投资学,9e,精要版,48772,48760,英文PPT Chap005.ppt 38页

CHAPTER5OptimalRiskyPortfolios 7-2TheInvestmentDecisionTop-downprocesswith3steps:Capitalallocationbetweentheriskyportfolioandrisk-freeassetAssetallocationacrossbroadassetclassesSecurityselectionofindividualassetswithineachassetclass 7-3DiversificationandPortfolioRiskMarketriskSystematicornondiversifiableFirm-specificriskDiversifiableornonsystematic 7-4Figure5.1PortfolioRiskasaFunctionoftheNumberofStocksinthePortfolio 7-5Figure5.2PortfolioDiversification 7-6CovarianceandCorrelationPortfolioriskdependsonthecorrelationbetweenthereturnsoftheassetsintheportfolioCovarianceandthecorrelationcoefficientprovideameasureofthewayreturnsoftwoassetsvary 7-7Two-SecurityPortfolio:Return 7-8=VarianceofSecurityD=VarianceofSecurityE=CovarianceofreturnsforSecurityDandSecurityETwo-SecurityPortfolio:Risk 7-9Two-SecurityPortfolio:RiskAnotherwaytoexpressvarianceoftheportfolio: 7-10D,E=CorrelationcoefficientofreturnsCov(rD,rE)=DEDED=StandarddeviationofreturnsforSecurityDE=StandarddeviationofreturnsforSecurityECovariance 7-11Rangeofvaluesfor1,2+1.0>r>-1.0Ifr=1.0,thesecuritiesareperfectlypositivelycorrelatedIfr=-1.0,thesecuritiesareperfectlynegativelycorrelatedCorrelationCoefficients:PossibleValues 7-12CorrelationCoefficientsWhenρDE=1,thereisnodiversificationWhenρDE=-1,aperfecthedgeispossible 7-13Table5.2ComputationofPortfolioVarianceFromtheCovarianceMatrix 7-14Three-AssetPortfolio 7-15Figure5.3PortfolioExpectedReturnasaFunctionofInvestmentProportions 7-16Figure5.4PortfolioStandardDeviationasaFunctionofInvestmentProportions 7-17TheMinimumVariancePortfolioTheminimumvarianceportfolioistheportfoliocomposedoftheriskyassetsthathasthesmalleststandarddeviation,theportfoliowithleastrisk.Whencorrelationislessthan+1,theportfoliostandarddeviationmaybesmallerthanthatofeitheroftheindividualcomponentassets.Whencorrelationis-1,thestandarddeviationoftheminimumvarianceportfolioiszero. 7-18Figure5.5PortfolioExpectedReturnasaFunctionofStandardDeviation 7-19Theamountofpossibleriskreductionthroughdiversificationdependsonthecorrelation.Theriskreductionpotentialincreasesasthecorrelationapproaches-1.Ifr=+1.0,noriskreductionispossible.Ifr=0,σPmaybelessthanthestandarddeviationofeithercomponentasset.Ifr=-1.0,arisklesshedgeispossible.CorrelationEffects 7-20Figure5.6TheOpportunitySetoftheDebtandEquityFundsandTwoFeasibleCALs 7-21TheSharpeRatioMaximizetheslopeoftheCALforanypossibleportfolio,P.Theobjectivefunctionistheslope:TheslopeisalsotheSharperatio. 7-22Figure5.7TheOpportunitySetoftheDebtandEquityFundswiththeOptimalCALandtheOptimalRiskyPortfolio 7-23Figure5.8DeterminationoftheOptimalOverallPortfolio 7-24Figure5.9TheProportionsoftheOptimalOverallPortfolio 7-25MarkowitzPortfolioSelectionModelSecuritySelectionThefirststepistodeterminetherisk-returnopportunitiesavailable.Allportfoliosthatlieontheminimum-variancefrontierfromtheglobalminimum-varianceportfolioandupwardprovidethebestrisk-returncombinations 7-26Figure5.10TheMinimum-VarianceFrontierofRiskyAssets 7-27MarkowitzPortfolioSelectionModelWenowsearchfortheCALwiththehighestreward-to-variabilityratio 7-28Figure5.11TheEfficientFrontierofRiskyAssetswiththeOptimalCAL 7-29MarkowitzPortfolioSelectionModelEveryoneinvestsinP,regardlessoftheirdegreeofriskaversion.Moreriskaverseinvestorsputmoreintherisk-freeasset.LessriskaverseinvestorsputmoreinP. 7-30CapitalAllocationandtheSeparationPropertyTheseparationpropertytellsusthattheportfoliochoiceproblemmaybeseparatedintotwoindependenttasksDeterminationoftheoptimalriskyportfolioispurelytechnical.AllocationofthecompleteportfoliotoT-billsversustheriskyportfoliodependsonpersonalpreference. 7-31Figure5.13CapitalAllocationLineswithVariousPortfoliosfromtheEfficientSet 7-32ThePowerofDiversificationRemember:Ifwedefinetheaveragevarianceandaveragecovarianceofthesecuritiesas: 7-33ThePowerofDiversificationWecanthenexpressportfoliovarianceas: 7-34Table5.4RiskReductionofEquallyWeightedPortfoliosinCorrelatedandUncorrelatedUniverses 7-35OptimalPortfoliosandNonnormalReturnsFat-taileddistributionscanresultinextremevaluesofVaRandESandencouragesmallerallocationstotheriskyportfolio.IfotherportfoliosprovidesufficientlybetterVaRandESvaluesthanthemean-varianceefficientportfolio,wemaypreferthesewhenfacedwithfat-taileddistributions. 7-36RiskPoolingandtheInsurancePrincipleRiskpooling:merginguncorrelated,riskyprojectsasameanstoreducerisk.increasesthescaleoftheriskyinvestmentbyaddingadditionaluncorrelatedassets.Theinsuranceprinciple:riskincreaseslessthanproportionallytothenumberofpoliciesinsuredwhenthepoliciesareuncorrelatedSharperatioincreases 7-37RiskSharingAsriskyassetsareaddedtotheportfolio,aportionofthepoolissoldtomaintainariskyportfoliooffixedsize.Risksharingcombinedwithriskpoolingisthekeytotheinsuranceindustry.Truediversificationmeansspreadingaportfoliooffixedsizeacrossmanyassets,notmerelyaddingmoreriskybetstoanever-growingriskyportfolio. 7-38InvestmentfortheLongRunLongTermStrategyInvestintheriskyportfoliofor2years.Long-termstrategyisriskier.Riskcanbereducedbysellingsomeoftheriskyassetsinyear2.“Timediversification”isnottruediversification.ShortTermStrategyInvestintheriskyportfoliofor1yearandintherisk-freeassetforthesecondyear.