FRM-P1-1905-协会模拟试卷（题目+答案）

FRM

PRACTICE

EXAMPARTI

FRMPracticeExamPart1

2019FRMPartIPracticeExam–AnswerKey

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2.

C

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D

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D

76.

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47

FRMPracticeExamPart1

1.Ariskmanagerisdecidingbetweenbuyingafuturescontractonanexchangeandbuyingaforwardcontract

directlyfromacounterpartyonthesameunderlyingasset.Bothcontractswouldhavethesamematurityand

deliveryspecifications.Themanagerfindsthatthefuturespriceislessthantheforwardprice.Assumingno

arbitrageopportunityexists,andinterestratesareexpectedtoincrease,whatsinglefactoractingalonewould

bearealisticexplanationforthispricedifference?

A.Thefuturescontractislessliquidthantheforwardcontract.

B.Theforwardcontractcounterpartyismorelikelytodefault.

C.Thepriceoftheunderlyingassetisstronglynegativelycorrelatedwithinterestrates.

D.Thetransactioncostonthefuturescontractismorethanthatontheforwardcontract.

CorrectAnswer:

Explanation:

C

Whenanassetisstronglynegativelycorrelatedwithinterestrates,futurespriceswill

tendtobeslightlylowerthanforwardprices.Whentheunderlyingassetincreasesin

price,theimmediategainarisingfromthedailyfuturessettlementwilltendtobe

investedatalowerthanaveragerateofinterestduetothenegativecorrelation.Inthis

case,futureswouldsellforslightlylessthanforwardcontracts,whicharenotaffectedby

interestratemovementsinthesamemannersinceforwardcontractsdonothaveadaily

settlementfeature.

Theotherthreechoiceswouldallmostlikelyresultinthefuturespricebeinghigherthan

theforwardprice.

Section:

FinancialMarketsandProducts

Reference:

JohnC.Hull,Options,Futures,andOtherDerivatives,10thEdition(NewYork,NY:

Pearson,2017),Chapter5-DeterminationofForwardandFuturesPrices

LearningObjective:Explaintherelationshipbetweenforwardandfuturesprices.

48

FRMPracticeExamPart1

2.AtraderinthearbitrageunitofamultinationalbankfindsthatafinancialassetistradingatUSD1,000,the

priceofa1-yearfuturescontractonthatassetisUSD1,020,andthepriceofa2-yearfuturescontractis

USD1,045.Assumethattherearenocashflowsfromtheassetfor2years.Ifthetermstructureofrisk-free

interestratesisflatat2%peryear,whichofthefollowingisanappropriatearbitragestrategy?

A.Short1-yearfuturescontractsandlong2-yearfuturescontracts

B.Short2-yearfuturescontractsandlong1-yearfuturescontracts

C.Short1-yearfuturescontractsandlongtheunderlyingassetfundedbyborrowingfor1yearat2%per

year

D.Short2-yearfuturescontractsandlongtheunderlyingassetfundedbyborrowingfor2yearsat2%per

year

CorrectAnswer:

Explanation:

D

The1-yearfuturespriceshouldbe1,000∗�0.02*1=1,020.20

The2-yearfuturespriceshouldbe1,000∗�0.02*2=1,040.81

Thecurrent2-yearfuturespriceinthemarketisovervaluedcomparedtothetheoretical

price.Tolockinaprofit,thetraderwouldshortthe2-yearfutures,borrowUSD1,000at

2%,andbuytheunderlyingasset.Attheendofthe2ndyear,thetraderwouldsellthe

assetatUSD1,045andreturntheborrowedmoneywithinterest,whichwouldbe1,000∗

�0.02*2=1,040.81,resultinginaUSD4.19gain.

Section:

FinancialMarketsandProducts

Reference:

JohnC.Hull,Options,Futures,andOtherDerivatives,10thEdition(NewYork,NY:

Pearson,2017),Chapter5-DeterminationofForwardandFuturesPrices

LearningObjective:Calculatetheforwardpricegiventheunderlyingasset’sspotprice,anddescribean

arbitrageargumentbetweenspotandforwardprices.

