金融风险管理师(FRM)2012考试真题

QuestionbankMonteCarloMethodsLetNbeannx1vectorofindependentdrawsfromastandardnormaldistribution,andletVbeacovariancematrixofmarkettime-seriesdata.Then,ifLisadiagonalmatrixoftheeigenvaluesofV,EisamatrixoftheeigenvectorsofV,andCCistheCholeskyfactorizationofV,whichofthefollowingwouldgenerateanormallydistributedrandomvectorwithmeanzeroandcovariancematrixVtobeusedinaMonteCarlosimulation?NC'CNNCELECannotbedeterminedfromdatagivenConsiderastockthatpaysnodividends,hasavolatilityof25%paandanexpectedreturnof13%pa.ThecurrentstockpriceisSO=$30.ThisimpliesthemodelSt+1=St(l+0.13At+0.25yAte),whereeisastandardnormalrandomvariable.Toimplementthissimulation,yougenerateapathofthestockpricebystartingatt=0,generatingasamplefore,updatingthestockpriceaccordingtothemodel,incrementingtby1andrepeatingthisprocessuntiltheendofthehorizonisreached.Whichofthefollowingstrategiesforgeneratingasampleforewillimplementthissimulationproperly?Generateasampleforebyusingtheinverseofthestandardnormalcumulativedistributionofasamplevaluedrawnfromauniformdistributionbetween0and1.Generateasampleforebysamplingfromanormaldistributionwithmean0.13andstandarddeviation0.25.Generateasampleforebyusingtheinverseofthestandardnormalcumulativedistributionofasamplevaluedrawnfromauniformdistributionbetween0and1.UseCholeskydecompositiontocorrelatethissamplewiththesamplefromtheprevioustimeinterval.Generateasampleforebysamplingfromanormaldistributionwithmean0.13andstandarddeviation0.25.UseCholeskydecompositiontocorrelatethissamplewiththesamplefromtheprevioustimeinterval.Continuingwiththepreviousquestion,youhaveimplementedthesimulationprocessdiscussedaboveusingatimeintervalAt=0.001,andyouareanalyzingthefollowingstockpricepathgeneratedbyyourimplementation. tSt—1eAS030.000.09300.03130.030.84930.21230.230.96170.23330.470.24600.06430.530.47690.12530.650.71410.18Giventhissample,whichofthefollowingsimulationstepsmostlikelycontainsanerror.CalculationtoupdatethestockpriceGenerationofrandomsamplevalueforeCalculationofthechangeinstockpriceduringeachperiodNoneoftheaboveInthegeometricBrownianmotionprocessforavariableS,Sisnormallydistributed.dln(S)isnormallydistributed.dS/Sisnormallydistributed.Sislognormallydistributed.IonlyII,III,andIVIVonlyIIIandIVConsiderthatastockpriceSthatfollowsageometricBrownianmotiondS=aSdt+bSdz,withbstrictlypositive.Whichofthefollowingstatementsisfalse?Ifthedriftaispositive,thepriceoneyearfromnowwillbeabovetoday'sprice.Theinstantaneousrateofreturnonthestockfollowsanormaldistribution.ThestockpriceSfollowsalognormaldistribution.Thismodeldoesnotimposemeanreversion.TheVasicekmodeldefinesarisk-neutralprocessforrwhichisdr=a(b-r)dt+adz,wherea,b,andoareconstant,andrrepresentstherateofinterest.FromthisequationwecanconcludethatthemodelisaMonteCarlo-typemodelSingle-factorterm-structuremodelTwo-factorterm-structuremodelDecisiontreemodelTheterma(b-r)inthepreviousquestionrepresentswhichterm?GammaStochasticReversionVegaWhichgroupofterm-structuremodelsdotheHo-Lee,Hull-White,andHeath,Jarrow,andMortonmodelsbelongto?No-arbitragemodelsTwo-factormodelsLognormalmodelsDeterministicmodelsAplausiblestochasticprocessfortheshort-termrateisoftenconsideredtobeonewheretherateispulledbacktosomelong-runaveragelevel.Whichoneofthefollowingterm-structuremodelsdoesnotincludethischaracteristic?TheVasicekmodelTheHo-LeemodelTheHull-WhitemodelTheCox-Ingersoll-RossmodelWhichofthefollowingstatementsaboutMonteCarlosimulationisfalse?MonteCarlosimulationcanbeusedwithalognormaldistribution.MonteCarlosimulationcangeneratedistributionsforportfoliosthatcontainonlylinearpositions.OnedrawbackofMonteCarlosimulationisthatitiscomputationallyveryintensive.Assumingtheunderlyingprocessisnormal,thestandarderrorresultingfromMonteCarlosimulationisinverselyrelatedtothesquarerootofthenumberoftrials.AriskmanagerhasbeenrequestedtoprovidesomeindicationofaccuracyofaMonteCarlosimulation.Using1,000replicationsofanormallydistributedvariableS,therelativeerrorintheone-day99%VARis5%.Undertheseconditions,Using1,000replicationsofalongoptionpositiononSshouldcreatealargerrelativeerror.Using10,000replicationsshouldcreatealargerrelativeerror.Usinganothersetof1,000replicationswillcreateanexactmeasureof5.0%forrelativeerror.Using1,000replicationsofashortoptionpositiononSshouldcreatealargerrelativeerror.ThemeasurementerrorinVAR,duetosamplingvariation,shouldbegreaterwithMoreobservationsandahighconfidencelevel(e.g.,99%)FewerobservationsandahighconfidencelevelMoreobservationsandalowconfidencelevel(e.g.,95%)Fewerobservationsandalowconfidencelevelletthepdff(x)bepositiveatx=-1,0,1andzeroelsewhere.iff(0)=0.25,findE(x2)iff(0)=0.25andifE(X)=0.25,determinef(-1)andf(1)Onecardisdrawnfromastandard52carddeck.Indescribingtheoccurrenceoftwopossibleevents,anAceandaKing,thesetwoeventsaresaidtobe:independentmutuallyexclusiverandomvariablesrandomlyindependent.WhichofthefollowingisNOTapossibleprobability?25/1001.2510Amongtwenty-fivearticles,ninearedefective,sixhavingonlyminordefectsandthreehavingmajordefects.Determinetheprobabilitythatanarticleselectedatrandomhasmajordefectsgiventhatithasdefects.1/8Amongtwenty-fivearticleseightaredefective,sixhavingonlyminordefectsandtwohavingmajordefects.Determinetheprobabilitythatanarticleselectedatrandomhasmajordefectsgiventhatithasdefects..08 (c)1/3.25 (d).24Adormitoryoncampushouses200students.120aremale,50areupperdivisionstudents,and40areupperdivisionmalestudents.Astudentisselectedatrandom.Theprobabilityofselectingalowerdivisionstudent,giventhestudentisafemale,is:(a)7/8 (d)7/20(b)7/15 (e)1/42/5Whichofthefollowingstatementsregardinglinearregressionisfalse?Heteroskedasticityoccurswhenthevarianceofresidualsisnotthesameacrossallobservationsinthesample.Unconditionalheteroskedasticityleadstoinefficientestimates,whereasconditionalheteroskedasticitycanleadtoproblemswithbothinferenceandestimation.Serialcorrelationoccurswhentheresidualtermsarecorrelatedwitheachother.Multicollinearityoccurswhenahighcorrelationexistsbetweenoramongtwoormoreoftheindependentvariablesinamultipleregression.Considertwostocks,AandB.Assumetheirannualreturnsarejointlynormallydistributed,themarginaldistributionofeachstockhasmean2%andstandarddeviation10%,andthecorrelationis0.9.WhatistheexpectedannualreturnofstockAiftheannualreturnofstockBis3%?2%2.9%4.7%1.1%Considerthefollowinglinearregressionmodel:Y=a+bX+e.Supposea=0.05,b=1.2,SD(Y)=0.26,SD(e)=0.1,whatisthecorrelationbetweenXandY?0.9230.8520.7010.462Underwhatcircumstancescouldtheexplanatorypowerofregressionanalysisbeoverstated?Theexplanatoryvariablesarenotcorrelatedwithoneanother.Thevarianceoftheerrortermdecreasesasthevalueofthedependentvariableincreases.Theerrortermisnormallydistributed.Animportantexplanatoryvariableisomittedthatinfluencestheexplanatoryvariablesincluded,andthedependentvariable.Whatdoesahypothesistestatthe5%significancelevelmean?P(notrejectH0|H0istrue)=0.05P(notrejectH0|H0isfalse)=0.05P(rejectH0|H0istrue)=0.05P(rejectH0|H0isfalse)=0.05Assumewecalculateaone-weekVARforanaturalgaspositionbyrescal-ingthedailyVARusingthesquare-rootrule.Letusnowassumethatwedeterminethetrugaspriceprocesstobemean-revertingandrecalculatetheVAR.Whichofthefollowingstatementsistrue?TherecalculatedVARwillbelessthantheoriginalVAR.TherecalculatedVARwillbeequaltotheoriginalVAR.TherecalculatedVARwillbegreaterthantheoriginalVAR.ThereisnonecessaryrelationbetweentherecalculatedVARandtheoriginalVAR.Onamultiple-choiceexamwithfourchoicesforeachofsixquestions,whatistheprobabilitythatastudentgetsfewerthantwoquestionscorrectsimplybyguessing?0.46%23.73%35.60%53.39%1. Thecurrentyieldonabondisequalto .annualinterestdividedbythecurrentmarketpricetheyieldtomaturityannualinterestdividedbytheparvaluetheinternalrateofreturnAnswer:ADifficulty:EasyRationale:Aiscurrentyieldandisquotedassuchinthefinancialpress.Ifa7%couponbondistradingfor$975.00,ithasacurrentyieldof percent.A)

B)

C)D)Answer:DA)

B)

C)D)Answer:D7.248.537.18Difficulty:EasyRationale:70/975=7.18.Ifa6%couponbondistradingfor$950.00,ithasacurrentyieldof percent.A)

B)

C)D)A)

B)

C)D)6.0Answer:BDifficulty:EasyAnswer:BRationale:60/950=6.3.Ifan8%couponbondistradingfor$1025.00,ithasacurrentyieldof percent.7.9Answer:ADifficulty:EasyRationale:80/1025=7.8.Ifa7.5%couponbondistradingfor$1050.00,ithasacurrentyieldof percent.7.0Answer:CDifficulty:EasyRationale:75/1050=7.1.Acouponbondpaysannualinterest,hasaparvalueof$1,000,maturesin4years,hasacouponrateof10%,andhasayieldtomaturityof12%.Thecurrentyieldonthisbondis .10.65%10.45%10.95%10.52%Answer:ADifficulty:ModerateRationale:FV=1000,n=4,PMT=100,i=12,PV=939.25;$100/$939.25=10.65%.

7.Acouponbondpaysannualinterest,hasaparvalueof$1,000,maturesin12years,hasacouponrateof11%,andhasayieldtomaturityof12%.ThecurrentyieldonthisbondisA)10.39%B)10.43%C)10.58%D)10.66%Answer:DDifficulty:ModerateRationale:FV=1000,n=12,PMT=110,i=12,PV=938.06;$100/$938.06=10.66%.8.Ofthefollowingfourinvestments, isconsideredthesafest.A)corporatebondsB)U.S.AgencyissuesC)TreasurybondsD)TreasurybillsAnswer:DDifficulty:EasyRationale:OnlyTreasuryissuesareinsuredbytheU.S.government;theshorter-termtheinstrument,thesafertheinstrument.9.Toearnahighratingfromthebondratingagencies,afirmshouldhaveA)alowtimesinterestearnedratioB)alowdebttoequityratioC)ahighquickratioD)BandCAnswer:DDifficulty:EasyRationale:Highvaluesforthetimesinterestandquickratiosandalowdebttoequityratioaredesirableindicatorsofsafety.10.Atissue,couponbondstypicallysell .A)aboveparvalueB)belowparC)atornearparvalueD)atavalueunrelatedtoparAnswer:CDifficulty:EasyRationale:Iftheinvestmentbankerhasappraisedthemarketandthequalityofthebondcorrectly,thebondwillsellatornearpar(unlessinterestrateshavechangedverydramaticallyandveryquicklyaroundthetimeofissuance).11.Accruedinterestisquotedinthebondpriceinthefinancialpress.mustbepaidbythebuyerofthebondandremittedtothesellerofthebond.mustbepaidtothebrokerfortheinconvenienceofsellingbondsbetweenmaturitydates.AandB.Answer:BDifficulty:ModerateRationale:Accruedinterestmustbepaidbythebuyer,butisnotincludedinthequotationspageprice.12.Theinvoicepriceofabondthatabuyerwouldpayisequaltotheaskedpriceplusaccruedinterest.theaskedpricelessaccruedinterest.thebidpriceplusaccruedinterest.thebidpricelessaccruedinterest.Answer:ADifficulty:EasyRationale:Thebuyerofabondwillbuyattheaskedpriceandwillalsobeinvoicedforanyaccruedinterestduetotheseller.1. Whichofthefollowingstatementsregardingrisk-averseinvestorsistrue?Theyonlycareabouttherateofreturn.Theyacceptinvestmentsthatarefairgames.Theyonlyacceptriskyinvestmentsthatofferriskpremiumsovertherisk-freerate.Theyarewillingtoacceptlowerreturnsandhighrisk.Answer:CDifficulty:Moderate2. Whichofthefollowingstatementsis(are)true?Risk-averseinvestorsrejectinvestmentsthatarefairgames.Risk-neutralinvestorsjudgeriskyinvestmentsonlybytheexpectedreturns.Risk-averseinvestorsjudgeinvestmentsonlybytheirriskiness.Risk-lovinginvestorswillnotengageinfairgames.IonlyIIonlyIandIIonlyIIandIIIonlyAnswer:CDifficulty:ModerateRationale:Risk-averseinvestorsconsiderariskyinvestmentonlyiftheinvestmentoffersariskpremium.Risk-neutralinvestorslookonlyatexpectedreturnswhenmakinganinvestmentdecision.Inthemean-standarddeviationgraphanindifferencecurvehasa slope.negativezeropositivenortheastAnswer:CDifficulty:EasyRationale:Therisk-returntrade-offisoneinwhichgreaterriskistakenifgreaterreturnscanbeexpected,resultinginapositiveslope.Inthemean-standarddeviationgraph,whichoneofthefollowingstatementsistrueregardingtheindifferencecurveofarisk-averseinvestor?Itisthelocusofportfoliosthathavethesameexpectedratesofreturnanddifferentstandarddeviations.Itisthelocusofportfoliosthathavethesamestandarddeviationsanddifferentratesofreturn.Itisthelocusofportfoliosthatofferthesameutilityaccordingtoreturnsandstandarddeviations.Itconnectsportfoliosthatofferincreasingutilitiesaccordingtoreturnsandstandarddeviations.Answer:CDifficulty:ModerateRationale:Indifferencecurvesplottrade-offalternativesthatprovideequalutilitytotheindividual(inthiscase,thetrade-offsaretherisk-returncharacteristicsoftheportfolios).Inareturn-standarddeviationspace,whichofthefollowingstatementsis(are)trueforrisk-averseinvestors?(Theverticalandhorizontallinesarereferredtoastheexpectedreturn-axisandthestandarddeviation-axis,respectively.)Aninvestor'sownindifferencecurvesmightintersect.Indifferencecurveshavenegativeslopes.Inasetofindifferencecurves,thehighestoffersthegreatestutility.Indifferencecurvesoftwoinvestorsmightintersect.IandIIonlyIIandIIIonlyIandIVonlyIIIandIVonlynoneoftheaboveAnswer:DDifficulty:ModerateRationale:Aninvestor'sindifferencecurvesareparallel,andthuscannotintersectandhavepositiveslopes.Thehighestindifferencecurve(theoneinthemostnorthwesternposition)offersthegreatestutility.Indifferencecurvesofinvestorswithsimilarrisk-returntrade-offsmightintersect.Eliasisarisk-averseinvestor.Davidisalessrisk-averseinvestorthanElias.Therefore,forthesamerisk,DavidrequiresahigherrateofreturnthanElias.forthesamereturn,EliastolerateshigherriskthanDavid.forthesamerisk,EliasrequiresalowerrateofreturnthanDavid.forthesamereturn,DavidtolerateshigherriskthanElias.Answer:DDifficulty:ModerateRationale:Themoreriskaversetheinvestor,thelessriskthatistolerated,givenarateofreturn.Whenaninvestmentadvisorattemptstodetermineaninvestor'srisktolerance,whichfactorwouldtheybeleastlikelytoassess?theinvestor'spriorinvestingexperiencetheinvestor'sdegreeoffinancialsecuritytheinvestor'stendencytomakeriskyorconservativechoicesthelevelofreturntheinvestorpreferstheinvestor'sfeelingaboutlossAnswer:DDifficulty:ModerateUsethefollowingtoanswerquestions8-9:Assumeaninvestorwiththefollowingutilityfunction:U=E(r)-3/2(s2).Tomaximizeherexpectedutility,shewouldchoosetheassetwithanexpectedrateofreturnof andastandarddeviationof ,respectively.12%;20%10%;15%10%;10%8%;10%noneoftheaboveAnswer:CDifficulty:ModerateRationale:U=0.10-3/2(0.10)2=8.5%;highestutilityofchoices.Tomaximizeherexpectedutility,whichoneofthefollowinginvestmentalternativeswouldshechoose?Aportfoliothatpays10percentwitha60percentprobabilityor5percentwith40percentprobability.Aportfoliothatpays10percentwith40percentprobabilityor5percentwitha60percentprobability.Aportfoliothatpays12percentwith60percentprobabilityor5percentwith40percentprobability.Aportfoliothatpays12percentwith40percentprobabilityor5percentwith60percentprobability.Answer:CDifficulty:DifficultRationale:U(c)=9.02%;highestutilityofpossibilities.Aportfoliohasanexpectedrateofreturnof0.15andastandarddeviationof0.15.Therisk-freerateis6percent.Aninvestorhasthefollowingutilityfunction:U=E(r)-(A/2)s2.WhichvalueofAmakesthisinvestorindifferentbetweentheriskyportfolioandtherisk-freeasset?5678Answer:DDifficulty:DifficultRationale:0.06=0.15-A/2(0.15)2;0.06-0.15=-A/2(0.0225);-0.09=-0.01125A;A=8;U=0.15-8/2(0.15)2=6%;U(Rf)=6%.Accordingtothemean-variancecriterion,whichoneofthefollowinginvestmentsdominatesallothers?E(r)=0.15;Variance=0.20E(r)=0.10;Variance=0.20E(r)=0.10;Variance=0.25E(r)=0.15;Variance=0.25Answer:ADifficulty:DifficultRationale:Agivesthehighestreturnwiththeleastrisk;returnperunitofriskis.75,whichdominatesthereward-riskratiofortheotherchoices.Considerariskyportfolio,A,withanexpectedrateofreturnof0.15andastandarddeviationof0.15,thatliesonagivenindifferencecurve.Whichoneofthefollowingportfoliosmightlieonthesameindifferencecurve?E(r)=0.15;Standarddeviation=0.20E(r)=0.15;Standarddeviation=0.10E(r)=0.10;Standarddeviation=0.10E(r)=0.20;Standarddeviation=0.15Answer:CDifficulty:DifficultRationale:PortfolioAhasarewardtoriskratioof1.0;portfolioCistheonlychoicewiththesamerisk-returntradeoff.Usethefollowingtoanswerquestions13-15:investmentExpectedReturnE(r)■StandardDevi^hcir.50..50.-210.160-.240；21(A/2)s2,whereA=4.0.13.A)B)C)D)Answer:CBasedontheutilityfunctionabove,whichinvestmentwouldyouselect?1234Difficulty:DifficultRationale:U(c)=0.21-4/2(0.16)2=15.88(highestutilityofchoices).14.A)B)C)D)Whichinvestmentwouldyouselectifyouwereriskneutral?1234Answer:DDifficulty:DifficultRationale:Ifyouareriskneutral,youronlyconcerniswithreturn,notrisk.Thevariable(A)intheutilityfunctionrepresentsthe:investor'sreturnrequirement.investor'saversiontorisk.certainty-equivalentrateoftheportfolio.minimumrequiredutilityoftheportfolio.Answer:BDifficulty:ModerateRationale:Aisanarbitraryscalefactorusedtomeasureinvestorrisktolerance.ThehigherthevalueofA,themoreriskaversetheinvestor.Theexactindifferencecurvesofdifferentinvestorscannotbeknownwithperfectcertainty.canbecalculatedpreciselywiththeuseofadvancedcalculus.althoughnotknownwithperfectcertainty,doallowtheadvisortocreatemoresuitableportfoliosfortheclient.AandC.Answer:DDifficulty:EasyRationale:Indifferencecurvescannotbecalculatedprecisely,butthetheorydoesallowforthecreationofmoresuitableportfoliosforinvestorsofdifferinglevelsofrisktolerance.Theriskinessofindividualassetsshouldbeconsideredfortheassetinisolation.shouldbeconsideredinthecontextoftheeffectonoverallportfoliobinedwiththeriskinessofotherindividualassets(intheproportionstheseassetsconstituteoftheentireportfolio)shouldbetherelevantriskmeasure.BandC.noneoftheabove.Answer:DDifficulty:EasyRationale:Therelevantriskisportfoliorisk;thus,theriskinessofanindividualsecurityshouldbeconsideredinthecontextoftheportfolioasawhole.Afairgamewillnotbeundertakenbyarisk-averseinvestor.isariskyinvestmentwithazeroriskpremium.isarisklessinvestment.BothAandBaretrue.BothAandCaretrue.Answer:DDifficulty:ModerateRationale:Afairgameisariskyinvestmentwithapayoffexactlyequaltoitsexpectedvalue.Sinceitoffersnoriskpremium,itwillnotbeacceptabletoarisk-averseinvestor.Thepresenceofriskmeansthatinvestorswilllosemoney.morethanoneoutcomeispossible.thestandarddeviationofthepayoffislargerthanitsexpectedvalue.finalwealthwillbegreaterthaninitialwealth.terminalwealthwillbelessthaninitialwealth.Answer:BDifficulty:EasyRationale:Thepresenceofriskmeansthatmorethanoneoutcomeispossible.Theutilityscoreaninvestorassignstoaparticularportfolio,otherthingsequal,willdecreaseastherateofreturnincreases.willdecreaseasthestandarddeviationincreases.willdecreaseasthevarianceincreases.willincreaseasthevarianceincreases.willincreaseastherateofreturnincreases.Answer:EDifficulty:EasyRationale:Utilityisenhancedbyhigherexpectedreturnsanddiminishedbyhigherrisk.Thecertaintyequivalentrateofaportfolioistheratethatarisk-freeinvestmentwouldneedtoofferwithcertaintytobeconsideredequallyattractiveastheriskyportfolio.theratethattheinvestormustearnforcertaintogiveuptheuseofhismoney.theminimumrateguaranteedbyinstitutionssuchasbanks.D) theratethatequates“A”intheutilityfunctionwiththeaverageriskaversioncoefficientforallrisk-averseinvestors.E) representedbythescalingfactor“-.005”intheutilityfunction.Answer:ADifficulty:ModerateAccordingtothemean-variancecriterion,whichofthestatementsbelowiscorrect?InvestmentE©StandardDeviationA10%疏B21曙11%C2WD2磁1伪InvestmentBdominatesInvestmentA.InvestmentBdominatesInvestmentC.InvestmentDdominatesalloftheotherinvestments.InvestmentDdominatesonlyInvestmentB.InvestmentCdominatesinvestmentA.Answer:BDifficulty:ModerateRationale:Thisquestionteststhestudent'sunderstandingofhowtoapplythemean-variancecriterion.Steveismorerisk-aversethanEdie.OnagraphthatshowsSteveandEdie'sindifferencecurves,whichofthefollowingistrue?Assumethatthegraphshowsexpectedreturnontheverticalaxisandstandarddeviationonthehorizontalaxis.SteveandEdie'sindifferencecurvesmightintersect.Steve'sindifferencecurveswillhaveflatterslopesthanEdie's.Steve'sindifferencecurveswillhavesteeperslopesthanEdie's.SteveandEdie'sindifferencecurveswillnotintersect.Steve'sindifferencecurveswillbedownwardslopingandEdie'swillbeupwardsloping.IandVIandIIIIIIandIVIandIIIIandIVAnswer:BDifficulty:ModerateRationale:Thisquestiontestswhetherthestudentunderstandsthegraphicalpropertiesofindifferencecurvesandhowtheyrelatetothedegreeofrisktolerance.TheCapitalAllocationLinecanbedescribedastheinvestmentopportunitysetformedwithariskyassetandarisk-freeasset.investmentopportunitysetformedwithtworiskyassets.lineonwhichlieallportfoliosthatofferthesameutilitytoaparticularinvestor.lineonwhichlieallportfolioswiththesameexpectedrateofreturnanddifferentstandarddeviations.noneoftheabove.Answer:ADifficulty:ModerateRationale:TheCALhasaninterceptequaltotherisk-freerate.Itisastraightlinethroughthepointrepresentingtherisk-freeassetandtheriskyportfolio,inexpected-return/standarddeviationspace.WhichofthefollowingstatementsregardingtheCapitalAllocationLine(CAL)isfals?eTheCALshowsrisk-returncombinations.TheslopeoftheCALequalstheincreaseintheexpectedreturnofariskyportfolioperunitofadditionalstandarddeviation.TheslopeoftheCALisalsocalledthereward-to-variabilityratio.TheCALisalsocalledtheefficientfrontierofriskyassetsintheabsenceofarisk-freeasset.BothAandDaretrue.Answer:DDifficulty:ModerateRationale:TheCALconsistsofcombinationsofariskyassetandarisk-freeassetwhoseslopeisthereward-to-variabilityratio;thus,allstatementsexceptdaretrue.Giventhecapitalallocationline,aninvestor'soptimalportfolioistheportfoliothatmaximizesherexpectedprofit.maximizesherrisk.minimizesbothherriskandreturn.maximizesherexpectedutility.noneoftheabove.Answer:DDifficulty:ModerateRationale:Bymaximizingexpectedutility,theinvestorisobtainingthebestrisk-returnrelationshipspossibleandacceptableforher.Aninvestorinvests30percentofhiswealthinariskyassetwithanexpectedrateofreturnof0.15andavarianceof0.04and70percentinaT-billthatpays6percent.Hisportfolio'sexpectedreturnandstandarddeviationare and ,respectively.A)0.114;0.12B)0.087;0.06C)0.295;0.12D)0.087;0.12E)noneoftheaboveAnswer:BDifficulty:ModerateRationale:E(rP)=0.3(15%)+0.7(6%)=8.7%;sP=0.3(0.04)1/2=6%.Usethefollowingtoanswerquestions28-31:Youinvest$100inariskyassetwithanexpectedrateofreturnof0.12andastandarddeviationof0.15andaT-billwitharateofreturnof0.05.Whatpercentagesofyourmoneymustbeinvestedintheriskyassetandtherisk-freeasset,respectively,toformaportfoliowithanexpectedreturnof0.09?A)85%and15%B)75%and25%C)67%and33%D)57%and43%E)cannotbedeterminedAnswer:DDifficulty:ModerateRationale:9%=w1(12%)+(1-w1)(5%);9%=12%w1+5%-5%w1;4%=7%w1;w1=0.57;1-w1=0.43;0.57(12%)+0.43(5%)=8.99%.Whatpercentagesofyourmoneymustbeinvestedintherisk-freeassetandtheriskyasset,respectively,toformaportfoliowithastandarddeviationof0.06?A)30%and70%B)50%and50%C)60%and40%D)40%and60%E)cannotbedeterminedAnswer:CDifficulty:ModerateRationale:0.06=x(0.15);x=40%inriskyasset.Aportfoliothathasanexpectedoutcomeof$115isformedbyinvesting$100intheriskyasset.investing$80intheriskyassetand$20intherisk-freeasset.borrowing$43attherisk-freerateandinvestingthetotalamount($143)intheriskyasset.investing$43intheriskyassetand$57intherisklessasset.Suchaportfoliocannotbeformed.Answer:CDifficulty:DifficultRationale:For$100,(115-100)/100=15%;.15=w1(.12)+(1-w1)(.05);.15=.12w1+.05-.05w1;0.10=0.07w1;w1=1.43($100)=$143;(1-w1)$100=-$43.TheslopeoftheCapitalAllocationLineformedwiththeriskyassetandtherisk-freeassetisequalto0.4667.0.800.41667.Cannotbedetermined.Answer:ADifficulty:ModerateRationale:(0.12-0.05)/0.15=0.4667.ConsideraT-billwitharateofreturnof5percentandthefollowingriskysecurities:SecurityA:E(r)=0.15;Variance=0.04SecurityB:E(r)=0.10;Variance=0.0225SecurityC:E(r)=0.12;Variance=0.01SecurityD:E(r)=0.13;Variance=0.0625Fromwhichseto