投资学课后习题答案.docx

投资学课后习题答案.docx

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投资学课后习题答案

投资学试题及答案

investmentexamⅠ

AllQuestionshaveEqualMarksAttemptany2questions2HoursAllowed

Include:

Formulasheet,

PresentValueTables,

StandardnormaldistributionTables.

1.Assumethatyouareafundmanagerofariskyportfoliowithanexpectedreturnof18%andastandarddeviationof28%.Risk-freemoneymarketfundsarealsoavailabletoinvestorsandtheseareexpectedtoprovideareturnof8%.Youhaveaclientthatchoosestoinvest70%ofhisportfolioinyourfundandtheremaining30%inamoneymarketfund.

a.Whatistheexpectedvalueandstandarddeviationoftherateofreturnonhisportfolio?

（15%）

b.Whatistherewardtovariabilityratioofyourportfolioandthatofyourclient’s?

（15%）

c.CalculatetheslopeoftheCapitalAllocationLine（CAL）ofyourportfolioandshow,usinganexpectedreturn-standarddeviationdiagram,thepositionofyourclientonyourfund’sCAL.（15%）

d.Yourclientdecidestoinvesttheproportionyofhisinvestmentbudgetinyourportfolio,whereyissetsothattheoverallexpectedreturnis16%.Whatistheproportionyandwhatisthestandarddeviationoftherateofreturnonyourclient’sportfolio?

（15%）

e.YourclientmentionstoyouthatheknowsofseveralpassivelymanagedFT-AllShareIndextrackerfundsthatyieldanexpectedrateofreturnof13%withastandarddeviationof25%.Explain,possiblywiththeaidofadiagram,whyyourfundhasadvantagesoverthetrackerfundsandwhyitmaynotbeintheclient’sbestintereststoswitchthe70%ofhisportfoliocurrentlyinvestedinyourfundtothetrackerfund.（20%）

f.Calculatethemaximumfeeyoucouldchargetheclient（asapercentageoftheinvestmentinyourfund,deductedattheendoftheyear）whilststillleavinghimatleastaswelloffinvestinginyourfundasinthetrackerfund.（20%）

2.ThemarketconsensusisthatPROSPECTSPlchasareturnoninvestment（k）of17%andabetacoefficient（）of1.4.PROSPECTSplanstomaintainindefinitelyitstraditionalretentionratio（b）of0.6.Thisyearsearningspershare（E）was72p,anddividendshavejustbeenpaid.Themarketequityriskpremiumisforecasttobe6%,andthecurrentinterestrateonshorttermgovernmentbondsis5%.

a.Usingthecapitalassetpricingmodel（CAPM）,whatrateofreturn（r）areinvestorsexpectingforinvestinginPROSPECTS?

（10%）

b.Whatisthecompany’sexpectedrateofgrowth（g）?

（10%）

c.Usingthedividenddiscountmodel（Gordon’sgrowthmodel）,whatisthevalueofaPROSPECTSshare（P0）?

（10%）

d.WhatisthecurrenttrailingPrice/Earnings（PE）ratio?

（10%）

e.WhatisthepresentvalueofPROSPECTSgrowthopportunities（PVGO）?

（15%）

f.Ifthecompanychangeditspayoutpolicyandstartedtodistributeallearningsasdividends,whatwouldbethenewshareprice（P0）?

Brieflydiscusswhythesharepriceisnowdifferenttowhatitwaswhenthecompanymaintainedaretentionratioof0.6（partcabove）.（15%）

g.DiscusstheassumptionsunderlyingGordon’sgrowthmodel,andthelimitationsofthemodel.（30%）

3.On1January2002,themarketvalueofa12%gilt（governmentbond）is£107.30.Thegiltpaysasemi-annualcoupon,withthefirstpaymenton1July2002.Thebondwillberedeemedatparvalueon1January2004.

a.i.Whatisthecurrentannualinterestyieldonthebond,aswouldbequotedintheFinancialTimes?

（7%）

ii.Whatistheeffectiveannualinterestyield?

（7%）

b.Whatisthesemiannualyieldtomaturity（YTM,alternativelyknownastheredemptionyield）onthebond?

（10%）

c.Whatisthedurationofthebond?

Note:

Duration（D）

D=[1/P]*[1*C1/（1+y）+2*C2/（1+y）2+3*C3/（1+y）3+...N*CN/（1+y）N]（15%）

d.IfmarketinterestrateschangeinstantaneouslysothattherequiredsemiannualYTMrisesby1.5percentagepoints,byhowmuchwillthevalueofthebondchange,basedonthedurationmeasure?

（15%）

e.Explainwhydurationmaynotprovideanaccuratemeasureoftheextenttowhichbondvalueschangewithchanginginterestrates（theinterestratesensitivityofthebond）.（30%）

f.BrieflyexplainhowtheyieldonindexlinkedgiltscanbeusedtoforecastUKinflationrates.（16%）

4.Attempttoanswereachofthefollowing10（itox）questionsconcerningderivativeinstrumentsandtheiruses:

i.Describethegeneraldifferencesbetweenacalloptionandafuturescontract.（10%）

ii.Howarecalloptionsusedbyspeculators?

Describetheconditionsinwhichtheirstrategywouldbackfire.（10%）

iii.Howareputoptionsusedbyspeculators?

Describetheconditionsinwhichtheirstrategywouldbackfire.（10%）

iv.Describethemaximumlossthatcouldoccurforapurchaserofacalloption.（10%）

v.Underwhatconditionswouldspeculatorssellacalloption?

（10%）

vi.Whatistherisktospeculatorswhosellputoptions?

