Corporate Finance 第7版 答案Ch011完整版

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Chapter11:AnAlternativeViewofRiskandReturn:

TheArbitragePricingTheory

11.1 RealGNPwashigherthananticipated.SincereturnsarepositivelyrelatedtothelevelofGNP,returnsshouldrisebasedonthisfactor.

Inflationwasexactlytheamountanticipated.Sincetherewasnosurpriseinthisannouncement,itwillnotaffectLewis-Stridenreturns.

InterestRatesarelowerthananticipated.Sincereturnsarenegativelyrelatedtointerestrates,thelowerthanexpectedrateisgoodnews.Returnsshouldriseduetointerestrates.

ThePresident’sdeathisbadnews.Althoughthepresidentwasexpectedtoretire,hisretirementwouldnotbeeffectiveforsixmonths.Duringthatperiodhewouldstillcontributetothefirm.Hisuntimelydeathmeanthatthosecontributionswouldnotbemade.Sincehewasgenerallyconsideredanassettothefirm,hisdeathwillcausereturnstofall.

Thepoorresearchresultsarealsobadnews.SinceLewis-Stridenmustcontinuetotestthedrug,itwillnotgointoproductionasearlyasexpected.Thedelaywillaffectexpectedfutureearnings,andthusitwilldampenreturnsnow.

TheresearchbreakthroughispositivenewsforLewisStriden.Sinceitwasunexpected,itwillcausereturnstorise.

Thecompetitor’sannouncementisalsounexpected,butitisnotawelcomesurprise.ThisannouncementwilllowerthereturnsonLewis-Striden.

Systematicriskisriskthatcannotbediversifiedawaythroughformationofaportfolio.Generally,systematicriskfactorsarethosefactorsthataffectalargenumberoffirmsinthemarket,however,thosefactorswillnotnecessarilyaffectallfirmsequally.ThesystematicfactorsinthelistarerealGNP,inflationandinterestrates.

Unsystematicriskisthetypeofriskthatcanbediversifiedawaythroughportfolioformation.Unsystematicriskfactorsarespecifictothefirmorindustry.Surprisesinthesefactorswillaffectthereturnsofthefirminwhichyouareinterested,buttheywillhavenoeffectonthereturnsoffirmsinadifferentindustryandperhapslittleeffectonotherfirmsinthesameindustry.ForLewis-Striden,theunsystematicriskfactorsarethepresident’sabilitytocontributetothefirm,theresearchresultsandthecompetitor.

11.2 a. Letm=systematicriskportionofreturn:

b. Let=theunsystematicportionofrisk,sincethenewswasonlyaboutthisfirm:

c. TotalReturn=Expectedreturn,plus2thecomponentsofunexpectedreturn:thesystematicriskportionofreturnandtheunsystematicportion:

11.3 a. Letm=systematicriskportionofreturn:

b. Let=theunsystematicportionofrisk:

c. TotalReturn:

11.4 a. Themarketmodelisspecifiedby:

soapplyingthattoeachStock:

StockA:

StockB:

StockC:

11.4 (continued)

b. Sincewedon'thavetheactualmarketreturnorunsystematicrisk,wewillgetaformulawiththosevaluesasunknowns:

c. Now,continuingwiththeMarketModel(asinparta),when=15%,andall=0:

i.returnsofindividualstocks:

ii.returnoftheportfolio:

AlternateSolutionforreturnonportfolio,whereistheweightintheportfolioofstocki:

11.5 a. Sincefivestockshavethesameexpectedreturnsandthesamebetas,theportfolioalsohasthesameexpectedreturnandbeta.However,theunsystematicrisksmightbedifferent:

b.

11.6 Todeterminewhichinvestmentinvestorwouldprefer,youmustcomputethevarianceofportfolioscreatedbymanystocksfromeithermarket.Note,becauseyouknowthatdiversificationisgood,itisreasonabletoassumethatonceaninvestorchosethemarketinwhichheorshewillinvest,heorshewillbuymanystocksinthatmarket.

Known:

Assume:

Theweightofeachstockis1/N;

thatis,foralli.

IfaportfolioiscomposedofNstockseachforming1/Nproportionoftheportfolio,thereturnontheportfoliois1/NtimesthesumofthereturnsontheNstocks.

