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LecturePresentationSoftware

toaccompany

InvestmentAnalysisand

PortfolioManagement

SeventhEdition

by

FrankK.Reilly&KeithC.BrownChapter9LecturePresentationSoftware1Chapter9–MultifactorModelsofRiskandReturnQuestionstobeanswered:Whatisthearbitragepricingtheory(APT)andwhatareitssimilaritiesanddifferencesrelativetotheCAPM?WhatarethemajorassumptionsnotrequiredbytheAPTmodelcomparedtotheCAPM?HowdoyoutesttheAPTbyexamininganomaliesfoundwiththeCAPM?Chapter9–MultifactorModels2Chapter9-MultifactorModelsofRiskandReturnWhataretheempiricaltestresultsrelatedtotheAPT?WhydosomeauthorscontendthattheAPTmodelisuntestable?WhataretheconcernsrelatedtothemultiplefactorsoftheAPTmodel?Chapter9-MultifactorModels3Chapter9-MultifactorModelsofRiskandReturnWhataremultifactormodelsandhowarerelatedtotheAPT?Whatarethestepsnecessaryindevelopingausablemultifactormodel?Whatarethemultifactormodelsinpractice?Howisriskestimatedinamultifactorsetting?Chapter9-MultifactorModels4ArbitragePricingTheory(APT)CAPMiscriticizedbecauseofthedifficultiesinselectingaproxyforthemarketportfolioasabenchmarkAnalternativepricingtheorywithfewerassumptionswasdeveloped:ArbitragePricingTheoryArbitragePricingTheory(APT)5ArbitragePricingTheory-APTThreemajorassumptions: 1.Capitalmarketsareperfectlycompetitive 2.Investorsalwaysprefermorewealthtolesswealthwithcertainty 3.ThestochasticprocessgeneratingassetreturnscanbeexpressedasalinearfunctionofasetofKfactorsorindexesArbitragePricingTheory-APT6AssumptionsofCAPM

ThatWereNotRequiredbyAPTAPTdoesnotassumeAmarketportfoliothatcontainsallriskyassets,andismean-varianceefficientNormallydistributedsecurityreturnsQuadraticutilityfunction

AssumptionsofCAPM

ThatWere7ArbitragePricingTheory(APT)Fori=1toNwhere:=returnonassetiduringaspecifiedtimeperiodRiArbitragePricingTheory(APT)8ArbitragePricingTheory(APT)Fori=1toNwhere:=returnonassetiduringaspecifiedtimeperiod=expectedreturnforassetiRiEiArbitragePricingTheory(APT)9ArbitragePricingTheory(APT)Fori=1toNwhere:=returnonassetiduringaspecifiedtimeperiod=expectedreturnforasseti=reactioninasseti’sreturnstomovementsinacommonfactorRiEibikArbitragePricingTheory(APT)10ArbitragePricingTheory(APT)Fori=1toNwhere:=returnonassetiduringaspecifiedtimeperiod=expectedreturnforasseti=reactioninasseti’sreturnstomovementsinacommonfactor=acommonfactorwithazeromeanthatinfluencesthereturnsonallassetsRiEibikArbitragePricingTheory(APT)11ArbitragePricingTheory(APT)Fori=1toNwhere:=returnonassetiduringaspecifiedtimeperiod=expectedreturnforasseti=reactioninasseti’sreturnstomovementsinacommonfactor=acommonfactorwithazeromeanthatinfluencesthereturnsonallassets=auniqueeffectonasseti’sreturnthat,byassumption,iscompletelydiversifiableinlargeportfoliosandhasameanofzeroRiEibikArbitragePricingTheory(APT)12ArbitragePricingTheory(APT)Fori=1toNwhere:=returnonassetiduringaspecifiedtimeperiod=expectedreturnforasseti=reactioninasseti’sreturnstomovementsinacommonfactor=acommonfactorwithazeromeanthatinfluencesthereturnsonallassets=auniqueeffectonasseti’sreturnthat,byassumption,iscompletelydiversifiableinlargeportfoliosandhasameanofzero=numberofassetsRiEibikNArbitragePricingTheory(APT)13ArbitragePricingTheory(APT)Multiplefactorsexpectedtohaveanimpactonallassets:ArbitragePricingTheory(APT)14ArbitragePricingTheory(APT)Multiplefactorsexpectedtohaveanimpactonallassets:InflationArbitragePricingTheory(APT)15ArbitragePricingTheory(APT)Multiplefactorsexpectedtohaveanimpactonallassets:InflationGrowthinGNPArbitragePricingTheory(APT)16ArbitragePricingTheory(APT)Multiplefactorsexpectedtohaveanimpactonallassets:InflationGrowthinGNPMajorpoliticalupheavalsArbitragePricingTheory(APT)17ArbitragePricingTheory(APT)Multiplefactorsexpectedtohaveanimpactonallassets:InflationGrowthinGNPMajorpoliticalupheavalsChangesininterestratesArbitragePricingTheory(APT)18ArbitragePricingTheory(APT)Multiplefactorsexpectedtohaveanimpactonallassets:InflationGrowthinGNPMajorpoliticalupheavalsChangesininterestratesAndmanymore….ArbitragePricingTheory(APT)19ArbitragePricingTheory(APT)Multiplefactorsexpectedtohaveanimpactonallassets:InflationGrowthinGNPMajorpoliticalupheavalsChangesininterestratesAndmanymore….ContrastwithCAPMinsistencethatonlybetaisrelevantArbitragePricingTheory(APT)20ArbitragePricingTheory(APT)BikdeterminehoweachassetreactstothiscommonfactorEachassetmaybeaffectedbygrowthinGNP,buttheeffectswilldifferInapplicationofthetheory,thefactorsarenotidentifiedSimilartotheCAPM,theuniqueeffectsareindependentandwillbediversifiedawayinalargeportfolioArbitragePricingTheory(APT)21ArbitragePricingTheory(APT)APTassumesthat,inequilibrium,thereturnonazero-investment,zero-systematic-riskportfolioiszerowhentheuniqueeffectsarediversifiedawayTheexpectedreturnonanyasseti(Ei)canbeexpressedas:ArbitragePricingTheory(APT)22ArbitragePricingTheory(APT)where:=theexpectedreturnonanassetwithzerosystematicriskwhere=theriskpremiumrelatedtoeachofthecommonfactors-forexampletheriskpremiumrelatedtointerestrateriskbi=thepricingrelationshipbetweentheriskpremiumandasseti-thatishowresponsiveassetiistothiscommonfactorKArbitragePricingTheory(APT)23ExampleofTwoStocks

andaTwo-FactorModel=changesintherateofinflation.Theriskpremiumrelatedtothisfactoris1percentforevery1percentchangeintherate=percentgrowthinrealGNP.Theaverageriskpremiumrelatedtothisfactoris2percentforevery1percentchangeintherate=therateofreturnonazero-systematic-riskasset(zerobeta:boj=0)is3percentExampleofTwoStocks

andaT24ExampleofTwoStocks

andaTwo-FactorModel=theresponseofassetXtochangesintherateofinflationis0.50=theresponseofassetYtochangesintherateofinflationis2.00=theresponseofassetXtochangesinthegrowthrateofrealGNPis1.50=theresponseofassetYtochangesinthegrowthrateofrealGNPis1.75ExampleofTwoStocks

andaT25ExampleofTwoStocks

andaTwo-FactorModel

=.03+(.01)bi1+(.02)bi2Ex=.03+(.01)(0.50)+(.02)(1.50)=.065=6.5%

Ey=.03+(.01)(2.00)+(.02)(1.75)=.085=8.5%ExampleofTwoStocks

andaT26Roll-RossStudyThemethodologyusedinthestudyisasfollows:Estimatetheexpectedreturnsandthefactorcoefficientsfromtime-seriesdataonindividualassetreturnsUsetheseestimatestotestthebasiccross-sectionalpricingconclusionimpliedbytheAPTTheauthorsconcludedthattheevidencegenerallysupportedtheAPT,butacknowledgedthattheirtestswerenotconclusiveRoll-RossStudyThemethodology27Extensionsofthe

