2020年FRM练习考试第一部分：五月考试水平测试题

2020

FRM

®

PRE-STUDY

PracticeExamPartI

2020FRMLearningObjectives

/frm

1

Updated01/21/20

2020FRMPre-StudyPracticeExamPartI

TableofContents

Introductionto2020FRMPartIPre-StudyPracticeExam3

2020FRMPartIPre-StudyPracticeExam–StatisticalReferenceTable4

2020FRMPartIPre-StudyPracticeExam–SpecialInstructionsandDefinitions5

2020FRMPartIPre-StudyPracticeExam–CandidateAnswerSheet6

2020FRMPartIPre-StudyPracticeExam–Questions7

2020FRMPartIPre-StudyPracticeExam–AnswerKey17

2020FRMPartIPre-StudyPracticeExam–Answers&Explanations18

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2020FRMPre-StudyPracticeExamPartI

Introduction

TheFRMExamisapractice-orientedexamination.Itsquestionsarederivedfromacombinationof

theory,assetforthinthecorereadings,and“real-world”workexperience.Candidatesareexpectedto

understandriskmanagementconceptsandapproachesandhowtheywouldapplytoariskmanager’s

day-to-dayactivities.

TheFRMExamisalsoacomprehensiveexamination,testingariskprofessionalonanumberofrisk

managementconceptsandapproaches.Itisveryrarethatariskmanagerwillbefacedwithanissuethatcan

immediatelybeslottedintoonecategory.Intherealworld,ariskmanagermustbeabletoidentifyany

numberofrisk-relatedissuesandbeabletodealwiththemeffectively.

The2020FRMPre-StudyPartIandPartIIPracticeExamshavebeendevelopedtoaidcandidatesintheir

preparationfortheFRMExaminMayandNovember2020.ThesePracticeExamsarebasedonasampleof

questionsfrompriorFRMExamsandaresuggestiveofthequestionsthatwillbeonthe2020FRMExam.

The2020FRMPre-StudyPartIPracticeExamcontains25multiple-choicequestionsandthe2020FRM

Pre-StudyPartIIPracticeExamcontains20multiple-choicequestions.

The2020FRMPracticeExamsdonotnecessarilycoveralltopicstobetestedinthe2020FRMExamas

anytestsamplesfromtheuniverseoftestablepossibleknowledgepoints.However,thequestions

selectedforinclusioninthePracticeExamswerechosentobebroadlyreflectiveofthematerialassigned

for2020aswellastorepresentthestyleofquestionthattheFRMCommitteeconsidersappropriate

basedonassignedmaterial.

Foracompletelistofcurrenttopics,corereadings,andkeylearningobjectives,candidatesshould

refertothe2020FRMExamStudyGuideand2020FRMLearningObjectives.

CorereadingswereselectedbytheFRMCommitteetoassistcandidatesintheirreviewofthesubjects

coveredbytheExam.QuestionsfortheFRMExamarederivedfromthecorereadings.Itisstrongly

suggestedthatcandidatesstudythesereadingsindepthpriortosittingfortheExam.

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2020FRMPre-StudyPracticeExamPartI

4

2020FRMPre-StudyPracticeExamPartI

SpecialInstructionsandDefinitions

1.Unlessotherwiseindicated,interestratesareassumedtobecontinuouslycompounded.

2.Unlessotherwiseindicated,optioncontractsareassumedtobeononeunitoftheunderlyingasset.

