CFA二级经典题-固定收益-标准版

Fixedincome

CFA二级原版书课后题

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Reading32

TheTermStructureandInterestRateDynamics

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Example

Aone-yearzero-couponbondyields4.0%.Thetwo-andthree-yearzero-

couponbondsyield5.0%and6.0%respectively.

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Example

Therateforaone-yearloanbeginninginoneyearisclosestto:

A.4.5%.

B.5.0%.

C.6.0%.

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Example

Answer:C

Fromtheforwardratemodel,wehave

=[1+r(1)]1[1+f(1,1)]1

[1+r(2)]2

Usingtheone-andtwo-yearspotrates,wehave

(1+0.05)2

(1+0.04)

(1+.05)2

=(1+.04)1[1+f(1,1)]1,so

−1

=f(1,1)=6.010%

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Example

Theforwardrateforatwo-yearloanbeginninginoneyearisclosestto:

A.5.0%

B.6.0%

C.7.0%

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Example

Answer:C

Fromtheforwardratemodel,

=[1+r(1)]1[1+f(1,2)]2

[1+r(3)]3

Usingtheoneandthree-yearspotrates,wefind

(1+0.06)3

(1+0.04)

(1+0.06)3

=(1+0.04)1[1+f(1,2)]2,so

−1

=f(1,2)=7.014%

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Example

Theforwardrateforaone-yearloanbeginningintwoyearsisclosestto:

A.6.0%

B.7.0%

C.8.0%

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Example

Answer:C

Fromtheforwardratemodel,

=[1+r(2)]2[1+f(2,1)]1

[1+r(3)]3

Usingthetwoandthree-yearspotrates,wefind

(1+0.06)3

(1+0.05)

(1+0.06)3

=(1+0.05)2[1+f(2,1)]1,so

−1

=f(2,1)=8.029%

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Example

Thefive-yearspotrateisnotgivenabove;however,theforwardpriceforatwo-

yearzero-couponbondbeginninginthreeyearsisknowntobe0.8479.The

pricetodayofafive-yearzero-couponbondisclosestto:

A.0.7119.

B.0.7835.

C.0.9524.

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Example

Answer:A

WecanconvertspotratestospotpricestofindP(3)==0.8396.The

forwardpricingmodelcanbeusedtofindthepriceofthefive-yearzeroas

P(T*+T)=P(T*)F(T*,T),soP(5)=P(3)F(3,2)=0.8396×0.8479=0.7119.

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Example

Theone-yearspotrater(1)=4%,theforwardrateforaone-yearloan

beginninginoneyearis6%,andtheforwardrateforaone-yearloanbeginning

intwoyearsis8%.Whichofthefollowingratesisclosesttothethree-yearspot

rate?

A.4.0%

B.6.0%

C.8.0%

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Example

Answer:B

Applyingtheforwardratemodel,wefind

[1+r(3)]3

=[1+r(1)]1[1+f(1,1)]1[1+f(2,1)]1

So[1+r(3)]3

=(1+0.04)1(1+0.06)1(1+0.08)1,

3

1.19063

=r(3)=5.987%.

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Example

Theone-yearspotrater(1)=5%andtheforwardpriceforaone-yearzero-

couponbondbeginninginoneyearis0.9346.Thespotpriceofatwo-year

zero-couponbondisclosestto:

A.0.87.

B.0.89.

C.0.93.

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Example

Answer:B

Wecanconvertspotratestospotpricesandusetheforwardpricingmodel,

sohaveP(1)=1=0.9524.TheforwardpricingmodelisP(T*+T)=

1.05

P(T*)F(T*,T)soP(2)=P(1)F(1,1)=0.9524×0.9346=0.8901.

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Example

Inatypicalinterestrateswapcontract,theswaprateisbestdescribedasthe

interestrateforthe:

A.fixed-ratelegoftheswap.

B.floating-ratelegoftheswap.

C.differencebetweenthefixedandfloatinglegsoftheswap.

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Example

Answer:A

Theswaprateistheinterestrateforthefixed-ratelegofaninterestrate

swap.

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Example

Atwo-yearfixed-for-floatingLiborswapis1.00%andthetwo-yearUSTreasury

bondisyielding0.63%.Theswapspreadisclosestto:

A.37bps.

B.100bps.

C.163bps.

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Example

Answer:A

Theswapspread=1.00%−0.63%=0.37%or37bps.

