06年FRM考试试题及参考答案51140真题.docx
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06年FRM考试试题及参考答案51140真题.docx
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06年FRM考试试题及参考答案51140真题
50.Supposethedailyreturnsofaportfolioandabenchmarkportfolioitisreplicatingareasfollows:
PortfolioReturn(bps)BenchmarkPortfolioReturn(bps)
Day13430
Day2-89-87
Day3108102
Day47070
Whatisthetrackingerroroverthefourdayperiod?
a.3.16bps
b.2bps
c.10bps
d.2.39bps
Answer:
a
a.Correct.
Trackingerroristhestandarddeviationofthedifferencebetweenthereturnofthemanagedportfolioandthebenchmarkportfolio.
TE=sigma(RP-RB)=[E[(RP-RB)2]-E(RP-RB)2]1/2
and
E[RP-RB]=(4+(-2)+6+0)/4=2.00
E[(RP-RB)]2=(16+4+36+0)/4=14.00
So,
TE=(14.00-4.00)1/2=3.16bps.
b.Incorrect.
Thissolutionincorrectlysetsthetrackingerrorequaltotheaveragedifferencebetweenthereturnofthemanagedportfolioandthebenchmarkportfolio.Trackingerroristhestandarddeviationofthedifferencebetweenthereturnofthemanagedportfolioandthebenchmarkportfolio.
c.Incorrect.
Thissolutionincorrectlysetsthetrackingerrorequaltothevarianceofthedifferencebetweenthereturnofthemanagedportfolioandthebenchmarkportfolio.Trackingerroristhestandarddeviationofthedifferencebetweenthereturnofthemanagedportfolioandthebenchmarkportfolio.
d.Incorrect.
Thissolutionincorrectlysetsthetrackingerrorequaltothedifferencebetweenthestandarddeviationofthereturnofthemanagedportfolioandthestandarddeviationofthereturnofthebenchmarkportfolio.Trackingerroristhestandarddeviationofthedifferencebetweenthereturnofthemanagedportfolioandthebenchmarkportfolio.
Reference:
NoelAmencandVeroniqueLeSourd,PortfolioTheoryandPerformanceAnalysis(WestSussex:
Wiley,2003).,Chapter4–TheCapitalAssetPricingModelandItsApplicationtoPerformanceMeasurement
51.Youaregiventhefollowinginformationaboutaninterestrateswap:
•2-yearTerm
•Semi-annualpayment
•FixedRate=6%
•FloatingRate=LIBOR+50basispoints.
•NotionalprincipalUSD10million.
CalculatethenetcouponexchangeforthefirstperiodifLIBORis5%atthebeginningoftheperiodand5.5%attheendoftheperiod.
a.FixedratepayerpaysUSD0.
b.FixedratepayerpaysUSD25,000.
c.FixedratepayerpaysUSD50,000.
d.FixedratepayerreceivesUSD25,000.0
Answer:
b
a.Incorrect.ThecandidateincorrectlyusestheLIBORrateattheendoftheperiod.
b.Correct.FixedratepayerpaysUSD25,000.SeeBELOWfordetails.
c.Incorrect.Thecandidateforgetstoaddthe50basispointstothebeginningLIBORrate.
d.Incorrect.Thecandidateisconfusedaboutthecashflowdirection.Anetpositivepaymentispaidbythefixedratepayer,notreceiving.
ComputationalDetailsforNumericalAnswer:
•Fixedratepayerpays6%,therefore(0.06/2)x10million=USD300,000.
•Interestrateswapshavepaymentsinarrears.FloatingratepayerpaysLIBORrateatthebeginningofperiod+0.50%,i.e.5%+0.50%=5.5%.
Thereforethefloatingratepayment=(0.055/2)x10million=USD275,000.
•ThenetpaymentofUSD25,000ispaidbythefixedratepayer.
Reference:
JohnHull,Options,Futures,andOtherDerivatives,6thed.(NewYork:
PrenticeHall,2006).,
Chapter7–Swaps
52.WhichofthefollowingisalimitationofusingtheCapitalAssetPricingModeltomeasureequityrequirementsforoperationalrisk?
a.Measurementerrorinseparatelymeasuringleveredandun-leveredbeta
b.Timelagsinvbariablesliketaxandregulationbeingreflectedinhistoricalbetaestimates.
c.Requiresdetailedknowledgeofprofitandlossaccountingtogofrombetatoaspecificmeasureofoperationalrisk.
d.Alloftheabove.
Answer:
d
Explanation:
Thisisnotagoodwaytomeasureoperationalrisk,andthesearejustthreeofthe
reasonswhy.
Reference:
EllenDavis,ed,TheAdvancedMeasurementApproachtoOperationalRisk,(London:
RiskBooks,2006).,
Chapter4–OperationalRiskEconomicCapitalMeasurement:
MathematicalModelsforAnalysingLoss
Data,byGeneAlvarez
53.Assumethataportfoliounderperformeditsbenchmarkby2%inthemostrecentmonth.Inthisscenario,
a.Alphais“-2%”asitreferstotheOutperformance/UnderperformanceGap.
b.Duetounderperformance,Alphaisdefinitelynegativeandcannotbepositive.
c.AlphamaybepositiveornegativedependinguponBetaandRiskFreeRate.
d.Alphais2%.
Answer:
c
a.Incorrect.TotalPortfolioReturnequalsto,RiskFreeReturn
i.e.RFR+[Betax(Indexreturn–RFR)]+Alpha.
Thisway,AlphaisresidualafterreducingRFRandIndexorMarketRelatedReturnfromTotalReturn.ItneednotbeequaltoUnderperformanceGapof“-2%”.
b.Incorrect.IfBetaofPortfolioismuchlower,MarketRelatedReturnwillalsobelower.
ThismayresultinaPositiveAlphainspiteofUnderperformance.
c.Correct.AmuchlowerBetawillreduceMarketRelatedReturnandinturn,mayincreasetheresidualAlphatopositivefigure.Similarly,ahigherbetamayresultinhighershareofMarketrelatedreturnimplyingaNegativeAlpha.Hence,AlphamaymoveanywheredependinguponthelevelsofBetaandRFR.
d.Incorrect.AlphacanbeanyfiguredependinguponlevelsofBetaandRFR.Alphaneednotbeequaltodifferenceinreturnofportfolioandindex.
Reference:
NoelAmencandVeroniqueLeSourd,PortfolioTheoryandPerformanceAnalysis(WestSussex:
Wiley,2003).,Chapter4–TheCapitalAssetPricingModelandItsApplicationtoPerformanceMeasurement
54.Whichofthefollowingstatementsisfalse?
a.European-styledcallandputoptionsaremostaffectedbychangesinvegawhentheyareatthe-money.
b.ThedeltaofaEuropean-styledputoptiononanunderlyingstockwouldmovetowardszeroasthepriceoftheunderlyingstockrises.
c.Thegammaofanat-the-moneyEuropean-styledoptiontendstoincreaseastheremainingmaturityoftheoptiondecreases.
d.Comparedtoanat-the-moneyEuropean-styledcalloption,anout-of-themoneyEuropeanoptionwiththesamestrikepriceandremainingmaturitywouldhaveagreaternegativevaluefortheta.
Answer:
d
a.Correct.Vegaishighestforat-the-moneyoptions.
b.Correct.ThedeltaforaEuropeanputoptionisnegative,andthelikelihoodofexercisedecreases,i.e.,deltamovestowardszero,asthepriceoftheunderlyingstockincreases.
c.Correct.Gammaincreasesasthetimetomaturitydecreases.Astimetomaturityapproacheszero,gammaapproachesinfinity.
d.Incorrect.Thetaislargeandnegativeforanat–the-moneyEuropean-styledoption,whilstthetaisclosetozerowhenthepricefortheunderlyingstockisverylow.Thereforethethetaforanout-ofthe–moneyEuropeanstyledcalloptionwouldhavealowernegativevaluecomparedtothatofanat-the-moneyEuropean-styledcalloption.
Reference:
JohnHull,Options,Futures,andOtherDerivatives,6thed.(NewYork:
PrenticeHall,2006).,
Chapter15–TheGreekLetters
55.Youaregiventhefollowinginformationaboutaporfolioandareaskedtomakearecommendationabouthowtoreallocatetheportfoliotoimprovetherisk/returntradeoff?
Asset
Expected
return
Standard
Deviation
Current
Weight
Covarianceof
Portfolioand
AssetIReturns
Marginal
Return
Marginal
Risk
MarginalReturn/
Marginalrisk
Risk
Contribution
Asset1
7.10%
17.00%
38.70%
1.43%
3.10%
13.99%
22.17%
5.41%
Asset2
8.00%
40.60%
6.20%
2.44%
4.00%
23.93%
16.71%
1.48%
Asset3
6.70%
44.80%
5.50%
2.39%
2.70%
23.39%
11.55%
1.29%
Asset4
6.90%
21.40%
14.60%
1.41%
2.90%
13.86%
20.92%
2.02%
Riskfree
4.00%
0.00%
35.00%
0.00%
Whichofthefollowingrecommendationswillimprovetherisk/returntradeofoftheporfolio?
a.Increasetheallocationstoassets1and3anddecreasetheallocationtoassets2and4.
b.Increasetheallocationstoassets1and2anddecreasetheallocationtoassets3and4.
c.Increasetheallocationstoassets2and3anddecreasetheallocationtoassets1and4.
d.Increasetheallocationstoassets1and4anddecreasetheallocationtoassets2and3.
Answer:
d
A.Incorrect.Asset3shouldbedecreasedsinceithasthelowestmarginalreturn-to-marginalriskratio.
B.Incorrect.Asset4shouldbeincreasedsinceithasthehighestmarginalreturn-to-marginalriskratio.
C.Incorrect.Asset4shouldbeincreasedsinceithasthehighestmarginalreturn-to-marginalriskratio.
D.Correct.Aportfoliooptimizingtherisk-rewardtradeoffhasthepropertythattheratioofthemarginalreturntomarginalriskofeachassetisequal.Therefore,thisoptionistheonlyrecommendationthatwillmovetheratiosintherightdirection.
56.BankOmega’sforeigncurrencytradingdeskiscomposedof2dealers;dealerA,whoholdsalongpositionof10millionCHFagainsttheUSD,anddealerB,whoholdsalongpositionof10millionSGDagainsttheUSD.ThecurrentspotratesforUSD/CHFandUSD/SGDare1.2350and1.5905respectively.Usingthevariance/covarianceapproach,youworkedoutthe1day,95%VARofdealerAtobeUSD77,632andthatofdealerBtobeUSD27,911.IfthecorrelationcoefficientbetweentheSGDandCHFis+0.602andassumingthatthesearetheonlytradingexposuresfordealerAanddealerB,whatwouldyoureportasthe1day,95%VARofBankOmega’sforeigncurrencytradingdeskusingthevariance/covarianceapproach?
a.USD97,027
b.USD105,543
c.USD113,932
d.Cannotbedeterminedduetoinsufficientdata
Answer:
a
a.NotethatthequestionasksfortheVARnumbertobeexpressedinUSD.Therefore,thefirststepistoconverttheforeigncurrencypositionsintermsofUSD.
DealerA’spositioninUSD:
10,000,000/1.2350=USD8,097,166
DealerB’spositioninUSD:
10,000,000/1.5905=USD6,287,331
Giventhat
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