3.bp(s)=basispoint(s)

4.CAPM=capitalassetpricingmodel

5.CCP=centralcounterpartyorcentralclearingcounterparty

6.CDO=collateralizeddebtobligation(s)

7.CDS=creditdefaultswap(s)

8.CEO,CFO,CIO,andCROare:chiefexecutive,financial,investment,andriskofficers,respectively

9.CVA=creditvalueadjustment

10.ERM=enterpriseriskmanagement

11.ES=expectedshortfall

12.EWMA=exponentiallyweightedmovingaverage

13.GARCH=generalizedauto-regressiveconditionalheteroskedasticity

14.LIBOR=Londoninterbankofferedrate

15.MBS=mortgage-backed-security(securities)

16.OIS=overnightindexedswap

17.OTC=over-the-counter

18.RAROC=risk-adjustedreturnoncapital

19.VaR=value-at-risk

20.Thefollowingacronymsareusedforselectedcurrencies:

AcronymCurrency

Acronym

GBP

Currency

AUD

BRL

Australiandollar

Britishpoundsterling

Indianrupee

Japaneseyen

Singaporedollar

USdollar

Brazilianreal

Canadiandollar

Chineseyuan

euro

INR

CAD

CNY

EUR

JPY

SGD

USD

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2020FRMPre-StudyPracticeExamPartI

2020FRMPartIPre-StudyPracticeExam–CandidateAnswerSheet

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

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18.

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25.

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2020FRMPre-StudyPracticeExamPartI

1.AnanalystisevaluatingtheperformanceofaportfolioofSingaporeanequitiesthatisbenchmarkedtothe

StraitsTimesIndex(STI).Theanalystcollectsthefollowinginformationabouttheportfolioandthebenchmark

index:

Expectedreturnoftheportfolio

Volatilityofreturnsoftheportfolio

ExpectedreturnoftheSTI

7.6%

11.5%

4.0%

8.7%

2.3%

1.7%

VolatilityofreturnsoftheSTI

Risk-freerateofreturn

BetaofportfoliorelativetoSTI

WhatistheSharperatioofthisportfolio?

A.0.036

B.0.047

C.0.389

D.0.461

2.Ananalystwantstopricea9-monthfuturescontractonastockindex.Thecurrentpriceoftheindexis

USD700andthecontinuouslycompoundedrisk-freerateis4.0%peryear.Ifthestocksunderlyingtheindex

provideacontinuouslycompoundeddividendyieldof2.5%peryear,whatistheno-arbitragepriceofthe

9-monthfuturescontract?

A.USD692.17

B.USD707.92

C.USD710.58

D.USD721.32

7

2020FRMPre-StudyPracticeExamPartI

3.SupposetheRussell2000Indexhasanexpectedannualreturnof7.8%andvolatilityof9.8%.Supposethe

AlphaIndustrialFundhasanexpectedannualreturnof7.1%andvolatilityof7.9%andisbenchmarkedagainst

theRussell2000Index.AccordingtotheCAPM,iftherisk-freerateis3.2%peryear,whatisthebetaofthe

AlphaIndustrialFund?

A.0.85

B.0.95

C.1.13

D.1.23

4.Ariskmanagerisevaluatingthepricesensitivityofaninvestment-gradecallablebondusingthefirm’s

valuationsystem.Thetablebelowpresentsinformationonthebondaswellasontheembeddedoption.The

currentinterestrateenvironmentisflatat4%.

ValueinUSDperUSD100facevalue

InterestRateLevel

3.95%

CallableBond

97.9430

CallOption

2.1972

4.00%

97.8910

2.1090

4.05%

97.8566

2.0035

Theconvexityofthecallablebondcanbeestimatedas:

A.0.180

B.0.360

C.179.792

D.719.167

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2020FRMPre-StudyPracticeExamPartI

5.Afixed-incomeportfoliomanagerpurchasesaseasoned6%agencyMBSwithaweightedaverageloanageof

50months.ThecurrentbalanceontheloansatthebeginningofthismonthisUSD22million,andthe

conditionalprepaymentrateisassumedtobeconstantat5%peryear.Whichofthefollowingisclosesttothe

anticipatedprincipalprepaymentthismonth?

A.USD22,558

B.USD66,000

C.USD91,667

D.USD93,830

6.AportfoliomanagerisexaminingdataregardingvariousindexfuturescontractstradedattheCMEGroup.