49

FRMPracticeExamPart1

3.Thepriceofa6-month,USD25.00strikeprice,European-styleputoptiononastockisUSD3.00.Thestock

priceisUSD26.00.Aspecialone-timedividendofUSD1.00isexpectedin3months.Thecontinuously

compoundedrisk-freerateforallmaturitiesis5%peryear.Whichofthefollowingisclosesttothevalueofa

European-stylecalloptiononthesameunderlyingstockwithastrikepriceofUSD25.00andatimeto

maturityof6months?

A.USD2.37

B.USD3.01

C.USD3.63

D.USD4.62

CorrectAnswer:

Explanation:

C

Fromtheequationforput-callparity,thiscanbesolvedbythefollowingequation:

c=S+p-PV(K)-PV(D)

0

wherePVrepresentsthepresentvalue,sothat

PV(K)=K∗e-rtandPV(D)=D∗e-rt

Where:

pistheputprice=USD3.00,

cisthecallprice=tobedetermined,

Kisthestrikepriceoftheputoption=USD25.00,

Disthedividend,

Sisthecurrentstockprice=USD26.00.

0

tisthetimetothenextdividend=0.25.

CalculatingPV(K),thepresentvalueofthestrikepriceresultsinavalueof25.00∗�-0.05*0.5

or24.3827,whilePV(D)isequalto1.00∗�-0.05*0.25=0.9876.

Hence,c=26.00+3.00–24.3827–0.9876=USD3.6297.

Aisincorrect.USD2.37isthevalueoftheputoptionifthequestionisswitched

(misinterpreted)suchthatthepriceofthecalloptionistakenasUSD3.00andtheput-

callparityformulaisused.

Bisincorrect.USD3.01istheoptionpriceifthestrikeprice,notthepresentvalueofthe

strikeprice,isusedintheput-callparityformula.

Disincorrect.USD4.62isthevalueofthecalloptionifthedividendpaymentisignored.

FinancialMarketsandProducts

Section:

Reference:

JohnC.Hull,Options,Futures,andOtherDerivatives,10thEdition(NewYork,NY:

Pearson,2017),Chapter11-PropertiesofStockOptions

LearningObjective:Explainput-callparityandapplyittothevaluationofEuropeanandAmericanstock

optionswithdividendsandwithoutdividends.

50

FRMPracticeExamPart1

4.Whichofthefollowingstatementsregardingacorporatetrusteenamedinacorporatebondindentureis

correct?

A.Thetrusteehastheauthoritytodeclareadefaultiftheissuermissesapayment.

B.Thetrusteemaytakeactionbeyondtheindenturetoprotectbondholders.

C.Thetrusteemustactattherequestofasufficientnumberofbondholders.

D.Thetrusteeispaidbythebondholdersortheirrepresentatives.

CorrectAnswer:

Explanation:

A

AccordingtotheTrustIndentureAct,ifacorporateissuerfailstopayinterestor

principal,thetrusteemaydeclareadefaultandtakesuchactionasmaybenecessaryto

protecttherightsofbondholders.Trusteescanonlyperformtheactionsindicatedinthe

indenture,butaretypicallyundernoobligationtoexercisethepowersgrantedbythe

indentureevenattherequestofbondholders.Thetrusteeispaidbythedebtissuer,not

bybondholdersortheirrepresentatives.

Section:

FinancialMarketsandProducts

Reference:

FrankFabozzi(Editor),TheHandbookofFixedIncomeSecurities,8thEdition(NewYork:

McGrawHill,2012),Chapter12-CorporateBonds

LearningObjective:Describeabondindentureandexplaintheroleofthecorporatetrusteeinabond

indenture.

51

FRMPracticeExamPart1

5.Pear,Inc.isamanufacturerthatisheavilydependentonplasticpartsshippedfromMalaysia.Pearwantsto

hedgeitsexposuretoplasticpriceshocksoverthenext7.5months.Futurescontracts,however,arenot

readilyavailableforplastic.Aftersomeresearch,Pearidentifiesfuturescontractsonothercommodities

whosepricesarecloselycorrelatedtoplasticprices.FuturesonCommodityAhaveacorrelationof0.85with

thepriceofplastic,andfuturesonCommodityBhaveacorrelationof0.92withthepriceofplastic.Futureson

bothCommodityAandCommodityBareavailablewith6-monthand9-monthexpirations.Ignoringliquidity

considerations,whichcontractwouldbethebesttominimizebasisrisk?

A.FuturesonCommodityAwith6monthstoexpiration

B.FuturesonCommodityAwith9monthstoexpiration

C.FuturesonCommodityBwith6monthstoexpiration

D.FuturesonCommodityBwith9monthstoexpiration

CorrectAnswer:

Explanation:

D

Explanation:Inordertominimizebasisrisk,oneshouldchoosethefuturescontractwith

thehighestcorrelationtopricechanges,andtheonewiththeclosestmaturity,

preferablyexpiringafterthedurationofthehedge.

Section:

FinancialMarketsandProducts

Reference:

JohnC.Hull,Options,Futures,andOtherDerivatives,10thEdition(NewYork:NY:

Pearson,2017),Chapter3-HedgingStrategiesUsingFutures

LearningObjective:Definethebasisandexplainthevarioussourcesofbasisrisk,andexplainhowbasisrisks

arisewhenhedgingwithfutures.

52

FRMPracticeExamPart1

6.AcurrencyanalystisexaminingtheexchangeratebetweentheUSdollarandtheeuroandisgiventhe

following:

•

•

•

CurrentUSDperEUR1exchangerate:1.13

CurrentUSD-denominated1-yearrisk-freeinterestrate:2.7%peryear

CurrentEUR-denominated1-yearrisk-freeinterestrate:1.7%peryear

Accordingtotheinterestrateparitytheorem,whatisthe2-yearforwardUSDperEUR1exchangerate?

A.1.1076

B.1.1188

C.1.1414

D.1.1528

CorrectAnswer:

Explanation:

D

Theforwardrate,F,isgivenbytheinterestrateparityequation:

t

�=�∗�

where;

Sisthespotexchangerate,

0

ristheUSDrisk-freerate,

ristheEURrisk-freerate,and

f

tisthetimetodelivery.

Substitutingthevaluesintheequation:

�=1.13∗�(..)=1.1528

Aisincorrect.USD1.1076perEUR1isthe2-yearforwardexchangeratewhenthe1-year

risk-freeratesforthetwocountriesareswitchedintheformula.

Bisincorrect.USD1.1188perEUR1isthe1-yearforwardexchangeratewhenthe1-year

risk-freeratesforthetwocountriesareswitchedintheformula.

Cisincorrect.USD1.1414perEUR1isthe1-yearforwardexchangerate,notthe2-year

forwardrate.

Section:

FinancialMarketsandProducts

Reference:

JohnC.Hull,Options,Futures,andOtherDerivatives,10thEdition(NewYork,NY:

Pearson,2017).Chapter5.DeterminationofForwardandFuturesPrices

LearningObjective:Calculateaforwardforeignexchangerateusingtheinterestrateparityrelationship.

53

FRMPracticeExamPart1

7.AninvestorsellsaJanuary2019callonthestockofXYZLimitedwithastrikepriceofUSD50forUSD10,and

buysaJanuary2019callonthesameunderlyingstockwithastrikepriceofUSD60forUSD2.Whatisthe

nameofthisstrategy,andwhatisthemaximumprofitandlosstheinvestorcouldincuratexpiration?

Strategy

MaximumProfit

USD8

MaximumLoss

USD2

USD2

USD2

Unlimited

A.Bearspread

B.Bearspread

C.Bullspread

D.Bullspread

Unlimited

USD8

USD8

CorrectAnswer:

Explanation:

A

Thisstrategyofbuyingacalloptionatahigherstrikepriceandsellingacalloptiononthe

samesecuritywiththesamematurityatalowerstrikepriceisknownasabearspread.

Toestablishabullspread,onewouldbuyacalloptionatalowerpriceandsellacall

optiononthesamesecuritywiththesamematurityatahigherstrikeprice.

Thecostofthebearspreadstrategywillbe:

USD-10+USD2=USD-8(anegativecost,whichrepresentsaninflowofUSD8tothe

investor)

ThemaximumpayoffoccurswhenthestockpriceS≤USD50andisequaltoUSD8(the

T

cashinflowfromestablishingtheposition)asnoneoftheoptionswillbeexercised.The

maximumlossoccurswhenthestockpriceS≥USD60atexpiration,asbothoptionswill

T

beexercised.TheinvestorwouldthenbeforcedtosellXYZsharesatUSD50tomeetthe

obligationsonthecalloptionsold,butcouldexercisethesecondcalltobuytheshares

backatUSD60foralossofUSD-10.However,sincetheinvestorreceivedaninflowof

USD8byestablishingthestrategy,thetotalprofitwouldbeUSD8-USD10=USD-2.