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Example

Theswapspreadisquotedas50bps.Ifthefive-yearUSTreasurybondis

yielding2%,theratepaidbythefixedpayerinafive-yearinterestrateswapis

closestto:

A.0.50%.

B.1.50%.

C.2.50%.

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Example

Answer:C

Thefixedlegofthefive-yearfixed-for-floatingswapwillbeequaltothe

five-yearTreasuryrateplustheswapspread:2%+0.5%=2.5%.

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Example

Ifthethree-monthT-billratedropsandtheLiborrateremainsthesame,the

relevantTEDspread:

A.increases.

B.decreases.

C.doesnotchange.

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Example

Answer:A

TheTEDspreadisthedifferencebetweenthethree-monthLiborrateand

thethree-monthTreasurybillrate.IftheT-billratefallsandLibordoesnot

change,theTEDspreadwillincrease.

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Example

GiventheyieldcurveforUSTreasuryzero-couponbonds,whichspreadismost

helpfulpricingacorporatebond?The:

A.Z-Spread.

B.TEDspread.

C.Libor–OISspread.

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Example

Answer:A

TheZ-spreadisthesingleratewhich,whenaddedtotheratesofthespot

yieldcurve,willprovidethecorrectdiscountratestopriceaparticularrisky

bond.

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Example

Afour-yearcorporatebondwitha7%couponhasaZ-spreadof200bps.

Assumeaflatyieldcurvewithaninterestrateforallmaturitiesof5%andannual

compounding.Thebondwillmostlikelysell:

A.closetopar.

B.atapremiumtopar.

C.atadiscounttopar.

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Example

Answer:A

The200bpsZ-spreadcanbeaddedtothe5%ratesfromtheyieldcurveto

pricethebond.Theresulting7%discountratewillbethesameforallofthe

bond’scash-flows,sincetheyieldcurveisflat.A7%couponbondyielding

7

%willbepricedatpar.

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Example

TheZ-spreadofBondAis1.05%andtheZ-spreadofBondBis1.53%.Allelse

equal,whichstatementbestdescribestherelationshipbetweenthetwobonds?

A.BondBissaferandwillsellatalowerprice.

B.BondBisriskierandwillsellatalowerprice.

C.BondAisriskierandwillsellatahigherprice.

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Example

Answer:B

ThehigherZ-spreadforBondBimpliesitisriskierthanBondA.Thehigher

discountratewillmakethepriceofBondBlowerthanBondA.

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Example

Whichtermstructuremodelcanbecalibratedtocloselyfitanobservedyield

curve?

A.TheHo–LeeModel

B.TheVasicekModel

C.TheCox–Ingersoll–RossModel

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Example

Answer:A

TheHo–Leemodelisarbitrage-freeandcanbecalibratedtocloselymatch

theobservedtermstructure.

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Case:JaneNguyen

JaneNguyenisaseniorbondtraderandChristineAlexanderisajuniorbond

traderforaninvestmentbank.Nguyenisresponsibleforherowntrading

activitiesandalsoforprovidingassignmentstoAlexanderthatwilldevelopher

skillsandcreateprofitabletradeideas.Exhibit1presentsthecurrentparand

spotrates.

Exhibit1.CurrentParandSpotRates

Maturity

ParRate

2.50%

2.99%

3.48%

3.95%

4.37%

SpotRate

Oneyear

Twoyears

Threeyears

Fouryears

Fiveyears

2.50%

3.00%

3.50%

4.00%

Note:Parandspotratesarebasedonannual-couponsovereignbonds.

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Case:JaneNguyen

NguyengivesAlexandertwoassignmentsthatinvolveresearchingvarious

questions:

Assignment1:Whatistheyieldtomaturityoftheoption-free,defaultrisk–

freebondpresentedinExhibit2?Assumethatthebondisheldtomaturity,

andusetheratesshowninExhibit1.

Exhibit2.SelectedDatafor$1,000ParBond

BondName

BondZ

Maturity(T)

Threeyears

Coupon

6.00%

Note:TermsaretodayforaT-yearloan.

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Case:JaneNguyen

Assignment2:Assumingthattheprojectedspotcurvetwoyearsfrom

todaywillbebelowthecurrentforwardcurve,isBondZfairlyvalued,

undervalued,orovervalued?

