第十章收益和风险CAPM课件

10.1IndividualSecuritiesThecharacteristicsofindividualsecuritiesthatareofinterestarethe:ExpectedReturnVarianceandStandardDeviationCovarianceandCorrelation10.2ExpectedReturn,Variance,andCovariance

Considerthefollowingtworiskyassetworld.Thereisa1/3chanceofeachstateoftheeconomyandtheonlyassetsareastockfundandabondfund.10.2ExpectedReturn,Variance,andCovariance10.2ExpectedReturn,Variance,andCovariance10.2ExpectedReturn,Variance,andCovariance10.2ExpectedReturn,Variance,andCovariance10.2ExpectedReturn,Variance,andCovariance10.2ExpectedReturn,Variance,andCovariance10.2ExpectedReturn,Variance,andCovariance10.2ExpectedReturn,Variance,andCovariance10.3TheReturnandRiskforPortfoliosNotethatstockshaveahigherexpectedreturnthanbondsandhigherrisk.Letusturnnowtotherisk-returntradeoffofaportfoliothatis50%investedinbondsand50%investedinstocks.10.3TheReturnandRiskforPortfoliosTherateofreturnontheportfolioisaweightedaverageofthereturnsonthestocksandbondsintheportfolio:10.3TheReturnandRiskforPortfoliosTherateofreturnontheportfolioisaweightedaverageofthereturnsonthestocksandbondsintheportfolio:10.3TheReturnandRiskforPortfoliosTherateofreturnontheportfolioisaweightedaverageofthereturnsonthestocksandbondsintheportfolio:10.3TheReturnandRiskforPortfoliosTheexpectedrateofreturnontheportfolioisaweightedaverageoftheexpectedreturnsonthesecuritiesintheportfolio.10.3TheReturnandRiskforPortfoliosThevarianceoftherateofreturnonthetworiskyassetsportfolioiswhereBSisthecorrelationcoefficientbetweenthereturnsonthestockandbondfunds.10.3TheReturnandRiskforPortfoliosObservethedecreaseinriskthatdiversificationoffers.Anequallyweightedportfolio(50%instocksand50%inbonds)haslessriskthanstocksorbondsheldinisolation.10.4TheEfficientSetforTwoAssetsWecanconsiderotherportfolioweightsbesides50%instocksand50%inbonds…100%bonds100%stocks10.4TheEfficientSetforTwoAssetsWecanconsiderotherportfolioweightsbesides50%instocksand50%inbonds…100%bonds100%stocks10.4TheEfficientSetforTwoAssets100%stocks100%bondsNotethatsomeportfoliosare“better”thanothers.Theyhavehigherreturnsforthesamelevelofriskorless.Thesecompromisetheefficientfrontier.Two-SecurityPortfolioswithVariousCorrelations100%bondsreturn100%stocks=0.2=1.0=-1.0PortfolioRisk/ReturnTwoSecurities:CorrelationEffectsRelationshipdependsoncorrelationcoefficient-1.0<

r

<+1.0Thesmallerthecorrelation,thegreatertheriskreductionpotentialIfr=+1.0,noriskreductionispossiblePortfolioRiskasaFunctionoftheNumberofStocksinthePortfolioNondiversifiablerisk;SystematicRisk;MarketRiskDiversifiableRisk;NonsystematicRisk;FirmSpecificRisk;UniqueRisknInalargeportfoliothevariancetermsareeffectivelydiversifiedaway,butthecovariancetermsarenot.Thusdiversificationcaneliminatesome,butnotalloftheriskofindividualsecurities.Portfoliorisk10.5TheEfficientSetforManySecuritiesConsideraworldwithmanyriskyassets;wecanstillidentifytheopportunitysetofrisk-returncombinationsofvariousportfolios.returnPIndividualAssets10.5TheEfficientSetforManySecuritiesGiventheopportunitysetwecanidentifytheminimumvarianceportfolio.returnPminimumvarianceportfolioIndividualAssets10.5TheEfficientSetforManySecuritiesThesectionoftheopportunitysetabovetheminimumvarianceportfolioistheefficientfrontier.returnPminimumvarianceportfolioefficientfrontierIndividualAssetsOptimalRiskyPortfoliowithaRisk-FreeAssetInadditiontostocksandbonds,consideraworldthatalsohasrisk-freesecuritieslikeT-bills100%bonds100%stocksrfreturn10.7RisklessBorrowingandLendingNowinvestorscanallocatetheirmoneyacrosstheT-billsandabalancedmutualfund100%bonds100%stocksrfreturnBalancedfundCML10.7RisklessBorrowingandLending

