投资学第10版习题答案06分析解析

Chapter6-CapitalAllocationtoRiskyAssets6-1Copyright©2014McGraw-HillEducation.Allrightsreserved.NoreproductionordistributionwithoutthepriorwrittenconsentofMcGraw-HillEducation.CHAPTER6:CAPITALALLOCATIONTORISKYASSETSPROBLEMSETS1.(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=$118,421b.Iftheportfolioispurchasedfor$118,421andprovidesanexpectedcashinflowof$135,000,thentheexpectedrateofreturn[E(r)]isasfollows:$118,421×[1+E(r)]=$135,000Therefore,E(r)=14%.Theportfoliopriceissettoequatetheexpectedrateofreturnwiththerequiredrateofreturn.c.IftheriskpremiumoverT-billsisnow12%,thentherequiredreturnis:6%+12%=18%Thepresentvalueoftheportfolioisnow:$135,000/1.18=$114,407d.Foragivenexpectedcashflow,portfoliosthatcommandgreaterriskChapter6-CapitalAllocationtoRiskyAssets6-2Copyright©2014McGraw-HillEducation.Allrightsreserved.NoreproductionordistributionwithoutthepriorwrittenconsentofMcGraw-HillEducation.premiumsmustsellatlowerprices.Theextradiscountfromexpectedvalueisapenaltyforrisk.5.WhenwespecifyutilitybyU=E(r)–0.5Aσ2,theutilitylevelforT-billsis:0.07Theutilitylevelfortheriskyportfoliois:U=0.12–0.5×A×(0.18)2=0.12–0.0162×AInorderfortheriskyportfoliotobepreferredtobills,thefollowingmusthold:0.12–0.0162A0.07A0.05/0.0162=3.09Amustbelessthan3.09fortheriskyportfoliotobepreferredtobills.6.PointsonthecurvearederivedbysolvingforE(r)inthefollowingequation:U=0.05=E(r)–0.5Aσ2=E(r)–1.5σ2ThevaluesofE(r),giventhevaluesofσ2,aretherefore:2E(r)0.000.00000.050000.050.00250.053750.100.01000.065000.150.02250.083750.200.04000.110000.250.06250.14375Theboldlineinthegraphonthenextpage(labeledQ6,forQuestion6)depictstheindifferencecurve.7.RepeatingtheanalysisinProblem6,utilityisnow:U=E(r)–0.5Aσ2=E(r)–2.0σ2=0.05Theequal-utilitycombinationsofexpectedreturnandstandarddeviationarepresentedinthetablebelow.Theindifferencecurveistheupwardslopinglineinthegraphonthenextpage,labeledQ7(forQuestion7).2E(r)0.000.00000.05000.050.00250.05500.100.01000.07000.150.02250.09500.200.04000.13000.250.06250.1750Chapter6-CapitalAllocationtoRiskyAssets6-3Copyright©2014McGraw-HillEducation.Allrightsreserved.NoreproductionordistributionwithoutthepriorwrittenconsentofMcGraw-HillEducation.TheindifferencecurveinProblem7differsfromthatinProblem6inslope.WhenAincreasesfrom3to4,theincreasedriskaversionresultsinagreaterslopefortheindifferencecurvesincemoreexpectedreturnisneededinordertocompensateforadditionalσ.E(r)5U(Q6,A=3)U(Q7,A=4)U(Q8,A=0)U(Q9,A0)8.Thecoefficientofriskaversionforariskneutralinvestoriszero.Therefore,thecorrespondingutilityisequaltotheportfolio’sexpectedreturn.Thecorrespondingindifferencecurveintheexpectedreturn-standarddeviationplaneisahorizontalline,labeledQ8inthegraphabove(seeProblem6).9.Arisklover,ratherthanpenalizingportfolioutilitytoaccountforrisk,derivesgreaterutilityasvarianceincreases.Thisamountstoanegativecoefficientofriskaversion.Thecorrespondingindifferencecurveisdownwardslopinginthegraphabove(seeProblem6),andislabeledQ9.Chapter6-CapitalAllocationtoRiskyAssets6-4Copyright©2014McGraw-HillEducation.Allrightsreserved.NoreproductionordistributionwithoutthepriorwrittenconsentofMcGraw-HillEducation.10.Theportfolioexpectedreturnandvariancearecomputedasfollows:(1)WBills(2)rBills(3)WIndex(4)rIndexrPortfolio(1)×(2)+(3)×(4)Portfolio(3)×20%2Portfolio0.05%1.013.0%13.0%=0.13020%=0.200.04000.250.813.011.4%=0.11416%=0.160.02560.450.613.09.8%=0.09812%=0.120.01440.650.413.08.2%=0.0828%=0.080.00640.850.213.06.6%=0.0664%=0.040.00161.050.013.05.0%=0.0500%=0.000.000011.ComputingutilityfromU=E(r)–0.5×Aσ2=E(r)–σ2,wearriveatthevaluesinthecolumnlabeledU(A=2)inthefollowingtable:WBillsWIndexrPortfolioPortfolio2PortfolioU(A=2)U(A=3)0.01.00.1300.200.04000.0900.07000.20.80.1140.160.02560.0884.07560.40.60.0980.120.01440.0836.07640.60.40.0820.080.00640.0756.07240.80.20.0660.040.00160.0644.06361.00.00.05