Aftercompletingherassignments,AlexanderasksaboutNguyen’scurrent

tradingactivities.Nguyenstatesthatshehasatwo-yearinvestmenthorizonand

willpurchaseBondZaspartofastrategytoridetheyieldcurve.Exhibit1shows

Nguyen’syieldcurveassumptionsimpliedbythespotrates.

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Case:JaneNguyen

BasedonExhibit1,thefive-yearspotrateisclosestto:

A.4.40%

B.4.45%

C.4.50%

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Case:JaneNguyen

Answer:B

Thefive-yearspotrateisdeterminedbyusingforwardsubstitutionand

usingtheknownvaluesoftheone-year,two-year,three-year,andfour-year

spotratesasfollows:

0

.0437

0.0437

1.0302

0.0437

1.0353

0.0437

1.0404

1+0.0437

1

=

+

+

+

+

1

.025

1+푟5

5

1

0

.0437

5

푟5=

−1=4.453%

.8394

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Case:JaneNguyen

BasedonExhibit1,themarketismostlikelyexpecting:

A.deflation.

B.inflation.

C.noriskpremiums.

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Case:JaneNguyen

Answer:B

Thespotratesimplyanupward-slopingyieldcurve,r(3)>r(2)>r(1).

Becausenominalyieldsincorporateapremiumforexpectedinflation,an

upward-slopingyieldcurveisgenerallyinterpretedasreflectingamarket

expectationofincreasing,oratleastlevel,futureinflation(associatedwith

relativelystrongeconomicgrowth).

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Case:JaneNguyen

BasedonExhibit1,theforwardrateofaone-yearloanbeginninginthreeyears

isclosestto:

A.4.17%.

B.4.50%.

C.5.51%.

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Case:JaneNguyen

Answer:C

Aone-yearloanbeginninginthreeyears,orf(3,1),iscalculatedasfollows:

3

+1

3

1

1

+푟3+1

=1+푟3

1+푓3,1

1

4

.040=1.0351+푓3,1

3

1

4

1

.04

푓3,1=

−1=5.514%

1

.0353

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Case:JaneNguyen

BasedonExhibit1,whichofthefollowingforwardratescanbecomputed?

A.Aone-yearloanbeginninginfiveyears

B.Athree-yearloanbeginninginthreeyears

C.Afour-yearloanbeginninginoneyear

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Case:JaneNguyen

Answer:C

Exhibit1providesfiveyearsofparrates,fromwhichthespotratesforr(1),

r(2),r(3),r(4),andr(5)canbederived.Thustheforwardratef(1,4)canbe

calculatedasfollows:

1

+푟5

+푟1

5

4

푓1,4=

−1

1

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Case:JaneNguyen

ForAssignment1,theyieldtomaturityforBondZisclosesttothe:

A.one-yearspotrate.

B.two-yearspotrate.

C.three-yearspotrate.

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Case:JaneNguyen

Answer:C

Theyieldtomaturity,y(3),ofBondZshouldbeaweightedaverageofthe

spotratesusedinthevaluationofthebond.Becausethebond’slargest

cashflowoccursinYear3,r(3)willhaveagreaterweightthanr(1)andr(2)

indeterminingy(3).

Usingthespotrates:

$

60

$60

$1,060

푃푟푖푐푒=

+

+

=$1,071.16

1

.0251

1.0302

1.0353

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Case:JaneNguyen

Usingtheyieldtomaturity:

60

+푦31

$

$60

$1,060

푃푟푖푐푒=

+

+

=$1,071.16

1

1+푦32

1+푦33

Usingacalculator,thecomputeresultisy(3)=3.46%,whichisclosestto

thethree-yearspotrateof3.50%.

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Case:JaneNguyen

ForAssignment2,AlexandershouldconcludethatBondZiscurrently:

A.undervalued.

B.fairlyvalued.

C.overvalued.

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Case:JaneNguyen

Answer:A

Alexanderprojectsthatthespotcurvetwoyearsfromtodaywillbebelow

thecurrentforwardcurve,whichimpliesthatherexpectedfuturespotrates

beyondtwoyearswillbelowerthanthequotedforwardrates.Alexander

wouldperceiveBondZtobeundervaluedinthesensethatthemarketis

effectivelydiscountingthebond’spaymentsatahigherratethanshewould

andthebond’smarketpriceisbelowherestimateofintrinsicvalue.

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Case:JaneNguyen

BychoosingtobuyBondZ,Nguyenismostlikelymakingwhichofthefollowing

assumptions?

