CFA一級押題-數(shù)量-打印版

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QuantitativeMethods

Q-1.

Thevalueinsixyearsof$75,000investedtodayatastatedannualinterestrateof7%

compoundedquarterlyisclosestto:

A.$112,555.

B.$113,330.

C.$113,733.

Q-2.

Thepresentvalue(PV)ofaninvestmentwiththefollowingyear-endcashflows(CF)

anda12%requiredannualrateofreturnisclosestto:

Year

CashFlow(€)

100,000

1

2

5

150,000

–10,000

A.€201,747.

B.€203,191.

C.€227,573.

Q-3.

Aninvestmentpays€300annuallyforfiveyears,withthefirstpaymentoccurring

today.Thepresentvalue(PV)oftheinvestmentdiscountedata4%annualrateis

closestto:

A.€1,336.

B.€1,389.

C.€1,625.

Q-4.

Whichofthefollowinggroupsbestillustratesapopulation?

A.The500companiesintheS&P500Index.

B.TheNYSE-listedstocksintheDowJonesIndustrialAverage.

C.TheLehmanAggregateBondIndexasarepresentationoftheUSbondmarket.

Q-5.

Amutualfundhasthereturnfrequencydistributionshowninthefollowingtable.

ReturnInterval(%)

AbsoluteFrequency

–10.0to–7.0

–7.0to–4.0

–4.0to–1.0

–1.0to+2.0

+2.0to+5.0

3

7

10

12

23

1

-9

+5.0to+8.0

5

Whichofthefollowingstatementsiscorrect?

A.Therelativefrequencyoftheinterval“–1.0to+2.0”is20%.

B.Therelativefrequencyoftheinterval“+2.0to+5.0”is23%.

C.Thecumulativerelativefrequencyoftheinterval“+5.0to+8.0”is91.7%.

Q-6.

Thereturnsofafundareasfollows:

Year

1

Return(%)

?20.60

15.00

0.50

2

3

4

9.80

5

4.60

Themeanabsolutedeviation(MAD)ofreturnsforthefundisclosestto:

A.13.69%.

B.9.53%.

C.11.91%.

Q-7.

Forapositivelyskewedunimodaldistribution,whichofthefollowingmeasuresismost

accuratelydescribedasthelargest?

A.Median.

B.Mean.

C.Mode.

Q-8.

Whenanalyzinginvestmentreturns,whichofthefollowingstatementsiscorrect?

A.Thegeometricmeanwillexceedthearithmeticmeanforaserieswithnon-zerovariance.

B.Thegeometricmeanmeasuresaninvestment’scompoundrateofgrowthovermultiple

periods.

C.Thearithmeticmeanaccuratelyestimatesaninvestment’sterminalvalueovermultiple

periods.

Q-9.

TheprobabilityofEventAis40%.TheprobabilityofEventBis60%.Thejoint

probabilityofABis40%.Theprobability(P)thatAorBoccurs,orbothoccur,isclosest

to:

A.40%.

B.84%.

C.60%.

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Q-10.

Whichofthefollowingcorrelationcoefficientsindicatestheweakestlinearrelationship

betweentwovariables?

A.-0.67.

B.-0.24.

C.0.33.

Q-11.

Afirmwillselecttwooffourvicepresidentstobeaddedtotheinvestmentcommittee.

Howmanydifferentgroupsoftwoarepossible?

A.6.

B.12.

C.24.

Q-12.

Asampleof25observationshasameanof8andastandarddeviationof15.The

standarderrorofthesamplemeanisclosestto:

A.1.60.

B.3.00.

C.3.06.

Q-13.

Althoughheknowssecurityreturnsarenotindependent,acolleaguemakestheclaim

thatbecauseofthecentrallimittheorem,ifwediversifyacrossalargenumberof

investments,theportfoliostandarddeviationwilleventuallyapproachzeroas

becomeslarge.Ishecorrect?

n

A.Yes.

B.No.

C.Notenoughinformationprovidedtoanswer.

Q-14.

Supposewetakearandomsampleof30companiesinanindustrywith200companies.

Wecalculatethesamplemeanoftheratioofcashflowtototaldebtfortheprioryear.

Wefindthatthisratiois23percent.Subsequently,welearnthatthepopulationcash

flowtototaldebtratio(takingaccountofall200companies)is26percent.Whatisthe

explanationforthediscrepancybetweenthesamplemeanof23percentandthe

populationmeanof26percent?

A.Samplingerror.

B.Bias.

C.Alackofconsistency.

