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AnAlternativeViewofRiskandReturnTheArbitragePricingTheory KeyConceptsandSkills Understandthedecompositionofasecurity sreturnintoexpectedandunexpectedcomponentsDiscusstherelativeimportanceofsystematicandunsystematicriskindeterminingaportfolio sreturnCompareandcontrasttheCAPMandArbitragePricingTheory ChapterOutline 11 1FactorModels Announcements Surprises andExpectedReturns11 2Risk SystematicandUnsystematic11 3SystematicRiskandBetas11 4PortfoliosandFactorModels11 5BetasandExpectedReturns11 6TheCapitalAssetPricingModelandtheArbitragePricingTheory11 7EmpiricalApproachestoAssetPricing ArbitragePricingTheory Arbitragearisesifaninvestorcanconstructazeroinvestmentportfoliowithasureprofit Sincenoinvestmentisrequired aninvestorcancreatelargepositionstosecurelargelevelsofprofit Inefficientmarkets profitablearbitrageopportunitieswillquicklydisappear 11 1FactorModels Announcements Surprises andExpectedReturns Thereturnonanysecurityconsistsoftwoparts First theexpectedreturnsSecond theunexpectedorriskyreturnsAwaytowritethereturnonastockinthecomingmonthis FactorModels Announcements Surprises andExpectedReturns Anyannouncementcanbebrokendownintotwoparts theanticipated orexpected partandthesurprise orinnovation Announcement Expectedpart Surprise Theexpectedpartofanyannouncementisthepartoftheinformationthemarketusestoformtheexpectation R ofthereturnonthestock Thesurpriseisthenewsthatinfluencestheunanticipatedreturnonthestock U 11 2Risk SystematicandUnsystematic Asystematicriskisanyriskthataffectsalargenumberofassets eachtoagreaterorlesserdegree Anunsystematicriskisariskthatspecificallyaffectsasingleassetorsmallgroupofassets Unsystematicriskcanbediversifiedaway Examplesofsystematicriskincludeuncertaintyaboutgeneraleconomicconditions suchasGNP interestratesorinflation Ontheotherhand announcementsspecifictoasinglecompanyareexamplesofunsystematicrisk Risk SystematicandUnsystematic SystematicRisk m NonsystematicRisk n 2 Totalrisk Wecanbreakdownthetotalriskofholdingastockintotwocomponents systematicriskandunsystematicrisk 11 3SystematicRiskandBetas Thebetacoefficient b tellsustheresponseofthestock sreturntoasystematicrisk IntheCAPM bmeasurestheresponsivenessofasecurity sreturntoaspecificriskfactor thereturnonthemarketportfolio Weshallnowconsiderothertypesofsystematicrisk SystematicRiskandBetas Forexample supposewehaveidentifiedthreesystematicrisks inflation GNPgrowth andthedollar eurospotexchangerate S Ourmodelis SystematicRiskandBetas Example Supposewehavemadethefollowingestimates bI 2 30bGNP 1 50bS 0 50Finally thefirmwasabletoattracta superstar CEO andthisunanticipateddevelopmentcontributes1 tothereturn SystematicRiskandBetas Example Wemustdecidewhatsurprisestookplaceinthesystematicfactors Ifitwerethecasethattheinflationratewasexpectedtobe3 butinfactwas8 duringthetimeperiod then FI Surpriseintheinflationrate actual expected 8 3 5 SystematicRiskandBetas Example IfitwerethecasethattherateofGNPgrowthwasexpectedtobe4 butinfactwas1 then FGNP SurpriseintherateofGNPgrowth actual expected 1 4 3 SystematicRiskandBetas Example Ifitwerethecasethatthedollar eurospotexchangerate S wasexpectedtoincreaseby10 butinfactremainedstableduringthetimeperiod then FS Surpriseintheexchangerate actual expected 0 10 10 SystematicRiskandBetas Example Finally ifitwerethecasethattheexpectedreturnonthestockwas8 then 11 4PortfoliosandFactorModels Nowletusconsiderwhathappenstoportfoliosofstockswheneachofthestocksfollowsaone factormodel WewillcreateportfoliosfromalistofNstocksandwillcapturethesystematicriskwitha1 factormodel Theithstockinthelisthasreturn RelationshipBetweentheReturnontheCommonFactor ExcessReturn Excessreturn ThereturnonthefactorF Ifweassumethatthereisnounsystematicrisk thenei 0 RelationshipBetweentheReturnontheCommonFactor ExcessReturn Excessreturn ThereturnonthefactorF Ifweassumethatthereisnounsystematicrisk thenei 0 RelationshipBetweentheReturnontheCommonFactor ExcessReturn Excessreturn ThereturnonthefactorF Differentsecuritieswillhavedifferentbetas PortfoliosandDiversification Weknowthattheportfolioreturnistheweightedaverageofthereturnsontheindividualassetsintheportfolio PortfoliosandDiversification Thereturnonanyportfolioisdeterminedbythreesetsofparameters Inalargeportfolio thethirdrowofthisequationdisappearsastheunsystematicriskisdiversifiedaway PortfoliosandDiversification Sothereturnonadiversifiedportfolioisdeterminedbytwosetsofparameters Theweightedaverageofexpectedreturns TheweightedaverageofthebetastimesthefactorF Inalargeportfolio theonlysourceofuncertaintyistheportfolio ssensitivitytothefactor 11 5BetasandExpectedReturns Thereturnonadiversifiedportfolioisthesumoftheexpectedreturnplusthesensitivityoftheportfoliotothefactor RelationshipBetweenb ExpectedReturn Ifshareholdersareignoringunsystematicrisk onlythesystematicriskofastockcanberelatedtoitsexpectedreturn RelationshipBetweenb ExpectedReturn Expectedreturn b A B C D SML 11 6TheCapitalAssetPricingModelandtheArbitragePricingTheory APTappliestowelldiversifiedportfoliosandnotnecessarilytoindividualstocks WithAPTitispossibleforsomeindividualstockstobemispriced notlieontheSML APTismoregeneralinthatitgetstoanexpectedreturnandbetarelationshipwithouttheassumptionofthemarketportfolio APTcanbeextendedtomultifactormodels 11 7EmpiricalApproachestoAssetPricing BoththeCAPMandAPTarerisk basedmodels Empiricalmethodsarebasedlessontheoryandmoreonlookingforsomeregularitiesinthehistoricalrecord Beawarethatcorrelationdoesnotimplycausality Relatedtoempirica

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