A.BondZwillbeheldtomaturity.

B.Thethree-yearforwardcurveisabovethespotcurve.

C.Futurespotratesdonotaccuratelyreflectfutureinflation.

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Case:JaneNguyen

Answer:B

Nguyen’sstrategyistoridetheyieldcurve,whichisappropriatewhenthe

yieldcurveisupwardsloping.TheyieldcurveimpliedbyExhibit1isupward

sloping,whichimpliesthatthethree-yearforwardcurveisabovethecurrent

spotcurve.Whentheyieldcurveslopesupward,asabondapproaches

maturityor“rollsdowntheyieldcurve,”thebondisvaluedatsuccessively

loweryieldsandhigherprices.

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Case:LauraMathews

LauraMathewsrecentlyhiredRobertSmith,aninvestmentadviseratShireGate

Advisers,toassistherininvesting.Mathewsstatesthatherinvestmenttime

horizonisshort,approximatelytwoyearsorless.Smithgathersinformationon

spotratesforon-the-runannual-coupongovernmentsecuritiesandswap

spreads,aspresentedinExhibit1.ShireGateAdvisersrecentlypublisheda

reportforitsclientsstatingitsbeliefthat,basedontheweaknessinthefinancial

markets,interestrateswillremainstable,theyieldcurvewillnotchangeitslevel

orshapeforthenexttwoyears,andswapspreadswillalsoremainunchanged.

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Case:LauraMathews

Exhibit1.GovernmentSpotRatesandSwapSpreads

Maturity(years)

1

2

3

4

Government

spotrate

2.25%

2.70%

3.30%

4.05%

Swapspread

0.25%

0.30%

0.45%

0.70%

SmithdecidestoexaminethefollowingthreeinvestmentoptionsforMathews:

Investment1:Buyagovernmentsecuritythatwouldhaveanannualized

returnthatisnearlyriskfree.Smithisconsideringtwopossible

implementations:atwo-yearinvestmentoracombinationoftwoone-year

investments.

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Case:LauraMathews

Investment2:Buyafour-year,zero-couponcorporatebondandthensellit

aftertwoyears.Smithillustratesthereturnsfromthisstrategyusingthe

swaprateasaproxyforcorporateyields.

Investment3:Buyalower-quality,two-yearcorporatebondwithacoupon

rateof4.15%andaZ-spreadof65bps.

WhenSmithmeetswithMathewstopresentthesechoices,Mathewstellshim

thatsheissomewhatconfusedbythevariousspreadmeasures.Sheiscurious

toknowwhetherthereisonespreadmeasurethatcouldbeusedasagood

indicatoroftheriskandliquidityofmoneymarketsecuritiesduringtherecent

past.

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Case:LauraMathews

InhispresentationofInvestment1,Smithcouldshowthatundertheno-

arbitrageprinciple,theforwardpriceofaone-yeargovernmentbondtobe

issuedinoneyearisclosestto:

A.0.9662.

B.0.9694.

C.0.9780.

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Case:LauraMathews

Answer:B

Theforwardpricingmodelisbasedontheno-arbitrageprincipleandis

usedtocalculateabond’sforwardpricebasedonthespotyieldcurve.The

spotcurveisconstructedbyusingannualizedratesfromoption-freeand

defaultrisk–freezero-couponbonds.

Equation2:P(T*+T)=P(T*)F(T*,T);weneedtosolveforF(1,1).

P(1)=1/(1+0.0225)1

andP(2)=1/(1+0.0270)2,

F(1,1)=P(2)/P(1)=0.9481/0.9780=0.9694.

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Case:LauraMathews

InpresentingInvestment1,usingShireGateAdvisers’interestrateoutlook,

Smithcouldshowthatridingtheyieldcurveprovidesatotalreturnthatismost

likely:

A.lowerthanthereturnonamaturity-matchingstrategy.

B.equaltothereturnonamaturity-matchingstrategy.

C.higherthanthereturnonamaturity-matchingstrategy.

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Case:LauraMathews

Answer:C

Whenthespotcurveisupwardslopinganditslevelandshapeare

expectedtoremainconstantoveraninvestmenthorizon(ShireGate

Advisers’view),buyingbondswithamaturitylongerthantheinvestment

horizon(i.e.,ridingtheyieldcurve)willprovideatotalreturngreaterthan

thereturnonamaturity-matchingstrategy.