Witharisk-freeassetavailableandtheefficientfrontieridentified,wechoosethecapitalallocationlinewiththesteepestslopereturnPefficientfrontierrfCML10.8MarketEquilibrium

Withthecapitalallocationlineidentified,allinvestorschooseapointalongtheline—somecombinationoftherisk-freeassetandthemarketportfolioM.Inaworldwithhomogeneousexpectations,Misthesameforallinvestors.returnPefficientfrontierrfMCMLTheSeparationProperty

TheSeparationPropertystatesthatthemarketportfolio,M,isthesameforallinvestors—theycanseparatetheirriskaversionfromtheirchoiceofthemarketportfolio.returnPefficientfrontierrfMCMLTheSeparationProperty

Investorriskaversionisrevealedintheirchoiceofwheretostayalongthecapitalallocationline—notintheirchoiceoftheline.returnPefficientfrontierrfMCMLMarketEquilibriumJustwheretheinvestorchoosesalongtheCapitalAssetLinedependsonhisrisktolerance.ThebigpointthoughisthatallinvestorshavethesameCML.100%bonds100%stocksrfreturnBalancedfundCMLMarketEquilibriumAllinvestorshavethesameCMLbecausetheyallhavethesameoptimalriskyportfoliogiventherisk-freerate.100%bonds100%stocksrfreturnOptimalRiskyPorfolioCMLTheSeparationProperty

Theseparationpropertyimpliesthatportfoliochoicecanbeseparatedintotwotasks:(1)determinetheoptimalriskyportfolio,and(2)selectingapointontheCML.100%bonds100%stocksrfreturnOptimalRiskyPorfolioCMLOptimalRiskyPortfoliowithaRisk-FreeAssetBytheway,theoptimalriskyportfoliodependsontherisk-freerateaswellastheriskyassets.100%bonds100%stocksreturnFirstOptimalRiskyPortfolioSecondOptimalRiskyPortfolioCML0CML1DefinitionofRiskWhenInvestorsHoldtheMarketPortfolioResearchershaveshownthatthebestmeasureoftheriskofasecurityinalargeportfolioisthebeta(b)ofthesecurity.Betameasurestheresponsivenessofasecuritytomovementsinthemarketportfolio.EstimatingbwithregressionSecurityReturnsReturnonmarket%Ri=a

i+biRm+eiSlope=biCharacteristicLineEstimatesofbforSelectedStocksStockBetaBankofAmerica1.55BorlandInternational2.35Travelers,Inc.1.65DuPont1.00Kimberly-ClarkCorp.0.90Microsoft1.05GreenMountainPower0.55HomestakeMining0.20Oracle,Inc.0.49TheFormulaforBetaClearly,yourestimateofbetawilldependuponyourchoiceofaproxyforthemarketportfolio.10.9RelationshipbetweenRiskandExpectedReturn(CAPM)ExpectedReturnontheMarket:Expectedreturnonanindividualsecurity:MarketRiskPremiumThisappliestoindividualsecuritiesheldwithinwell-diversifiedportfolios.ExpectedReturnonanIndividualSecurityThisformulaiscalledtheCapitalAssetPricingModel(CAPM)Assumebi=0,thentheexpectedreturnisRF.Assume

bi=1,thenExpectedreturnonasecurity=Risk-freerate+Betaofthesecurity×MarketriskpremiumRelationshipBetweenRisk&ExpectedReturnExpectedreturnb1.0RelationshipBetweenRisk&ExpectedReturnExpectedreturnb1.510.10SummaryandConclusionsThischaptersetsforththeprinciplesofmodernportfoliotheory.TheexpectedreturnandvarianceonaportfoliooftwosecuritiesAandBaregivenbyByvaryingwA,onecantraceouttheefficientsetofportfolios.Wegraphedtheefficientsetforthetwo-assetcaseasacurve,pointingoutthatthedegreeofcurvaturereflectsthediversificationeffect:thelowerthecorrelationbetweenthetwosecurities,thegreaterthedive