WhenthestockpriceisUSD50<S≤USD60,onlythecalloptionsoldbytheinvestor

T

wouldbeexercised,hencethepayoffwillbe50-S.Sincetheinflowfromestablishing

T

theoriginalstrategywasUSD8,thenetprofitwillbe58-S,whichwouldalwaysbe

T

higherthanUSD-2.

Section:

FinancialMarketsandProducts

Reference:

JohnC.Hull,Options,Futures,andOtherDerivatives,10thEdition(NewYork,NY:

Pearson,2017),Chapter11-PropertiesofStockOptions

LearningObjective:Identifyandcomputeupperandlowerboundsforoptionpricesonnon-dividendand

dividendpayingstocks.

54

FRMPracticeExamPart1

8.AnanalystistryingtogetsomeinsightintotherelationshipbetweenthereturnonstockLMD(RLMD,t)andthe

returnontheS&P500index(RS&P,t).Usinghistoricaldata,theanalystestimatesthefollowing:

AnnualmeanreturnforLMD

11%

7%

AnnualmeanreturnforS&P500index

AnnualvolatilityforS&P500indexreturns

CovariancebetweenthereturnsofLMDandS&P500index

18%

6%

Assumetheanalystusesthesamedatatoestimatetheregressionmodelgivenby:

RLMD,t=α+β∗RS&P,t+εt

Usingtheordinaryleastsquarestechnique,whichofthefollowingmodelswilltheanalystobtain?

A.RLMD,t=-0.02+0.54RS&P,t

B.RLMD,t=-0.02+1.85RS&P,t

C.RLMD,t=0.04+0.54RS&P,t

D.RLMD,t=0.04+1.85RS&P,t

CorrectAnswer:

Explanation:

B

TheregressioncoefficientsforamodelspecifiedbyY=bX+a+εareobtainedusingthe

formulas:

b=CovXY/S2

X

and

a=E(Y)–b*E(X)

Inthisexample:CovXY=0.06

S=0.18

X

E(Y)=0.11

E(X)=0.07

Then:

b=0.06/(0.18)2=1.85

a=0.11–(1.85*0.07)=-0.02

whereεrepresentstheerrorterm.

Section:

QuantitativeAnalysis

Reference:

JamesStockandMarkWatson,IntroductiontoEconometrics,BriefEdition(Boston,MA:

Pearson,2008),Chapter4–LinearRegressionwithOneRegressor

LearningObjective:Explainhowregressionanalysisineconometricsmeasurestherelationshipbetween

dependentandindependentvariables.

55

FRMPracticeExamPart1

9.Forasampleof400firms,therelationshipbetweencorporaterevenue(Y)andtheaverageyearsof

i

experienceperemployee(X)ismodeledasfollows:

i

Y=β+β*X+ε,

i=1,2...,400

i

1

2

i

i

Ananalystwantstotestthejointnullhypothesisthatβ=0andβ=0atthe95%confidencelevel.Thep-

1

2

valueforthet-statisticforβis0.07,andthep-valueforthet-statisticforβis0.06.Thep-valuefortheF-

1

2

statisticfortheregressionis0.045.Whichofthefollowingstatementsiscorrect?

A.Theanalystcanrejectthejointnullhypothesisbecauseeachβisdifferentfrom0atthe95%confidence

level.

B.Theanalystcannotrejectthejointnullhypothesisbecauseneitherβisdifferentfrom0atthe95%

confidencelevel.

C.TheanalystcanrejectthejointnullhypothesisbecausetheF-statisticissignificantatthe95%confidence

level.

D.TheanalystcannotrejectthejointnullhypothesisbecausetheF-statisticisnotsignificantatthe95%

confidencelevel.

CorrectAnswer:

Explanation:

C

Thet-testwouldnotbesufficienttotestthejointnullhypothesis.Inordertotestthe

jointnullhypothesis,examinetheF-statistic,whichinthiscaseisstatisticallysignificantat

the95%confidencelevel.Thus,thejointnullhypothesiscanberejected.

Section:

QuantitativeAnalysis

Reference:

JamesStockandMarkWatson,IntroductiontoEconometrics,Briefedition(Boston,MA:

Pearson,2008),Chapter7-HypothesisTestsandConfidenceIntervalsinMultiple

Regression

LearningObjective:Interprettestsofasinglerestrictioninvolvingmultiplecoefficients;InterprettheF-

statistic.

56

FRMPracticeExamPart1

10.Afixed-incomeportfoliomanagercurrentlyholdsaportfolioofbondsofvariouscompanies.Assumingall

thesebondshavethesameannualizedprobabilityofdefaultandthatthedefaultsareindependent,the

numberofdefaultsinthisportfoliooverthenextyearfollowswhichtypeofdistribution?

A.Bernoulli

B.Lognormal

C.Binomial

D.Exponential

CorrectAnswer:

Explanation:

C

Theresultwouldfollowabinomialdistributionasthereisafixednumberofrandom

variables,eachwiththesameannualizedprobabilityofdefault.ItisnotaBernoulli

distribution,asaBernoullidistributionwoulddescribethelikelihoodofdefaultofoneof

theindividualbondsratherthanoftheentireportfolio(i.e.Abinomialdistribution

essentiallydescribesagroupofBernoullidistributedvariables).

Section:

QuantitativeAnalysis

Reference:

MichaelMiller,MathematicsandStatisticsforFinancialRiskManagement,2ndEdition

(Hoboken,NJ:JohnWiley&Sons,2013),Chapter4-Distributions

LearningObjective:Distinguishthekeypropertiesamongthefollowingdistributions:uniformdistribution,

Bernoullidistribution,Binomialdistribution,Poissondistribution,normaldistribution,

lognormaldistribution,Chi-squareddistribution,Student’st-distribution,andF-

distributions,andidentifycommonoccurrencesofeachdistribution.

57

FRMPracticeExamPart1

11.AnanalysthasbeenaskedtocheckforarbitrageopportunitiesintheTreasurybondmarketbycomparingthe

cashflowsofselectedbondswiththecashflowsofcombinationsofotherbonds.Ifa1-yearzero-couponbond

ispricedatUSD98anda1-yearbondpayingan8%couponsemi-annuallyispricedatUSD103,usinga

replicationapproach,whatshouldbethepriceofa1-yearTreasurybondthatpaysacouponof6%semi-

annually?

A.USD99.3

B.USD101.1

C.USD101.8

D.USD103.9

CorrectAnswer:

Explanation:

C

Todeterminetheprice(F)ofthe6%couponbondbyreplication,whereFandFarethe

3

1

2

weightfactorsinthereplicatingportfolioforthezero-couponbondandthe8%coupon

bond,respectively,correspondingtotheproportionsofthezero-couponbondandthe

8%couponbondtobeheld,andgivena1-yearhorizon:

Thethreeequationsbelowexpresstherequirementthatthecashflowsofthereplicating

portfolio,oneachcashflowdate(t,inyears),beequaltothecashflowofthe6%coupon

bond:

Time(t=0):98*F+103*F=F……………Equation(1)

1

2

3

Time(t=0.5):0*F+4*F=3...…………….Equation(2)

1

2

Time(t=1.0):100*F+104*F=103…...Equation(3)

1

2

FromEquation(2),F=3/4=0.75

2

SubstitutingthevalueofFinEquation(3):100*F+104*0.75=103,giving,F=0.25

2

1

1

PluggingthevaluesofFandFinEquation(1),wedetermineF=98*0.25+103*0.75=

1

2

3

101.75

Aisincorrect.USD99.25isthepriceofthe1-year6%couponTreasurybondiftheweight

factors,FandF,areswitchedinEquation(1).

1

2

Bisincorrect.USD101.07isthepriceofthe1-year6%couponTreasurybondiftheyield-

to-maturityofthe1-year8%couponTreasurybondisusedinitspricingandthezero-

couponTreasurybondisignoredinthereplication.

Disincorrect.USD103.91isthepriceofthe1-year6%couponTreasurybondiftheyield-

to-maturityofthezero-couponTreasurybondisusedinitspricingandthe1-year8%

couponTreasurybondisignoredinthereplication.

Section:

ValuationandRiskModels

Reference:

BruceTuckmanandAngelSerrat,FixedIncomeSecurities:ToolsforToday’sMarkets,3rd

Edition(Hoboken,NJ:JohnWiley&Sons,2011),Chapter1-Prices,DiscountFactors,and

Arbitrage

LearningObjective:Constructareplicatingportfoliousingmultiplefixedincomesecuritiestomatchthecash

flowsofagivenfixedincomesecurity.

58

FRMPracticeExamPart1

12.IfthecurrentmarketpriceofastockisUSD60,whichofthefollowingoptionsonthestockhasthehighest

gamma?

A.Longcalloptionexpiringin5dayswithstrikepriceofUSD30

B.Longcalloptionexpiringin5dayswithstrikepriceofUSD60

C.Longcalloptionexpiringin30dayswithstrikepriceofUSD30

D.Longcalloptionexpiringin30dayswithstrikepriceofUSD60

CorrectAnswer:

Explanation:

B

Gammaisdefinedastherateofchangeofanoption’sdeltawithrespecttothepriceof

theunderlyingasset,orthesecondderivativeoftheoptionpricewithrespecttothe

assetprice.Therefore,thehighestgammaisobservedinshortermaturityandat-the-

moneyoptions,sinceoptionswiththesecharacteristicsaremuchmoresensitiveto

changesintheunderlyingassetprice.Thegammaishighestforashortermaturitycall

optionbecausedelta’smovetowardeither0or+1.00ismoreimminent.

Thecorrectchoiceisacalloptionbothat-the-moneyandwiththeshortermaturity.

ValuationandRiskModels

Section:

Reference:

JohnC.Hull,Options,Futures,andOtherDerivatives,10thEdition(NewYork,NY:

Pearson,2017),Chapter19-TheGreekLetters

LearningObjective:Defineanddescribetheta,gamma,vega,andrhoforoptionpositions.

59

FRMPracticeExamPart1

13.Aninvestmentadvisorisadvisingawealthyclient.TheclientwouldliketoinvestUSD500,000inabondrated

atleastAA.TheadvisorisconsideringbondsissuedbyCompanyX,CompanyY,andCompanyZ,andwantsto

chooseabondthatsatisfiestheclient’sratingrequirement,butalsohasthehighestyieldtomaturity.The

advisorhasgatheredthefollowinginformation:

Company/Bond

Bondrating

Annualcouponrate(%)

Timetomaturityinyears

Price(USD)

X

AA+

3.50

5

975

1,000

Y

A+

3.56

5

973

1,000

Z

AAA

3.38

5

989

1,000

Parvalue(USD)

Assumingsemi-annualcouponpayments,whichbondshouldtheinvestmentadvisorpurchasefortheclient?

A.BondX

B.BondY

C.BondZ

D.EitherBondXorBondZ

CorrectAnswer:

Explanation:

A

Toreachthecorrectanswer,findthebondwiththehighestyieldtomaturity(YTM)that

qualifiesforinclusionintheclient’sportfolio.AlthoughwecancalculatetheYTMforeach

bondusingabusiness/financialcalculator,itisunnecessarytodosointhiscase.Ofthe

threebonds,BondYdoesnotqualifyfortheportfolioasitsratingofA+isbelowtheAA

ratingrequiredbytheclient.ThisleavesBondXandBondZonly.Comparingthetwo

bonds,BondXpaysahighercouponthanBondZ,yetitischeaperaswell.Therefore,the

yieldonBondXishigher.

Toformallycalculatetheyield,youcouldalsousethefollowingequationdescribingthe

relationshipbetweenpriceandyield:

where,

P=Bondpricey=YTM

c=Couponrate

T=Termtomaturityinyears

F=Facevalueofthebond

Usingthisequation(oranequivalentcalculatorfunction),theYTMfortheXbondequals

4.06%,whiletheYTMfortheZbondequals3.62%.Usingabusiness/financialcalculator

for:

BondX:N=2*5=10;FV=1,000;PMT=(0.0350/2)*1,000=17.5;PV=-975;y=2.0287*2

=4.0575%

BondY:N=2*5=10;FV=1,000;PMT=(0.0356/2)*1,000=17.8;PV=-973;y=2.0819*2

=4.1637%

60

FRMPracticeExamPart1

BondZ:N=2*5=10;FV=1,000;PMT=(0.0338/2)*1,000=16.9;PV=-989;y=1.8113*2=

3.6225%

Section:

ValuationandRiskModels

Reference:

BruceTuckmanandAngelSerrat,FixedIncomeSecurities:ToolsforToday’sMarkets,3rd

Edition(Hoboken,NJ:JohnWiley&Sons,2011),Chapter3-Returns,SpreadsandYields

LearningObjective:Computeabond'sYTMgivenabondstructureandprice.

61

FRMPracticeExamPart1

14.Anassetmanagerataninsurancecompanyisconsideringmakingafixed-incomeinvestmentandholdingitfor

2years.Themanageriscomparingtwobondissuesthathaveequalyieldtomaturityatorigination.Oneisa

semi-annualcouponbondpaying7%,maturingin2years,andpricedatUSD101.86.Theotherisazero-

couponbond,alsomaturingin2years,andpricedatUSD88.85.Themanagerisuncertainabouttheoutlook

forinterestratesoverthenext2yearsbutwillincorporatetheforecastofthecompany’seconomistwhen

makingtheinvestmentdecision.Assumingnodefaultrisk,taximplications,orliquidityconstraints,whichof

thefollowingstatementsiscorrect?

A.Themanagershouldbeindifferenttowardsthebondsiftheinterestrateisexpectedtorisesinceboth

bondshavethesameyieldandcashflows.

B.Themanagershouldpreferthezero-couponbondiftheinterestrateisexpectedtoriseinthefuture.

C.Themanagershouldpreferthezero-couponbondiftheexpectedaverageinterestrateoverthenext2

yearsislessthan6%.

D.Themanagershouldpreferthecouponbondiftheexpectedaverageinterestrateoverthenext2yearsis

lessthan6%.

CorrectAnswer:

Explanation:

C

Ciscorrect.Thecurrentannualyieldonboththecouponandzero-couponbondsarethe

sameatapproximately6%(5.9992%).Ifratesarehigherthan6%thenthecouponbond

wouldbepreferredduetohigherreinvestmentincomeon3intermediatecouponstobe

received.

Aisincorrect.Iftheinterestrateisexpectedtorise,couponbondswouldbemore

attractivebecauseinvestorscanreinvestthecouponathigherinterestrates.

Bisincorrect.Iftheinterestrateisexpectedtorise,couponbondswouldbemore

attractivebecauseinvestorscanreinvestthecouponathigherinterestrates.

Disincorrect.Iftheinterestratefallsbelowtheyieldtomaturity,thecouponbond

wouldhavelowerreinvestmentincomeandbecomelessattractive.

Section:

FinancialMarketsandProducts

Reference:

FrankFabozzi(Editor),TheHandbookofFixedIncomeSecurities,8thEdition(NewYork:

McGraw-Hill,2012),Chapter12-CorporateBonds

LearningObjective:Describezero-couponbondsandexplaintherelationshipbetweenoriginal-issuediscount

andreinvestmentrisk.

62

FRMPracticeExamPart1

15.Aportfoliomanagerbought600calloptionsonanon-dividend-payingstock,withastrikepriceofUSD60,for

USD3each.ThecurrentstockpriceisUSD62withadailystockreturnvolatilityof1.82%,andthedeltaofthe

optionis0.5.Usingthedelta-normalapproachtocalculateVaR,whatisanapproximationofthe1-day95%

VaRofthisposition?

A.USD54

B.USD557

C.USD787

D.USD1,114

CorrectAnswer:

Explanation:

B

Thedeltaoftheoptionis0.5.The1-day95%VaRof1shareoftheunderlying=1.82%*

1.645*62=USD1.8562

Therefore,theVaRofoneoptionis:

0.5*1.8562=USD0.9281,andmultiplyingby600unitsprovidesthe1-day95%VaRof

theentireposition:USD556.86.

Aisincorrect.USD53.8902istheresultobtainedbyignoringdeltaandusingthecall

optionprice,notstockprice,todetermineVaRofposition:VaR=0.0182*1.645*600*3=

USD53.8902.

Cisincorrect.USD787.40istheresultobtainedwhentheVaRofthepositionis

incorrectlycalculatedatthe99%confidencelevel(VaR=0.0182*2.326*62*0.5*600=

USD787.3975).

Disincorrect.USD1,113.72istheresultobtainedwhend