Whichofthefollowingobservationswouldtheportfoliomanagermostlikelyviewasapotentialproblem?

A.Thevolumeinaspecificcontractisgreaterthantheopeninterest.

B.Onespecificcontractisofamuchsmallersizethantheothers.

C.Thepriorsettlementpriceforaspecificcontractisabovetheopeningprice.

D.Inaspecificcontract,thelastdayonwhichtradingcanoccurisnotspecified.

7.Ananalystisexaminingaportfoliothatconsistsof2,500subprimemortgagesand800primemortgages.Of

thesubprimemortgages,500arelateontheirpayments.Oftheprimemortgages,64arelateontheir

payments.Iftheanalystrandomlyselectsamortgagefromtheportfolioanditiscurrentlylateonits

payments,whatistheprobabilitythatitisasubprimemortgage?

A.60%

B.67%

C.75%

D.89%

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2020FRMPre-StudyPracticeExamPartI

8.TRSC,atrustcompanyspecializingincorporateinvestments,isbroughtinasacorporatetrusteeforarecent

bondissuemadebyBanko,asmallinvestmentbank.WhichofthefollowingstatementsaboutTRSCandits

roleasapartytotheindentureiscorrect?

A.TRSCmustmonitorBanko’sfinancialsituationtoforeseeanycovenantbreaches.

B.Whendeemednecessary,TRSCshouldtakeactionbeyondthetermsoftheindentureinordertoprotect

bondholders.

C.TRSCmusttakeactionaccordingtothetermsoftheindenturewheneveritisrequestedbybondholders.

D.TRSCispaidbyBankotorepresenttheinterestsofthebondholders.

9.AnanalysthasbeenaskedtocheckforarbitrageopportunitiesintheTreasurybondmarketbycomparingthe

cashflowsofselectedbondswiththecashflowsofcombinationsofotherbonds.Ifa1-yearzero-couponbond

ispricedatUSD97anda1-year7%couponbondwithsemi-annualpaymentsispricedatUSD102,usinga

replicationapproach,whatshouldbethepriceofa1-year6%couponTreasurybondthatpayssemi-annually?

A.USD97.71

B.USD101.04

C.USD101.29

D.USD102.86

10.AnItalianbankentersintoa6-monthforwardcontractwithanimportertosellGBP80millionin6monthsata

rateofEUR1.13perGBP1.Ifin6monthstheexchangerateisEUR1.12perGBP1,whatisthepayofftothe

bankfromtheforwardcontract?

A.EUR-800,000

B.EUR-400,000

C.EUR400,000

D.EUR800,000

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2020FRMPre-StudyPracticeExamPartI

11.Ariskmanagerisdecidingbetweenbuyingafuturescontractonanexchangeandbuyingaforwardcontract

directlyfromacounterpartyonthesameunderlyingasset.Bothcontractswouldhavethesamematurityof

2yearsandthesamedeliveryspecifications.Themanagerfindsthatthefuturespriceishigherthanthe

forwardprice.Assumingnoarbitrageopportunityexists,andinterestratesareexpectedtoincrease,what

singlefactoractingalonewouldbearealisticexplanationforthispricedifference?

A.Thefuturescontractislessliquidthantheforwardcontract.

B.Theforwardcontractcounterpartyislesslikelytodefaultthanthecounterpartyinthefutures

transaction.

C.Thetransactioncostonthefuturescontractishigherthanthatontheforwardcontract.

D.Thepriceoftheunderlyingassetisstronglypositivelycorrelatedwithinterestrates.

12.AriskmanageratFirmSPCistestingaportfolioforheteroskedasticityusingtheWhitetest.Theportfoliois

modeledasfollows:

푌=훼+훽푋+휖푖

푖

1푖

Theresidualsarecomputedasfollows:

̂

휖̂=푌−훼̂−훽푋

푖푖1푖

WhichofthefollowingcorrectlydepictsthesecondstepintheWhitetestfortheportfolio?

A.

B.

C.

D.

2

2

휖

휖

휖

휖

̂=훾+훾푋+훾푋+휂푖

푖011푖21푖

2

푖

2

푖

2

푖

2

̂

=훾푋+훾푋+휂푖

11푖21푖

̂

=훾+훾푋+휂푖

011푖

2

̂

=훾+훾푋+휂푖

011푖

13.Supposethatthecorrelationofthereturnofaportfoliowiththereturnofitsbenchmarkis0.7,thevolatilityof

thereturnoftheportfoliois6.5%,andthevolatilityofthereturnofthebenchmarkis5.0%.Whatisthebeta

oftheportfoliowithrespecttoitsbenchmark?

A.-0.91

B.0.64

C.0.80

D.0.91

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2020FRMPre-StudyPracticeExamPartI

14.Ariskmanageratamajorglobalbankisconductingatimeseriesanalysisofequityreturns.Themanager

wantstoknowwhetherthetimeseriesiscovariancestationary.Whichofthefollowingstatementsdescribes

oneoftherequirementsforatimeseriestobecovariancestationary?

A.Thedistributionofatimeseriesshouldhaveakurtosisvaluenear3.0,ensuringnofattailswilldistort

stationarity.

B.Thedistributionofatimeseriesshouldhaveaskewnessvaluenear0,sothatitsmeanwillfallinthe

centerofthedistribution.

C.Theautocovariancesofacovariancestationarytimeseriesdependonlyonthelag,h,between

observations,notontime.

D.Whentheautocovariancefunctionisasymmetricwithrespecttodisplacement,τ,forwardlooking

stationaritycanbeachieved.

15.AriskmanageriscalculatingtheVaRofafundwithadatasetof50weeklyreturns.Themeanweeklyreturn

estimatedfromthesampleis8%withastandarddeviationof17%.Assumingthatweeklyreturnsare

independentandidenticallydistributed,whatisthestandarddeviationofthemeanweeklyreturn?

A.0.4%

B.0.7%

C.2.4%

D.10.0%

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2020FRMPre-StudyPracticeExamPartI

16.Ananalystwantstopricea1-year,European-stylecalloptiononcompanyREX’sstockusingtheBlack-Scholes-

Merton(BSM)model.REXannouncesthatitwillpayadividendofUSD1.25pershareonanex-dividenddate

1monthfromnowandhasnofurtherdividendpayoutplans.TherelevantinformationfortheBSMmodel

inputsareinthefollowingtable.

Currentstockprice(S)

USD60

12%peryear

3.5%peryear

USD60

0

Stockpricevolatility(σ)

Risk-freerate(r)

Calloptionexerciseprice(K)

N(d1)

0.570143

N(d2)

0.522623

Whatisthepriceofthe1-yearcalloptiononthestock?

A.USD2.40

B.USD3.22

C.USD3.97

D.USD4.81

17.Anactuaryataninsurancecompanyisaskedtoestimateanordinaryleastsquaresestimation(OLS)regression

modeltoanalyzecompanyperformance.Theactuaryisconcernedthatimportantvariablescouldbeomitted

intheOLSregressionmodel,resultinginomittedvariablebiaswhichwouldreducetheaccuracyoftheresult.

Whendoesomittedvariablebiasoccur?

A.Omittedvariablebiasoccurswhentheomittedvariableiscorrelatedwithalloftheincludedindependent

variablesandisadeterminantofthedependentvariable.

B.Omittedvariablebiasoccurswhentheomittedvariableiscorrelatedwithatleastoneoftheincluded

independentvariablesandisadeterminantofthedependentvariable.

C.Omittedvariablebiasoccurswhentheomittedvariableisindependentoftheincludedindependent

variablesandisadeterminantofthedependentvariable.

D.Omittedvariablebiasoccurswhentheomittedvariableisindependentoftheincludedindependent

variablesbutisnotadeterminantofthedependentvariable.

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2020FRMPre-StudyPracticeExamPartI

18.Thecurrentpriceofa6-month,USD30.00strikeprice,European-styleputoptiononastockisUSD4.00.The

currentstockpriceisUSD32.00.Aspecialone-timedividendofUSD0.75pershareisexpectedin3months.

Thecontinuouslycompoundedrisk-freerateforallmaturitiesis3.5%peryear.Whichofthefollowingis

closesttotheno-arbitragevalueofaEuropean-stylecalloptiononthesameunderlyingstockwithastrike

priceofUSD30.00andatimetomaturityof6months?

A.USD2.22

B.USD5.26

C.USD5.78

D.USD6.52

QUESTIONS19AND20REFERTOTHEFOLLOWINGINFORMATION:

Ariskmanagerisconsideringwritinga6-monthAmerican-styleputoptiononanon-dividendpayingstockY.The

currentstockpriceisUSD30,andthestrikepriceoftheoptionisUSD32.Tofindtheno-arbitragepriceofthe

option,themanagerusesatwo-stepbinomialtreemodel.Thestockpricecangoupordownby15%eachperiod.

Themanager’sviewisthatthestockpricehasa60%probabilityofgoingupeachperiodanda40%probabilityof

goingdowneachperiod.Theannualrisk-freerateis4%withcontinuouscompounding.

19.Whatistherisk-neutralprobabilityofthestockpricegoingupinasinglestep?

A.16.0%

B.46.7%

C.53.4%

D.84.0%

20.Theno-arbitragepriceofthe6-monthoptionisclosestto:

A.USD2.00

B.USD3.51

C.USD3.66

D.USD3.69

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2020FRMPre-StudyPracticeExamPartI

21.Ajunioranalystatabankisaskedtoprovidesuggestionsonpotentialmetricsthebankcanuseinitscapital

managementprogram.Theanalystpreparesapresentationdiscussingtheadvantagesanddisadvantagesof

theRAROCmetric.Whichofthefollowingstatementsismostappropriatefortheanalysttoincludeinthe

presentation?

A.RAROCwillmakeiteasiertocomparetheprofitabilityofbusinessdivisionsthatrequiredifferentlevelsof

capital.

B.RAROCallowsthefirmtobenchmarkitsperformanceagainstoperatingtargetssetbyindustrypeers.

C.RAROCisaneffectiveforward-lookingtooltomodelpotentialextremelossesduringstressscenarios.

D.Anactivityisaddingvaluetothebank’sshareholdersifitscostofequitycapitalishigherthanitsRAROC.

22.ThecollapseofLong-TermCapitalManagement(LTCM)isaclassicriskmanagementcasestudy.Whichofthe

followingstatementsaboutriskmanagementatLTCMiscorrect?

A.LTCM’stradersdidnotrespondquicklyenoughtochangesinmarketvolatilityasthereweresignificant

barriersthatblockedtheflowofinformation.

B.LTCMfailedtoaccountfortheilliquidityofitslargestpositionsinitsriskcalculations.

C.LTCM’suseofhighleverageisevidenceofpoorriskmanagement.

D.LTCMdidnotrunanystressscenariosonitsVaRmodel.

23.AportfolioofinvestmentsecuritiesforaregionalbankhasacurrentmarketvalueofUSD3,700,000witha

dailyvarianceof0.0004.Assumingthereare250tradingdaysinayearandtheportfolioreturnsare

independentandfollowthesamenormaldistributionwithzeromean,whatistheestimateoftheannualVaR

atthe95%confidencelevel?

A.USD38,494

B.USD121,730

C.USD1,924,720

D.USD2,721,519

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2020FRMPre-StudyPracticeExamPartI

24.BankPZRenteredintoa2-yearinterestrateswapcontractonSeptember7,2016.Accordingtotheswap,Bank

PZRwouldreceivea4.10%fixedrateandpayLIBORplus1.30%onanotionalamountofUSD7.5million.

