CFA特許金融分析師-CFA一級-強化練習題（參考）-01-QuantitativeMethod

CFA特許金融分析師-CFA一級-強化練習題（參考）-01-QuantitativeMethod[單選題]1.Apopulationhasanon-normaldistributionwithm（江南博哥）eanμandvarianceσ^2.Thesamplingdistributionofthesamplemeancomputedfromsamplesoflargesizefromthatpopulationwillhave:A.thesamedistributionasthepopulationdistribution.B.itsmeanapproximatelyequaltothepopulationmean.C.itsvarianceapproximatelyequaltothepopulationvariance.正確答案：B參考解析：Biscorrect.Givenapopulationdescribedbyanyprobabilitydistribution(normalornon-normal)withfinitevariance,thecentrallimittheoremstatesthatthesamplingdistributionofthesamplemeanwillbeapproximatelynormal,withthemeanapproximatelyequaltothepopulationmean,whenthesamplesizeislarge.[單選題]2.Thecovarianceofreturnsispositivewhenthereturnsontwoassetstendto:A.havethesameexpectedvalues.B.beabovetheirexpectedvalueatdifferenttimes.C.beonthesamesideoftheirexpectedvalueatthesametime.正確答案：C參考解析：Ciscorrect.Thecovarianceofreturnsispositivewhenthereturnsonbothassetstendtobeonthesameside(aboveorbelow)theirexpectedvaluesatthesametime,indicatinganaveragepositiverelationshipbetweenreturns.[單選題]3.Astockispricedat$100.00andfollowsaone-periodbinomialprocesswithanupmovethatequals1.05andadownmovethatequals0.97.If1millionBernoullitrialsareconducted,andtheaverageterminalstockpriceis$102.00,theprobabilityofanupmove(p)isclosestto:A.0.375.B.0.500.C.0.625.正確答案：C參考解析：Ciscorrect.Theprobabilityofanupmove(p)canbefoundbysolvingtheequation:(p)uS＋(1–p)dS=(p)105＋(1–p)97=102.Solvingforpgives8p=5,sothatp=0.625.[單選題]4.Abankquotesastatedannualinterestrateof4.00%.Ifthatrateisequaltoaneffectiveannualrateof4.08%,thenthebankiscompoundinginterest:A.daily.B.quarterly.C.semiannually.正確答案：A參考解析：Aiscorrect.Theeffectiveannualrate(EAR)whencompoundeddailyis4.08%.[單選題]5.Ananalystisexaminingalargesamplewithanunknownpopulationvariance.Totestthehypothesisthatthehistoricalaveragereturnonanindexislessthanorequalto6%,whichofthefollowingisthemostappropriatetest?A.One-tailedz-testB.Two-tailedz-testC.One-tailedF-test正確答案：A參考解析：Aiscorrect.Ifthepopulationsampledhasunknownvarianceandthesampleislarge,az-testmaybeused.Hypothesesinvolving“greaterthan”or“l(fā)essthan”postulationsareone-sided(one-tailed).Inthissituation,thenullandalternativehypothesesarestatedasH0:μ≤6%andHa:μ>6%,respectively.Aone-tailedt-testisalsoacceptableinthiscase.[單選題]6.Whichofthefollowingshouldbeusedtotestthedifferencebetweenthevariancesoftwonormallydistributedpopulations?A.t-testB.F-testC.Pairedcomparisonstest正確答案：B參考解析：Biscorrect.AnF-testisusedtoconducttestsconcerningthedifferencebetweenthevariancesoftwonormallydistributedpopulationswithrandomindependentsamples.[單選題]7.Asportscar,purchasedfor￡200,000,isfinancedforfiveyearsatanannualrateof6%compoundedmonthly.Ifthefirstpaymentisdueinonemonth,themonthlypaymentisclosestto:A.￡3,847.B.￡3,867.C.￡3,957.正確答案：B參考解析：Biscorrect,calculatedasfollows(whereAisannuityandPVispresentvalue):[單選題]8.Givenaportfoliooffivestocks,howmanyuniquecovarianceterms,excludingvariances,arerequiredtocalculatetheportfolioreturnvariance?A.10B.20C.25正確答案：A參考解析：Aiscorrect.Acovariancematrixforfivestockshas5×5=25entries.Subtractingthe5diagonalvariancetermsresultsin20off-diagonalentries.Becauseacovariancematrixissymmetrical,only10entriesareunique(20/2=10).