（10%）

vii.Identifythefactorsaffectingthepremiumpaidonacalloption.Describehoweachfactoraffectsthesizeofthepremium.（10%）

viii.Identifythefactorsaffectingthepremiumpaidonaputoption.Describehoweachfactoraffectsthesizeofthepremium.（10%）

ix.Howcanfinancialinstitutionswithstockportfoliosusestockoptionswhentheyexpectstockpricestorisesubstantiallybutdonotyethavesufficientfundstopurchasemorestock?

（10%）

x.WhywouldafinancialinstitutionholdingABCstockconsiderbuyingaputoptiononthisstockratherthansimplysellthestock?

（10%）

5.Considerthetwo（excessreturns）index-modelregressionresultsforthefollowing2stocksgiveninthetablebelow:

StockA

StockB

Indexmodelregressionestimates

1.5%+1.2（rm-rf）

2.5%+0.8（rm-rf）

R2

0.602

0.450

ResidualStandardDeviation（e）

12.4%

21.1%

StandardDeviationofexcessreturns

23.1%

26.7%

Therisk-freerateovertheperiodwas6%andthemarket’saveragereturnwas14%.

a.Calculatethefollowingstatisticsforeachstockandcommentonthedifferencesbetweenthem:

i.Alpha.

ii.Appraisalratio.

iii.Sharpemeasure.

iv.Treynormeasure.

（50%）

b.Whichstockisthebestchoice（andexplainwhy）underthefollowingcircumstances?

i.Thisistheonlyriskyassettobeheldbytheinvestor.

ii.Thisstockwillbemixedwiththerestoftheinvestor’sportfoliocurrentlycomposedsolelyofholdingsinthemarketindexfund.

iii.Thisisoneofmanystocksthattheinvestorisanalysingtoformanactivelymanagedstockportfolio.

（25%）

c.Itisoftensuggestedthatfundmanagerperformanceshouldbeevaluatedoveranentiremarketcycle.Discusstheplausibilityofthisnotionandanyargumentsthatappeartocontradictit.（25%）

6.Supposethereare3well-diversifiedportfolioswiththecharacteristicsasshowninthetablebelow:

Security

Price

E（R）

Beta

A

£3.00

10%

1.00

B

£4.00

12%

1.20

C

£2.00

13%

1.10

a.Showwhetherthereisanarbitrageopportunityimpliedbythesenumbers.Indicatemathematicallyhowtotakeadvantageofit.（60%）

b.ExplainthemaindifferencebetweentheMarketmodelandtheCAPM.（20%）

c.ExplainhowtheCAPMdiffersfromtheAPTmodel.（20%）

SolutionstoInvestmentexamⅠ

1.a.Expectedreturn=.3⨯8%+.7⨯18%=15%peryear.

Standarddeviation=.7⨯28%=19.6%

b.Yourreward-to-variabilityratio==.357

c.Client'sreward-to-variabilityratio==.3571

d.E（rC）=rf+E[（rP）–rf]y=8+l0y

Iftheexpectedreturnoftheportfolioisequalto16%,thensolvingforyweget:

16=8+10y,andy==.8Therefore,togetanexpectedreturnof16%theclientmustinvest80%oftotalfundsintheriskyportfolioand20%inT-bills.

σC=.8⨯σP=.8⨯28%=22.4%peryear

e.SlopeoftheCML==.20

Thediagramfollows.Myfundallowsaninvestortoachieveahighermeanforanygivenstandarddeviationthanwouldapassivestrategy,i.e.,ahigherexpectedreturnforanygivenlevelofrisk.

f.With70%ofhismoneyinmyfund'sportfoliotheclientgetsameanreturnof15%peryearandastandarddeviationof19.6%peryear.Ifheshiftsthatmoneytothepassiveportfolio（whichhasanexpectedreturnof13%andstandarddeviationof25%）,hisoverallexpectedreturnandstandarddeviationbecome:

E（rC）=rf+.7[E（rM）-rf]

Inthiscase,rf=8%andE（rM）=13%.Therefore,

E（rC）=8+.7⨯（13–8）=11.5%

Thestandarddeviationofthecompleteportfoliousingthepassiveportfoliowouldbe:

σC=.7⨯σM=.7⨯25%=17.5%

Therefore,theshiftentailsadeclineinthemeanfrom14%to11.5%andadeclineinthestandarddeviationfrom19.6%to17.5%.Sincebothmeanreturnandstandarddeviationfall,itisnotyetclearwhetherthemoveisbeneficialorharmful.Thedisadvantageoftheshiftisthatifmyclientiswillingtoacceptameanreturnonhistotalportfolioof11.5%,hecanachieveitwithalowerstandarddeviationusingmyfundportfolio,ratherthanthepassiveportfolio.Toachieveatargetmeanof11.5%,wefirstwritethemeanofthecompleteportfolioasafunctionoftheproportionsinvestedinmyfundportfolio,y:

E（rC）=8+y（18-8）=8+10y

Becauseourtargetis:

E（rC）=11.5%,theproportionthatmustbeinvestedinmyfundisdeterminedasfollows:

11.5=8+10y,y==.35

Thestandarddeviationoftheportfoliowouldbe:

σC=y⨯28%=.35⨯28%=9.8%.Thus,byusingmyportfolio,thesame11.5%expectedreturncanbeachievedwithastandarddeviationofonly9.8%asopposedtothestandarddeviationof17.5%usingthepassiveportfolio.

Thefeewouldreducethereward-to-variabilityratio,i.e.,theslopeoftheCAL.Clientswillbeindifferentbetweenmyfundandthepassiveportfolioiftheslopeoftheafter-feeCALandtheCMLareequal.Letfdenotethefee.

SlopeofCALwithfee==

SlopeofCML（whichrequiresnofee）==.20.

Settingtheseslopesequalweget:

=.20

10-f=28