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Case:LauraMathews

InpresentingInvestment2,Smithshouldshowatotalreturnclosestto:

A.4.31%.

B.5.42%.

C.6.53%.

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Case:LauraMathews

Answer:C

Theswapspreadisacommonwaytoindicatecreditspreadsinamarket.

Thefour-yearswaprate(fixedlegofaninterestrateswap)canbeusedas

anindicationofthefour-yearcorporateyield.Ridingtheyieldcurveby

purchasingafour-yearzero-couponbondwithayieldof4.75%{i.e.,4.05%

+

0.70%,[P4=100/(1+0.0475)4=83.058]}andthensellingitwhenit

becomesatwo-yearzero-couponbondwithayieldof3.00%{i.e.,2.70%+

0

6

.30%,[P2=100/(1+0.0300)2=94.260]}producesanannualreturnof

.53%:(94.260/83.058)0.5–1.0=0.0653.

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Case:LauraMathews

ThebondinInvestment3ismostlikelytradingatapriceof:

A.100.97.

B.101.54.

C.104.09.

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Case:LauraMathews

Answer:B

TheZ-spreadistheconstantbasispointspreadthatisaddedtothe

default-freespotcurvetopriceariskybond.AZ-spreadof65bpsfora

particularbondwouldimplyaddingafixedspreadof65bpstomaturities

alongthespotcurvetocorrectlypricethebond.Therefore,forthetwo-

yearbond,r(1)=2.90%(i.e.,2.25%+0.65%),r(2)=3.35%(i.e.,2.70%+

0

.65%),andthepriceofthebondwithanannualcouponof4.15%isas

follows:

P=4.15/(1+0.029)1

+4.15/(1+0.0335)2+100/(1+0.0335)2,

P=101.54.

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Case:LauraMathews

ThemostappropriateresponsetoMathewsquestionregardingaspread

measureisthe:

A.Z-spread.

B.Treasury–Eurodollar(TED)spread.

C.Libor–OIS(overnightindexedswap)spread.

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Case:LauraMathews

Answer:C

TheLibor–OISspreadisconsideredanindicatoroftheriskandliquidityof

moneymarketsecurities.Thisspreadmeasuresthedifferencebetween

LiborandtheOISrate.

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Case:RowanMadison

RowanMadisonisajunioranalystatCardinalCapital.SageWinter,asenior

portfoliomanagerandMadison’ssupervisor,meetswithMadisontodiscuss

interestratesandreviewtwobondpositionsinthefirm’sfixed-incomeportfolio.

WinterbeginsthemeetingbyaskingMadisontostateherviewsontheterm

structureofinterestrates.Madisonresponds:

“Yieldsareareflectionofexpectedspotratesandriskpremiums.Investors

demandriskpremiumsforholdinglong-termbonds,andtheseriskpremiums

increasewithmaturity.”

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Case:RowanMadison

WinternextasksMadisontodescribefeaturesofequilibriumandarbitrage-free

termstructuremodels.Madisonrespondsbymakingthefollowingstatements:

Statement1:“Equilibriumtermstructuremodelsarefactormodelsthatusethe

observedmarketpricesofareferencesetoffinancialinstruments,assumedto

becorrectlypriced,tomodelthemarketyieldcurve.”

Statement2:“Incontrast,arbitrage-freetermstructuremodelsseektodescribe

thedynamicsofthetermstructurebyusingfundamentaleconomicvariables

thatareassumedtoaffectinterestrates.”

WinterasksMadisonaboutherpreferencesconcerningtermstructuremodels.

Madisonstates:

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Case:RowanMadison

“Ipreferarbitrage-freemodels.Eventhoughequilibriummodelsrequirefewer

parameterstobeestimatedrelativetoarbitrage-freemodels,arbitrage-free

modelsallowfortime-varyingparameters.Ingeneral,thisallowanceleadsto

arbitrage-freemodelsbeingabletomodelthemarketyieldcurvemore

preciselythanequilibriummodels.”

WintertellsMadisonthat,basedonrecentchangesinspreads,sheisconcerned

aboutaperceivedincreaseincounterpartyriskintheeconomyanditseffecton

theportfolio.MadisonasksWinter:

“Whichspreadmeasureshouldweusetoassesschangesincounterpartyriskin

theeconomy?”

