CFA特許金融分析師-CFA一級-數(shù)量

CFA特許金融分析師-CFA一級-數(shù)量[單選題]1.Thepresentvalue(PV)ofaninvestmentwiththefollowingyear-endcashflows（江南博哥）(CF)anda12%requiredannualrateofreturnisclosestto:CF1=100,000eurodollarforyear1;CF2=150,000eurodollarforyear2;CF3=CF4=0eurodollarforyear3&4;CF5=-10,000eurodollarforyear5.A.€201,747.B.€203,191.C.€227,573.正確答案：B參考解析：Biscorrect,asshowninthefollowingtable.B正確。BAIIPlus計算器，CF頁面下，2NDCE/C清楚歷史記錄，依次按：CFo=0C01=100,000F01=1C02=150,000F02=1C03=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=1NPV頁面下：I=12CPTNPV=203,190.52[單選題]2.Considerthefollowing20itemslistedinascendingorder:Themedianvalueoftheitemsisclosestto:A.4.B.5.C.3.正確答案：A參考解析：Themedianisthevalueofthemiddleitemofasetofitemsthathasbeensortedintoascendingordescendingorder.Inaneven-numberedsample,wedefinethemedianasthemeanofthevaluesofitemsoccupyingthen/2and(n+2)/2positions(thetwomiddleitems).Then/2itemisthe10thitemandthe(n+2)/2itemisthe11thitem.Thevalueofthe10thitemis3;thevalueofthe11thitemis5.Themeanof3and5is4.中位數(shù)是按升序或降序排序的一組項的中間項的值。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（中間兩個項目）的項目值的平均值。在題干中，n/2項是第10項，（n＋2）/2項是第11項。因為第10項的值是3；第11項的值是5。3和5的平均數(shù)是(3＋5）/2=4。[單選題]3.Whenwecalculatethekurtosis,whatisthepowerofthekurtosis?A.2.B.3.C.4.正確答案：C參考解析：Samplekurtosisismeasuredusingdeviationsraisedtothefourthpower.樣本峰度是用提高到四次方的偏差來測量的。[單選題]4.Thecovarianceofreturnsispositivewhenthereturnsontwoassetstendto:A.havethesameexpectedvalues.B.beabovetheirexpectedvalueatdifferenttimes.C.beonthesamesideoftheirexpectedvalueatthesametime.正確答案：C參考解析：：Ciscorrect.Thecovarianceofreturnsispositivewhenthereturnsonbothassetstendtobeonthesameside(aboveorbelow)theirexpectedvaluesatthesametime,indicatinganaveragepositiverelationshipbetweenreturns.：C正確。當(dāng)兩種資產(chǎn)的收益同時趨于同一方向(高于或低于)期望值時，收益的協(xié)方差為正，說明收益之間的平均正相關(guān)關(guān)系。[單選題]5.Themeanmonthlyreturnandthestandarddeviationforthreeindustrysectorsareshowninthefollowingexhibit.Basedonthecoefficientofvariation,theriskiestsectoris:A.utilities.B.materials.C.industrials.正確答案：B參考解析：Biscorrect.Thecoefficientofvariation(CV)istheratioofthestandarddeviationtothemean,whereahigherCVimpliesgreaterriskperunitofreturn.B正確。變異系數(shù)(CV)是標(biāo)準(zhǔn)差與均值的比值，變異系數(shù)越大，單位收益的風(fēng)險越大。CV(UTIL)=s/X=1.23%/2.10%=0.59.CV(MATR)=s/X=1.35%/1.25%=1.08.CV(INDU)=s/X=1.52%/3.01%=0.51.[單選題]6.AtthebeginningofYearX,aninvestorallocatedhisretirementsavingsintheassetclassesshowninthefollowingexhibitandearnedareturnforYearXasalsoshown.TheportfolioreturnforYearXisclosestto:A.5.1%.B.5.3%.C.6.3%.正確答案：C參考解析：：Ciscorrect.Theportfolioreturnmustbecalculatedastheweightedmeanreturn,wheretheweightsaretheallocationsineachassetclass:(0.20×8%)＋(0.40×12%)＋【0.25×(-3%)】＋(0.15×4%)=6.25%,or≈6.3%.去年，一位投資者將他的退休儲蓄分配到如下表所示的資產(chǎn)類別中。問2015年的投資組合收益率最接近多少。