Roll-RossStudyCho,Elton,andGruberexaminedthenumberoffactorsinthereturn-generatingprocessthatwerepricedDhrymes,Friend,andGultekin(DFG)reexaminedtechniquesandtheirlimitationsandfoundthenumberoffactorsvarieswiththesizeoftheportfolioExtensionsofthe

Roll-RossS28TheAPTandAnomaliesSmall-firmeffectReinganum-resultsinconsistentwiththeAPTChen-supportedtheAPTmodeloverCAPMJanuaryanomalyGultekin-APTnotbetterthanCAPMBurmeisterandMcElroy-effectnotcapturedbymodel,butstillrejectedCAPMinfavorofAPTTheAPTandAnomaliesSmall-fir29Shanken’sChallengetoTestabilityoftheAPTIfreturnsarenotexplainedbyamodel,itisnotconsideredrejectionofamodel;howeverifthefactorsdoexplainreturns,itisconsideredsupportAPThasnoadvantagebecausethefactorsneednotbeobservable,soequivalentsetsmayconformtodifferentfactorstructuresEmpiricalformulationoftheAPTmayyielddifferentimplicationsregardingtheexpectedreturnsforagivensetofsecuritiesThus,thetheorycannotexplaindifferentialreturnsbetweensecuritiesbecauseitcannotidentifytherelevantfactorstructurethatexplainsthedifferentialreturnsShanken’sChallengetoTestabi30AlternativeTestingTechniquesJobsonproposesAPTtestingwithamultivariatelinearregressionmodelBrownandWeinsteinproposeusingabilinearparadigmOthersproposenewmethodologiesAlternativeTestingTechniques31MultifactorModelsandRiskEstimation Inamultifactormodel,theinvestorchoosestheexactnumberandidentityofriskfactorsMultifactorModelsandRiskEs32MultifactorModelsandRiskEstimationMultifactorModelsinPracticeMacroeconomic-BasedRiskFactorModelsMultifactorModelsandRiskEs33MultifactorModelsandRiskEstimationMultifactorModelsinPracticeMacroeconomic-BasedRiskFactorModelsMicroeconomic-BasedRiskFactorModelsMultifactorModelsandRiskEs34MultifactorModelsandRiskEstimationMultifactorModelsinPracticeMacroeconomic-BasedRiskFactorModelsMicroeconomic-BasedRiskFactorModelsExtensionsofCharacteristic-BasedRiskFactorModelsMultifactorModelsandRiskEs35EstimatingRiskinaMultifactorSetting:ExamplesEstimatingExpectedReturnsforIndividualStocksEstimatingRiskinaMultifact36EstimatingRiskinaMultifactorSetting:ExamplesEstimatingExpectedReturnsforIndividualStocksComparingMutualFundRiskExposuresEstimatingRiskinaMultifact37TheInternet

