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1、Chapter10ArbitragePricingTheyMultifactModelsofRiskReturn101Copyright?2014McGrawHillEducation.Allrightsreserved.NoreproductiondistributionwithoutthepriwrittenconsentofMcGrawHillEducation.CHAPTER10:ARBITRAGEPRICINGTHEYMULT

2、IFACTMODELSOFRISKRETURNPROBLEMSETS1.Therevisedestimateoftheexpectedrateofreturnonthestockwouldbetheoldestimateplusthesumoftheproductsoftheunexpectedchangeineachfacttimestherespectivesensitivitycoefficient:Revisedestimate

3、=12%[(12%)(0.53%)]=15.5%NotethattheIPestimateiscomputedas:1(5%3%)theIRestimateiscomputedas:0.5(8%5%).2.TheAPTfactsmustcrelatewithmajsourcesofuncertaintyi.e.sourcesofuncertaintythatareofconcerntomanyinvests.Researcherssho

4、uldinvestigatefactsthatcrelatewithuncertaintyinconsumptioninvestmentopptunities.GDPtheinflationrateinterestratesareamongthefactsthatcanbeexpectedtodetermineriskpremiums.Inparticularindustrialproduction(IP)isagoodindicato

5、fchangesinthebusinesscycle.ThusIPisacidatefafactthatishighlycrelatedwithuncertaintiesthathavetodowithinvestmentconsumptionopptunitiesintheeconomy.3.Anypatternofreturnscanbeexplainedifwearefreetochooseanindefinitelylargen

6、umberofexplanatyfacts.Ifatheyofassetpricingistohavevalueitmustexplainreturnsusingareasonablylimitednumberofexplanatyvariables(i.e.systematicfactssuchasunemploymentlevelsGDPoilprices).4.Equation10.11applieshere:E(rp)=rfβP

7、1[E(r1)?rf]βP2[E(r2)–rf]Weneedtofindtheriskpremium(RP)feachofthetwofacts:RP1=[E(r1)?rf]RP2=[E(r2)?rf]Indertodosowesolvethefollowingsystemoftwoequationswithtwounknowns:.31=.06(1.5RP1)(2.0RP2).27=.06(2.2RP1)[(–0.2)RP2]Thes

8、olutiontothissetofequationsisRP1=10%RP2=5%ThustheexpectedreturnbetarelationshipisE(rP)=6%(βP110%)(βP25%)Chapter10ArbitragePricingTheyMultifactModelsofRiskReturn103Copyright?2014McGrawHillEducation.Allrightsreserved.Norep

9、roductiondistributionwithoutthepriwrittenconsentofMcGrawHillEducation.Fn=20stocks(i.e.long10stockssht10stocks)theinvestwillhavea$100000position(eitherlongsht)ineachstock.marketexposureiszerobutfirmspecificriskhasnotbeenf

10、ullydiversified.Thevarianceofdollarreturnsfromthepositionsinthe20stocksis20[(1000000.30)2]=18000000000Thestarddeviationofdollarreturnsis$134164.b.Ifn=50stocks(25stockslong25stockssht)theinvestwillhavea$40000positionineac

11、hstockthevarianceofdollarreturnsis50[(400000.30)2]=7200000000Thestarddeviationofdollarreturnsis$84853.Similarlyifn=100stocks(50stockslong50stockssht)theinvestwillhavea$20000positionineachstockthevarianceofdollarreturnsis

12、100[(200000.30)2]=3600000000Thestarddeviationofdollarreturnsis$60000.Noticethatwhenthenumberofstocksincreasesbyafactof5(i.e.from20to100)starddeviationdecreasesbyafactof=2.23607(from5$134164to$60000).8.a.)(σσβσ2222eM??881

13、25)208.0(σ2222????A50010)200.1(σ2222????B97620)202.1(σ2222????Cb.Ifthereareaninfinitenumberofassetswithidenticalacteristicsthenawelldiversifiedptfolioofeachtypewillhaveonlysystematicrisksincethenonsystematicriskwillappro

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