C正確。投資組合的回報須以加權(quán)平均回報計算，其中的權(quán)重是每種資產(chǎn)類別的配置:(0.20×8%)＋(0.40×12%)＋【0.25×(-3%)】＋(0.15×4%)=6.25%或≈6.3%。[單選題]7.Ananalystisusingthedatainthefollowingexhibittoprepareastatisticalreport.Thecumulativerelativefrequencyforthebin-1.71%≤x＜2.03%isclosestto:A.0.250.B.0.333.C.0.583.正確答案：C參考解析：Ciscorrect.Thecumulativerelativefrequencyofabinidentifiesthefractionofobservationsthatarelessthantheupperlimitofthegivenbin.Itisdeterminedbysummingtherelativefrequenciesfromthelowestbinuptoandincludingthegivenbin.Thefollowingexhibitshowstherelativefrequenciesforallthebinsofthedatafromthepreviousexhibit:Thebin-1.71%≤x＜2.03%hasacumulativerelativefrequencyof0.583..根據(jù)題目中表格信息，題目問：區(qū)間-1.71%≤x＜2.03%對應(yīng)的累積相對頻率是多少？一個區(qū)間的累積相對頻率，應(yīng)該包含“小于給定區(qū)間上限”的觀測值的部分。它是由最低區(qū)間到并包括給定區(qū)間的相對頻率之和決定的。表中顯示了題目表中所有數(shù)據(jù)區(qū)間的相對頻率。區(qū)間-1.71%≤x＜2.03%對應(yīng)的累積相對頻率為0.583。補充：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題目問的一個區(qū)間是-1.71至2.03，差值為3.74于是18.66可以分成？個3.74的區(qū)間呢？18.66/3.74=5個第一個upperlimit是-5.45=-9.19＋3.74[單選題]8.Annualreturnsandsummarystatisticsforthreefundsarelistedinthefollowingexhibit:Thefundthatshowsthehighestabsolutedispersionis:A.FundPQRifthemeasureofdispersionistherange.B.FundXYZifthemeasureofdispersionisthevariance.C.FundABCifthemeasureofdispersionisthemeanabsolutedeviation.正確答案：C參考解析：Ciscorrect.Themeanabsolutedeviation(MAD)ofFundABC’sreturnsisgreaterthantheMADofbothoftheotherfunds.Thenumbersshownforvarianceareunderstoodtobein“percentsquared”termssothatwhentakingthesquareroot,theresultisstandarddeviationinpercentageterms.Alternatively,byexpressingstandarddeviationandvarianceindecimalform,onecanavoidtheissueofunits;indecimalform,thevariancesforFundABC,FundXYZ,andFundPQRare0.0317,0.0243,and0.0110,respectively.C正確。ABC基金回報的平均絕對偏差(MAD)大于其他兩個基金的MAD。ABC基金的MAD=[|-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)|＋|11-(-10.8)|]/5=9.8%PQR基金的MAD=[|-14-(-5)|＋|-18-(-5)|＋|6-(-5)|＋|-2-(-5)|＋|3-(-5)|]/5=8.8%A和B錯誤: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，結(jié)果就是百分比的標(biāo)準(zhǔn)偏差?；蛘?，用小數(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0.0110。[單選題]9.Foracreditcard,itcharges15%compoundedmonthly.Itseffectiveannualrateisclosetto?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.USandSpanishbondshavereturnstandarddeviationsof0.64and0.56,respectively.Ifthecorrelationbetweenthetwobondsis0.24,thecovarianceofreturnsisclosestto:A.0.086.B.0.335.C.0.390.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.：A正確。協(xié)方差是標(biāo)準(zhǔn)差和相關(guān)系數(shù)的乘積，用以下公式計算：Cov(美國債券的回報,西班牙債券的回報)=σ(美國國債)×σ(西班牙債券)×ρ(美國債券的回報,西班牙債券的回報)=0.64×0.56×0.24=0.086。[單選題]11.Whichofthefollowingisapropertyoftwodependentevents?A.Thetwoeventsmustoccursimultaneously.B.Theprobabilityofoneeventinfluencestheprobabilityoftheotherevent.C.Theprobabilityofthetwoeventsoccurringistheproductofeachevent’sprobability.