[單選題]9.WhichofthefollowingisaTypeIerror?A.RejectingatruenullhypothesisB.RejectingafalsenullhypothesisC.Failingtorejectafalsenullhypothesis正確答案：A參考解析：Aiscorrect.ThedefinitionofaTypeIerroriswhenatruenullhypothesisisrejected.[單選題]10.Afterestimatingtheprobabilitythataninvestmentmanagerwillexceedhisbenchmarkreturnineachofthenexttwoquarters,ananalystwantstoforecasttheprobabilitythattheinvestmentmanagerwillexceedhisbenchmarkreturnoverthetwo-quarterperiodintotal.Assumingthateachquarter’sperformanceisindependentoftheother,whichprobabilityruleshouldtheanalystselect?A.AdditionruleB.MultiplicationruleC.Totalprobabilityrule正確答案：B參考解析：Biscorrect.Becausetheeventsareindependent,themultiplicationruleismostappropriateforforecastingtheirjointprobability.ThemultiplicationruleforindependenteventsstatesthatthejointprobabilityofbothAandBoccurringisP(AB)=P(A)P(B).[單選題]11.Whichofthefollowinggroupsbestillustratesapopulation?A.The500companiesintheS&P500IndexB.TheNYSE-listedstocksintheDowJonesIndustrialAverageC.TheLehmanAggregateBondIndexasarepresentationoftheUSbondmarket正確答案：A參考解析：Aiscorrect.Apopulationisdefinedasallmembersofaspecifiedgroup.TheS&P500Indexconsistsof500companies,sothisgroupisthepopulationofcompaniesintheindex.BisincorrectbecausethereareseveralDowJonescomponentstocksthatarenottradedontheNYSE,makingtheNYSEgroupasubsetofthetotalpopulationofstocksincludedintheDowJonesaverage.CisincorrectbecausealthoughtheLehmanAggregateBondIndexisrepresentativeoftheUSbondmarket,itisasamplingofbondsinthatmarketandnottheentirepopulationofbondsinthatmarket.[單選題]12.Overthepast240months,aninvestor’sportfoliohadameanmonthlyreturnof0.79%,withastandarddeviationofmonthlyreturnsof1.16%.AccordingtoChebyshev’sinequality,theminimumnumberofthe240monthlyreturnsthatfallintotherangeof-0.95%to2.53%isclosestto:A.80.B.107.C.133.正確答案：C參考解析：Ciscorrect.AccordingtoChebyshev’sinequality,theproportionoftheobservationswithinkstandarddeviationsofthearithmeticmeanisatleast1–1/k^2forallk>1.Theupperlimitoftherangeis2.53%,whichis2.53-0.79=1.74%abovethemean.Thelowerlimitis-0.95,whichis0.79-(-0.95)=1.74%belowthemean.Asaresult,k=1.74/1.16=1.50standarddeviations.Becausek=1.50,theproportionofobservationswithintheintervalisatleast1–1/1.5^2=1–0.444=0.556,or55.6%.Thus,thenumberofobservationsinthegivenrangeisatleast240×55.6%,whichis≈133.[單選題]13.Thevalueofateststatisticisbestdescribedasthebasisfordecidingwhetherto:A.rejectthenullhypothesis.B.acceptthenullhypothesis.C.rejectthealternativehypothesis.正確答案：A參考解析：Aiscorrect.Calculatedusingasample,ateststatisticisaquantitywhosevalueisthebasisfordecidingwhethertorejectthenullhypothesis.[單選題]14.Incontrasttonormaldistributions,lognormaldistributions:A.areskewedtotheleft.B.haveoutcomesthatcannotbenegative.C.aremoresuitablefordescribingassetreturnsthanassetprices.正確答案：B參考解析：Biscorrect.Bydefinition,lognormalrandomvariablescannothavenegativevalues.[單選題]15.Forasamplesizeof65withameanof31takenfromanormallydistributedpopulationwithavarianceof529,a99%confidenceintervalforthepopulationmeanwillhavealowerlimitclosestto:A.23.64.B.25.41.C.30.09.正確答案：A參考解析：Aiscorrect.Tosolve,usethestructureofConfidenceinterval=Pointestimate±Reliabilityfactor×Standarderror,which,foranormallydistributedpopulationwithknownvariance,isrepresentedbythefollowingformula:[單選題]16.Theprobabilityofaneventgiventhatanothereventhasoccurredisa:A.jointprobability.B.marginalprobability.C.conditionalprobability.正確答案：C參考解析：Ciscorrect.Aconditionalprobabilityistheprobabilityofaneventgiventhatanothereventhasoccurred.[單選題]17.Aportfoliomanagerannuallyoutperformsherbenchmark60%ofthetime.Assumingindependentannualtrials,whatistheprobabilitythatshewilloutperformherbenchmarkfourormoretimesoverthenextfiveyears?A.0.26B.0.34C.0.48正確答案：B參考解析：Biscorrect.Tocalculatetheprobabilityof4yearsofoutperformance,usetheformula:Usingthisformulatocalculatetheprobabilityin4of5years,n=5,x=4andp=0.60.Therefore,Theprobabilityofoutperforming4ormoretimesisp(4)+p(5)=0.2592+0.0778=0.3370[單選題]18.Johnpurchased60%ofthestocksinaportfolio,whileAndrewpurchasedtheother40%.HalfofJohn’sstock-picksareconsideredgood,whileafourthofAndrew’sareconsideredtobegood.Ifarandomlychosenstockisagoodone,whatistheprobabilityJohnselectedit?A.0.40.B.0.30.C.0.75.正確答案：C參考解析：Usingtheinformationofthestockbeinggood,theprobabilityisupdatedtoaconditionalprobability:P(John|good)=P(goodandJohn)/P(good).P(goodandJohn)=P(good|John)×P(John)=0.5×0.6=0.3.P(goodandAndrew)=0.25×0.40=0.10.P(good)=P(goodandJohn)+P(goodandAndrew)=0.40.P(John|good)=P(goodandJohn)/P(good)=0.3/0.4=0.75.[單選題]19.JillBattenisanalyzinghowthereturnsonthestockofStellarEnergyCorp.arerelatedwiththepreviousmonth'spercentchangeintheUSConsumerPriceIndexforEnergy(CPIENG).Basedon248observations,shehascomputedthesamplecorrelationbetweentheStellarandCPIENGvariablestobe-0.1452.Shealsowantstodeterminewhetherthesamplecorrelationisstatisticallysignificant.Thecriticalvaluefortheteststatisticatthe0.05levelofsignificanceisapproximately1.96.BattenshouldconcludethatthestatisticalrelationshipbetweenStellarandCPIENGis:A.significant,becausethecalculatedteststatistichasalowerabsolutevaluethanthecriticalvaluefortheteststatistic.B.significant,becausethecalculatedteststatistichasahigherabsolutevaluethanthecriticalvaluefortheteststatistic.C.notsignificant,becausethecalculatedteststatistichasahigherabsolutevaluethanthecriticalvaluefortheteststatistic.正確答案：B參考解析：Biscorrect.ThecalculatedteststatisticisBecausetheabsolutevalueoft=-2.30177isgreaterthan1.96,thecorrelationcoefficientisstatisticallysignificant.[單選題]20.Arandomnumberbetweenzeroandoneisgeneratedaccordingtoacontinuousuniformdistribution.Whatistheprobabilitythatthefirstnumbergeneratedwillhaveavalueofexactly0.30?A.0%B.30%C.70%正確答案：A參考解析：Aiscorrect.Theprobabilityofgeneratingarandomnumberequaltoanyfixedpointunderacontinuousuniformdistributioniszero.[單選題]21.Indescriptivestatistics,anexampleofaparameteristhe:A.medianofapopulation.B.meanofasampleofobservations.C.standarddeviationofasampleofobservations.正確答案：A參考解析：Aiscorrect.Anydescriptivemeasureofapopulationcharacteristicisreferredtoasaparameter.[單選題]22.Areturndistributionwithfrequentsmallgainsandafewextremelossesismostlikelytobecalled:A.leptokurtic.B.positivelyskewed.C.negativelyskewed.正確答案：C參考解析：Ciscorrect.Areturndistributionwithnegativeskewhasfrequentsmallgainsandafewextremelosses.Aisincorrectbecausealeptokurticdistributionismorepeakedwithfattertails,whichexhibitbothextremegainsandlosses.Bisincorrectbecauseareturndistributionwithpositiveskewhasfrequentsmalllossesandafewextremegains.[單選題]23.Aperpetualpreferredstockmakesitsfirstquarterlydividendpaymentof$2.00infivequarters.Iftherequiredannualrateofreturnis6%compoundedquarterly,thestock’spresentvalueisclosestto:A.