投资学第10版习题答案09.docx

投资学第10版习题答案09.docx

《投资学第10版习题答案09.docx》由会员分享，可在线阅读，更多相关《投资学第10版习题答案09.docx（12页珍藏版）》请在冰豆网上搜索。

投资学第10版习题答案09

CHAPTER9:

THECAPITALASSETPRICINGMODEL

PROBLEMSETS

1.

2.Ifthesecurity’scorrelationcoefficientwiththemarketportfoliodoubles（withallothervariablessuchasvariancesunchanged）,thenbeta,andthereforetheriskpremium,willalsodouble.Thecurrentriskpremiumis:

14%–6%=8%

Thenewriskpremiumwouldbe16%,andthenewdiscountrateforthesecuritywouldbe:

16%+6%=22%

Ifthestockpaysaconstantperpetualdividend,thenweknowfromtheoriginaldatathatthedividend（D）mustsatisfytheequationforthepresentvalueofaperpetuity:

Price=Dividend/Discountrate

50=D/0.14⇒D=50⨯0.14=$7.00

Atthenewdiscountrateof22%,thestockwouldbeworth:

$7/0.22=$31.82

Theincreaseinstockriskhaslowereditsvalueby36.36%.

3.a.False.β=0impliesE（r）=rf,notzero.

b.False.Investorsrequireariskpremiumonlyforbearingsystematic（undiversifiableormarket）risk.Totalvolatility,asmeasuredbythestandarddeviation,includesdiversifiablerisk.

c.False.Yourportfolioshouldbeinvested75%inthemarketportfolioand25%inT-bills.Then:

4.TheexpectedreturnisthereturnpredictedbytheCAPMforagivenlevelofsystematicrisk.

5.AccordingtotheCAPM,$1DiscountStoresrequiresareturnof13%basedonitssystematicrisklevelofβ=1.5.However,theforecastedreturnisonly12%.Therefore,thesecurityiscurrentlyovervalued.

Everything$5requiresareturnof10%basedonitssystematicrisklevelofβ=1.0.However,theforecastedreturnis11%.Therefore,thesecurityiscurrentlyundervalued.

6.Correctanswerischoicea.Theexpectedreturnofastockwithaβ=1.0must,onaverage,bethesameastheexpectedreturnofthemarketwhichalsohasaβ=1.0.

7.Correctanswerischoicea.Betaisameasureofsystematicrisk.Sinceonlysystematicriskisrewarded,itissafetoconcludethattheexpectedreturnwillbehigherforKaskin’sstockthanforQuinn’sstock.

8.Theappropriatediscountratefortheprojectis:

rf+β×[E（rM）–rf]=.08+[1.8⨯（.16–.08）]=.224,or22.4%

Usingthisdiscountrate:

Annuityfactor（22.4%,10years）]=$18.09

Theinternalrateofreturn（IRR）fortheprojectis35.73%.RecallfromyourintroductoryfinanceclassthatNPVispositiveifIRR>discountrate（or,equivalently,hurdlerate）.ThehighestvaluethatbetacantakebeforethehurdlerateexceedstheIRRisdeterminedby:

.3573=.08+β×（.16–.08）⇒β=.2773/.08=3.47

9.a.CalltheaggressivestockAandthedefensivestockD.Betaisthesensitivityofthestock’sreturntothemarketreturn,i.e.,thechangeinthestockreturnperunitchangeinthemarketreturn.Therefore,wecomputeeachstock’sbetabycalculatingthedifferenceinitsreturnacrossthetwoscenariosdividedbythedifferenceinthemarketreturn:

b.Withthetwoscenariosequallylikely,theexpectedreturnisanaverageofthetwopossibleoutcomes:

E（rA）=0.5⨯（–.02+.38）=.18=18%

E（rD）=0.5⨯（.06+.12）=.09=9%

c.TheSMLisdeterminedbythemarketexpectedreturnof[0.5×（.25+.05）]=15%,withβM=1,andrf=6%（whichhasβf=0）.Seethefollowinggraph:

Theequationforthesecuritymarketlineis:

E（r）=.06+β×（.15–.06）

d.Basedonitsrisk,theaggressivestockhasarequiredexpectedreturnof:

E（rA）=.06+2.0×（.15–.06）=.24=24%

Theanalyst’sforecastofexpectedreturnisonly18%.Thusthestock’salphais:

αA=actuallyexpectedreturn–requiredreturn（givenrisk）

=18%–24%=–6%

Similarly,therequiredreturnforthedefensivestockis:

E（rD）=.06+0.3×（.15–.06）=8.7%

Theanalyst’sforecastofexpectedreturnforDis9%,andhence,thestockhasapositivealpha:

αD=Actuallyexpectedreturn–Requiredreturn（givenrisk）

=.09–.087=+0.003=+0.3%

Thepointsforeachstockplotonthegraphasindicatedabove.

e.Thehurdlerateisdeterminedbytheprojectbeta（0.3）,notthefirm’sbeta.Thecorrectdiscountrateis8.7%,thefairrateofreturnforstockD.

10.Notpossible.PortfolioAhasahigherbetathanPortfolioB,buttheexpectedreturnforPortfolioAislowerthantheexpectedreturnforPortfolioB.Thus,thesetwoportfolioscannotexistinequilibrium.

11.Possible.IftheCAPMisvalid,theexpectedrateofreturncompensatesonlyforsystematic（market）risk,representedbybeta,ratherthanforthestandarddeviation,whichincludesnonsystematicrisk.Thus,PortfolioA’slowerrateofreturncanbepairedwithahigherstandarddeviation,aslongasA’sbetaislessthanB’s.

12.Notpossible.Thereward-to-variabilityratioforPortfolioAisbetterthanthatofthemarket.ThisscenarioisimpossibleaccordingtotheCAPMbecausetheCAPMpredictsthatthemarketisthemostefficientportfolio.Usingthenumberssupplied:

PortfolioAprovidesabetterrisk-rewardtrade-offthanthemarketportfolio.

13.Notpossible.PortfolioAclearlydominatesthemarketportfolio.PortfolioAhasbothalowerstandarddeviationandahigherexpectedreturn.

14.Notpossible.TheSMLforthisscenariois:

E（r）=10+β×（18–10）

Portfolioswithbetaequalto1.5haveanexpectedreturnequalto:

E（r）=10+[1.5×（18–10）]=22%

TheexpectedreturnforPortfolioAis16%;thatis,PortfolioAplotsbelowtheSML（αA=–6%）and,hence,isanoverpricedportfolio.ThisisinconsistentwiththeCAPM.

15.Notpossible.TheSMListhesameasinProblem14.Here,PortfolioA’srequiredreturnis:

.10+（.9×.08）=17.2%

Thisisgreaterthan16%.PortfolioAisoverpricedwithanegativealpha:

αA=–1.2%

16.Possible.TheCMListhesameasinProblem12.PortfolioAplotsbelowtheCML,asanyassetisexpectedto.ThisscenarioisnotinconsistentwiththeCAPM.

17.Sincethestock’sbetaisequalto1.2,itsexpectedrateofreturnis:

.06+[1.2⨯（.16–.06）]=18%

18.Theseriesof$1,000paymentsisaperpetuity.Ifbetais0.5,thecashflowshouldbediscountedattherate:

.06+[0.5×（.16–.06）]=.11=11%

PV=$1,000/0.11=$9,090.91

If,however,betaisequalto1,thentheinvestmentshouldyield16%,andthepricepaidforthefirmshouldbe:

PV=$1,000/0.16=$6,250

Thedifference,$2,840.91,istheamountyouwilloverpayifyouerroneouslyassumethatbetais0.5ratherthan1.