正確答案：B參考解析：：Biscorrect.Theprobabilityoftheoccurrenceofoneisrelatedtotheoccurrenceoftheother.Ifwearetryingtoforecastoneevent,informationaboutadependenteventmaybeuseful.這題問：如果兩個事件是dependent不獨立的，以下哪個說法正確？A說：兩個事件一定同時發(fā)生，翻譯成數(shù)學(xué)公式就是P(AB）=100%。這句話本身是不對的?？梢耘e一個反例。兩個事件不獨立，說明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，此時說明AB一定不能同時發(fā)生，此時AB是互斥事件，P(AB）=0.B說：一個事件會受到另外事件發(fā)生的影響，這個是dependentevent的定義。dependentevent是不獨立事件，也就是兩件事件的發(fā)生是互相影響的。C說：兩件事情發(fā)生的概率是兩個事件各自概率的乘積，翻譯成數(shù)學(xué)公式就是P(AB）=P(A)*P(B)。只有獨立事件才有P(AB）=P(A)*P(B)，這里說的是不獨立事件，所以C的說法也是錯誤的。[單選題]12.Iftherisk-freerateisequaltozeroandthemeanislessthanthestandarddeviation,comparedwithSharpratio,thecoefficientofvariationis:A.Greater.B.Same.C.Less.正確答案：A參考解析：Sharperatio=[expectedreturn(mean)–risk-freerate]/standarddeviation=mean/standarddeviation;CV=standarddeviation/expectedreturn.Themeanislessthanthestandarddeviation,socomparedwithSharpratio,thecoefficientofvariationisgreater.夏普比率=[預(yù)期回報（平均值）-無風(fēng)險比率]/標(biāo)準(zhǔn)差=平均值/標(biāo)準(zhǔn)差；變異系數(shù)=標(biāo)準(zhǔn)差/預(yù)期回報。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,shefindsthat70%ofthebondswillreceivea“good”rating,implyingthattheyarelesslikelytofail.Ofthebondsthatfailed,only50%hada“good”rating.UseBayes’formulatopredicttheprobabilityoffailuregivena“good”rating.(Hint,letP(A)betheprobabilityoffailure,P(B)betheprobabilityofa“good”rating,P(B|A)bethelikelihoodofa“good”ratinggivenfailure,andP(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,theprobabilityoffailuregivena“good”ratingiswhereP(A)=0.20=probabilityoffailureP(B)=0.70=probabilityofa“good”ratingP(B|A)=0.50=probabilityofa“good”ratinggivenfailureWiththeseestimates,theprobabilityoffailuregivena“good”ratingisIftheanalystusesthebankruptcypredictionmodelasaguide,theprobabilityoffailuredeclinesfrom20%to14.3%.B正確。題目考察的就是貝葉斯公式的運用。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”評級的概率為：P(B)=0.70在給定債券破產(chǎn)的前提下獲得“良好”評級的概率為：P(B|A)=0.50那么，根據(jù)貝葉斯公式，在獲得“良好”評級的前提下，債券破產(chǎn)概率：[單選題]14.Abarchartthatorderscategoriesbyfrequencyindescendingorderandincludesalinedisplayingcumulativerelativefrequencyisreferredtoasa:A.ParetoChart.B.groupedbarchart.C.frequencypolygon.正確答案：A參考解析：Aiscorrect.AbarchartthatorderscategoriesbyfrequencyindescendingorderandincludesalinedisplayingcumulativerelativefrequencyiscalledaParetoChart.AParetoChartisusedtohighlightdominantcategoriesorthemostimportantgroups.Bisincorrectbecauseagroupedbarchartorclusteredbarchartisusedtopresentthefrequencydistributionoftwocategoricalvariables.Cisincorrectbecauseafrequencypolygonisusedtodisplayfrequencydistributions.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.Ananalystdevelopsthefollowingcovariancematrixofreturns:Thecorrelationofreturnsbetweenthehedgefundandthemarketindexisclosestto:A.0.005.B.0.073.C.0.764.正確答案：C參考解析：：Ciscorrect.ThecorrelationbetweentworandomvariablesRiandRjisdefinedasρ(Ri,Rj)=Cov(Ri,Rj)/[σ(Ri)σ(Rj)].Usingthesubscriptitorepresenthedgefundsandthesubscriptjtorepresentthemarketindex,thestandarddeviationsareσ(Ri)=2561/2=16andσ(Rj)=811/2=9.Thus,ρ(Ri,Rj)=Cov(Ri,Rj)/[σ(Ri)σ(Rj)]=110/(16×9)=0.764.：C正確。兩個隨機變量之間的相關(guān)性Ri和Rj被定義為ρ(Ri,Rj)=Cov(Ri,Rj)/(σ(Ri)σ(Rj)]。使用下標(biāo)代表對沖基金和下標(biāo)j代表市場指數(shù),標(biāo)準(zhǔn)偏差是σ(Ri)=256^(1/2)=16和σ(Rj)=81^(1/2)=9。因此,ρ(Ri,Rj)=Cov(Ri,Rj)/(σ(Ri)σ(Rj)]=110/(16×9)=0.764。[單選題]16.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.：A正確。這里要求的是exceedingsales的oddsfor。所以for后面的“exceedingsales”就是對應(yīng)的事件該事件發(fā)生的概率題干給出是0.167.oddsfor=P(E)/[1-P(E)]=0.167/(1-0.167)=0.2[單選題]17.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.：B正確。相關(guān)系數(shù)在＋1附近表現(xiàn)出很強的正線性，而在-1附近表現(xiàn)出很強的負線性。相關(guān)性為0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.Whichprobabilityestimatemostlikelyvariesgreatlybetweenpeople?A.AnaprioriprobabilityB.AnempiricalprobabilityC.Asubjectiveprobability正確答案：C參考解析：Ciscorrect.Asubjectiveprobabilitydrawsonpersonalorsubjectivejudgmentthatmaybewithoutreferencetoanyparticulardata.C正確。主觀概率利用個人或主觀判斷，與任何特定數(shù)據(jù)可能無關(guān)。[單選題]19.Datavaluesthatarecategoricalandnotamenabletobeingorganizedinalogicalorderaremostlikelytobecharacterizedas:A.ordinaldata.B.discretedata.C.nominaldata.正確答案：C參考解析：Ciscorrect.Nominaldataarecategoricalvaluesthatarenotamenabletobeingorganizedinalogicalorder.Aisincorrectbecauseordinaldataarecategoricaldatathatcanbelogicallyorderedorranked.Bisincorrectbecausediscretedataarenumericalvaluesthatresultfromacountingprocess;thus,theycanbeorderedinvariousways,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，因為排序數(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，因為離散數(shù)據(jù)是計數(shù)過程中產(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￥250,000investedatastatedannualrateof3%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):方法一（對應(yīng)）BAIIplus金融計算器不可以直接計算：log以x為底y的對數(shù)，不過有l(wèi)n這個功能，ln表示的是log以e為底?？梢允褂谩皳Q底公式”，1.040353^t=4求t，計算過程如下：用計算器求EAR：1.2ND22NDCE/C2.NOM：3ENTER3.↓↓C/Y：365ENTER4.↑CPT：EFF=3.045326計算t年（先算年再轉(zhuǎn)換成月，如果先計算再轉(zhuǎn)換成月不知1個月=?天）250,000x(1＋EAR)^t=1,000,0001.03045326^t=4log(1.03045326)4=t利用換底公式：[Log()4]/[Log()1.03045326]=tLn4/Ln1.03045326=t分別用計算器計算Ln4和Ln1.03045326：按：4Ln得1.386294；1.03045326Ln得0.0299999；t=46.211704(年)計算月的個數(shù)：n=tx12=46.211704x12=554.540453方法二（繞開Ln）因為PMT=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N可以是天，也可以是年按天來算：PV=-250,000，F(xiàn)V=1,000,000，PMT=0，I/Y=3/365，CPTN=16,687.27453Numberofmonths=16,687.27453/365x12=46.21171104x12=554.5405按年來算：PV=-250,000，F(xiàn)V=1,000,000，PMT=0，I/Y=3.045326，CPTN=46.2117Numberofmonths=46.2117x12=554.5404[單選題]21.Theprobabilityofaneventgiventhatanothereventhasoccurredisa:A.jointprobability.B.marginalprobability.C.conditionalprobability.正確答案：C參考解析：：Ciscorrect.Aconditionalprobabilityistheprobabilityofaneventgiventhatanothereventhasoccurred.：C正確。條件概率是一個事件在另一個事件已經(jīng)發(fā)生的情況下發(fā)生的概率。[單選題]22.Whichvaluationtoolisrecommendedtobeusedifthegoalistomakecomparisonsofthreeormorevariablesovertime?A.HeatmapB.BubblelinechartC.Scatterplotmatrix正確答案：B參考解析：Biscorrect.Abubblelinechartisaversionofalinechartwheredatapointsarereplacedwithvarying-sizedbubblestorepresentathirddimensionofthedata.Alinechartisveryeffectiveatvisualizingtrendsinthreeormorevariablesovertime.Aisincorrectbecauseaheatmapdifferentiateshighvaluesfromlowvaluesandreflectsthecorrelationbetweenvariablesbutdoesnothelpinmakingcomparisonsofvariablesovertime.Cisincorrectbecauseascatterplotmatrixisausefultoolfororganizingscatterplotsbetweenpairsofvariables,makingiteasytoinspectallpairwiserelationshipsinonecombinedvisual.However,itdoesnothelpinmakingcomparisonsofthesevariablesovertime.B是正確的。氣泡線圖是折線圖的一個版本，其中數(shù)據(jù)點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或更多變量隨時間變化的趨勢方面非常有效。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，但無助于隨時間變化的變量間比較。C是不正確的，散點圖矩陣是組織變量對之間散點圖的有用工具，可以方便地在一個組合視覺中檢查所有成對關(guān)系。然而，隨著時間的推移，這無助于對這些變量進行比較。[單選題]23.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):C正確。方法一：FV=PV(1＋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.IfvariableAhasameanof－0.56,variableBhasameanof0.23,andthecovariancebetweenthetwovariablesispositive,thecorrelationbetweenthesetwovariablesis:A.negative.B.zero.C.positive.正確答案：C參考解析：Ciscorrect.Thecorrelationcoefficientispositivebecausethecovarianceispositive.Thefactthatoneorbothvariableshaveanegativemeandoesnotaffectthesignofthecorrelationcoefficient.因為協(xié)方差為正，所以相關(guān)系數(shù)為正。一個或兩個變量的平均值均為負并不影響相關(guān)系數(shù)的符號。故選項C是正確的[單選題]25.HimariFukumotohasjoinedanewfirmandisselectingmutualfundsinthefirm’spensionplan.If10mutualfundsareavailable,andsheplanstoselectfour,howmanydifferentsetsofmutualfundscanshechoose?A.210B.720C.5,040正確答案：A參考解析：Aiscorrect.Thenumberofcombinationsisthenumberofwaystopickfourmutualfundsoutof10withoutregardtoorder,whichisA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.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):B正確。在BNG模式下，計算4筆學(xué)費在t=18時間點上的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時間點：FV18=PV18=183,650.5975，N=18，I/Y=6，PMT=0，CPTPV=64,340.8456[單選題]27.Givena€1,000,000investmentforfouryearswithastatedannualrateof3%compoundedcontinuously,thedifferenceinitsinterestearningscomparedwiththesameinvestmentcompoundeddailyisclosestto:A.€1.B.€6.C.€455.正確答案：B參考解析：Biscorrect.Thedifferencebetweencontinuouscompoundinganddailycompoundingis€127,496.85–€127,491.29=€5.56,or≈€6,asshowninthefollowingcalculations.Withcontinuouscompounding,theinvestmentearns(wherePVispresentvalue)Withdailycompounding,theinvestmentearns: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*e^(rs*N)=€1,000,000*e^(0.03*4)–€1,000,000=€1,127,496.85–€1,000,000=€127,496.85以日計息，這個投資的收益為:€1,000,000*(10.03/365)^(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，直接計算結(jié)果帶入第三排鍵)：PV=1,000,000，N=365*4，I/Y=3/365，PMT=0，CPTFV=-1,127,491.29PV=1,000,000，N=4，I/Y=(e^3%-1)*100，PMT=0，CPTFV=-1,127,496.85[單選題]28.Ananalystdevelopedtwoscenarioswithrespecttotherecoveryof$100,000principalfromdefaultedloans:Theamountoftheexpectedrecoveryisclosestto:A.$36,400.B.$63,600.C.$81,600.正確答案：B參考解析：：Biscorrect.IfScenario1occurs,theexpectedrecoveryis60%($50,000)40%($30,000)=$42,000,andifScenario2occurs,theexpectedrecoveryis90%($80,000)10%($60,000)=$78,000.Weightingbytheprobabilityofeachscenario,theexpectedrecoveryis40%($42,000)60%($78,000)=$63,600.Alternatively,firstcalculatingtheprobabilityofeachamountoccurring,theexpectedrecoveryis(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)生場景1，預(yù)期的恢復(fù)是60%($50,000)40%($30,000)=$42,000，如果發(fā)生場景2，預(yù)期的恢復(fù)是90%($80,000)10%($60,000)=$78,000。按照每種情況的概率進行加權(quán)，預(yù)期復(fù)蘇為40%(42,000美元)60%(78,000美元)=63,600美元?；蛘撸紫扔嬎忝總€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)=$63,600。[單選題]29.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).：A正確。五只股票的協(xié)方差矩陣有5×5=25項。減去5個對角線方差項，得到20個非對角線項。因為協(xié)方差矩陣是對稱的，所以只有10個協(xié)方差項是唯一的(20/2=10)。[單選題]30.Acorrelationof0.34betweentwovariables,XandY,isbestdescribedas: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，表明這兩個變量正相關(guān)變化的。因此，選項B是正確的[單選題]31.Publishedratingsonstocksrangingfrom1(strongsell)to5(strongbuy)areexamplesofwhichmeasurementscale?A.OrdinalB.ContinuousC.Nominal正確答案：A參考解析：Aiscorrect.Ordinalscalessortdataintocategoriesthatareorderedwithrespecttosomecharacteristicandmayinvolvenumberstoidentifycategoriesbutdonotassurethatthedifferencesbetweenscalevaluesareequal.Thebuyratingscaleindicatesthatastockranked5isexpectedtoperformbetterthanastockranked4,butittellsusnothingabouttheperformancedifferencebetweenstocksranked4and5comparedwiththeperformancedifferencebetweenstocksranked1and2,andsoon.A是正確的。排序數(shù)據(jù)可對觀測值進行排序并分類，涉及到的數(shù)字僅用來識別類別，但不能確保類別間的差異是相等的。買入評級量表表明，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.Whichofthefollowingriskpremiumsismostrelevantinexplainingthedifferenceinyieldsbetween30-yearbondsissuedbytheUSTreasuryand30-yearbondsissuedbyasmallprivateissuer?A.InflationB.MaturityC.Liquidity正確答案：C參考解析：：Ciscorrect.USTreasurybondsarehighlyliquid,whereasthebondsofsmallissuerstradeinfrequentlyandtheinterestrateincludesaliquiditypremium.Thisliquiditypremiumreflectstherelativelyhighcosts(includingtheimpactonprice)ofsellingaposition.：C正確。美國國債的流動性很強，而小型發(fā)行人的債券交易較少，其利率包含流動性溢價。這種流動性溢價反映了賣出頭寸的相對較高成本(考慮了流動性對于債券本身價格的影響)。[單選題]33.Amanagerwillselect20bondsoutofhisuniverseof100bondstoconstructaportfolio.Whichformulaprovidesthenumberofpossibleportfolios?A.PermutationformulaB.MultinomialformulaC.Combinationformula正確答案：C參考解析：：Ciscorrect.Thecombinationformulaprovidesthenumberofwaysthatrobjectscanbechosenfromatotalofnobjects,whentheorderinwhichtherobjectsarelisteddoesnotmatter.Theorderofthebondswithintheportfoliodoesnotmatter.：C正確。組合公式提供了從總共n個對象中選擇r個對象的方法的數(shù)量，而r個對象的排列順序并不重要。投資組合中債券的順序并不重要。[單選題]34.Whichofthefollowingstatementsismostaccurate?Ifthecovarianceofreturnsbetweentwoassetsis0.0023,then:A.theassets’riskisnearzero.B.theassetreturnsareunrelated.C.theassetreturnshaveapositiverelationship.正確答案：C參考解析：：Ciscorrect.Thecovarianceofreturnsispositivewhenthereturnsonbothassetstendtobeonthesameside(aboveorbelow)theirexpectedvaluesatthesametime.：C正確。當(dāng)兩種資產(chǎn)的回報率趨向于同一水平(高于或低于期望值)時，回報率的協(xié)方差為正。[單選題]35.Ananalystcalculatedtheexcesskurtosisofastock’sreturnsas-0.75.Fromthisinformation,weconcludethatthedistributionofreturnsis:A.normallydistributed.B.thin-tailedcomparedtothenormaldistribution.C.fat-tailedcomparedtothenormaldistribution.正確答案：B參考解析：Biscorrect.Thedistributionisthin-tailedrelativetothenormaldistributionbecausetheexcesskurtosisislessthanzero.選項B是正確的。由于分布的超額峰度是小于0的，那么可以得出：該分布相對于正態(tài)分布是低峰的，即低峰瘦尾。[單選題]36.Whichofthefollowingisapotentialproblemwithinterpretingacorrelationcoefficient?A.OutliersB.SpuriouscorrelationC.Bothoutliersandspuriouscorrelation正確答案：C參考解析：Ciscorrect.Bothoutliersandspuriouscorrelationarepotentialproblemswithinterpretingcorrelationcoefficients.異常值和偽相關(guān)都是解釋相關(guān)系數(shù)的潛在問題。因此，選項C是正確的[單選題]37.Ananalystproducesthefollowingjointprobabilityfunctionforaforeignindex(FI)andadomesticindex(DI).Thecovarianceofreturnsontheforeignindexandthereturnsonthedomesticindexisclosestto:A.26.39.B.26.56.C.28.12.正確答案：B參考解析：Biscorrect.Thecovarianceis26.56,calculatedasfollows.First,expectedreturnsareB正確。協(xié)方差為26.56，計算方法如下:首先，預(yù)期回報是:E(RFI)=(0.25×25)＋(0.50×15)＋(0.25×10)=6.25＋7.50＋2.50=16.25和E(RDI)=(0.25×30)＋(0.50×25)＋(0.25×15)=7.50＋12.50＋3.75=23.75。CovarianceisCov(RFI,RDI)=0.25[(25–16.25)(30–23.75)]＋0.50[(15–16.25)(25–23.75)]＋0.25[(10–16.25)(15–23.75)]=13.67＋(–0.78)＋13.67=26.56.[單選題]38.Themedianisclosestto:A.34.51.B.100.49.C.102.98.正確答案：B參考解析：Biscorrect.Themedianisindicatedwithinthebox,whichisthe100.49inthisdiagram.中位數(shù)，指的就是箱體中間的那條線所對應(yīng)的數(shù)值，也就是圖中的100.49.[單選題]39.Giventhefollowingtimelineandadiscountrateof4%ayearcompoundedannually,thepresentvalue(PV),asoftheendofYear5(PV5),ofthecashflowreceivedattheendofYear20isclosestto:A.$22,819.B.$27,763.C.