Paymentsweretobemadeevery6months.Thetablebelowdisplaystheactualannual6-monthLIBORrates

overthe2-yearperiod:

Date

6-monthLIBOR

2.46%

Sep7,2016

Mar7,2017

Sept7,2017

Mar7,2018

Sep7,2018

1.13%

0.79%

0.42%

0.56%

Assumingnodefault,howmuchdidBankPZRreceiveonSeptember7,2018?

A.USD12,750

B.USD75,375

C.USD84,000

D.USD89,250

25.TheCFOofapubliclytradedcomputermanufacturingcompanyisassessingtheconcernsandmotivationsof

differentstakeholdergroupswithrespecttothefirm’shedgingstrategies.Whichofthefollowingstatements

iscorrect?

A.Ifthefirm’sequityinvestorsholdawell-diversifiedportfolioofinvestments,theywouldtypicallyprefer

thatthefirmhedgerisksspecifictothecomputerindustry.

B.Debtinvestorswouldtypicallypreferthatthecompanyusehedgingstrategiestoincreasethestabilityof

itsrevenuestream.

C.Thefirmshouldtypicallynothedgetheforeignexchangeriskoflong-termcontractstointernational

customers.

D.Equityinvestorswouldtypicallynotrewardthefirmforusinghedgingtoreduceitstaxexposureovera

multi-yearperiod.

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2020FRMPre-StudyPracticeExamPartI

2020FRMPartIPre-StudyPracticeExam–AnswerSheet

1.

2.

D

B

A

D

D

D

D

D

C

D

D

A

D

C

C

B

B

C

C

C

A

B

C

D

B

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

17

2020FRMPre-StudyPracticeExamPartI

1.AnanalystisevaluatingtheperformanceofaportfolioofSingaporeanequitiesthatisbenchmarkedtothe

StraitsTimesIndex(STI).Theanalystcollectsthefollowinginformationabouttheportfolioandthebenchmark

index:

Expectedreturnoftheportfolio

Volatilityofreturnsoftheportfolio

ExpectedreturnoftheSTI

7.6%

11.5%

4.0%

8.7%

2.3%

1.7%

VolatilityofreturnsoftheSTI

Risk-freerateofreturn

BetaofportfoliorelativetoSTI

WhatistheSharperatioofthisportfolio?

A.0.036

B.0.047

C.0.389

D.0.461

CorrectAnswer:

Explanation:

D

TheSharperatiofortheportfoliois:

퐸푥푝푒푐푡푒푑푟푒푡푢푟푛표푓푝표푟푡푓표푙−푅

푓푟푒푒푟푎푡푒7.6%−2.3%

=

=0.461

푉표푙푎푡

표푓푟푒푡푢푟푛푠표푓푝표푟푡푓표푙

11.5%

Section:

FoundationsofRiskManagement

Reference:

GlobalAssociationofRiskProfessionals.FoundationsofRiskManagement.NewYork,NY:

Pearson,2019.Chapter5.ModernPortfolioTheory(MPT)andtheCapitalAssetPricing

Model(CAPM).

LearningObjective:Calculate,compare,andinterpretthefollowingperformancemeasures:theSharpe

performanceindex,theTreynorperformanceindex,theJensenperformanceindex,the

trackingerror,informationratio,andSortinoratio.

18

2020FRMPre-StudyPracticeExamPartI

2.Ananalystwantstopricea9-monthfuturescontractonastockindex.Thecurrentpriceoftheindexis

USD700andthecontinuouslycompoundedrisk-freerateis4.0%peryear.Ifthestocksunderlyingtheindex

provideacontinuouslycompoundeddividendyieldof2.5%peryear,whatistheno-arbitragepriceofthe

9-monthfuturescontract?

A.USD692.17

B.USD707.92

C.USD710.58

D.USD721.32

CorrectAnswer:

Explanation:

B

Theformulaforcomputingtheforwardpriceonafinancialassetis:

F0,T=Se(r−q)T

0

whereSisthespotpriceoftheasset=USD700,risthecontinuouslycompoundedrisk-

0

freeinterestrate=4.0%,qisthecontinuousdividendyieldontheasset=2.5%,andTis

timeuntildeliverydateinyears=9/12=0.75.

Theno-arbitragefuturespriceiscomputedasfollows:

(0.04−0.025)∗0.75

퐹=700∗푒

0

=707.9195

Aisincorrect.USD692.17istheresultobtainedwhentherisk-freerateanddividend

yieldareswitchedintheformulafora9-monthfuturesprice

Cisincorrect.USD710.58isthefuturespricein1year,not9months.

Disincorrect.USD721.31istheresultobtainedwhenthedividendyieldisnot

considered.

Section:

FinancialMarketsandProducts

Reference:

GlobalAssociationofRiskProfessionals.FinancialMarketsandProducts.NewYork,NY:

Pearson,2019.Chapter10.PricingFinancialForwardsandFutures.

LearningObjective:Calculatetheforwardpricegiventheunderlyingasset’sspotprice,anddescribean

arbitrageargumentbetweenspotandforwardprices.

19

2020FRMPre-StudyPracticeExamPartI

3.SupposetheRussell2000Indexhasanexpectedannualreturnof7.8%andvolatilityof9.8%.Supposethe

AlphaIndustrialFundhasanexpectedannualreturnof7.1%andvolatilityof7.9%andisbenchmarkedagainst

theRussell2000Index.AccordingtotheCAPM,iftherisk-freerateis3.2%peryear,whatisthebetaofthe

AlphaIndustrialFund?

A.0.85

B.0.95

C.1.13

D.1.23

CorrectAnswer:

Explanation:

A

SincethecorrelationorcovariancebetweentheAlphaIndustrialFundandtheRussell

2000Indexisnotknown,CAPMmustbeusedtobackoutthebeta:

E(R)=R+*E(R)−R

,

i

F

i

M

F

where

E(R)istheexpectedannualreturnofthefund,

i

isthebetaofthefundwiththemarketindex(theRussell2000Index),

i

Ristherisk-freerateperyear,

F

E(R)istheexpectedannualreturnofthemarket(inthiscase,theRussell2000

M

Index).

Therefore,

7.1%=3.2%+*(7.8%–3.2%).

i

Hence,

=(7.1%–3.2%)/(7.8%–3.2%)=0.85.

i

Section:

FoundationsofRiskManagement

Reference:

GlobalAssociationofRiskProfessionals.FoundationsofRiskManagement.NewYork,NY:

Pearson,2019.Chapter5.ModernPortfolioTheory(MPT)andtheCapitalAssetPricing

Model(CAPM).

LearningObjective:ApplytheCAPMincalculatingtheexpectedreturnonanasset;Interpretbetaand

calculatethebetaofasingleassetorportfolio.

20

2020FRMPre-StudyPracticeExamPartI

4.Ariskmanagerisevaluatingthepricesensitivityofaninvestment-gradecallablebondusingthefirm’s

valuationsystem.Thetablebelowpresentsinformationonthebondaswellasontheembeddedoption.The

currentinterestrateenvironmentisflatat4%.

ValueinUSDperUSD100facevalue

InterestRateLevel

3.95%

CallableBond

97.9430

CallOption

2.1972

4.00%

97.8910

2.1090

4.05%

97.8566

2.0035

Theconvexityofthecallablebondcanbeestimatedas:

A.0.180

B.0.360

C.179.792

D.719.167

CorrectAnswer:

Explanation:

D

Convexityisdefinedasthesecondderivativeoftheprice-ratefunctiondividedbythe

priceofthebond.Toestimateconvexity,onemustfirstestimatethedifferenceinbond

priceperdifferenceintheratefortwoseparaterateenvironments,oneastephigher

thanthecurrentrateandoneasteplower.Onemustthenestimatethechangeacross

thesetwovaluesperdifferenceinrate.Thisisgivenbytheformula:

P−PP−P

1

0

−

0

−1

1

r

r

1

P−2P+P

C=

*

=

*

1

0

−1

r

P

0

(r)

2

P

0

where∆risthechangeintherateinonestep;inthiscase,0.05%.Therefore,thebest

estimateofconvexityis:

97.8566−2*97.891097.9430

*

97.8910

+

1

C=

=719.1672

(0.0005)

2

Aisincorrect.0.1798istheresultobtainedwhenthechangeinyieldintheformulais

takenas0.10%insteadofthesquareof0.05%.

Bisincorrect.0.3596istheresultobtainedwhenthechangeinyieldintheformulais

takenas0.05%insteadofthesquareof0.05%.

Cisincorrect.179.7918istheresultobtainedwhenthechangeinyieldintheformulais

takenasthesquareof0.10%insteadofthesquareof0.05%.

Section:

ValuationandRiskModels

Reference:

GlobalAssociationofRiskProfessionals.ValuationandRiskModels.NewYork,NY:

Pearson,2019.Chapter12.ApplyingDuration,Convexity,andDV01.

21

2020FRMPre-StudyPracticeExamPartI

LearningObjective:Define,compute,andinterprettheconvexityofafixedincomesecuritygivenachangein

yieldandtheresultingchangeinprice.

5.Afixed-incomeportfoliomanagerpurchasesaseasoned6%agencyMBSwithaweightedaverageloanageof

50months.ThecurrentbalanceontheloansatthebeginningofthismonthisUSD22million,andthe

conditionalprepaymentrateisassumedtobeconstantat5%peryear.Whichofthefollowingisclosesttothe

anticipatedprincipalprepaymentthismonth?

A.USD22,558

B.USD66,000

C.USD91,667

D.USD93,830

CorrectAnswer:

Explanation:

D

Theconditionalprepaymentrate(CPR)isrelatedtothesinglemonthlymortalityrate

(SMM)asfollows:

CPR=1–(1–SMM)12.Andso,

SMM=1–(1–CPR)1/12=1–(1–0.05)1/12=0.004265=0.4265%.

Therefore,

theanticipatedprincipalprepaymentisequaltothepercentageofprincipaloutstanding

atthebeginningofthemonththatisanticipatedtobeprepaidduringthemonth=

22,000,000*0.004265=USD93,830.

Aisincorrect.USD22,558istheresultofusinganincorrectformula:SMM=1–(1–

CPR)1/50.

Bisincorrect.USD66,000istheoutcomeofcomputing5%oftheannualcoupon

paymentbasedonthecurrentbalance=USD22,000,000*0.06*0.05=USD66,000.

Cisincorrect.USD91,667istheresultofmultiplyingUSD22,000,000by5%/12.

FinancialMarketsandProducts

Section:

Reference:

GlobalAssociationofRiskProfessionals.FinancialMarketsandProducts.NewYork,NY:

Pearson,2019.Chapter18.MortgagesandMortgage-BackedSecurities.

Learning

Calculateafixedratemortgagepayment,anditsprincipalandinterestcomponents.

Objectives:

Calculateweightedaveragecoupon,weightedaveragematurity,singlemonthlymortality

rate(SMM),andconditionalprepaymentrate(CPR)foramortgagepool.

22

2020FRMPre-StudyPracticeExamPartI

6.AportfoliomanagerisexaminingdataregardingvariousindexfuturescontractstradedattheCMEGroup.

Whichofthefollowingobservationswouldtheportfoliomanagermostlikelyviewasapotentialproblem?

A.Thevolumeinaspecificcontractisgreaterthantheopeninterest.

B.Onespecificcontractisofamuchsmallersizethantheothers.

C.Thepriorsettlementpriceforaspecificcontractisabovetheopeningpr