19.UsingtheSML:

.04=.06+β×（.16–.06）⇒β=–.02/.10=–0.2

20.r1=19%;r2=16%;β1=1.5;β2=1

a.Todeterminewhichinvestorwasabetterselectorofindividualstockswelookatabnormalreturn,whichistheex-postalpha;thatis,theabnormalreturnisthedifferencebetweentheactualreturnandthatpredictedbytheSML.Withoutinformationabouttheparametersofthisequation（risk-freerateandmarketrateofreturn）wecannotdeterminewhichinvestorwasmoreaccurate.

b.Ifrf=6%andrM=14%,then（usingthenotationalphafortheabnormalreturn）:

α1=.19–[.06+1.5×（.14–.06）]=.19–.18=1%

α2=.16–[.06+1×（.14–.06）]=.16–.14=2%

Here,thesecondinvestorhasthelargerabnormalreturnandthusappearstobethesuperiorstockselector.Bymakingbetterpredictions,thesecond

investorappearstohavetiltedhisportfoliotowardunderpricedstocks.

c.Ifrf=3%andrM=15%,then:

α1=.19–[.03+1.5×（.15–.03）]=.19–.21=–2%

α2=.16–[.03+1×（.15–.03）]=.16–.15=1%

Here,notonlydoesthesecondinvestorappeartobethesuperiorstockselector,butthefirstinvestor’spredictionsappearvalueless（orworse）.

21.a.Sincethemarketportfolio,bydefinition,hasabetaof1,itsexpectedrateofreturnis12%.

b.β=0meansnosystematicrisk.Hence,thestock’sexpectedrateofreturninmarketequilibriumistherisk-freerate,5%.

c.UsingtheSML,thefairexpectedrateofreturnforastockwithβ=–0.5is:

Theactuallyexpectedrateofreturn,usingtheexpectedpriceanddividendfornextyearis:

Becausetheactuallyexpectedreturnexceedsthefairreturn,thestockisunderpriced.

22.Inthezero-betaCAPMthezero-betaportfolioreplacestherisk-freerate,andthus:

E（r）=8+0.6（17–8）=13.4%

23.a.E（rP）=rf+βP×[E（rM）–rf]=5%+0.8（15%−5%）=13%

α=14%-13%=1%

Youshouldinvestinthisfundbecausealphaispositive.

b.Thepassiveportfoliowiththesamebetaasthefundshouldbeinvested80%inthemarket-indexportfolioand20%inthemoneymarketaccount.Forthisportfolio:

E（rP）=（0.8×15%）+（0.2×5%）=13%

14%−13%=1%=α

24.a.WewouldincorporateliquidityintotheCCAPMinamanneranalogoustothewayinwhichliquidityisincorporatedintotheconventionalCAPM.Inthelattercase,inadditiontothemarketriskpremium,expectedreturnisalsodependentontheexpectedcostofilliquidityandthreeliquidity-relatedbetaswhichmeasurethesensitivityof:

（1）thesecurity’silliquiditytomarketilliquidity;

（2）thesecurity’sreturntomarketilliquidity;and,（3）thesecurity’silliquiditytothemarketreturn.AsimilarapproachcanbeusedfortheCCAPM,exceptthattheliquiditybetaswouldbemeasuredrelativetoconsumptiongrowthratherthantheusualmarketindex.

b.Asinpart（a）,nontradedassetswouldbeincorporatedintotheCCAPMinafashionsimilartopart（a）.Replacethemarketportfoliowithconsumptiongrowth.Theissueofliquidityismoreacutewithnontradedassetssuchasprivatelyheldbusinessesandlaborincome.

Whileownershipofaprivatelyheldbusinessisanalogoustoownershipofanilliquidstock,expectagreaterdegreeofilliquidityforthetypicalprivatebusiness.Iftheownerofaprivatelyheldbusinessissatisfiedwiththedividendspaidoutfromthebusiness,thenthelackofliquidityisn