第十一章 套利定价理论

McGraw-Hill/IrwinCopyright©2002byTheMcGraw-HillCompanies,Inc.Allrightsreserved.11-0ChapterOutline11.1FactorModels:Announcements,Surprises,andExpectedReturns11.2Risk:SystematicandUnsystematic11.3SystematicRiskandBetas11.4PortfoliosandFactorModels11.5BetasandExpectedReturns11.6TheCapitalAssetPricingModelandtheArbitragePricingTheory11.7ParametricApproachestoAssetPricing11.8SummaryandConclusionsMcGraw-Hill/IrwinCopyright©2002byTheMcGraw-HillCompanies,Inc.Allrightsreserved.11-1ArbitragePricingTheoryArbitrage-arisesifaninvestorcanconstructazeroinvestmentportfoliowithasureprofit.•Sincenoinvestmentisrequired,aninvestorcancreatelargepositionstosecurelargelevelsofprofit.•Inefficientmarkets,profitablearbitrageopportunitieswillquicklydisappear.McGraw-Hill/IrwinCopyright©2002byTheMcGraw-HillCompanies,Inc.Allrightsreserved.11-211.1FactorModels:Announcements,Surprises,andExpectedReturns•Thereturnonanysecurityconsistsoftwoparts.–Firsttheexpectedreturns–Secondistheunexpectedorriskyreturns.•Awaytowritethereturnonastockinthecomingmonthis:returntheofpartunexpectedtheisreturntheofpartexpectedtheiswhereURURRMcGraw-Hill/IrwinCopyright©2002byTheMcGraw-HillCompanies,Inc.Allrightsreserved.11-311.1FactorModels:Announcements,Surprises,andExpectedReturns•Anyannouncementcanbebrokendownintotwoparts,theanticipatedorexpectedpartandthesurpriseorinnovation:•Announcement=Expectedpart+Surprise.•Theexpectedpartofanyannouncementispartoftheinformationthemarketusestoformtheexpectation,Rofthereturnonthestock.Thesurpriseisthenewsthatinfluencestheunanticipatedreturnonthestock,U.McGraw-Hill/IrwinCopyright©2002byTheMcGraw-HillCompanies,Inc.Allrightsreserved.11-411.2Risk:SystematicandUnsystematic•Asystematicriskisanyriskthataffectsalargenumberofassets,eachtoagreaterorlesserdegree.•Anunsystematicriskisariskthatspecificallyaffectsasingleassetorsmallgroupofassets.•Unsystematicriskcanbediversifiedaway.•Examplesofsystematicriskincludeuncertaintyaboutgeneraleconomicconditions,suchasGNP,interestratesorinflation.•Ontheotherhand,announcementsspecifictoacompany,suchasagoldminingcompanystrikinggold,areexamplesofunsystematicrisk.McGraw-Hill/IrwinCopyright©2002byTheMcGraw-HillCompanies,Inc.Allrightsreserved.11-511.2Risk:SystematicandUnsystematicSystematicRisk;mNonsystematicRisk;nTotalrisk;UWecanbreakdowntherisk,U,ofholdingastockintotwocomponents:systematicriskandunsystematicrisk:riskicunsystemattheisrisksystematictheiswherebecomesεmεmRRURRMcGraw-Hill/IrwinCopyright©2002byTheMcGraw-HillCompanies,Inc.Allrightsreserved.11-611.3SystematicRiskandBetas•Thebetacoefficient,b,tellsustheresponseofthestock’sreturntoasystematicrisk.•IntheCAPM,bmeasuredtheresponsivenessofasecurity’sreturntoaspecificriskfactor,thereturnonthemarketportfolio.)()(2,MMiiRRRCovb•Weshallnowconsidermanytypesofsystematicrisk.McGraw-Hill/IrwinCopyright©2002byTheMcGraw-HillCompanies,Inc.Allrightsreserved.11-711.3SystematicRiskandBetas•Forexample,supposewehaveidentifiedthreesystematicrisksonwhichwewanttofocus:1.Inflation2.GDPgrowth3.Thedollar-eurospotexchangerate,S($,€)•Ourmodelis:riskicunsystemattheisbetarateexchangespottheisbetaGDPtheisbetainflationtheisεβββεFβFβFβRRεmRRSGDPISSGDPGDPIIMcGraw-Hill/IrwinCopyright©2002byTheMcGraw-HillCompanies,Inc.Allrightsreserved.11-8SystematicRiskandBetas:Example•Supposewehavemadethefollowingestimates:1.bI=-2.302.bGDP=1.503.bS=0.50.•Finally,thefirmwasabletoattracta“superstar”CEOandthisunanticipateddevelopmentcontributes1%tothereturn.εFβFβFβRRSSGDPGDPII%1ε%150.050.130.2SGDPIFFFRRMcGraw-Hill/IrwinCopyright©2002byTheMcGraw-HillCompanies,Inc.Allrightsreserved.11-9SystematicRiskandBetas:ExampleWemustdecidewhatsurprisestookplaceinthesystematicfactors.Ifitwasthecasethattheinflationratewasexpectedtobeby3%,butinfactwas8%duringthetimeperiod,thenFI=Surpriseintheinflationrate=actual–expected=8%-3%=5%%150.050.130.2SGDPIFFFRR%150.050.1%530.2SGDPFFRRMcGraw-Hill/IrwinCopyright©2002byTheMcGraw-HillCompanies,Inc.Allrightsreserved.11-10SystematicRiskandBetas:ExampleIfitwasthecasethattherateofGDPgrowthwasexpectedtobe4%,butinfactwas1%,thenFGDP=SurpriseintherateofGDPgrowth=actual–expected=1%-4%=-3%%150.050.1%530.2SGDPFFRR%150.0%)3(50.1%530.2SFRRMcGraw-Hill/IrwinCopyright©2002byTheMcGraw-HillCompanies,Inc.Allrightsreserved.11-11SystematicRiskandBetas:ExampleIfitwasthecasethatdollar-eurospotexchangerate,S($,€),wasexpectedtoincreaseby10%,butinfactremainedstableduringthetimeperiod,thenFS=Surpriseintheexchangerate=actual–expected=0%-10%=-10%%150.0%)3(50.1%530.2SFRR%1%)10(50.0%)3(50.1%530.2RRMcGraw-Hill/IrwinCopyright©2002byTheMcGraw-HillCompanies,Inc.Allrightsreserved.11-12SystematicRiskandBetas:ExampleFinally,ifitwasthecasethattheexpectedreturnonthestockwas8%,then%150.0%)3(50.1%530.2SFRR%12%1%)10(50.0%)3(50.1%530.2%8RR%8RMcGraw-Hill/IrwinCopyright©2002byTheMcGraw-HillCompanies,Inc.Allrightsreserved.11-1311.4PortfoliosandFactorModels•Nowletusconsiderwhathappenstoportfoliosofstockswheneachofth