收益管理与风险控制(英文版).pptx

收益管理与风险控制(英文版).pptx

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ChapterOutline,10.1IndividualSecurities10.2ExpectedReturn,Variance,andCovariance10.3TheReturnandRiskforPortfolios10.4TheEfficientSetforTwoAssets10.5TheEfficientSetforManySecurities10.6Diversification:

AnExample10.7RisklessBorrowingandLending10.8MarketEquilibrium10.9RelationshipbetweenRiskandExpectedReturn（CAPM）10.10SummaryandConclusions,10.1IndividualSecurities,Thecharacteristicsofindividualsecuritiesthatareofinterestarethe:

ExpectedReturnVarianceandStandardDeviationCovarianceandCorrelation,10.2ExpectedReturn,Variance,andCovariance,Considerthefollowingtworiskyassetworld.Thereisa1/3chanceofeachstateoftheeconomyandtheonlyassetsareastockfundandabondfund.,10.2ExpectedReturn,Variance,andCovariance,10.2ExpectedReturn,Variance,andCovariance,10.2ExpectedReturn,Variance,andCovariance,10.2ExpectedReturn,Variance,andCovariance,10.2ExpectedReturn,Variance,andCovariance,10.2ExpectedReturn,Variance,andCovariance,10.2ExpectedReturn,Variance,andCovariance,10.2ExpectedReturn,Variance,andCovariance,10.3TheReturnandRiskforPortfolios,Notethatstockshaveahigherexpectedreturnthanbondsandhigherrisk.Letusturnnowtotherisk-returntradeoffofaportfoliothatis50%investedinbondsand50%investedinstocks.,10.3TheReturnandRiskforPortfolios,Therateofreturnontheportfolioisaweightedaverageofthereturnsonthestocksandbondsintheportfolio:

10.3TheReturnandRiskforPortfolios,Therateofreturnontheportfolioisaweightedaverageofthereturnsonthestocksandbondsintheportfolio:

10.3TheReturnandRiskforPortfolios,Therateofreturnontheportfolioisaweightedaverageofthereturnsonthestocksandbondsintheportfolio:

10.3TheReturnandRiskforPortfolios,Theexpectedrateofreturnontheportfolioisaweightedaverageoftheexpectedreturnsonthesecuritiesintheportfolio.,10.3TheReturnandRiskforPortfolios,Thevarianceoftherateofreturnonthetworiskyassetsportfoliois,whereBSisthecorrelationcoefficientbetweenthereturnsonthestockandbondfunds.,10.3TheReturnandRiskforPortfolios,Observethedecreaseinriskthatdiversificationoffers.Anequallyweightedportfolio（50%instocksand50%inbonds）haslessriskthanstocksorbondsheldinisolation.,10.4TheEfficientSetforTwoAssets,Wecanconsiderotherportfolioweightsbesides50%instocksand50%inbonds,100%bonds,100%stocks,10.4TheEfficientSetforTwoAssets,Wecanconsiderotherportfolioweightsbesides50%instocksand50%inbonds,100%bonds,100%stocks,10.4TheEfficientSetforTwoAssets,100%stocks,100%bonds,Notethatsomeportfoliosare“better”thanothers.Theyhavehigherreturnsforthesamelevelofriskorless.,Thesecompromisetheefficientfrontier.,Two-SecurityPortfolioswithVariousCorrelations,100%bonds,return,100%stocks,=0.2,=1.0,=-1.0,PortfolioRisk/ReturnTwoSecurities:

CorrelationEffects,Relationshipdependsoncorrelationcoefficient-1.0r+1.0Thesmallerthecorrelation,thegreatertheriskreductionpotentialIfr=+1.0,noriskreductionispossible,PortfolioRiskasaFunctionoftheNumberofStocksinthePortfolio,Nondiversifiablerisk;SystematicRisk;MarketRisk,DiversifiableRisk;NonsystematicRisk;FirmSpecificRisk;UniqueRisk,n,Inalargeportfoliothevariancetermsareeffectivelydiversifiedaway,butthecovariancetermsarenot.,Thusdiversificationcaneliminatesome,butnotalloftheriskofindividualsecurities.,Portfoliorisk,10.5TheEfficientSetforManySecurities,Consideraworldwithmanyriskyassets;wecanstillidentifytheopportunitysetofrisk-returncombinationsofvariousportfolios.,return,P,IndividualAssets,10.5TheEfficientSetforManySecurities,Giventheopportunitysetwecanidentifytheminimumvarianceportfolio.,return,P,minimumvarianceportfolio,IndividualAssets,10.5TheEfficientSetforManySecurities,Thesectionoftheopportunitysetabovetheminimumvarianceportfolioistheefficientfrontier.,return,P,minimumvarianceportfolio,efficientfrontier,IndividualAssets,OptimalRiskyPortfoliowithaRisk-FreeAsset,Inadditiontostocksandbonds,consideraworldthatalsohasrisk-freesecuritieslikeT-bills,100%bonds,100%stocks,rf,return,10.7RisklessBorrowingandLending,NowinvestorscanallocatetheirmoneyacrosstheT-billsandabalancedmutualfund,100%bonds,100%stocks,rf,return,Balancedfund,CML,10.7RisklessBorrowingandLending,Witharisk-freeassetavailableandtheefficientfrontieridentified,wechoosethecapitalallocationlinewiththesteepestslope,return,P,efficientfrontier,rf,CML,10.8MarketEquilibrium,Withthecapitalallocationlineidentified,allinvestorschooseapointalongthelinesomecombinationoftherisk-freeassetandthemarketportfolioM.Inaworldwithhomogeneousexpectations,Misthesameforallinvestors.,return,P,efficientfrontier,rf,M,CML,TheSeparationProperty,TheSeparationPropertystatesthatthemarketportfolio,M,isthesameforallinvestorstheycanseparatetheirriskaversionfromtheirchoiceofthemarketportfolio.,return,P,efficientfrontier,rf,M,CML,TheSeparationProperty,Investorriskaversionisrevealedintheirchoiceofwheretostayalongthecapitalallocationlinenotintheirchoiceoftheline.,return,P,efficientfrontier,rf,M,CML,MarketEquilibrium,JustwheretheinvestorchoosesalongtheCapitalAssetLinedependsonhisrisktolerance.ThebigpointthoughisthatallinvestorshavethesameCML.,100%bonds,100%stocks,rf,return,Balancedfund,CML,MarketEquilibrium,AllinvestorshavethesameCMLbecausetheyallhavethesameoptimalriskyportfoliogiventherisk-freerate.,100%bonds,100%stocks,rf,return,OptimalRiskyPorfolio,CML,TheSeparationProperty,Theseparationpropertyimpliesthatportfoliochoicecanbeseparatedintotwotasks:

（1）determinetheoptimalriskyportfolio,and

（2）selectingapointontheCML.,100%bonds,100%stocks,rf,return,OptimalRiskyPorfolio,CML,OptimalRiskyPortfoliowithaRisk-FreeAsset,Bytheway,theoptimalriskyportfoliodependsontherisk-freerateaswellastheriskyassets.,100%bonds,100%stocks,return,FirstOptimalRiskyPortfolio,SecondOptimalRiskyPortfolio,CML0,CML1,DefinitionofRiskWhenInvestorsHoldtheMarketPortfolio,Researchershaveshownthatthebestmeasureoftheriskofasecurityinalargeportfolioisthebeta（b）ofthesecurity.Betameasurestheresponsivenessofasecuritytomovementsinthemarketportfolio.,Estimatingbwithregression,SecurityReturns,Returnonmarket%,Ri=ai+biRm+ei,Slope=bi,CharacteristicLine,EstimatesofbforSelectedStocks,TheFormulaforBeta,Clearly,yourestimateofbetawilldependuponyourchoiceofaproxyforthemarketportfolio.,10.9RelationshipbetweenRiskandExpectedReturn（CAPM）,ExpectedReturnontheMarket:

Expectedreturnonanindividualsecurity:

MarketRiskPremium,Thisappliestoindividualsecuritiesheldwithinwell-diversifiedportfolios.,ExpectedReturnonanIndividualSecurity,ThisformulaiscalledtheCapitalAssetPricingModel（CAPM）,Assumebi=0,thentheexpectedreturnisRF.Assumebi=1,then,RelationshipBetweenRisk&ExpectedReturn,Expectedreturn,b,1.0,RelationshipBetweenRisk&ExpectedReturn,Expectedreturn,b,1.5,10.10SummaryandConclusions,Thischaptersetsforththeprinciplesofmodernportfoliotheory.TheexpectedreturnandvarianceonaportfoliooftwosecuritiesAandBaregivenby,ByvaryingwA,onecantraceouttheefficientsetofportfolios.Wegraphedtheefficientsetforthetwo-assetcaseasacurve,pointingoutthatthedegreeofcurvaturereflectsthediversificationeffect:

thelowerthecorrelationbetweenthetwosecurities,thegreaterthediversification.Thesamegeneralshapeholdsinaworldofmanyassets.,10.10SummaryandConclusions,Theefficientsetofriskyassetscanbecombinedwithrisklessborrowingandlending.Inthiscase,arationalinvestorwillalwayschoosetoholdtheportfolioofriskysecuritiesrepresentedbythemarketportfolio.,Thenwithborrowingorlending,theinvestorselectsapointalongtheCML.,10.10SummaryandConclusions,Thecontributionofasecuritytotheriskofawell-diversifiedportfolioisproportionaltothecovarianceofthesecuritysreturnwiththemarketsreturn.Thiscontributioniscalledthebeta.,TheCAPMstatesthattheexpectedreturnonasecurityispositivelyrelatedtothesecuritysbeta: