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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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