$31.B.$126.C.$133.正確答案：B參考解析：Biscorrect.Thevalueoftheperpetuityoneyearfromnowiscalculatedas:PV=A/r,wherePVispresentvalue,Aisannuity,andrisexpressedasaquarterlyrequiredrateofreturnbecausethepaymentsarequarterly.[單選題]24.Foralumpsuminvestmentof￥250,000investedatastatedannualrateof3%compoundeddaily,thenumberofmonthsneededtogrowthesumto￥1,000,000isclosestto:A.555.B.563.C.576.正確答案：A參考解析：Aiscorrect.Theeffectiveannualrate(EAR)iscalculatedasfollows:SolvingforNonafinancialcalculatorresultsin(whereFVisfuturevalueandPVispresentvalue):[單選題]25.Whichofthefollowingcorrelationcoefficientsindicatestheweakestlinearrelationshipbetweentwovariables?A.–0.67B.–0.24C.0.33正確答案：B參考解析：Biscorrect.Correlationsnear+1exhibitstrongpositivelinearity,whereascorrelationsnear–1exhibitstrongnegativelinearity.Acorrelationof0indicatesanabsenceofanylinearrelationshipbetweenthevariables.Thecloserthecorrelationisto0,theweakerthelinearrelationship.[單選題]26.Anincreaseinsamplesizeismostlikelytoresultina:A.widerconfidenceinterval.B.decreaseinthestandarderrorofthesamplemean.C.lowerlikelihoodofsamplingfrommorethanonepopulation.正確答案：B參考解析：Biscorrect.Allelsebeingequal,asthesamplesizeincreases,thestandarderrorofthesamplemeandecreasesandthewidthoftheconfidenceintervalalsodecreases.[單選題]27.Allelsebeingequal,asthecorrelationbetweentwoassetsapproaches+1.0,thediversificationbenefits:A.decrease.B.staythesame.C.increase.正確答案：A參考解析：Aiscorrect.Asthecorrelationbetweentwoassetsapproaches+1,diversificationbenefitsdecrease.Inotherwords,anincreasinglypositivecorrelationindicatesanincreasinglystrongpositivelinearrelationshipandfewerdiversificationbenefits.[單選題]28.Asthet-distribution’sdegreesoffreedomdecrease,thet-distributionmostlikely:A.exhibitstailsthatbecomefatter.B.approachesastandardnormaldistribution.C.becomesasymmetricallydistributedarounditsmeanvalue.正確答案：A參考解析：Aiscorrect.Astandardnormaldistributionhastailsthatapproachzerofasterthanthet-distribution.Asdegreesoffreedomincrease,thetailsofthet-distributionbecomelessfatandthet-distributionbeginstolookmorelikeastandardnormaldistribution.Butasdegreesoffreedomdecrease,thetailsofthet-distributionbecomefatter.[單選題]29.Ifanestimatorisconsistent,anincreaseinsamplesizewillincreasethe:A.accuracyofestimates.B.efficiencyoftheestimator.C.unbiasednessoftheestimator.正確答案：A參考解析：Aiscorrect.Aconsistentestimatorisoneforwhichtheprobabilityofestimatesclosetothevalueofthepopulationparameterincreasesassamplesizeincreases.Morespecifically,aconsistentestimator’ssamplingdistributionbecomesconcentratedonthevalueoftheparameteritisintendedtoestimateasthesamplesizeapproachesinfinity.[單選題]30.Whichofthefollowingrepresentsacorrectstatementaboutthep-value?A.Thep-valueofferslesspreciseinformationthandoestherejectionpointsapproach.B.Alargerp-valueprovidesstrongerevidenceinsupportofthealternativehypothesis.C.Ap-valuelessthanthespecifiedlevelofsignificanceleadstorejectionofthenullhypothesis.正確答案：C參考解析：Ciscorrect.Thep-valueisthesmallestlevelofsignificanceatwhichthenullhypothesiscanberejectedforagivenvalueoftheteststatistic.Thenullhypothesisisrejectedwhenthep-valueislessthanthespecifiedsignificancelevel.