Tofindthevarianceoftherespectiveportfoliosinthe2markets,weneedtousethedefinitionofvariancefromStatistics:

Inourcase:

11.6 (continued)

Notehowever,tousethis,firstwemustfindand.So,usingtheassumptionaboutequalweightsandthensubstitutingintheknownequationfor:

Also,recallfromStatisticsapropertyofExpectedValue:

whereaisaconstant,andarerandomvariables,then

and

.

Nowusetheabovetofind:

11.6 (continued)

Next,substitutebothoftheseresultsintotheoriginalequationforvariance:

Finally,sincewecanhaveasmanystocksineachmarketaswewant,

inthelimit,as,,

soweget:

andsince,andtheproblemstatesthat

Sonow,summarizewhatwehavesofar:

andfinallywecanbeginansweringthequestionsa,b,&cforvariousvaluesofthecorrelations:

11.6 (continued)

a. Substituteintotherespectivevarianceformulas:

Since,(andexpectedreturnsareequal)ariskaverseinvestorwillprefertoinvestinthesecondmarket.

b.

Since,ariskaverseinvestorwillprefertoinvestinthesecondmarket.

c.

Since,ariskaverseinvestorwillbeindifferentbetweeninvestinginthetwomarkets.

d. Sincetheexpectedreturnsareequal,indifferenceimpliesthatthevariancesoftheportfoliosinthetwomarketsarealsoequal.So,setthevarianceequationsequal,andsolveforthecorrelationofonemarketintermsoftheother:

Therefore,foranysetofcorrelationsthathavethisrelationship(asfoundinpartc),ariskaverseinvestorwillbeindifferentbetweenthetwomarkets.

11.7 a. Inordertofindstandarddeviation(notatedhere,s),youmustfirstfindtheVariance,since.RecallfromStatisticsapropertyofVariance:

whereaisaconstant,andarerandomvariables,then

and

.

Theproblemstatesthatreturn-generationcanbedescribedby:

Realizethatarerandomvariables,andareconstants.Then,applytheabovepropertiestothismodel,andyouget:

andnowfindsforeachasset(percentshavebeenconvertedheretodecimal*):

*Notethatbecauseoftakingthesquareroot,thereispotentialhereforgettingconfusedaboutthepercent.Keepinmindthat"percent"isonlyfortheconvenienceofpresentation.Itisalwaysagoodideatoconverttodecimalbeforedoingcalculations,anddoyourworkindecimals.Thenyoucanconvertbacktopercentforthefinalanswer.

11.7 (continued)

b.i: Fromaboveformulaforvariance,notethatas,soyouget:

So,thevariancesfortheassetsare(noconfusionabout%here,soyoucanjuststayin%):

b.ii. Usethemodel:,whichistheCAPM(orAPTModelwhenthereisonefactorandthatfactoristheMarket).

ComparetheseresultsforexpectedassetreturnsasperCAPMorAPTwiththeexpectedreturnsgiveninthetable.ThisshowsthatassetsA&Bareaccuratelypriced,butassetCisoverpriced(themodelshowsthereturnshouldbehigher).Thus,rationalinvestorswillnotholdassetC.

b.iii. Ifshortsellingisallowed,rationalinvestorswillsellshortassetC,causingthepriceofassetCtodecreaseuntilnoarbitrageopportunityexists.Inotherwords,thepriceofassetCshoulddecreaseuntilthereturnbecomes14.25%.

11.8 a. Let theproportionofSecurity1intheportfolioand

theproportionofSecurity2intheportfolio

andnotethatsincetheweightsmustsumto1.0,

.

RecallfromChapter10thatthebetaforaportfolio(orinthiscasethebetaforafactor)istheweightedaverageofthesecuritybetas,so

Now,applytheconditiongiveninthehintthatthereturnoftheportfoliodoesnotdependon.Thismeansthattheportfoliobetaforthatfactorwillbe0:

andsolvingforand:

Thus,sellshortSecurity1andbuySecurity2.

Tofindtheexpectedreturnonthatportfolio,use

soapplyingtheabove:

11.8 (continued)

b. Followingthesamelogicasinparta,wehave

and

Thus,sellshortSecurity4andbuySecurity3.Then,

Notethatsincebothandare0,thisisariskfreeportfolio!

c. Theportfolioinpartbprovidesariskfreereturnof10%,whichishigherthanthe5%returnprovidedbytheriskfreesecurity.Totakeadvantageofthisopportunity,borrowattheriskfreerateof5%andinves