博迪第八版投资学第十章课后习题答案Word格式.doc

博迪第八版投资学第十章课后习题答案Word格式.doc

《博迪第八版投资学第十章课后习题答案Word格式.doc》由会员分享，可在线阅读，更多相关《博迪第八版投资学第十章课后习题答案Word格式.doc（8页珍藏版）》请在冰点文库上搜索。

E（rp）=rf+bP1[E（r1）-rf]+bP2[E（r2）–rf]

Weneedtofindtheriskpremium（RP）foreachofthetwofactors:

RP1=[E（r1）-rf]andRP2=[E（r2）-rf]

Inordertodoso,wesolvethefollowingsystemoftwoequationswithtwounknowns:

31=6+（1.5´

RP1）+（2.0´

RP2）

27=6+（2.2´

RP1）+[（–0.2）´

RP2]

Thesolutiontothissetofequationsis:

RP1=10%andRP2=5%

Thus,theexpectedreturn-betarelationshipis:

E（rP）=6%+（bP1´

10%）+（bP2´

5%）

5. TheexpectedreturnforPortfolioFequalstherisk-freeratesinceitsbetaequals0.

ForPortfolioA,theratioofriskpremiumtobetais:

（12-6）/1.2=5

ForPortfolioE,theratioislowerat:

（8–6）/0.6=3.33

Thisimpliesthatanarbitrageopportunityexists.Forinstance,youcancreateaPortfolioGwithbetaequalto0.6（thesameasE’s）bycombiningPortfolioAandPortfolioFinequalweights.TheexpectedreturnandbetaforPortfolioGarethen:

E（rG）=（0.5´

12%）+（0.5´

6%）=9%

bG=（0.5´

1.2）+（0.5´

0）=0.6

ComparingPortfolioGtoPortfolioE,Ghasthesamebetaandhigherreturn.Therefore,anarbitrageopportunityexistsbybuyingPortfolioGandsellinganequalamountofPortfolioE.Theprofitforthisarbitragewillbe:

rG–rE=[9%+（0.6´

F）]-[8%+（0.6´

F）]=1%

Thatis,1%ofthefunds（longorshort）ineachportfolio.

6. Substitutingtheportfolioreturnsandbetasintheexpectedreturn-betarelationship,weobtaintwoequationswithtwounknowns,therisk-freerate（rf）andthefactorriskpremium（RP）:

12=rf+（1.2´

RP）

9=rf+（0.8´

Solvingtheseequations,weobtain:

rf=3%andRP=7.5%

7. a. Shortinganequally-weightedportfolioofthetennegative-alphastocksandinvestingtheproceedsinanequally-weightedportfolioofthetenpositive-alphastockseliminatesthemarketexposureandcreatesazero-investmentportfolio.DenotingthesystematicmarketfactorasRM,theexpecteddollarreturnis（notingthattheexpectationofnon-systematicrisk,e,iszero）:

$1,000,000´

[0.02+（1.0´

RM）]-$1,000,000´

[（–0.02）+（1.0´

RM）]

=$1,000,000´

0.04=$40,000

Thesensitivityofthepayoffofthisportfoliotothemarketfactoriszerobecausetheexposuresofthepositivealphaandnegativealphastockscancelout.（NoticethatthetermsinvolvingRMsumtozero.）Thus,thesystematiccomponentoftotalriskisalsozero.Thevarianceoftheanalyst’sprofitisnotzero,however,sincethisportfolioisnotwelldiversified.

Forn=20stocks（i.e.,long10stocksandshort10stocks）theinvestorwillhavea$100,000position（eitherlongorshort）ineachstock.Netmarketexposureiszero,butfirm-specificriskhasnotbeenfullydiversified.Thevarianceofdollarreturnsfromthepositionsinthe20stocksis:

20´

[（100,000´

0.30）2]=18,000,000,000

Thestandarddeviationofdollarreturnsis$134,164.

b. Ifn=50stocks（25stockslongand25stocksshort）,theinvestorwillhavea$40,000positionineachstock,andthevarianceofdollarreturnsis:

50´

[（40,000´

0.30）2]=7,200,000,000

Thestandarddeviationofdollarreturnsis$84,853.

Similarly,ifn=100stocks（50stockslongand50stocksshort）,theinvestorwillhavea$20,000positionineachstock,andthevarianceofdollarreturnsis:

100´

[（20,000´

0.30）2]=3,600,000,000

Thestandarddeviationofdollarreturnsis$60,000.

Noticethat,whenthenumberofstocksincreasesbyafactorof5（i.e.,from20to100）,standarddeviationdecreasesbyafactorof=2.23607（from$134,164to$60,000）.

8. a.

b.Ifthereareaninfinitenumberofassetswithidenticalcharacteristics,thenawell-diversifiedportfolioofeachtypewillhaveonlysystematicrisksincethenon-systematicriskwillapproachzerowithlargen.Themeanwillequalthatoftheindividual（identical）stocks.

c. Thereisnoarbitrageopportunitybecausethewell-diversifiedportfoliosallplotonthesecuritymarketline（SML）.Becausetheyarefairlypriced,thereisnoarbitrage.