[單選題]31.Ahypothesistestforanormally-distributedpopulationata0.05significancelevelimpliesa:A.95%probabilityofrejectingatruenullhypothesis.B.95%probabilityofaTypeIerrorforatwo-tailedtest.C.5%criticalvaluerejectionregioninatailofthedistributionforaone-tailedtest.正確答案：C參考解析：Ciscorrect.Foraone-tailedhypothesistest,thereisa5%criticalvaluerejectionregioninonetailofthedistribution.[單選題]32.Aclientrequires￡100,000oneyearfromnow.Ifthestatedannualrateis2.50%compoundedweekly,thedepositneededtodayisclosestto:A.￡97,500.B.￡97,532.C.￡97,561.正確答案：B參考解析：Biscorrectbecause￡97,531representsthepresentvalue(PV)of￡100,000receivedoneyearfromtodaywhentoday’sdepositearnsastatedannualrateof2.50%andinterestcompoundsweekly,asshowninthefollowingequation(whereFVisfuturevalue):[單選題]33.Thevalueinsixyearsof$75,000investedtodayatastatedannualinterestrateof7%compoundedquarterlyisclosestto:A.$112,555.B.$113,330.C.$113,733.正確答案：C參考解析：Ciscorrect,asshowninthefollowing(whereFVisfuturevalueandPVispresentvalue):[單選題]34.Foratwo-sidedconfidenceinterval,anincreaseinthedegreeofconfidencewillresultin:A.awiderconfidenceinterval.B.anarrowerconfidenceinterval.C.nochangeinthewidthoftheconfidenceinterval.正確答案：A參考解析：Aiscorrect.Asthedegreeofconfidenceincreases(e.g.,from95%to99%),agivenconfidenceintervalwillbecomewider.Aconfidenceintervalisarangeforwhichonecanassertwithagivenprobability1–α,calledthedegreeofconfidence,thatitwillcontaintheparameteritisintendedtoestimate.[單選題]35.Whenevaluatingmeandifferencesbetweentwodependentsamples,themostappropriatetestisa:A.chi-squaretest.B.pairedcomparisonstest.C.z-test.正確答案：B參考解析：Biscorrect.Apairedcomparisonstestisappropriatetotestthemeandifferencesoftwosamplesbelievedtobedependent.[單選題]36.AlimitationofMonteCarlosimulationis:A.itsfailuretodo“whatif”analysis.B.thatitrequireshistoricalrecordsofreturnsC.itsinabilitytoindependentlyspecifycause-and-effectrelationships.正確答案：C參考解析：Ciscorrect.MonteCarlosimulationisacomplementtoanalyticalmethods.MonteCarlosimulationprovidesstatisticalestimatesandnotexactresults.Analyticalmethods,whenavailable,providemoreinsightintocause-and-effectrelationships[單選題]37.Theprobabilityofcorrectlyrejectingthenullhypothesisisthe:A.p-value.B.powerofatest.C.levelofsignificance.正確答案：B參考解析：Biscorrect.Thepowerofatestistheprobabilityofrejectingthenullhypothesiswhenitisfalse.[單選題]38.Whichparameterequalszeroinanormaldistribution?A.KurtosisB.SkewnessC.Standarddeviation正確答案：B參考解析：Biscorrect.Anormaldistributionhasaskewnessofzero(itissymmetricalaroundthemean).Anon-zeroskewnessimpliesasymmetryinadistribution.[單選題]39.Ananalystteststheprofitabilityofatradingstrategywiththenullhypothesisbeingthattheaverageabnormalreturnbeforetradingcostsequalszero.Thecalculatedt-statisticis2.802,withcriticalvaluesof±2.756atsignificancelevelα=0.01.Afterconsideringtradingcosts,thestrategy’sreturnisnearzero.Theresultsaremostlikely:A.statisticallybutnoteconomicallysignificant.B.economicallybutnotstatisticallysignificant.C.neitherstatisticallynoreconomicallysignificant.正確答案：A參考解析：Aiscorrect.Thehypothesisisatwo-tailedformulation.Thet-statisticof2.802fallsoutsidethecriticalrejectionpointsoflessthan–2.756andgreaterthan2.756,thereforethenullhypothesisisrejected;theresultisstatisticallysignificant.However,despitethestatisticalresults,tryingtoprofitonthestrategyisnotlikelytobeeconomicallymeaningfulbecausethereturnisnearzeroaftertransactioncosts[單選題]40.Areportonlong-termstockreturnsfocusedexclusivelyonallcurrentlypubliclytradedfirmsinanindustryismostlikelysusceptibleto:A.look-aheadbias.B.survivorshipbias.C.intergenerationaldatamining.