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TightropewalkerNikWallendamakesChicagocrossingshttp WallendaFall AnAlternativeViewofRiskandReturn TheArbitragePricingTheory Chapter12 Copyright 2010bytheMcGraw HillCompanies Inc Allrightsreserved McGraw Hill Irwin ChapterOutline 12 1Introduction12 2SystematicRiskandBetas12 3PortfoliosandFactorModels12 4BetasandExpectedReturns12 5TheCapitalAssetPricingModelandtheArbitragePricingTheory12 6EmpiricalApproachestoAssetPricing KeyConceptsandSkills Discusstherelativeimportanceofsystematicandunsystematicriskindeterminingaportfolio sreturnCompareandcontrasttheCAPMandArbitragePricingTheory ArbitragePricingTheory StephenRossFrancoModiglianiProfessorofFinancialEconomicsProfessorofFinanceattheMITSloanSchoolofManagement StephenRossFrancoModiglianiProfessorofFinancialEconomicsProfessorofFinanceattheMITSloanSchoolofManagement LawofOnePrice Arbitragearisesifaninvestorcanconstructazeroinvestmentportfoliowithasureprofit ArbitragePricingTheory Sincenoinvestmentisrequired aninvestorcancreatelargepositionstosecurelargelevelsofprofit Inefficientmarkets profitablearbitrageopportunitieswillquicklydisappear marketisatequilibrium Arbitrageisthebestexaminer TotalRisk Totalrisk systematicrisk unsystematicriskForwell diversifiedportfolios unsystematicriskisverysmall thetotalriskforadiversifiedportfolioisessentiallyequivalenttothesystematicrisk Risk SystematicandUnsystematic SystematicRisk m NonsystematicRisk n 2 Totalrisk b theresponseofthestock sreturntoasystematicrisk 12 2SystematicRiskandBetas B theresponseofthestock sreturntoasystematicrisk IntheCAPM bmeasurestheresponsivenessofasecurity sreturntoaspecificriskfactor thereturnonthemarketportfolio SystematicRiskandBetas threesystematicrisks inflation GNPgrowth andthedollar eurospotexchangerate S SystematicRiskandBetas Example Supposewehavemadethefollowingestimates bI 2 30bGNP 1 50bS 0 50unanticipateddevelopmentcontributes1 tothereturn SystematicRiskandBetas Example theinflationratewasexpectedtobe3 butinfactwas8 duringthetimeperiod then FI Surpriseintheinflationrate actual expected 8 3 5 SystematicRiskandBetas Example IftherateofGNPgrowthwasexpectedtobe4 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 12 3PortfoliosandFactorModels 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 12 4BetasandExpectedReturns RelationshipBetweenb ExpectedReturn CAPM Expectedreturn b A B C D SML securitymarketline Marketportfolioandthesinglefactor Expectedreturn b securitymarketline E R Rf B Rm Rf identicaltothatofCAPM E Rm 12 5TheCapitalAssetPricingModelandtheArbitragePricingTheory APTappliestowelldiversifiedportfoliosandnotnecessarilytoindividualstocks WithAPTitispossibleforsomeindividualstockstobemispriced notlieontheSML APTismoregeneralinthatitgetstoanexpectedreturnandbetarelationshipwithouttheassumptionofthemarketportfolio APTcanbeextendedtomultifactormodels 12 6EmpiricalApproachestoAssetPricing Botharerisk basedmodels Empiricalmethodsaremoreonlookingforsomeregularitiesinthehistoricalrecord Beawarethatcorrelationdoesnotimplycausality Valueportfolio lowP EGrowthportfolio HighP E NobelPrizeLaureateEugeneF FamainStockholm December2013 Fama French3 factormodel FamaandFrenchstartedwiththeobservationthattwoclassesofstockshavetendedtodobetterthanthemarketasawhole i smallcapsand ii stockswithahighbook to marketratio BtM customarilycalledvaluestocks contrastedwithgrowthstocks TheythenaddedtwofactorstoCAPMtoreflectaportfolio sexposu

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