepassiveriskyportfolioofferedanaverageriskpremiumof7.9%withastandarddeviationof20.8%,resultinginareward-to-volatilityratioof.38.HafizHoque