投资学第10版习题答案06.docx

投资学第10版习题答案06.docx

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投资学第10版习题答案06

CHAPTER6:

CAPITALALLOCATIONTORISKYASSETS

PROBLEMSETS

1.（e）Thefirsttwoanswerchoicesareincorrectbecauseahighlyriskaverseinvestorwouldavoidportfolioswithhigherriskpremiumsandhigherstandarddeviations.Inaddition,higherorlowerSharperatiosarenotanindicationofaninvestor'stoleranceforrisk.TheSharperatioissimplyatooltoabsolutelymeasurethereturnpremiumearnedperunitofrisk.

2.（b）Ahigherborrowingrateisaconsequenceoftheriskoftheborrowers’default.Inperfectmarketswithnoadditionalcostofdefault,thisincrementwouldequalthevalueoftheborrower’soptiontodefault,andtheSharpemeasure,withappropriatetreatmentofthedefaultoption,wouldbethesame.However,inrealitytherearecoststodefaultsothatthispartoftheincrementlowerstheSharperatio.Also,noticethatanswer（c）isnotcorrectbecausedoublingtheexpectedreturnwithafixedrisk-freeratewillmorethandoubletheriskpremiumandtheSharperatio.

3.Assumingnochangeinrisktolerance,thatis,anunchangedrisk-aversioncoefficient（A）,higherperceivedvolatilityincreasesthedenominatoroftheequationfortheoptimalinvestmentintheriskyportfolio（Equation6.7）.Theproportioninvestedintheriskyportfoliowillthereforedecrease.

4.a.Theexpectedcashflowis:

（0.5×$70,000）+（0.5×200,000）=$135,000.

Withariskpremiumof8%overtherisk-freerateof6%,therequiredrateofreturnis14%.Therefore,thepresentvalueoftheportfoliois:

$135,000/1.14=$118,421

b.Iftheportfolioispurchasedfor$118,421andprovidesanexpectedcashinflowof$135,000,thentheexpectedrateofreturn[E（r）]isasfollows:

$118,421×[1+E（r）]=$135,000

Therefore,E（r）=14%.Theportfoliopriceissettoequatetheexpectedrateofreturnwiththerequiredrateofreturn.

c.IftheriskpremiumoverT-billsisnow12%,thentherequiredreturnis:

6%+12%=18%

Thepresentvalueoftheportfolioisnow:

$135,000/1.18=$114,407

d.Foragivenexpectedcashflow,portfoliosthatcommandgreaterriskpremiumsmustsellatlowerprices.Theextradiscountfromexpectedvalueisapenaltyforrisk.

5.WhenwespecifyutilitybyU=E（r）–0.5Aσ2,theutilitylevelforT-billsis:

0.07

Theutilitylevelfortheriskyportfoliois:

U=0.12–0.5×A×（0.18）2=0.12–0.0162×A

Inorderfortheriskyportfoliotobepreferredtobills,thefollowingmusthold:

0.12–0.0162A>0.07⇒A<0.05/0.0162=3.09

Amustbelessthan3.09fortheriskyportfoliotobepreferredtobills.

6.PointsonthecurvearederivedbysolvingforE（r）inthefollowingequation:

U=0.05=E（r）–0.5Aσ2=E（r）–1.5σ2

ThevaluesofE（r）,giventhevaluesofσ2,aretherefore:

σ

σ2

E（r）

0.00

0.0000

0.05000

0.05

0.0025

0.05375

0.10

0.0100

0.06500

0.15

0.0225

0.08375

0.20

0.0400

0.11000

0.25

0.0625

0.14375

Theboldlineinthegraphonthenextpage（labeledQ6,forQuestion6）depictstheindifferencecurve.

7.RepeatingtheanalysisinProblem6,utilityisnow:

U=E（r）–0.5Aσ2=E（r）–2.0σ2=0.05

Theequal-utilitycombinationsofexpectedreturnandstandarddeviationarepresentedinthetablebelow.Theindifferencecurveistheupwardslopinglineinthegraphonthenextpage,labeledQ7（forQuestion7）.

σ

σ2

E（r）

0.00

0.0000

0.0500

0.05

0.0025

0.0550

0.10

0.0100

0.0700

0.15

0.0225

0.0950

0.20

0.0400

0.1300

0.25

0.0625

0.1750

TheindifferencecurveinProblem7differsfromthatinProblem6inslope.WhenAincreasesfrom3to4,theincreasedriskaversionresultsinagreaterslopefortheindifferencecurvesincemoreexpectedreturnisneededinordertocompensateforadditionalσ.

8.Thecoefficientofriskaversionforariskneutralinvestoriszero.Therefore,thecorrespondingutilityisequaltotheportfolio’sexpectedreturn.Thecorrespondingindifferencecurveintheexpectedreturn-standarddeviationplaneisahorizontalline,labeledQ8inthegraphabove（seeProblem6）.

9.Arisklover,ratherthanpenalizingportfolioutilitytoaccountforrisk,derivesgreaterutilityasvarianceincreases.Thisamountstoanegativecoefficientofriskaversion.Thecorrespondingindifferencecurveisdownwardslopinginthegraphabove（seeProblem6）,andislabeledQ9.

10.Theportfolioexpectedreturnandvariancearecomputedasfollows:

（1）

WBills

（2）

rBills

（3）

WIndex

（4）

rIndex

rPortfolio

（1）×

（2）+（3）×（4）

σPortfolio

（3）×20%

σ2Portfolio

0.0

5%

1.0

13.0%

13.0%=0.130

20%=0.20

0.0400

0.2

5

0.8

13.0

11.4%=0.114

16%=0.16

0.0256

0.4

5

0.6

13.0

9.8%=0.098

12%=0.12

0.0144

0.6

5

0.4

13.0

8.2%=0.082

8%=0.08

0.0064

0.8

5

0.2

13.0

6.6%=0.066

4%=0.04

0.0016

1.0

5

0.0

13.0

5.0%=0.050

0%=0.00

0.0000

11.Com