《金融学》（第二版） 课件 （英文） Chapter13 Capital Market Equilibrium

Chapter13:

CapitalMarket EquilibriumObjectiveTheTheoryoftheCAPMUseofCAPMinbenchmarkingUsingCAPMtodeterminecorrectratefordiscounting1Chapter13Contents13.1TheCapitalAssetPricingModelinBrief13.2DeterminingoftheRiskPremiumontheMarketPortfolio13.3BetaandRiskPremiumsonIndividualSecurities13.4UsingtheCAPMinPortfolioSelection13.5Valuation&RegulatingRatesofReturn13.6ModificationsandAlternativestotheCAPM2IntroductionCAPMisatheoryaboutequilibriumpricesinthemarketsforriskyassetsItisimportantbecauseitprovidesajustificationforthewidespreadpracticeofpassiveinvestingcalledindexingawaytoestimateexpectedratesofreturnforuseinevaluatingstocksandprojects313.1TheCapitalAssetPricingModelinBriefDevelopedinthe1960’sbySharp,andindependentlybyLintner,andMossinItanswersthequestionWhatwouldequilibriumriskpremiumsbeifpeoplehadthesamesetofforecastsofexpectedreturns,risk,andcorrelationsallchosetheirportfoliosaccordingtheprinciplesofefficientdiversification4Sowhat’swrongwithms-analysisTheassumptionsofthelastchapterappearedfullyacceptableInfactitmayappeartobepedantictomentionthematallWhydevelopanewmodelforrisk-returnifthepresentmodelain’tbroke?5ms-analysis:EstimationWedidnotspellitout,butifyourecallthemnemonicforobtainingtheportfoliovolatilityinthems-model,(givenn-sharesintheportfolio,)weneededn-means(noproblem)n-standarddeviations(noproblem)n*(n-1)/2correlations(?problem)6ms-analysis:EstimationAllparametersneedestimation,andtherearen*(n+1)/2+nparametersAssumeaportfolioof,say,2,000sharesrepresentthemarket,thenweneedtoestimatemorethan2,000,000parameters,mostofwhicharecorrelations7ms-analysis:EstimationRecallthatwhenyouestimateparameters,itisdonewithonlyagivenlevelofconfidenceConfidenceimproveswiththenumberofobservationsInpracticetheparametershavetimedependence,soolddataintroduceserrorFor2,000shares,anda99%confidence,about20,000parameterswillbeinerror8ms-analysis:EstimationTheerrorsmay,ormaynot,besignificanttoyourinvestmentdecision,buttheirexistencecallsforfurtheranalysisInanycase,thedatacollection,verification,andprocessing,isasignificantuseofanalyticalresources9ms-analysis:WishesAfterwehavetheestimatedparameters,findingtheoptimalportfoliorequiresquadraticprogramming,andthisagainrequiresheavyuseofcomputationalresourcesTheproblemissimilartoknowingthepositionandvelocityofeverystarintheMilkyWay,andattemptingtopredicttheirfuturesbycomputingindividualinteractions10ms-analysis:GuidancePrinciplesforSimplificationAnimportantprincipleoffinancialmodelingistocreateequationsthatcapturethekeyfactorsparsimoniouslyAnotherimportantprincipleistoattempttodevelopsimplemodelsLinearmodelsarethenpreferredtoquadraticmodels11TheAstrophysicsofFinanceIntheMilkyWayproblem,anastronomershouldspecifyexactlywhatneedstobepredicted,andgiveattentiontothevariablesthatmostaffectitSo,ifhewantstoknowwhenthenextstarwillcomecloseenoughtoSoltodisturbtheOortcloudthenclosestarsneedindividualanalysisdistantstarsmaybetreatedhomogeneously12SpecifyingtheModelInthelastchapterweexamineddiversifyingahomogenousportfolio,andweobservedthatthereweretwokindsofriskdiversifiableorindividualriskNondiversifiableormarketrisk13SpecifyingtheModelWealsoobservedthatinthelimitasthenumberofsecuritiesbecomeslarge,weobtainedtheformulaThisformulatellsusthatthecorrelationsareofcrucialimportanceintherelationshipbetweenaportfolioriskandthestockrisk14SpecifyingtheModelInthehomogenousmodel,wesawthattherewasindividual-andmarket-riskAssumethateachequity’sreturnisthecompositionoftworandomvariables:oneassociatedwiththemarket’sreturnoneassociatedwiththecompany-specificreturn15SpecifyingtheModel:AssumptionsCompany-specificreturnonanystockxisnotcorrelatedtothecompany-specificreturnonanyotherstockyiscorrelatedwiththemarketreturnTherisk-freerateisconstantduringtheinvestmenttheperiod16AssumptionsInvestorsforecastsagreewithrespecttoexpectations,standarddeviations,andcorrelationsofthereturnsofriskysecuritiesThereforeallinvestorsholdriskyassetsinthesamerelativeproportionsInvestorsbehaveoptimallyInequilibrium,pricesadjustsothataggregatedemandforeachsecurityisequaltoitssupply17MarketPortfolioSinceeveryinvestor’srelativeholdingsoftheriskysecurityisthesame,theonlywaytheassetmarketcanclearisifthoseoptimalrelativeproportionsaretheproportionsinwhichtheyarevaluedinthemarketplaceMarketPortfolio18CMLandtheCAPMCAPMsaysthatinequilibrium,anyinvestor’srelativeholdingofriskyassetswillbethesameasinthemarketportfolioDependingontheirriskaversions,differentinvestorsholdportfolioswithdifferentmixesofrisklessassetandthemarketportfolio19CAPMFormula20TheCapitalMarketLine21Activev.PassiveManagementCAPMimpliesthat,onaverage,theperformancesofactiveportfoliomanagersisequaltothatofpassivemanagersemployingjustthemarketportfolioandtherisk-freesecurityDiligentmanagersdooutperformpassivemanagers,butonlytothedegreethattheirdiligenceisrewarded22RewardOnlyforMarketRiskTheriskpremiumonanyindividualsecurityisproportionalonlytoitscontributiontotheriskofthemarketportfolio,anddoesnotdependonitsstand-aloneriskInvestorsarerewardedonlyforbearingmarketrisk2313.2DeterminingtheRiskPremiumontheMarketPortfolioCAPMstatesthattheequilibriumriskpremiumonthemarketportfolioistheproductofvarianceofthemarket,s2Mweightedaverageofthedegreeofriskaversionofholdersofrisk,A24CommentCAPMexplainsthedifferencebetweentherisklessinterestrateandtheexpectedrateofreturnonthemarketportfolio,butnottheirabsolutelevelsTheabsoluteleveloftheequilibriumexpectedrateofreturnonthemarketportfolioisdeterminedbysuchfactorsasexpectedproductivityhouseholdinter-temporalpreferencesforconsumption25Example:ToDetermine‘A’2613.3BetaandRiskPremiumsonIndividualSecuritiesIfriskisdefinedasthatmeasuresuchthatasitincreases,arisk-averseinvestorwouldhavetobecompensatedbyalargerexpectedreturninorderthatshewouldcontinuetoholditinheroptimalportfolio,thenthemeasureofasecurity’sriskisitsbeta,bbtellsyouhowmuchthesecurity’srateofreturnchangeswhenthereturnonthemarketportfoliochanges27Comment:b=1Asecuritywithab=1onaveragerisesandfallswiththemarketa10%(say)unexpectedrise(fall)inthemarketreturnpremiumwill,onaverage,resultina10%rise(fall)inthesecurity’sreturnpremium28Comment:b