Q-15.

A

small-capgrowthfund’smonthlyreturnsforthepast36monthshavebeen

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consistentlyoutperformingitsbenchmark.Ananalystisdeterminingwhetherthe

standarddeviationofmonthlyreturnsisgreaterthan6%.Whichofthefollowingbest

describesthehypothesistobetested?

A.H0:σ2≤0.36%

B.Ha:σ2>6%

C.H0:σ2≥0.36%

Q-16.

Willcoisamanufacturerinamaturecyclicalindustry.Duringthemostrecentindustry

cycle,itsnetincomeaveraged$30millionperyearwithastandarddeviationof$10

million(n=6observations).ManagementclaimsthatWillco’sperformanceduringthe

mostrecentcycleresultsfromnewapproachesandthatwecandismissprofitability

expectationsbasedonitsaverageornormalizedearningsof$24millionperyearin

priorcycles.Determinewhetherornottorejectthenullhypothesisatthe0.05

significancelevelinanone-tailedtest.

A.Rejectthenullhypothesis.

B.Donotrejectthenullhypothesis.

C.Notenoughinformationprovidedtoanswer.

Q-17.

Whichofthefollowingrepresentsacorrectstatementaboutthep-value?

A.Thep-valueofferslesspreciseinformationthandoestherejectionpointsapproach.

B.Alargerp-valueprovidesstrongerevidenceinsupportofthealternativehypothesis.

C.

A

p-valuelessthanthespecifiedlevelofsignificanceleadstorejectionofthenull

hypothesis.

Q-18.

Inwhichofthefollowingsituationswouldanon-parametrictestofahypothesismost

likelybeused?

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A.Thesampledataarerankedaccordingtomagnitude.

B.Thesampledatacomefromanormallydistributedpopulation.

C.Thetestvaliditydependsonmanyassumptionsaboutthenatureofthepopulation.

2

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QuantitativeMethods

Q-1.

Solution:C.

Asshowninthefollowing(whereFVisfuturevalueandPVispresentvalue):

FV=PV(1+rs/m)mN

FV6=$75,000(1+0.07/4)(4×6)

FV6=$113,733.21.

Quantitativemethod,Timevalueofmoney,EAR

Q-2.

Solution:B.

Asshowninthefollowingtable.

Year

CashFlow(€)

100,000

FormulaCF×(1+r)t

100,000(1.12)–1

150,000(1.12)–2

–10,000(1.12)–5

PVatYear0

89,285.71

119,579.08

–5,674.27

1

2

5

150,000

–10,000

2

03,190.52

Quantitativemethod,Timevalueofmoney,Annuity

Q-3.

Solution:B.

Asshowninthefollowingcalculationforanannuity(A)due:

BGN:PMT=300,N=5,I/Y=4,FV=0,CPTPV=-€1,388.97,or≈-€1,389.

Quantitativemethod,Timevalueofmoney,Annuity

Q-4.

Solution:A.

Apopulationisdefinedasallmembersofaspecifiedgroup.TheS&P500Indexconsistsof500

companies,sothisgroupisthepopulationofcompaniesintheindex.

BisincorrectbecausethereareseveralDowJonescomponentstocksthatarenottradedonthe

NYSE,makingtheNYSEgroupasubsetofthetotalpopulationofstocksincludedintheDow

Jonesaverage.

CisincorrectbecausealthoughtheLehmanAggregateBondIndexisrepresentativeoftheUS

bondmarket,itisasamplingofbondsinthatmarketandnottheentirepopulationofbondsin

thatmarket.

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Quantitativemethod,StatisticalConceptsandMarketReturns,Measurementscales

Q-5.

Solution:A.

Therelativefrequencyistheabsolutefrequencyofeachintervaldividedbythetotalnumberof

observations.Here,therelativefrequencyiscalculatedas:12/60=20%.

Bisincorrectbecausetherelativefrequencyofthisintervalis23/60=38.33%.

Cisincorrectbecausethecumulativerelativefrequencyofthelastintervalmustequal100%.

Quantitativemethod,StatisticalConceptsandMarketReturns,Measuresofcentraltendency

Q-6.

Solution:B.