正確答案：B參考解析：Biscorrect.Areportthatusesacurrentlistofstocksdoesnotaccountforfirmsthatfailed,merged,orotherwisedisappearedfromthepublicequitymarketinpreviousyears.Asaconsequence,thereportisbiased.Thistypeofbiasisknownassurvivorshipbias.[單選題]41.Amanagerwillselect20bondsoutofhisuniverseof100bondstoconstructaportfolio.Whichformulaprovidesthenumberofpossibleportfolios?A.PermutationformulaB.MultinomialformulaC.Combinationformula正確答案：C參考解析：Ciscorrect.Thecombinationformulaprovidesthenumberofwaysthatrobjectscanbechosenfromatotalofnobjects,whentheorderinwhichtherobjectsarelisteddoesnotmatter.Theorderofthebondswithintheportfoliodoesnotmatter.[單選題]42.Frequencydistributionssummarizedatain:A.atabulardisplay.B.overlappingintervals.C.arelativelylargenumberofintervals.正確答案：A參考解析：Aiscorrect.Afrequencydistributionisatabulardisplayofdatasummarizedintoarelativelysmallnumberofintervals.Bisincorrectbecauseintervalscannotoverlap.Eachobservationisplaceduniquelyintooneinterval.Cisincorrectbecauseafrequencydistributionissummarizedintoarelativelysmallnumberofintervals.[單選題]43.Aninvestmentpays€300annuallyforfiveyears,withthefirstpaymentoccurringtoday.Thepresentvalue(PV)oftheinvestmentdiscountedata4%annualrateisclosestto:A.€1,336.B.€1,389.C.€1,625.正確答案：B參考解析：Biscorrect,asshowninthefollowingcalculationforanannuity(A)due:[單選題]44.IftheprobabilitythatZolafCompanysalesexceedlastyear'ssalesis0.167,theoddsforexceedingsalesareclosestto:A.1to5.B.1to6.C.5to1.正確答案：A參考解析：Aiscorrect.GivenoddsforEofatob,theimpliedprobabilityofE=a/(a+b).Statedintermsofoddsatobwitha=1,b=5,theprobabilityofE=1/(1+5)=1/6=0.167.Thisresultconfirmsthataprobabilityof0.167forbeatingsalesisoddsof1to5.[單選題]45.Whichofthefollowingstatementsonp-valueiscorrect?A.Thep-valueisthesmallestlevelofsignificanceatwhichH0canberejected.B.Thep-valueindicatestheprobabilityofmakingaTypeIIerror.C.Thelowerthep-value,theweakertheevidenceforrejectingtheH0.正確答案：A參考解析：Aiscorrect.Thep-valueisthesmallestlevelofsignificance(α)atwhichthenullhypothesiscanberejected.[單選題]46.AMonteCarlosimulationcanbeusedto:A.directlyprovideprecisevaluationsofcalloptions.B.simulateaprocessfromhistoricalrecordsofreturns.C.testthesensitivityofamodeltochangesinassumptions.正確答案：C參考解析：Ciscorrect.AcharacteristicfeatureofMonteCarlosimulationisthegenerationofalargenumberofrandomsamplesfromaspecifiedprobabilitydistributionordistributionstorepresenttheroleofriskinthesystem.[單選題]47.WhichofthefollowingeventscanberepresentedasaBernoullitrial?A.TheflipofacoinB.TheclosingpriceofastockC.Thepickingofarandomintegerbetween1and10正確答案：A參考解析：Aiscorrect.Atrial,suchasacoinflip,willproduceoneoftwooutcomes.SuchatrialisaBernoullitrial.[單選題]48.Whenmakingadecisionininvestmentsinvolvingastatisticallysignificantresult,the:A.economicresultshouldbepresumedmeaningful.B.statisticalresultshouldtakepriorityovereconomicconsiderations.C.economiclogicforthefuturerelevanceoftheresultshouldbefurtherexplored.正確答案：C參考解析：Ciscorrect.Whenastatisticallysignificantresultisalsoeconomicallymeaningful,oneshouldfurtherexplorethelogicofwhytheresultmightworkinthefuture.[單選題]49.USandSpanishbondshavereturnstandarddeviationsof0.64and0.56,respectively.Ifthecorrelationbetweenthetwobondsis0.24,thecovarianceofreturnsisclosestto:A.0.086.B.0.670.C.0.781.正確答案：A參考解析：Aiscorrect.ThecovarianceistheproductofthestandarddeviationsandcorrelationusingtheformulaCov(USbondreturns,Spanishbondreturns)=σ(USbonds)×σ(Spanishbonds)×ρ(USbondreturns,Spanishbondreturns)=0.64×0.56×0.24=0.086.[單選題]50.Iftheprobabilitythataportfoliooutperformsitsbenchmarkinanyquarteris0.75,theprobabilitythattheportfoliooutperformsitsbenchmarkinthreeorfewerquartersoverthecourseofayearisclosestto:A.0.26B.0.42C.0.68正確答案：C參考解析：Ciscorrect.TheprobabilitythattheperformanceisatorbelowtheexpectationiscalculatedbyfindingF(3)=p(3)+p(2)+p(1)usingtheformula:Therefore,F(3)=p(3)+p(2)+p(1)+p(0)=0.42+0.20+0.06+0.004=0.684orapproximately68percent[單選題]51.Grandparentsarefundinganewborn’sfutureuniversitytuitioncosts,estimatedat$50,000/yearforfouryears,withthefirstpaymentdueasalumpsumin18years.Assuminga6%effectiveannualrate,therequireddeposittodayisclosestto:A.$60,699.B.$64,341.C.$68,201.正確答案：B參考解析：Biscorrect.First,findthepresentvalue(PV)ofanordinaryannuityinYear17thatrepresentsthetuitioncosts:Then,findthePVoftheannuityintoday’sdollars(whereFVisfuturevalue):[單選題]52.Whichofthefollowingstatementsismostaccurate?Ifthecovarianceofreturnsbetweentwoassetsis0.0023,then:A.theassets’riskisnearzero.B.theassetreturnsareunrelated.C.theassetreturnshaveapositiverelationship.正確答案：C參考解析：Ciscorrect.Thecovarianceofreturnsispositivewhenthereturnsonbothassetstendtobeonthesameside(aboveorbelow)theirexpectedvaluesatthesametime.[單選題]53.Whichofthefollowingassetsmostlikelyrequirestheuseofamultivariatedistributionformodelingreturns?A.AcalloptiononabondB.AportfoliooftechnologystocksC.Astockinamarketindex正確答案：B參考解析：Biscorrect.Multivariatedistributionsspecifytheprobabilitiesforagroupofrelatedrandomvariables.Aportfoliooftechnologystocksrepresentsagroupofrelatedassets.Accordingly,statisticalinterrelationshipsmustbeconsidered,resultingintheneedtouseamultivariatenormaldistribution.[單選題]54.Allelseequal,isspecifyingasmallersignificancelevelinahypothesistestlikelytoincreasetheprobabilityofaTypeIerrororTypeIIerror?A.TypeIerror(No)orTypeIIerror(No)B.TypeIerror(No)orTypeIIerror(Yes)C.TypeIerror(Yes)orTypeIIerror(No)正確答案：B參考解析：Biscorrect.SpecifyingasmallersignificanceleveldecreasestheprobabilityofaTypeIerror(rejectingatruenullhypothesis),butincreasestheprobabilityofaTypeIIerror(notrejectingafalsenullhypothesis).Asthelevelofsignificancedecreases,thenullhypothesisislessfrequentlyrejected.[單選題]55.Anestimatorwithanexpectedvalueequaltotheparameterthatitisintendedtoestimateisdescribedas:A.efficient.B.unbiased.C.consistent.正確答案：B參考解析：Biscorrect.Anunbiasedestimatorisoneforwhichtheexpectedvalueequalstheparameteritisintendedtoestimate.[單選題]56.Thelevelofsignificanceofahypothesistestisbestusedto:A.calculatetheteststatistic.B.definethetest’srejectionpoints.C.specifytheprobabilityofaTypeIIerror.正確答案：B參考解析：Biscorrect.Thelevelofsignificanceisusedtoestablishtherejectionpointsofthehypothesistest.[單選題]57.Asamplemeaniscomputedfromapopulationwithavarianceof2.45.Thesamplesizeis40.Thestandarderrorofthesamplemeanisclosestto:A.0.039.B.0.247.C.0.387.正確答案：B參考解析：Biscorrect.Takingthesquarerootoftheknownpopulationvariancetodeterminethepopulationstandarddeviation(σ)resul