InvestmentsOnlineTheInternet

InvestmentsOnlin38Futuretopics

Chapter10

AnalysisofFinancialStatementsFuturetopics

Chapter10Analy39LecturePresentationSoftware

toaccompany

InvestmentAnalysisand

PortfolioManagement

SeventhEdition

by

FrankK.Reilly&KeithC.BrownChapter9LecturePresentationSoftware40Chapter9–MultifactorModelsofRiskandReturnQuestionstobeanswered:Whatisthearbitragepricingtheory(APT)andwhatareitssimilaritiesanddifferencesrelativetotheCAPM?WhatarethemajorassumptionsnotrequiredbytheAPTmodelcomparedtotheCAPM?HowdoyoutesttheAPTbyexamininganomaliesfoundwiththeCAPM?Chapter9–MultifactorModels41Chapter9-MultifactorModelsofRiskandReturnWhataretheempiricaltestresultsrelatedtotheAPT?WhydosomeauthorscontendthattheAPTmodelisuntestable?WhataretheconcernsrelatedtothemultiplefactorsoftheAPTmodel?Chapter9-MultifactorModels42Chapter9-MultifactorModelsofRiskandReturnWhataremultifactormodelsandhowarerelatedtotheAPT?Whatarethestepsnecessaryindevelopingausablemultifactormodel?Whatarethemultifactormodelsinpractice?Howisriskestimatedinamultifactorsetting?Chapter9-MultifactorModels43ArbitragePricingTheory(APT)CAPMiscriticizedbecauseofthedifficultiesinselectingaproxyforthemarketportfolioasabenchmarkAnalternativepricingtheorywithfewerassumptionswasdeveloped:ArbitragePricingTheoryArbitragePricingTheory(APT)44ArbitragePricingTheory-APTThreemajorassumptions: 1.Capitalmarketsareperfectlycompetitive 2.Investorsalwaysprefermorewealthtolesswealthwithcertainty 3.ThestochasticprocessgeneratingassetreturnscanbeexpressedasalinearfunctionofasetofKfactorsorindexesArbitragePricingTheory-APT45AssumptionsofCAPM

ThatWereNotRequiredbyAPTAPTdoesnotassumeAmarketportfoliothatcontainsallriskyassets,andismean-varianceefficientNormallydistributedsecurityreturnsQuadraticutilityfunction

AssumptionsofCAPM

ThatWere46ArbitragePricingTheory(APT)Fori=1toNwhere:=returnonassetiduringaspecifiedtimeperiodRiArbitragePricingTheory(APT)47ArbitragePricingTheory(APT)Fori=1toNwhere:=returnonassetiduringaspecifiedtimeperiod=expectedreturnforassetiRiEiArbitragePricingTheory(APT)48ArbitragePricingTheory(APT)Fori=1toNwhere:=returnonassetiduringaspecifiedtimeperiod=expectedreturnforasseti=reactioninasseti’sreturnstomovementsinacommonfactorRiEibikArbitragePricingTheory(APT)49ArbitragePricingTheory(APT)Fori=1toNwhere:=returnonassetiduringaspecifiedtimeperiod=expectedreturnforasseti=reactioninasseti’sreturnstomovementsinacommonfactor=acommonfactorwithazeromeanthatinfluencesthereturnsonallassetsRiEibikArbitragePricingTheory(APT)50ArbitragePricingTheory(APT)Fori=1toNwhere:=returnonassetiduringaspecifiedtimeperiod=expectedreturnforasseti=reactioninasseti’sreturnstomovementsinacommonfactor=acommonfactorwithazeromeanthatinfluencesthereturnsonallassets=auniqueeffectonasseti’sreturnthat,byassumption,iscompletelydiversifiableinlargeportfoliosandhasameanofzeroRiEibikArbitragePricingTheory(APT)51ArbitragePricingTheory(APT)Fori=1toNwhere:=returnonassetiduringaspecifiedtimeperiod=expectedreturnforasseti=reactioninasseti’sreturnstomovementsinacommonfactor=acommonfactorwithazeromeanthatinfluencesthereturnsonallassets=auniqueeffectonasseti’sreturnthat,byassumption,iscompletelydiversifiableinlargeportfoliosandhasameanofzero=numberofassetsRiEibikNArbitragePricingTheory(APT)52ArbitragePricingTheory(APT)Multiplefactorsexpectedtohaveanimpactonallassets:ArbitragePricingTheory(APT)53ArbitragePricingTheory(APT)Multiplefactorsexpectedtohaveanimpactonallassets:InflationArbitragePricingTheory(APT)54ArbitragePricingTheory(APT)Multiplefactorsexpectedtohaveanimpactonallassets:InflationGrowthinGNPArbitragePricingTheory(APT)55ArbitragePricingTheory(APT)Multiplefactorsexpectedtohaveanimpactonallassets:InflationGrowthinGNPMajorpoliticalupheavalsArbitragePricingTheory(APT)56ArbitragePricingTheory(APT)Multiplefactorsexpectedtohaveanimpactonallassets:InflationGrowthinGNPMajorpoliticalupheavalsChangesininterestratesArbitragePricingTheory(APT)57ArbitragePricingTheory(APT)Multiplefactorsexpectedtohaveanimpactonallassets:InflationGrowthinGNPMajorpoliticalupheavalsChangesininterestratesAndmanymore….ArbitragePricingTheory(APT)58ArbitragePricingTheory(APT)Multiplefactorsexpectedtohaveanimpactonallassets:InflationGrowthinGNPMajorpoliticalupheavalsChangesininterestratesAndmanymore….ContrastwithCAPMinsistencethatonlybetaisrelevantArbitragePricingTheory(APT)59ArbitragePricingTheory(APT)BikdeterminehoweachassetreactstothiscommonfactorEachassetmaybeaffectedbygrowthinGNP,buttheeffectswilldifferInapplicationofthetheory,thefactorsarenotidentifiedSimilartotheCAPM,theuniqueeffectsareindependentandwillbediversifiedawayinalargeportfolioArbitragePricingTheory(APT)60ArbitragePricingTheory(APT)APTassumesthat,inequilibrium,thereturnonazero-investment,zero-systematic-riskportfolioiszerowhentheuniqueeffectsarediversifiedawayTheexpectedreturnonanyasseti(Ei)canbeexpressedas:ArbitragePricingTheory(APT)61ArbitragePricingTheory(APT)where:=theexpectedreturnonanassetwithzerosystematicriskwhere=theriskpremiumrelatedtoeachofthecommonfactors-forexampletheriskpremiumrelatedtointerestrateriskbi=thepricingrelationshipbetweentheriskpremiumandasseti-thatishowresponsiveassetiistothiscommonfactorKArbitragePricingTheory(APT)62ExampleofTwoStocks