9. a. Alongpositioninaportfolio（P）comprisedofPortfoliosAandBwillofferanexpectedreturn-betatradeofflyingonastraightlinebetweenpointsAandB.Therefore,wecanchooseweightssuchthatbP=bCbutwithexpectedreturnhigherthanthatofPortfolioC.Hence,combiningPwithashortpositioninCwillcreateanarbitrageportfoliowithzeroinvestment,zerobeta,andpositiverateofreturn.

b. Theargumentinpart（a）leadstothepropositionthatthecoefficientofb2mustbezeroinordertoprecludearbitrageopportunities.

10. a. E（r）=6+（1.2´

6）+（0.5´

8）+（0.3´

3）=18.1%

b.Surprisesinthemacroeconomicfactorswillresultinsurprisesinthereturnofthestock:

Unexpectedreturnfrommacrofactors=

[1.2（4–5）]+[0.5（6–3）]+[0.3（0–2）]=–0.3%

E（r）=18.1%−0.3%=17.8%

11. TheAPTrequired（i.e.,equilibrium）rateofreturnonthestockbasedonrfandthefactorbetasis:

requiredE（r）=6+（1´

2）+（0.75´

4）=16%

Accordingtotheequationforthereturnonthestock,theactuallyexpectedreturnonthestockis15%（becausetheexpectedsurprisesonallfactorsarezerobydefinition）.Becausetheactuallyexpectedreturnbasedonriskislessthantheequilibriumreturn,weconcludethatthestockisoverpriced.

12. Thefirsttwofactorsseempromisingwithrespecttothelikelyimpactonthefirm’scostofcapital.Botharemacrofactorsthatwouldelicithedgingdemandsacrossbroadsectorsofinvestors.Thethirdfactor,whileimportanttoPorkProducts,isapoorchoiceforamultifactorSMLbecausethepriceofhogsisofminorimportancetomostinvestorsandisthereforehighlyunlikelytobeapricedriskfactor.Betterchoiceswouldfocusonvariablesthatinvestorsinaggregatemightfindmoreimportanttotheirwelfare.Examplesinclude:

inflationuncertainty,short-terminterest-raterisk,energypricerisk,orexchangeraterisk.Theimportantpointhereisthat,inspecifyingamultifactorSML,wenotconfuseriskfactorsthatareimportanttoaparticularinvestorwithfactorsthatareimportanttoinvestorsingeneral;

onlythelatterarelikelytocommandariskpremiuminthecapitalmarkets.

13. Themaximumresidualvarianceistiedtothenumberofsecurities（n）intheportfoliobecause,asweincreasethenumberofsecurities,wearemorelikelytoencountersecuritieswithlargerresidualvariances.Thestartingpointistodeterminethepracticallimitontheportfolioresidualstandarddeviation,s（eP）,thatstillqualifiesasa‘well-diversifiedportfolio.’Areasonableapproachistocompares2（eP）tothemarketvariance,orequivalently,tocompares（eP）tothemarketstandarddeviation.Supposewedonotallows（eP）toexceedpsM,wherepisasmalldecimalfraction,forexample,0.05;

then,thesmallerthevaluewechooseforp,themorestringentourcriterionfordefininghowdiversifieda‘well-diversified’portfoliomustbe.

Nowconstructaportfolioofnsecuritieswithweightsw1,w2,…,wn,sothatSwi=1.Theportfolioresidualvarianceis:

s2（eP）=Sw12s2（ei）

Tomeetourpracticaldefinitionofsufficientlydiversified,werequirethisresidualvariancetobelessthan（psM）2.Asureandsimplewaytoproceedistoassumetheworst,thatis,assumethattheresidualvarianceofeachsecurityisthehighestpossiblevalueallowedundertheassumptionsoftheproblem:

s2（ei）=ns2M

Inthatcase:

s2（eP）=Swi2nsM2

Nowapplytheconstraint:

Swi2nsM2≤（psM）2

Thisrequiresthat:

nSwi2≤p2

Or,equivalently,that:

Swi2≤p2/n

Arelativelyeasywaytogenerateasetofwell-diversifiedportfoliosistouseportfolioweightsthatfollowageometricprogression,sincethecomputationsthenbecomerelativelystraightforward.Choosew1andacommonfactorqforthegeometricprogressionsuchthatq<

1.Therefore,theweightoneachstockisafractionqoftheweightonthepreviousstockintheseries.Thenthesumofntermsis:

Swi=w1（1–qn）/（1–q）=1

or:

w1=（1–q）/（1–qn）

Thesumofthensquaredweightsissimilarlyobtainedfromw12andacommongeometricprogressionfactorofq2.Therefore:

Swi2=w12（1–q2n）/（1–q2）

Substitutingforw1fromabove,weobtain:

Swi2=[（1–q）2/（1–qn）2]×

[（1–q2n）/（1–q2）]

Forsufficientdiversification,wechooseqsothat:

Forexample,continuetoassumethatp=0.05andn=1,000.Ifwechoose

q=0.9