³1Asecuritywithab

³1onaveragerisesandfallsmorethanthemarketWithab=1.3,a10%(say)unexpectedrise(fall)inthemarketreturnpremiumwill,onaverage,resultina13%rise(fall)inthesecurity’sreturnpremiumSuchasecurityissaidtobeaggressive29Comment:b

£1Asecuritywithab

£1onaveragerisesandfallslessthanthemarketWithab=0.7,a10%(say)unexpectedrise(fall)inthemarketreturnpremiumwill,onaverage,resultina7%rise(fall)inthesecurity’sreturnpremiumSuchasecurityissaidtobedefensive30CAPMRiskPremiumonanyAssetAccordingthetheCAPM,inequilibrium,theriskpremiumonanyassetisequaltheproductof

b(or‘Beta’)theriskpremiumonthemarketportfolio31TheSecurityMarketLine32SecurityMarketLineTheplotofasecurity’sriskpremium(orsometimessecurityreturns)againstsecuritybetaNotethattheslopeofthesecuritymarketlineisthemarketpremiumByCAPMtheory,allsecuritiesmustfallpreciselyontheSML(henceitsname)33PracticalExampleSomesimulateddatawasgeneratedundertheassumptionsthat:themarketportfolioreturnhasanexpectedvalueof0.15,avolatilityof0.20,andindex0=50thesharezhasareturnof0.12,avolatilityof0.25,andprice0=30(nodividends)thecorrelationbetweenthereturnsis0.90;andtherisk-freerateis0.053435DataSetUsedInordertodisplaythematerialclearly,onlyoneyearofdataisgenerated,andiscollectedmonthly,resultingin13setsofpricesInarealsimulation,muchmoredatamustbecollectedinordertoprovideanadequateconfidenceintervalforparameterestimates36TransformationofPricesintoReturnsThepricesaretransformedintomonthlyholdingperiodreturns(mhpr_Ind,andmhpr_Z)Themhprsaretransformedintoannualrates,compoundedannuallyTheannualratescompoundedannuallyaretransformedtoannualratescompoundedcontinuously37TableofPrices3839FinancialCalculatorsEverythingcouldhavebeendoneusingamodernstandard-issuefinancialorscientificcalculatorRemember,thecorrectratetouseistheannualratecompoundedcontinuously,andthatmonth-to-yearconversionsofstandarddeviationinvolveasquarerootof12Takecaretoenterthemarketrateastheindependentvariable,x40AccuracyIssueWeassumedthatthes’sandr’sareconstants,buttheyarerandomvariablestooInordertoachieveadequateconfidence,alargesampleisneededSmallmovementsinpricearemaskedbytransactionpricesTheresultisacompromisebetweencurrencyandconfidence41ModelandMeasuredValuesofStatisticalParameters42CommentTheillustratedtrajectoryistypicalformonthlydatacollectedoverayearCaution:avoidusingsmalldatasetstoestimateCAPMparameters43RegressionLineTheslopeoftheregressionlineofdependentstockagainstindependentmarketreturnsisbeta4445ObservationAllsecurities,(notjustefficientportfolios)plotontotheSML,iftheyarecorrectlypricedaccordingtotheCAPM46TheBetaofaPortfolioWhendeterminingtheriskofaportfoliousingstandarddeviationresultsinaformulathat’squitecomplexusingbeta,theformulaislinear47ComputingBetaHerearesomeusefulformulaeforcomputingbeta4813.4UsingtheCAPMinPortfolioSelectionWhetherornotCAPMisavalidtheory,indexingisattractivetoinvestorsbecausehistoricallyithasperformedbetterthanmostactivelymanagedportfoliositcostslesstoimplementthatactivemanagement49AParadoxResolvedThelastchapterposedaparadoxwithtwosecuritiesco-existing,onehavingalowerstandarddeviationandhigherreturnthantheotherIfweaccepttheCAPMasavalidtheory,wehavearesolutionBothsecuritieslieontheSML,andbothsecuritiesliebelowtheCML50s-riskandb-riskAsecurityhastwokindsofrisk:riskthatmaybediversifiedaway,andriskthatisassociatedwiththemarketTheCAPMtheorystatesthatthelowerreturnonthes-riskiersecurityimpliesthatithasalowerlevelofmarketb-risk,andthisistheonlyrelevantriskThes-riskiersecuritycontainsrelativelymore(irrelevant)security-specificrisk51ABrandManagerMostinvestorshavetheopportunitytoeliminatemostindividualriskfromtheirportfolio;butconsideraproductmanager’sexposuretoriskIfabrandmanager’sproductsperformwell,promotion,highersalary,andgreaterautonomyfollowperformbadly,humiliation,unemploymentandpovertyfollow52ABrandManagerNowassumethatanewproductisavailableforinclusioninthebrand,butgivenitsb-riskandexpectedreturn,itfallsbelowthesml,andhenceisnotintheinvestors’interestsThemanagerdiscoversthatthenewproductreduceshistotalrisk,andactsinhisowninterests(ratherthantheinvestors’),andacceptstheproduct(agencyproblem)53ThePortfolioManagerRemember(lastchapter)wehadnotresolvedtheissuehowtoevaluatetheperformanceofaportfoliomanager,butgiventheCAPMaresolutionisathandIfyourportfolioisproducingactualreturnswithalowerbetathanthesmlspecifies(withstatisticalsignificance),thenyoushouldcertainlynotbefired54ThePortfolioManagerThefurtherawelldiversifiedportfolioconsistentlyliesabove(below)thesml,thebetter(worse)thefundmanager’sperformanceThereareseveralmeasuresofthisdistance,butthistopicisbetterleftforanotherday55AlphaFundandtheSecurityMarketLine56AlphaFundandtheCapitalMarketLine57HowtoWinInvestmentGamesYoumayhavebeenaskedtotakepartinaninvestmentgamewhereyou‘given’$100,000tomanageforasemester;winnertakesallTheoverwhelmingchancesarethatthewinningstudentusespoorfinancialpractices58HowtoWinInvestmentGames(Continued)Thecriteriaofsuccessforthegamedifferssignificantlyfromreal-lifeinvesting,soyourstrategyforwinningislikelytobedifferentIfyoudiversifyawayunsystematicrisk--evenifyouhavesomekindofinformationaladvantageoveryourcompetition--youareveryunlikelytowinthegameTowin,youneedindividualrisktoseparateyoufromthecrowdUnlikearealinvestoryoudon’thaverealdownside-riskyourupside-potentialmaterializesonlybybeingfirst5913.5ValuationandRegulatingRatesofReturnBetamaybeusedtoobtainthediscountfactorforaprojectAssumeaprojectissimilartotheprojectsundertakenbyanotherfirm,‘Betaful’Betafulisfinancedby20%short-termdebt,and80%equity,anditsbis1.3(assumedebtisrisk-free)Youroptimalcapitalstructureis40%(risk-free)debt,and60%equity60ValuationandRegulatingRatesofReturnAssumethemarketrateis15%,andtherisk-freerateis5%ComputethebetaofBetaful’soperations61ValuationandRegulatingRatesofReturnBetaofBetaful’soperationsisequaltothebetaofournewoperationTofindtherequiredreturnonthenewproject,applytheCAPM62ValuationandRegulatingRatesofReturnAssumethatyourcompanyisjustavehicleforthenewproject,thenthebetaofyourunquotedequityis63ValuationandRegulatingRatesofReturnAssumethatyourcompanyhasanexpecteddividendof$6nextyear,andthatitwillgrowannuallyatarateof4%forever,thevalueofashareis64ValuationandRegulatingRatesofReturnRegulatorsusetheCAPMtoestablisha‘fair’rateofreturnoninvestedcapitalinpublicutilities,giventhelevelofrisk6513.6ModificationsandAlternativestotheCAPMStartinginthe1970sresearchersfoundthatCAPMdidnotseemtofullyexplainthestructureofexpectedreturnsonassets.Aconsensus