andaTwo-FactorModel=changesintherateofinflation.Theriskpremiumrelatedtothisfactoris1percentforevery1percentchangeintherate=percentgrowthinrealGNP.Theaverageriskpremiumrelatedtothisfactoris2percentforevery1percentchangeintherate=therateofreturnonazero-systematic-riskasset(zerobeta:boj=0)is3percentExampleofTwoStocks

andaT63ExampleofTwoStocks

andaTwo-FactorModel=theresponseofassetXtochangesintherateofinflationis0.50=theresponseofassetYtochangesintherateofinflationis2.00=theresponseofassetXtochangesinthegrowthrateofrealGNPis1.50=theresponseofassetYtochangesinthegrowthrateofrealGNPis1.75ExampleofTwoStocks

andaT64ExampleofTwoStocks

andaTwo-FactorModel

=.03+(.01)bi1+(.02)bi2Ex=.03+(.01)(0.50)+(.02)(1.50)=.065=6.5%

Ey=.03+(.01)(2.00)+(.02)(1.75)=.085=8.5%ExampleofTwoStocks

andaT65Roll-RossStudyThemethodologyusedinthestudyisasfollows:Estimatetheexpectedreturnsandthefactorcoefficientsfromtime-seriesdataonindividualassetreturnsUsetheseestimatestotestthebasiccross-sectionalpricingconclusionimpliedbytheAPTTheauthorsconcludedthattheevidencegenerallysupportedtheAPT,butacknowledgedthattheirtestswerenotconclusiveRoll-RossStudyThemethodology66Extensionsofthe

Roll-RossStudyCho,Elton,andGruberexaminedthenumberoffactorsinthereturn-generatingprocessthatwerepricedDhrymes,Friend,andGultekin(DFG)reexaminedtechniquesandtheirlimitationsandfoundthenumberoffactorsvarieswiththesizeoftheportfolioExtensionsofthe

Roll-RossS67TheAPTandAnomaliesSmall-firmeffectReinganum-resultsinconsistentwiththeAPTChen-supportedtheAPTmodeloverCAPMJanuaryanomalyGultekin-APTnotbetterthanCAPMBurmeisterandMcElroy-effectnotcapturedbymodel,butstillrejectedCAPMinfavorofAPTTheAPTandAnomaliesS

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