$28,873.正確答案：B參考解析：Biscorrect.ThePVinYear5ofa$50,000lumpsumpaidinYear20is$27,763.23(whereFVisfuturevalue):B正確。在END模式下，F(xiàn)V=50,000，N=15，I/Y=4，PMT=0，CPTPV=-27,763.23[單選題]40.TheaveragereturnforPortfolioAoverthepasttwelvemonthsis3%,withastandarddeviationof4%.TheaveragereturnforPortfolioBoverthissameperiodisalso3%,butwithastandarddeviationof6%.ThegeometricmeanreturnofPortfolioAis2.85%.ThegeometricmeanreturnofPortfolioBis:A.lessthan2.85%.B.equalto2.85%.C.greaterthan2.85%.正確答案：A參考解析：Aiscorrect.Themoredisperseadistribution,thegreaterthedifferencebetweenthearithmeticmeanandthegeometricmean.選項A是正確的。對于任何一個數(shù)據(jù)集來說，算術(shù)平均數(shù)是唯一的，而且其數(shù)值大小與數(shù)據(jù)集中每一個數(shù)據(jù)都有關(guān)，如果數(shù)據(jù)集中有異常值，將會使算術(shù)平均數(shù)發(fā)生很大的變化。因此，當(dāng)數(shù)據(jù)集越分散，對算數(shù)平均數(shù)的影響就越大，也就使得算術(shù)平均值和幾何平均值之間的差異越大。[單選題]41.ThefollowingexhibitshowstheannualMSCIWorldIndextotalreturnsfora10-yearperiod.ThefourthquintilereturnfortheMSCIWorldIndexisclosestto:A.20.65%.B.26.03%.C.27.37%.正確答案：B參考解析：Biscorrect.Quintilesdivideadistributionintofifths,withthefourthquintileoccurringatthepointatwhich80%oftheobservationsliebelowit.Thefourthquintileisequivalenttothe80thpercentile.Tofindtheythpercentile(Py),wefirstmustdetermineitslocation.Theformulaforthelocation(Ly)ofaythpercentileinanarraywithnentriessortedinascendingorderisLy=(n＋1)×(y/100).Inthiscase,n=10andy=80%,soL80=(10＋1)×(80/100)=11×0.8=8.8.Withthedataarrangedinascendingorder(－40.33%,－5.02%,9.57%,10.02%,12.34%,15.25%,16.54%,20.65%,27.37%,and30.79%),the8.8thpositionwouldbebetweenthe8thand9thentries,20.65%and27.37%,respectively.Usinglinearinterpolation,P80=X8＋(Ly–8)×(X9–X8),P80=20.65＋(8.8–8)×(27.37–20.65)=20.65＋(0.8×6.72)=20.65＋5.38=26.03%.五分位數(shù)把一個分布分成五分之三，而第四分位數(shù)出現(xiàn)在80%的觀察值低于它的地方。第四個五分位數(shù)相當(dāng)于第80個百分位數(shù)。要找到第yth百分位數(shù)(Py)，首先必須確定它的位置。按升序排列n個元素的數(shù)組中第y百分位的位置(Ly)公式為Ly=(n＋1)×(y/100)。此時，n=10,y=80%，所以L80=(10＋1)×(80/100)=11×0.8=8.8。數(shù)據(jù)按升序排列(－40.33%、－5.02%、9.57%、10.02%、12.34%、15.25%、16.54%、20.65%、27.37%和30.79%)，8.8位分別位于第8和第9項之間，分別為20.65%和27.37%。采用線性插值，P80=X8＋(Ly-8)×(X9-X8)，P80=20.65＋(8.8-8)×(27.37-20.65)=20.65＋(0.8×6.72)=20.65＋5.38=26.03%。[單選題]42.Theprobabilitydistributionforacompany‘ssalesis:Thestandarddeviationofsalesisclosestto:A.$9.81million.B.$12.20million.C.$32.40million.正確答案：A參考解析：Aiscorrect.Theanalystmustfirstcalculateexpectedsalesas0.05×$70+0.70×$40+0.25×$25=$3.50million+$28.00million+$6.25million=$37.75million.Aftercalculatingexpectedsales,wecancalculatethevarianceofsales:Thestandarddeviationofsalesisthusσ=($96.18)^1/2=$9.81million.A正確。分析師必須首先計算預(yù)期銷售額為0.05×$70＋0.70×$40＋0.25×$25=$37.75million。通過計算期望銷售額，可以計算出銷售額的方差:σ^2=P(70)(70-E(銷售))^2＋P(40)[40-E(銷售)]^2＋P(25)(25-E(銷售))^2=0.05(70-37.75)^2＋0.70(40-37.75)^2＋0.25(25-37.75)^2=52mil＋3.54mil＋40.6