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CFA特許金融分析師-CFA一級(jí)-數(shù)量

[單選題]1.Thepresentvalue(PV)ofaninvestmentwiththefollowing

year-endcashflows(江南博哥)(CF)anda12%requiredannualrate

ofreturnisclosest

YearCashFlow(€)

1100,000

2150,000

5-10,000

to:---------------------------------------------------------------

CF1=1OO,000eurodollarforyear1;CF2=150,000eurodollarforyear

2;CF3=CF4=0eurodollarforyear3&4;CF5=-10,000eurodollarfor

year5.

A.€201,747.

B.€203,191.

C.€227,573.

正確答案:B

參考解析:Biscorrect,asshowninthefollowing

CashFlowFormulaPVat

Year(€)CFx(Wr)rYearO

1100.000100,000(1.12)7=89.285.71

2150,00015OXM?(1.12)-2-119,579.08

5-10,000-10,000(1.12)-5?-5,674.27

203,190.52

table.

B正確。BAIIPlus計(jì)算器,CF頁(yè)面下,2NDCE/C清楚歷史記錄,依次按:

CFo=0C01=100,000F01=lC02=150,0001'02=lC03=0F03=2(表示第三筆現(xiàn)金流為

0,分別發(fā)生在第三年和第四年末,一共兩筆)C04=-10,000F04=lNPV頁(yè)面下:

A.4.

B.5.

C.3.

正確答案:A

參考解析:Themedianisthevalueofthemiddleitemofasetof

itemsthathasbeensortedintoascendingordescendingorder.Inan

even-numberedsample,wedefinethemedianasthemeanofthevalues

ofitemsoccupyingthen/2and(n+2)/2positions(thetwomiddle

items).Then/2itemisthe10thitemandthe(n+2)/2itemisthe

11thileni.ThevalueofIlie10lhiLemis3;LlievalueofIlie11Lh

itemis5.Themeanof3and5is4.中位數(shù)是按升序或降序排序的一組項(xiàng)

的中間項(xiàng)的值。在偶數(shù)樣本中,我們將中位數(shù)定義為占據(jù)n/2和(n+2)/2位

置(中間兩個(gè)項(xiàng)目)的項(xiàng)目值的平均值。在題干中,n/2項(xiàng)是第10項(xiàng),(n+

2)/2項(xiàng)是第11項(xiàng)。因?yàn)榈?0項(xiàng)的值是3;笫11項(xiàng)的值是5o3和5的平均

數(shù)是(3+5)/2=4o

[單選題]3.Whenwecalculatethekurtosis,whatisthepowerofthe

kurtosis?

A.2.

B.3.

C.4.

正確答案:C

參考解析:Samplekurtosisismeasuredusingdeviationsraisedtothe

fourthpower.樣本峰度是用提高到四次方的偏差來(lái)測(cè)量的。

[單選題]4.Thecovarianceofreturnsispositivewhenthereturnson

twoassetstendto:

A.havethesameexpectedvalues.

B.beabovetheirexpectedvalueatdifferenttimes.

C.beonthesamesideoftheirexpectedvalueatthesametime.

正確答案:C

參考解析::Ciscorrect.Thecovarianceofreturnsispositivewhen

thereturnsonbothassetstendtobeonthesameside(aboveor

below)theirexpectedvaluesatthesametime,indicatinganaverage

positiverelationshipbetweenreturns.:C正確。當(dāng)兩種資產(chǎn)E勺收益同

時(shí)趨于同一方向(高于或低于)期望值時(shí),收益的協(xié)方差為正,說(shuō)明收益之間的

平均正相關(guān)關(guān)系。

[單選題]5.Themeanmonthlyreturnandthestandarddeviationfor

threeindustrysectorsareshowninthefollowing

MeanMonthlyReturnStandardDeviationof

Sector(%)Return(%)

Utilities(UTIL)2.101.23

Materials(MATR)1.251.35

Industrials(INDU)3.011.52

exhibit.

Basedonthecoefficientofvariation,theriskiestsectoris:

A.utilities.

B.materials.

C.industrials.

正確答案:B

參考解析:Biscorrect.Thecoefficientofvariation(CV)isthe

ratioofthestandarddeviationtothemean,whereahigherCV

impliesgreaterriskperunitof

S

3UTIL=1澈=-

生,.。8

CVMATR

X1.25%

cy=上==o.5i

INDUx301%B正確。變異系數(shù)(CV)是標(biāo)準(zhǔn)

return.

差與均值的比值,變異系數(shù)越大,單位收益的風(fēng)險(xiǎn)越大。

CV(UTIL)=s/X=l.23%/2.10%=0.59.CV(MATR)=s/X=l.35%/1.25%=1.08.

CV(INDU)=s/X=l.52%/3.01%=0.51.

[單選題]6.AtthebeginningofYearX,aninvestorallocatedhis

retirementsavingsintheassetclassesshowninthefollowing

exhibitandearnedareturnforYearXasalso

AssetAllocationAssetClassReturn

AssetClass(%)(%)

Large*capUSequities20.08.0

Small-capUSequities40.0120

Emergingmarketequities25.0-3.0

High-yieldbonds15.04.0

shown.The

portfolioreturnforYearXisclosestto:

LowerLimitUpperLimitAbsoluteRelativeCumulativeRelative

(%)(%)FrequencyFrequencyFrequency

-9.19<-5.4510.0830.083

—5.454<-1.7120.1670.250

-1.714<2.0340.3330.583

2034<5.7730.2500333

5.77,29.5120.1671.000

exhibit:

Thebin-1.71%WxV2.03%hasacumulativerelativefrequencyof

0.583.

.根據(jù)題目中表格信息,題目問:區(qū)間-1.7設(shè)Wx<2.03%對(duì)應(yīng)的累積相對(duì)

頻率是多少?一個(gè)區(qū)間的累積相對(duì)頻率,應(yīng)該包含“小于給定區(qū)間上限”的觀

測(cè)值的部分。它是由最低區(qū)間到并包括給定區(qū)間的相對(duì)頻率之和決定的。表中

顯示了題目表中所有數(shù)據(jù)區(qū)間的相對(duì)頻率。區(qū)間-1.71%WxV2.03%對(duì)應(yīng)的

累積相對(duì)頻率為0.583。補(bǔ)充:數(shù)據(jù)中的最大值和最下值可以找到,差值為

9.47-(-9.19)=18.66題目問的一個(gè)區(qū)間是T.71至2.03,差值為3.74于是

18.66可以分成?個(gè)3.74的區(qū)間呢?18.66/3.74=5個(gè)第一個(gè)upperlimit是-

5.45=-9.19+3.74

[單選題]8.Annualreturnsandsunnnarystatisticsforthreefundsare

listedinthefollowing

AnnualReturns(%)

YearFundABCFundXYZFundPQR

Year1-20.0-33.0-140

Year223.0-120-18.0

Year3-14.0-12060

Year45.0-8.0-20

Year5-14.011.0ao

Mean-4.0-10.8—5.0

Standarddeviation17.815.6ias

exhibit:

Thefundthatshowsthehighestabsolutedispersionis:

A.FundPQRifthemeasureofdispersionistherange.

B.FundXYZifthemeasureofdispersionisthevariance.

C.FundABCifthemeasureofdispersionisthemeanabsolute

deviation.

正確答案:c

參考解析:Ciscorrect.Themeanabsolutedeviation(MAD)ofFund

ABC,sreturnsisgreaterthantheMADofbothoftheother

funds.

IL.

2用_

MAD=-----------,whereXisthearithmeticmeanoftheseries.

n

MADforFundABC=

卜20-+|23-(~4)卜卜14-(-4)|+|5-(-4肛14-(-4)|

—14a4

5

MADforFundXYZ=

|—33—(—10.8)|+|—12-(—10.8"+12-10.8)+|—8—(—10.8)|+|11—10.8)|

---------------------------------------------------------------------------------------------------------------------9.8%

5

MADforFundPQR=

卜14-(一米|-18-(-5)|4|6-(-5)|+|-2-(-5)|+|3-(-5)|_

----------------------------------------------------------------------------------------=0.0zo

5

AandBareincorrectbecausetherangeandvarianceofthethreefundsareas

follows:

FundABCFundXYZFundPQR

Range43%44%24%

Variance317243110

The

numbersshownforvarianceareunderstoodtobeinupercent

squared“termssothatwhentakingthesquareroot,theresultis

standarddeviationinpercentageterms.Alternatively,byexpressing

standarddeviationandvarianceindecimalform,onecanavoidthe

issueofunits;indecimalform,thevariancesforFundABC,FundXYZ,

andFundPQRare0.0317,0.0243,and0.0110,respectively.

C正確。ABC基金回報(bào)的平均絕對(duì)偏差(MAD)大于其他兩個(gè)基金的MADoABC基

金的MAD=[1-20-(-4)|+|23-(-4)|+|-14-(-4)|+|5-(-4)|+|-14-(-

4)|]/5=14.4%XYZ基金的MAD=[|-33-(-10.8)|+|-12-(-10.8)|+|-12-(-

10.8)|+|-8-(-10.8)|+|ll-(-10.8)|]/5=9.8%PQR基金的MAD=[|-14-(-5)|

+1-18-(-5)|+|6-(-5)|+|-2-(-5)|+|3-(-5)|]/5=8.8%A和B錯(cuò)誤:方差的

數(shù)字被理解為“百分比的平方”的形式,所以當(dāng)取平方根時(shí),結(jié)果就是百分比

的標(biāo)準(zhǔn)偏差?;蛘撸眯?shù)表示標(biāo)準(zhǔn)差和方差,就可以避免單位的問題;以小數(shù)

形式表示,基金ABC、基金XYZ和基金PQR的方差分別為0.0317、0.0243和

O.OllOo

[單選題]9.Foracreditcard,itcharges15%compoundedmonthly.Its

effectiveannualrateisclosetto?

A.15.78%

B.18.85%

C.16.08%

正確答案:C

參考解析:EAR=(1+15%/12)12-1=16.08%EAR=(1+15%/12)^12-1=16.08%

[單選題]10.USandSptniislibondshavereturnslciiidarddevialiojisof

0.64and0.56,respectively.Ifthecorrelationbetweenthetwobonds

is0.24,thecovarianceofreturnsisclosestto:

A.0.086.

B.0.335.

C.0.390.

正確答案:A

參考解析::Aiscorrect.Thecovarianceistheproductofthe

standarddeviationsandcorrelationusingtheformulaCov(USbond

returns,Spanishbondreturns)=。(USbonds)Xo(Spanishbonds)

Xp(USbondreturns,Spanishbondreturns)=0.64X0.56X0.24=

0.086.:A正確。協(xié)方差是標(biāo)準(zhǔn)差和相關(guān)系數(shù)的乘積,用以下公式計(jì)算:

Cov(美國(guó)債券的回報(bào),西班牙債券的回報(bào))二。(美國(guó)國(guó)債)義。(西班牙債券)XP

(美國(guó)債券的回報(bào),西班牙債券的回報(bào))=0.64X0.56X0.24=0.086。

[單選題]11.Whichofthefollowingisapropertyoftwodependent

events?

A.Thetwoeventsmustoccursimultaneously.

B.Theprobabilityofoneeventinfluencestheprobabilityofthe

otherevent.

C.Theprobabilityofthetwoeventsoccurringistheproductofeach

event'sprobability.

正確答案:B

參考解析::Biscorrect.Theprobabilityoftheoccurrenceofone

isrelatedtotheoccurrenceoftheother.Ifwearetryingto

forecastoneevent,informationaboutadependenteventmaybeuseful.

這題問:如果兩個(gè)事件是dependent不獨(dú)立的,以下哪個(gè)說(shuō)法正確?A說(shuō):兩個(gè)

事件一定同時(shí)發(fā)生,翻譯成數(shù)學(xué)公式就是P(AB)=1009k這句話本身是不對(duì)的。

可以舉一個(gè)反例。兩個(gè)事件不獨(dú)立,說(shuō)明AB的發(fā)生是互相影響的,但是這種影

響是什么未知。也有可能是A發(fā)生了B一定不發(fā)生,此時(shí)說(shuō)明AB一定不能同時(shí)

發(fā)生,此時(shí)AB是互斥事件,P(AB)=0.B說(shuō):一個(gè)事件會(huì)受到另外事件發(fā)生的影

響,這個(gè)是dependentevent的定義。dependentevent是不獨(dú)立事件,也就是

兩件事件的發(fā)生是互相影響的。C說(shuō):兩件事情發(fā)生的概率是兩個(gè)事件各自概率

的乘積,翻譯成數(shù)學(xué)公式就是P(AB)邛(A)*P(B)。只有獨(dú)立事件才有P(AB)

二P(A)*P(B),這里說(shuō)的是不獨(dú)立事件,所以C的說(shuō)法也是錯(cuò)誤的。

[單選題]12.Iftherisk-freerateisequaltozeroandthemeanis

lessthanthestandarddeviation,comparedwithSharpratio,the

coefficientofvariationis:

A.Greater.

B.Same.

C.Less.

正確答案:A

參考解析:Sharperatio=[expectedreturn(mean)-risk-free

rate]/standarddeviation=mean/standarddeviation;CV=standard

deviation/expectedreturn.Themeanislessthanthestandard

deviation,socomparedwithSharpratio,thecoefficientofvariation

isgreater,夏普比率:[預(yù)期回報(bào)(平均值)-無(wú)風(fēng)險(xiǎn)比率]/標(biāo)準(zhǔn)差二平均值/標(biāo)

準(zhǔn)差;變異系數(shù)二標(biāo)準(zhǔn)差/預(yù)期回報(bào)。與標(biāo)準(zhǔn)差相比,變異系數(shù)的值更大。

[單選題]13.Ananalystestimatesthat20%ofhigh-riskbondswillfail

(gobankrupt).Ifsheappliesabankruptcypredictionmodel,she

findsthat70%ofthebondswillreceivea“good”rating,implying

thatthoyarelesslikelytofail.Ofthebondsthatfailed,only50%

hada“good"rating.UseBayes'formulatopredicttheprobability

offailuregivena“good”rating.(Hint,letP(A)bethe

probabilityoffailure,P(B)betheprobabilityofa"good"rating,

P(B|A)bethelikelihoodofa“good”ratinggivenfailure,and

P(A|B)bethelikelihoodoffailuregivena“good”rating.)

A.5.7%

B.14.3%

C.28.6%

正確答案:B

參考解析:Biscorrect.WithBayes'formula,theprobabilityof

failuregivena“good"ratingiswhereP(A)=0.20=probabilityof

failureP(B)=0.70=probabilityofa“good”ratingP(BA)=0.50

=probabilityofa“good"ratinggivenfailureWiththeseestimates,

theprobabilityoffailuregivena“good”ratingisIftheanalyst

usesthebankruptcypredictionmodelasaguide,theprobabilityof

failuredeclinesfrom20%to14.3%.B正確。題目考察的就是貝葉斯公式的

運(yùn)用。根據(jù)題意可知:債券破產(chǎn)的概率:P(A)=0.20債券獲得“良好”評(píng)

級(jí)的概率為:P(B)=0.70在給定債券破產(chǎn)的前提下獲得“良好”評(píng)級(jí)的概率

為:P(B|A)=0.50那么,根據(jù)貝葉斯公式,在獲得“良好”評(píng)級(jí)的前提

下,債券破產(chǎn)概率:

[單選題]14.Abarchartthatorderscategoriesbyfrequencyin

descendingorderandincludesalinedisplayingcumulativerelative

frequencyisreferredtoasa:

A.ParetoChart.

B.groupedbarchart.

C.frequencypolygon.

正確答案:A

參考解析:Aiscorrect.Abarchartthatorderscategoriesby

frequencyindescendingorderandincludesalinedisplaying

cumulativerelativefrequencyiscalledaParetoChart.APareto

Chartisusedtohighlightdominantcategoriesorthemostimportant

groups.Bisincorrectbecauseagroupedbarchartorclusteredbar

chartisusedtopresentthefrequencydistributionoftwo

categoricalvariables.Cisincorrectbecauseafrequencypolygonis

usedtodisplayfrequencydistributions.A是正確的。將類別結(jié)果按頻率降

序排列并包含顯示累積相對(duì)頻率的線條的柱狀圖稱為帕累托圖。帕累托圖用于

突出主要類別或最重要的群體。

[單選題]15.Ananalystdevelopsthefollowingcovariancematrixof

HedgeFundMarketIndex

Hedgefund256110

Marketindex11081

returns:---------------------------------------------------------The

correlationofreturnsbetweenthehedgefundandthemarketindexis

closestto:

A.0.005.

B.0.073.

C.0.764.

正確答案:C

參考解析::Ciscorrect.Thecorrelationbetweentworandom

variablesRiandRjisdefinedasP(Ri,Rj)=Cov(Ri,Rj)/[o(Ri)o

(Rj)].Usingthesubscriptitorepresenthedgefundsandthe

subscriptjtorepresentthemarketindex,thestandarddeviations

areo(Ri)=2561/2=16ando(Rj)=811/2=9.Thus,P(Ri,Rj)=

Cov(Ri,Rj)/[o(Ri)。(Rj)]=110/(16X9)=0.764.:C正確。兩個(gè)隨

機(jī)變量之間的相關(guān)性Ri和Rj被定義為P(Ri,Rj)=Cov(Ri,Rj)/(o(Ri)

0(Rj)]o使用下標(biāo)代表對(duì)沖基金和下標(biāo)j代表市場(chǎng)指數(shù),標(biāo)準(zhǔn)偏差是。(Ri)二

25671/2)=16和。(Rj)=8171/2)=9。因此,P(Ri,Rj)=Cov(Ri,Rj)

/(o(Ri)o(Rj)]=110/(16X9)=0.764o

[單選題]16.IftheprobabilitythatZolafCompanysalesexceedlast

year'ssalesis0.167,theoddsforexceedingsalesareclosestto:

A.1to5.

B.1to6.

C.5lo1.

正確答案:A

參考解析::Aiscorrect.GivenoddsforEofatob,theimplied

probabilityofE=a/(a+b).Statedintermsofoddsatobwitha二

1,b=5,theprobabilityofE=1/(1+5)=1/6=0.167.Thisresult

confirmsthataprobabilityof0.167forbeatingsalesisoddsof1

to5.:A正確。這里要求的是exceedingsales的oddsfor。所以for后面

的“exceedingsales"就是對(duì)應(yīng)的事件該事件發(fā)生的概率題干給出是

0.167.oddsfor=P(E)/[l-P(E)]=0.167/(1-0.167)=0.2

[單選題]17.Whichofthefollowingcorrelationcoefficientsindicates

theweakestlinearrelationshipbetweentwovariables?

A.-0.67

B.-0.24

C.0.33

正確答案:B

參考解析::Biscorrect.Correlationsnear+1exhibitstrong

positivelinearity,whereascorrelationsnear-1exhibitstrong

negativelinearity.Acorrelationof0indicatesanabsenceofany

linearrelationshipbetweenthevariables.Thecloserthecorrelation

isto0,theweakerthelinearrelationship.:B正確。相關(guān)系數(shù)在+1

附近表現(xiàn)出很強(qiáng)的正線性,而在T附近表現(xiàn)出很強(qiáng)的負(fù)線性。相關(guān)性為。表示

變量之間不存在任何線性關(guān)系。相關(guān)性越接近0,線性關(guān)系越弱。

[單選題]18.Whichprobabilityestimatemostlikelyvariesgreatly

betweenpeople?

A.Anaprioriprobability

B.Anempiricalprobability

C.Asubjectiveprobability

正確答案:C

參考解析:Ciscorrect.Asubjectiveprobabilitydrawsonpersonalor

subjectivejudgmentthatmaybewithoutreferencetoanyparticular

data.C正確。主觀概率利用個(gè)人或主觀判斷,與任何特定數(shù)據(jù)可能無(wú)關(guān)。

[單選題]19.Datavaluesthatarecategoricalandnotamenabletobeing

organizedinalogicalorderaremostlikelytobecharacterizedas:

A.ordinaldata.

B.discretedata.

C.nominaldata.

正確答案:C

參考解析:Ciscorrect.Nominaldataarecategoricalvaluesthatare

notdiiieiiabletobeingorganizedinalogicalolder.AisincoriecL

becauseordinaldataarecategoricaldatathatcanbelogically

orderedorranked.Bisincorrectbecausediscretedataarenumerical

valuesthatresultfromacountingprocess;thus,theycanbeordered

invariousways,suchasfromhighesttolowestvalue.C是正確的。名

義數(shù)據(jù)是分類值,并不表示邏輯或者排列順序。A是不正確的,因?yàn)榕判驍?shù)據(jù)

是可以邏輯排序或排序的分類數(shù)據(jù)。B是不正確的,因?yàn)殡x散數(shù)據(jù)是計(jì)數(shù)過(guò)程

中產(chǎn)生的數(shù)值;因此,它們可以以各種方式排序,例如從最高值到最低值。

[單選題]20.Foralumpsuminvestmentof¥250,000investedata

statedannualrateof3%compoundeddaily,thenumberofmonths

neededtogrowthesumtoY1,000,000isclosestto:

A.555.

B.563.

C.576.

正確答案:A

參考解析:Aiscorrect.Theeffectiveannualrate(EAR)iscalculated

EAR=(1+Periodicinterestrate)"1-1

EARh(1?0.03/365)365-1

asfollows:EAR=(1.03045)-1=0.030453.3.O4S3%.1V皿forNonafinancial

calculatorresultsin(whereFVisfuturevalueandPVispresent

(1+0.030453)'=FVN/PV=Y1,000,000/Y250,000

=46.21years,whichmultipliedby12toconverttomonthsresultsin554.5,

val?ue\):or?*555months.

方法一(對(duì)應(yīng))BAHplus金融計(jì)算器不可以直接計(jì)算:log以x為底y的對(duì)

數(shù),不過(guò)有In這個(gè)功能,In表示的是log以e為底??梢允褂谩皳Q底公式”,

1.040353%二4求t,計(jì)算過(guò)程如下:用計(jì)算器求EAR:1.2ND22NDCE/C

2.NOM:3ENTER3.I!C/Y:365ENTER4.tCPT:EFF=3.045326計(jì)算t年

(先算年再轉(zhuǎn)換成月,如果先計(jì)算再轉(zhuǎn)換成月不知1個(gè)月二?天)250,000x(1+

EAR)^t=l,OOO,0001.03045326%=4log(1.03045326)4=t利用換底公式:

[Log()4]/[Log()1.03045326]=tLn4/Lnl.03045326=t分別用計(jì)算器計(jì)算Ln4

和LnL03045326:按:4Ln得L386294;L03045326Ln得0.0299999;

t=46.211704(年)計(jì)算月的個(gè)數(shù):n=txl2=46.211704x12=554.540453方法二

(繞開Ln)因?yàn)镻MT=0,表示現(xiàn)金流發(fā)生的頻率(一年多少次)沒有限制,N

(一共多少期)沒有限制,只要PMT和N匹配即可,此時(shí)N可以是天,也可以

是年按天來(lái)算:PV=-250,000,FV=1,000,000,PMT=0,I/Y=3/365,CPT

N=16,687.27453Numberofmonths=16,687.27453/365xl2=

46.21171104x12=554.5405按年來(lái)算:PV=-250,000,FV=l,000,000,PMT=0,

I/Y=3.045326,CPTNM6.2117Numberofinoiilhs=46.2117x12=554.5404

[單選題]21.Theprobabilityofaneventgiventhatanothereventhas

occurredisa:

A.jointprobability.

B.marginalprobability.

C.conditionalprobability.

正確答案:C

參考解析::Ciscorrect.Aconditionalprobabilityisthe

probabilityofaneventgiventhatanothereventhasoccurred.:C正

確。條件概率是一個(gè)事件在另一個(gè)事件已經(jīng)發(fā)生的情況下發(fā)生的概率,

[單選題]22.Whichvaluationtoolisrecommendedtobeusedifthegoal

istomakecomparisonsofthreeormorevariablesovertime?

A.Heatmap

B.Bubblelinechart

C.Scatterplotmatrix

正確答案:B

參考解析:Biscorrect.Abubblelinechartisaversionofaline

chartwheredatapointsarereplacedwithvarying-sizedbubblesto

representathirddimensionofthedata.Alinechartisvery

effectiveatvisualizingtrendsinthreeormorevariablesovertime.

Aisincorrectbecauseaheatmapdifferentiateshighvaluesfromlow

valuesandreflectsthecorrelationbetweenvariablesbutdoesnot

helpinmakingcomparisonsofvariablesovertime.Cisincorrect

becauseascatterplotmatrixisausefultoolfororganizing

scatterplotsbetweenpairsofvariables,makingiteasytoinspect

allpairwiserelationshipsinonecombinedvisual.However,itdoes

nothelpinmakingcomparisonsofthesevariablesovertime.B是正確

的。氣泡線圖是折線圖的一個(gè)版本,其中數(shù)據(jù)點(diǎn)被替換為不同大小的氣泡,以

表示數(shù)據(jù)的第三維。折線圖在可視化三個(gè)或更多變量隨時(shí)間變化的趨勢(shì)方面非

常有效。A是不正確的,熱力圖區(qū)分高值和低值,并反映變量之間的相關(guān)性,但

無(wú)助于隨時(shí)間變化的變量間比較。C是不正確的,散點(diǎn)圖矩陣是組織變量對(duì)之間

散點(diǎn)圖的有用工具,可以方便地在一個(gè)組合視覺中檢查所有成對(duì)關(guān)系。然而,

隨著時(shí)間的推移,這無(wú)助于對(duì)這些變量進(jìn)行比較。

[單選題]23.Thevalueinsixyearsof$75,000investedtodayata

statedannualinterestrateof7%compoundedquarterlyisclosestto:

A.$112,555.

B.$113,330.

C.$113,733.

正確答案:C

參考解析:Ciscorrect,asshowninthefollowing(whereFVisfuture

FV=PV^l+I)

FV6=$75,000^1+等廣"

FV=$113,733.21.

valueandPVispresentvalue):6C正確。方法一:

FV=PV(l+r/m)^(m*N),FV6=$75,000(1+0.07/4)-(4*6)=$113,733.21方法

二:PV=75,000,N=4*6,I/Y=7/4,PMT=0,CPTFV=113,733.21

[單選題]24.Considertwovariables,AandB.IfvariableAhasamean

of-0.56,variableBhasameanof0.23,andthecovariancebetween

thetwovariablesispositive,thecorrelationbetweenthesetwo

variablesis:

A.negative.

B.zero.

C.positive.

正確答案:C

參考解析:Ciscorrect.Thecorrelationcoefficientispositive

becausethecovarianceispositive.Thefactthatoneorboth

variableshaveanegativemeandoesnotaffectthesignofthe

correlationcoefficient.因?yàn)閰f(xié)方差為正,所以相關(guān)系數(shù)為正。一個(gè)或兩個(gè)

變量的平均值均為負(fù)并不影響相關(guān)系數(shù)的符號(hào)。故選項(xiàng)C是正確的

[單選題]25.HimariFukumotohasjoinedanewfirmandisselecting

mutualfundsinthefirm'spensionplan.If10mutualfundsare

available,andsheplanstoselectfour,howmanydifferentsetsof

mutualfundscanshechoose?

A.210

B.720

C.5,040

正確答案:A

參考解析:Aiscorrect.Thenumberofcombinationsisthenumaerof

waystopickfourmutualfundsoutof10withoutregardtoorder,

which

「10!10x9x8x7…

inC4=--------=-----------=210

(10-4)!4!4x3x2x1

is

A正確。組合數(shù),指的是不考慮順序的前提下,從10只共同基金中選擇4只的

方法數(shù)為:

[單選題]26.Grandparentsarefundinganewbornsfutureuniversity

tuitioncosts,estimatedat$50,000/yearforfouryears,withthe

firstpaymentdueasalumpsumin18years.Assuminga6%effective

annualrate,therequireddeposittodayisclosestto:

A.$60,699.

B.$64,341.

C.$68,201.

正確答案:B

參考角其析:Biscorrect.First,findthepresentvalue(PV)ofan

ordinaryannuityinYear17thatrepresentsthetuition

=$50,000x3.4651

costs:=$173,255.28.Then,findthePVoftheannuityintoday's

J?

(1+0.06)”

DV$173.255.28

dollars(whereFVisfuturevalue):^o2564-34085*5641341B正確。在BNG模

式下,計(jì)算4筆學(xué)費(fèi)在t二18時(shí)間點(diǎn)上的PV18:FV=0,N=4,I/Y=6,PMT=-

50,000,CPTPV18=183,650.5975在END模式下,將PV18折現(xiàn)到t=0時(shí)間點(diǎn):

FV18=PV18=183,650.5975,N=18,I/Y=6,PMT=0,CPTPV=64,340.8456

[單選題]27.Givena€1,000,000investmentforfouryearswitha

statedannualrateof3%compoundedcontinuously,thedifferencein

itsinterestearningscomparedwiththesameinvestmentcompounded

dailyisclosestto:

A.€1.

B.€6.

C.€455.

正確答案:B

參考解析:Biscorrect.Thedifferencebetweencontinuouscompounding

anddailycompoundingis€127,496.85-€127,491.29=€5.56,or%

€6,asshowninthefollowingcalculations.Withcontinuous

compounding,theinvestmentearns(wherePVispresent

-PV=€l,000,000e003(4)-€1,000,000

=€1,127,496.85-€1,000,000

value)=€127,4X85Withdailycompounding,the

€1,000,000(1+O.OS/SdS)36^4)-€1,000,000=€1,127,491.29-€1,000,000;

investmentearns:€127,49129,

方法一:連續(xù)復(fù)利和每日復(fù)利的差是:€127,496.85-€127,491.29=€5.56,

or^€6,相關(guān)計(jì)算如下所示。連續(xù)復(fù)利情況下,投資收益(PV表示的是現(xiàn)

值):PV*eXrs*N)二€1,000,000*^(0.03*4)-€1,000,000=€

1,127,496.85-€1,000,000=€127,496.85以日計(jì)息,這個(gè)投資的收益為:

€1,000,000*(10.03/365廠(365*4)-€1,000,000=€1,127,491.29-

€1,000,000=€127,491.29.方法二(注意不要保留小數(shù)帶入,直接計(jì)算結(jié)果

帶入第三排鍵):PV=1,OOO,000,N=365*4,I/Y=3/365,PMT=0,CPTFV=-

1,127,491.29PV=l,000,000,N=4,I/Y=(e^3%-l)*100,PMT=0,CPTFV=-

1,127,496.85

[單選題]28.Ananalystdevelopedtwoscenarioswithrespecttothe

recoveryof$100,000principalfromdefaulted

ProbabilityAmountProbability

ScenarioofScenario(%)Recovered($)ofAmount(%)

14050,00060

30,00040

26080,00090

60.00010

loans:----------—----------------Theamount

oftheexpectedrecoveryisclosestto:

A.$36,400.

B.$63,600.

C.$81,600.

正確答案:B

參考解析::Biscorrect.IfScenario1occurs,theexpected

recoveryis60%($50,000)40%($30,000)=$42,000,andifScenario2

occurs,theexpectedrecoveryis90%($80,000)10%($60,000)=$78,000.

Weightingbytheprobabilityofeachscenario,theexpectedrecovery

is40%($42,000)60%($78,000)=$63,600.Alternatively,first

calculaLinglliepiobabililyofeachainouiiloccuiiing,theexpected

recoveryis

(40%)(60%)($50,000)(40%)(40%)($30,000)(60%)(90%)($80,000)(60%)(10%)($

60,000)=$63,600.:B正確。如果發(fā)生場(chǎng)景1,預(yù)期的恢復(fù)是

60%($50,000)40%($30,000)=$42,000,如果發(fā)生場(chǎng)景2,預(yù)期的恢復(fù)是

90%($80,000)10%($60,000)=$78,000o按照每種情況的概率進(jìn)行加權(quán),預(yù)期復(fù)

蘇為40%(42,000美元)60%(78,000美元)=63,600美元?;蛘撸紫扔?jì)算每個(gè)

金額發(fā)生的概率,預(yù)期回收率為

(40%)(60%)($50,000)(40%)(40%)($30,000)(60%)(90%)($80,000)(60%)(10%)($

60,000)=$63,600o

[單選題]29.Givenaportfoliooffivestocks,howmanyunique

covarianceterms,excludingvariances,arerequiredtocalculatethe

portfolioreturnvariance?

A.10

B.20

C.25

正確答案:A

參考解析::Aiscorrect.Acovariancematrixforfivestockshas5

X5=25entries.Subtractingthe5diagonalvariancetermsresults

in20off-diagonalentries.Becauseacovariancematrixis

symmetrical,only10entriesareunique(20/2=10).:A正確。五只

股票的協(xié)方差矩陣有5X5二25項(xiàng)。減去5個(gè)對(duì)角線方差項(xiàng),得到20個(gè)非對(duì)角

線項(xiàng)。因?yàn)閰f(xié)方差矩陣是對(duì)稱的,所以只有10個(gè)協(xié)方差項(xiàng)是唯一的(20/2二

10)O

[單選題]30.Acorrelationof0.34betweentwovariables,XandY,is

bestdescribedas:

A.changesinXcausingchangesinY.

B.apositiveassociationbetweenXandY.

C.acurvilinearrelationshipbetweenXandY.

正確答案:B

參考解析:Biscorrect.Thecorrelationcoefficientispositive,

indicatingthatthetwoseriesmovetogether.相關(guān)系數(shù)為正,表明這兩個(gè)

變量正相關(guān)變化的。因此,選項(xiàng)B是正確的

[單選題]31.Publishedratingsonstocksrangingfrom1(strongsell)

to5(strongbuy)areexamplesofwhichmeasurementscale?

A.Ordinal

B.Continuous

C.Nominal

正確答案:A

參考解析:Aiscorrect.Ordinalscalessortdataintocategoriesthat

areorderedwithrespecttosomecharacteristicandmayinvolve

numberstoidentifycategoriesbutdonotassurethatthedifferences

betweenscalevaluesareequal.Thebuyratingscaleindicatesthata

stockranked5isexpectedtoperformbetterthanastockranked4,

butittellsusnothingabouttheperformancedifferencebetween

stocksranked4and5comparedwiththeperformancedifference

betweenstocksranked1and2,andsoon.A是正確的。排序數(shù)據(jù)可對(duì)觀測(cè)

值進(jìn)行排序并分類,涉及到的數(shù)字僅用來(lái)識(shí)別類別,但不能確保類別間的差異

是相等的。買入評(píng)級(jí)量表表明,排名5的股票預(yù)期表現(xiàn)優(yōu)于排名4的股票,但

它沒有告訴我們排名4和5的股票與排名1和2的股票相比的表現(xiàn)差異是怎樣

的。

[單選題]32.

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