博迪教學課件13

Chapter13:

CapitalMarket EquilibriumObjectiveTheTheoryoftheCAPMUseofCAPMinbenchmarkingUsingCAPMtodeterminecorrectratefordiscounting1Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallChapter13Contents13.1TheCapitalAssetPricingModelinBrief13.2DeterminingoftheRiskPremiumontheMarketPortfolio13.3BetaandRiskPremiumsonIndividualSecurities13.4UsingtheCAPMinPortfolioSelection13.5Valuation&RegulatingRatesofReturn13.6ModificationsandAlternativestotheCAPM2Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallIntroductionCAPMisatheoryaboutequilibriumpricesinthemarketsforriskyassetsItisimportantbecauseitprovidesajustificationforthewidespreadpracticeofpassiveinvestingcalledindexingawaytoestimateexpectedratesofreturnforuseinevaluatingstocksandprojects3Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall13.1TheCapitalAssetPricingModelinBriefDevelopedinthe1960’sbySharp,andindependentlybyLintner,andMossinItanswersthequestionWhatwouldequilibriumriskpremiumsbeifpeoplehadthesamesetofforecastsofexpectedreturns,risk,andcorrelationsallchosetheirportfoliosaccordingtheprinciplesofefficientdiversification4Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallSowhat’swrongwithms-analysisTheassumptionsofthelastchapterappearedfullyacceptableInfactitmayappeartobepedantictomentionthematallWhydevelopanewmodelforrisk-returnifthepresentmodelain’tbroke?5Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallms-analysis:EstimationWedidnotspellitout,butifyourecallthemnemonicforobtainingtheportfoliovolatilityinthems-model,(givenn-sharesintheportfolio,)weneededn-means(noproblem)n-standarddeviations(noproblem)n*(n-1)/2correlations(?problem)6Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallms-analysis:EstimationAllparametersneedestimation,andtherearen*(n+1)/2+nparametersAssumeaportfolioof,say,2,000sharesrepresentthemarket,thenweneedtoestimatemorethan2,000,000parameters,mostofwhicharecorrelations7Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallms-analysis:EstimationRecallthatwhenyouestimateparameters,itisdonewithonlyagivenlevelofconfidenceConfidenceimproveswiththenumberofobservationsInpracticetheparametershavetimedependence,soolddataintroduceserrorFor2,000shares,anda99%confidence,about20,000parameterswillbeinerror8Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallms-analysis:EstimationTheerrorsmay,ormaynot,besignificanttoyourinvestmentdecision,buttheirexistencecallsforfurtheranalysisInanycase,thedatacollection,verification,andprocessing,isasignificantuseofanalyticalresources9Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallms-analysis:WishesAfterwehavetheestimatedparameters,findingtheoptimalportfoliorequiresquadraticprogramming,andthisagainrequiresheavyuseofcomputationalresourcesTheproblemissimilartoknowingthepositionandvelocityofeverystarintheMilkyWay,andattemptingtopredicttheirfuturesbycomputingindividualinteractions10Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallms-analysis:GuidancePrinciplesforSimplificationAnimportantprincipleoffinancialmodelingistocreateequationsthatcapturethekeyfactorsparsimoniouslyAnotherimportantprincipleistoattempttodevelopsimplemodelsLinearmodelsarethenpreferredtoquadraticmodels11Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheAstrophysicsofFinanceIntheMilkyWayproblem,anastronomershouldspecifyexactlywhatneedstobepredicted,andgiveattentiontothevariablesthatmostaffectitSo,ifhewantstoknowwhenthenextstarwillcomecloseenoughtoSoltodisturbtheOortcloudthenclosestarsneedindividualanalysisdistantstarsmaybetreatedhomogeneously12Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallSpecifyingtheModelInthelastchapterweexamineddiversifyingahomogenousportfolio,andweobservedthatthereweretwokindsofriskdiversifiableorindividualriskNondiversifiableormarketrisk13Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallSpecifyingtheModelWealsoobservedthatinthelimitasthenumberofsecuritiesbecomeslarge,weobtainedtheformulaThisformulatellsusthatthecorrelationsareofcrucialimportanceintherelationshipbetweenaportfolioriskandthestockrisk14Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallSpecifyingtheModelInthehomogenousmodel,wesawthattherewasindividual-andmarket-riskAssumethateachequity’sreturnisthecompositionoftworandomvariables:oneassociatedwiththemarket’sreturnoneassociatedwiththecompany-specificreturn15Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallSpecifyingtheModel:AssumptionsCompany-specificreturnonanystockxisnotcorrelatedtothecompany-specificreturnonanyotherstockyiscorrelatedwiththemarketreturnTherisk-freerateisconstantduringtheinvestmenttheperiod16Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallAssumptionsInvestorsforecastsagreewithrespecttoexpectations,standarddeviations,andcorrelationsofthereturnsofriskysecuritiesThereforeallinvestorsholdriskyassetsinthesamerelativeproportionsInvestorsbehaveoptimallyInequilibrium,pricesadjustsothataggregatedemandforeachsecurityisequaltoitssupply17Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallMarketPortfolioSinceeveryinvestor’srelativeholdingsoftheriskysecurityisthesame,theonlywaytheassetmarketcanclearisifthoseoptimalrelativeproportionsaretheproportionsinwhichtheyarevaluedinthemarketplaceMarketPortfolio18Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallCMLandtheCAPMCAPMsaysthatinequilibrium,anyinvestor’srelativeholdingofriskyassetswillbethesameasinthemarketportfolioDependingontheirriskaversions,differentinvestorsholdportfolioswithdifferentmixesofrisklessassetandthemarketportfolio19Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallCAPMFormula20Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheCapitalMarketLine21Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallActivev.PassiveManagementCAPMimpliesthat,onaverage,theperformancesofactiveportfoliomanagersisequaltothatofpassivemanagersemployingjustthemarketportfolioandtherisk-freesecurityDiligentmanagersdooutperformpassivemanagers,butonlytothedegreethattheirdiligenceisrewarded22Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallRewardOnlyforMarketRiskTheriskpremiumonanyindividualsecurityisproportionalonlytoitscontributiontotheriskofthemarketportfolio,anddoesnotdependonitsstand-aloneriskInvestorsarerewardedonlyforbearingmarketrisk23Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall13.2DeterminingtheRiskPremiumontheMarketPortfolioCAPMstatesthattheequilibriumriskpremiumonthemarketportfolioistheproductofvarianceofthemarket,s2Mweightedaverageofthedegreeofriskaversionofholdersofrisk,A24Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallCommentCAPMexplainsthedifferencebetweentherisklessinterestrateandtheexpectedrateofreturnonthemarketportfolio,butnottheirabsolutelevelsTheabsoluteleveloftheequilibriumexpectedrateofreturnonthemarketportfolioisdeterminedbysuchfactorsasexpectedproductivityhouseholdinter-temporalpreferencesforconsumption25Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallExample:ToDetermine‘A’26Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall13.3BetaandRiskPremiumsonIndividualSecuritiesIfriskisdefinedasthatmeasuresuchthatasitincreases,arisk-averseinvestorwouldhavetobecompensatedbyalargerexpectedreturninorderthatshewouldcontinuetoholditinheroptimalportfolio,thenthemeasureofasecurity’sriskisitsbeta,bbtellsyouhowmuchthesecurity’srateofreturnchangeswhenthereturnonthemarketportfoliochanges27Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallComment:b=1Asecuritywithab=1onaveragerisesandfallswiththemarketa10%(say)unexpectedrise(fall)inthemarketreturnpremiumwill,onaverage,resultina10%rise(fall)inthesecurity’sreturnpremium28Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallComment:b