Themeanabsolutedeviation(MAD)forasampleiscalculatedasfollows:

Mean:=(?20.60%+15.00%+0.50%+9.80%+4.60%)/5=1.86%

DeviationsfromMean

AbsoluteDeviation(%)

|

|

|

|

|

?20.60%?1.86%|

15.00%?1.86%|

0.50%?1.86%|

9.80%?1.86%|

4.60%?1.86%|

22.46

13.14

1.36

7.94

2.74

Total

47.64

9.53

MAD=47.64/5

Cisincorrect.Itusestheterm“n–1”inthedenominatoroftheformulaofMAD:47.64%/(5-1)=

11.91%

Aisincorrect.Itisthesamplestandarddeviation{[(?20.60%?1.86%)2+(15.00%?1.86%)2+

(0.50%?1.86%)2+(9.80%?1.86%)2+(4.60%?1.86%)2]/(5-1)}0.5=13.69%.

QuantitativeMethod,StatisticalConceptsandMarketReturns,Absolutedispersion

Q-7.

Solution:B.

Forapositivelyskewedunimodaldistribution,themodeislessthanthemedian,whichisless

thanthemean.

Aisincorrect.Forthepositivelyskewedunimodaldistribution,themodeislessthanthemedian,

whichislessthanthemean.

Cisincorrect.Forthepositivelyskewedunimodaldistribution,themodeislessthanthemedian,

whichislessthanthemean.

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QuantitativeMethod,StatisticalConceptsandMarketReturns,Measuresofcentraltendency

Q-8.

Solution:B.

Thegeometricmeancompoundstheperiodicreturnsofeveryperiod,givingtheinvestoramore

accuratemeasureoftheterminalvalueofaninvestment.

QuantitativeMethod,StatisticalConceptsandMarketReturns,Measuresofcentraltendency

Q-9.

Solution:C.

P(AorB)=P(A)+P(B)?P(AB)=0.40+0.60?0.40=0.60or60%.

Aisincorrectbecauseitusesonlythejointprobabilityof40%=(0.60×0.40).

Bisincorrect;itisobtainedbyadding0.60and0.24toget0.84.

QuantitativeMethod,StatisticalConceptsandMarketReturns,Calculationrulesforprobabilities

Q-10.

Solution:B.

Correlationsnear+1exhibitstrongpositivelinearity,whereascorrelationsnear-1exhibitstrong

negativelinearity.Acorrelationof0indicatesanabsenceofanylinearrelationshipbetweenthe

variables.Thecloserthecorrelationisto0,theweakerthelinearrelationship.

QuantitativeMethod,StatisticalConceptsandMarketReturns,Factorial

Permutation

&

Combination

&

Q-11.

Solution:A.

Theanswerisfoundusingthecombinationformula

nCr=n!/(n-r)!r!

Here,n=4andr=2,sotheansweris4!/[(4-2)!2!]=24/[(2)×(2)]=6.Thisresultcanbeverified

byassumingtherearefourvicepresidents,VP-VP.Thesixpossibleadditionstotheinvestment

1

4

committeeareVP1andVP2,VP1andVP3,VP1andVP4,VP2andVP3,VP2andVP4,andVP3andVP4.

QuantitativeMethod,StatisticalConceptsandMarketReturns,Factorial

Permutation

&

Combination&

Q-12.

Solution:B.

Thestandarderrorofthesamplemean,whenthesamplestandarddeviationisknown,is:

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15?√25=3.00

Inthiscase,S

=

??

Aisincorrectandiscalculatedbydividing8bythesquarerootof25.

Cisincorrectandiscalculatedbydividing15bythesquarerootof24.

QuantitativeMethod,StatisticalConceptsandMarketReturns,Centrallimittheory

Q-13.

Solution:B.

Firsttheconclusiononthelimitofzeroiswrong;second,thesupportcitedfordrawingthe

conclusion(i.e.,thecentrallimittheorem)isnotrelevantinthiscontext.

QuantitativeMethod,StatisticalConceptsandMarketReturns,Centrallimittheory

Q-14.

Solution:A.

Thediscrepancyarisesfromsamplingerror.Samplingerrorexistswheneveronefailstoobserve

everyelementofthepopulation,becauseasamplestatisticcanvaryfromsampletosample.As

statedinthereading,thesamplemeanisanunbiasedestimator,aconsistentestimator,andan

efficientestimatorofthepopulationmean.Althoughthesamplemeanisanunbiasedestimator

ofthepopulationmean—theexpectedvalueofthesamplemeanequalsthepopulation

mean—becauseofsamplingerror,wedonotexpectthesamplemeantoexactlyequalthe

populationmeaninanyonesamplewemaytake.

QuantitativeMethod,StatisticalConceptsandMarketReturns,Biases

Q-15.

Solution:A.

Thisisaone-tailedhypothesistestingwitha“greaterthan