31Asecuritywithab

31onaveragerisesandfallsmorethanthemarketWithab=1.3,a10%(say)unexpectedrise(fall)inthemarketreturnpremiumwill,onaverage,resultina13%rise(fall)inthesecurity’sreturnpremiumSuchasecurityissaidtobeaggressive29Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallComment:b

￡1Asecuritywithab

￡1onaveragerisesandfallslessthanthemarketWithab=0.7,a10%(say)unexpectedrise(fall)inthemarketreturnpremiumwill,onaverage,resultina7%rise(fall)inthesecurity’sreturnpremiumSuchasecurityissaidtobedefensive30Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallCAPMRiskPremiumonanyAssetAccordingthetheCAPM,inequilibrium,theriskpremiumonanyassetisequaltheproductof

b(or‘Beta’)theriskpremiumonthemarketportfolio31Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheSecurityMarketLine32Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallSecurityMarketLineTheplotofasecurity’sriskpremium(orsometimessecurityreturns)againstsecuritybetaNotethattheslopeofthesecuritymarketlineisthemarketpremiumByCAPMtheory,allsecuritiesmustfallpreciselyontheSML(henceitsname)33Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallPracticalExampleSomesimulateddatawasgeneratedundertheassumptionsthat:themarketportfolioreturnhasanexpectedvalueof0.15,avolatilityof0.20,andindex0=50thesharezhasareturnof0.12,avolatilityof0.25,andprice0=30(nodividends)thecorrelationbetweenthereturnsis0.90;andtherisk-freerateis0.0534Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall35Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallDataSetUsedInordertodisplaythematerialclearly,onlyoneyearofdataisgenerated,andiscollectedmonthly,resultingin13setsofpricesInarealsimulation,muchmoredatamustbecollectedinordertoprovideanadequateconfidenceintervalforparameterestimates36Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTransformationofPricesintoReturnsThepricesaretransformedintomonthlyholdingperiodreturns(mhpr_Ind,andmhpr_Z)Themhprsaretransformedintoannualrates,compoundedannuallyTheannualratescompoundedannuallyaretransformedtoannualratescompoundedcontinuously37Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTableofPrices38Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall39Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallFinancialCalculatorsEverythingcouldhavebeendoneusingamodernstandard-issuefinancialorscientificcalculatorRemember,thecorrectratetouseistheannualratecompoundedcontinuously,andthatmonth-to-yearconversionsofstandarddeviationinvolveasquarerootof12Takecaretoenterthemarketrateastheindependentvariable,x40Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallAccuracyIssueWeassumedthatthes’sandr’sareconstants,buttheyarerandomvariablestooInordertoachieveadequateconfidence,alargesampleisneededSmallmovementsinpricearemaskedbytransactionpricesTheresultisacompromisebetweencurrencyandconfidence41Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallModelandMeasuredValuesofStatisticalParameters42Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallCommentTheillustratedtrajectoryistypicalformonthlydatacollectedoverayearCaution:avoidusingsmalldatasetstoestimateCAPMparameters43Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallRegressionLineTheslopeoftheregressionlineofdependentstockagainstindependentmarketreturnsisbeta44Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall45Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallObservationAllsecurities,(notjustefficientportfolios)plotontotheSML,iftheyarecorrectlypricedaccordingtotheCAPM46Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheBetaofaPortfolioWhendeterminingtheriskofaportfoliousingstandarddeviationresultsinaformulathat’squitecomplexusingbeta,theformulaislinear47Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallComputingBetaHerearesomeusefulformulaeforcomputingbeta48Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall13.4UsingtheCAPMinPortfolioSelectionWhetherornotCAPMisavalidtheory,indexingisattractivetoinvestorsbecausehistoricallyithasperformedbetterthanmostactivelymanagedportfoliositcostslesstoimplementthatactivemanagement49Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallAParadoxResolvedThelastchapterposedaparadoxwithtwosecuritiesco-existing,onehavingalowerstandarddeviationandhigherreturnthantheotherIfweaccepttheCAPMasavalidtheory,wehavearesolutionBothsecuritieslieontheSML,andbothsecuritiesliebelowtheCML50Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHalls-riskandb-riskAsecurityhastwokindsofrisk:riskthatmaybediversifiedaway,andriskthatisassociatedwiththemarketTheCAPMtheorystatesthatthelowerreturnonthes-riskiersecurityimpliesthatithasalowerlevelofmarketb-risk,andthisistheonlyrelevantriskThes-riskiersecuritycontainsrelativelymore(irrelevant)security-specificrisk51Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallABrandManagerMostinvestorshavetheopportunitytoeliminatemostindividualriskfromtheirportfolio;butconsideraproductmanager’sexposuretoriskIfabrandmanager’sproductsperformwell,promotion,highersalary,andgreaterautonomyfollowperformbadly,humiliation,unemploymentandpovertyfollow52Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallABrandManagerNowassumethatanewproductisavailableforinclusioninthebrand,butgivenitsb-riskandexpectedreturn,itfallsbelowthesml,andhenceisnotintheinvestors’interestsThemanagerdiscoversthatthenewproductreduceshistotalrisk,andactsinhisowninterests(ratherthantheinvestors’),andacceptstheproduct(agencyproblem)53Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallThePortfolioManagerRemember(lastchapter)wehadnotresolvedtheissuehowtoevaluatetheperformanceofaportfoliomanager,butgiventheCAPMaresolutionisathandIfyourportfolioisproducingactualreturnswithalowerbetathanthesmlspecifies(withstatisticalsignificance),thenyoushouldcertainlynotbefired54Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallThePortfolioManagerThefurtherawelldiversifiedportfolioconsistentlyliesabove(below)thesml,thebetter(worse)thefundmanager’sperformanceThereareseveralmeasuresofthisdistance,butthistopicisbetterleftforanotherday55Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallAlphaFundandtheSecurityMarketLine56Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallAlphaFundandtheCapitalMarketLine57Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallHowtoWinInvestmentGamesYoumayhavebeenaskedtotakepartinaninvestmentgamewhereyou‘given’$100,000tomanageforasemester;winnertakesallTheoverwhelmingchancesarethatthewinningstudentusespoorfinancialpractices58Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallHowtoWinInvestmentGames(Continued)Thecriteriaofsuccessforthegamedifferssignificantlyfromreal-lifeinvesting,soyourstrategyforwinningislikelytobedifferentIfyoudiversifyawayunsystematicrisk--evenifyouhavesomekindofinformationaladvantageoveryourcompetition--youareveryunlikelytowinthegameTowin,youneedindividualrisktoseparateyoufromthecrowdUnlikearealinvestoryoudon’thaverealdownside-riskyourupside-potentialmaterializesonlybybeingfirst59Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall13.5ValuationandRegulatingRatesofReturnBetamaybeusedtoobtainthediscountfactorforaprojectAssumeaprojectissimilartotheprojectsundertakenbyanotherfirm,‘Betaful’Betafulisfinancedby20%short-termdebt,and80%equity,anditsbis1.3(assumedebtisrisk-free)Youroptimalcapitalstructureis40%(risk-free)debt,and60%equity60Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallValuationandRegulatingRatesofReturnAssumethemarketrateis15%,andtherisk-freerateis5%ComputethebetaofBetaful’soperations61Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallValuationandRegulatingRatesofReturnBetaofBetaful’soperationsisequaltothebetaofournewoperationTofindtherequiredreturnonthenewproject,applytheCAPM62Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallValuationandRegulatingRatesofReturnAssumethatyourcompanyisjustavehicleforthenewproject,thenthebetaofyourunquotedequityis63Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallValuationandRegulatingRatesofReturnAssumethatyourcompanyhasanexpecteddividendof$6nextyear,andthatitwillgrowannuallyatarateof4%forever,thevalueofashareis64Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallValuationandRegulatingRatesofReturnRegulatorsusetheCAPMtoestablisha‘fair’rateofreturnoninvestedcapitalinpublicutilities,giventhelevelofrisk65Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall13.6ModificationsandAlternativestotheCAPMStartinginthe1970sresearchersfoundthatCAPMdidnotseemtofullyexplainthestructureofexpectedreturnsonassets.