Winterisalsoworriedabouttheeffectofyieldvolatilityontheportfolio.She

asksMadisontoidentifytheeconomicfactorsthataffectshort-termandlong-

termratevolatility.Madisonresponds:

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Case:RowanMadison

“Short-termratevolatilityismostlylinkedtouncertaintyregardingmonetary

policy,whereaslong-termratevolatilityismostlylinkedtouncertaintyregarding

therealeconomyandinflation.”

Finally,WinterasksMadisontoanalyzetheinterestrateriskportfoliopositions

ina5-yearanda20-yearbond.Winterrequeststhattheanalysisbebasedon

level,slope,andcurvatureastermstructurefactors.Madisonpresentsher

analysisinExhibit1.

Exhibit1.Three-FactorModelofTermStructure

TimetoMaturity(years)

Factor

5

20

Level

Steepness

Curvature

–0.4352%

–0.0515%

0.3963%

–0.5128%

–0.3015%

0.5227%

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Case:RowanMadison

WinterasksMadisontoperformtwoanalyses:

Analysis1:Calculatetheexpectedchangeinyieldonthe20-yearbond

resultingfromatwostandarddeviationincreaseinthesteepnessfactor.

Analysis2:Calculatetheexpectedchangeinyieldonthefive-yearbond

resultingfromaonestandarddeviationdecreaseinthelevelfactoranda

onestandarddeviationdecreaseinthecurvaturefactor.

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Case:RowanMadison

Madison’sviewsonthetermstructureofinterestratesaremostconsistentwith

the:

A.localexpectationstheory.

B.segmentedmarketstheory.

C.liquiditypreferencetheory.

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Case:RowanMadison

Answer:C

Liquiditypreferencetheoryassertsthatinvestorsdemandariskpremium,

intheformofaliquiditypremium,tocompensatethemfortheadded

interestraterisktheyfacewhenbuyinglong-maturitybonds.Thetheory

alsostatesthattheliquiditypremiumincreaseswithmaturity.

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Case:RowanMadison

WhichofMadison’sstatement(s)regardingequilibriumandarbitrage-freeterm

structuremodelsisincorrect?

A.Statement1only

B.Statement2only

C.BothStatement1andStatement2

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Case:RowanMadison

Answer:C

BothstatementsareincorrectbecauseMadisonincorrectlydescribesboth

typesofmodels.Equilibriumtermstructuremodelsarefactormodelsthat

seektodescribethedynamicsofthetermstructurebyusingfundamental

economicvariablesthatareassumedtoaffectinterestrates.Arbitrage-free

termstructuremodelsuseobservedmarketpricesofareferencesetof

financialinstruments,assumedtobecorrectlypriced,tomodelthemarket

yieldcurve.

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Case:RowanMadison

IsMadisoncorrectindescribingkeydifferencesinequilibriumandarbitrage-

freemodelsastheyrelatetothenumberofparametersandmodelaccuracy?

A.Yes

B.No,sheisincorrectaboutwhichtypeofmodelrequiresfewerparameter

estimates

C.No,sheisincorrectaboutwhichtypeofmodelismorepreciseatmodeling

marketyieldcurves

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Case:RowanMadison

Answer:A

ConsistentwithMadison’sstatement,equilibriumtermstructuremodels

requirefewerparameterstobeestimatedrelativetoarbitrage-freemodels,

andarbitrage-freemodelsallowfortime-varyingparameters.Consequently,

arbitrage-freemodelscanmodelthemarketyieldcurvemoreprecisely

thanequilibriummodels.

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Case:RowanMadison

ThemostappropriateresponsetoMadison’squestionregardingthespread

measureisthe:

A.Z-spread.

B.Treasury–Eurodollar(TED)spread.

C.Libor–OIS(overnightindexedswap)spread.

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Case:RowanMadison

Answer:B

TheTEDspread,calculatedasthedifferencebetweenLiborandtheyieldon

aT-billofmatchingmaturity,isanindicatorofperceivedcreditriskinthe

generaleconomy.Anincrease(decrease)intheTEDspreadsignalsthat

lendersbelievetheriskofdefaultoninterbankloansisincreasing

(decreasing).Therefore,theTEDspreadcanbethoughtofasameasureof

counterpartyrisk.

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Case:RowanMadison

IsMadison’sresponseregardingthefactorsthataffectshort-termandlong-

termratevolatilitycorrect?

Yes

No,sheisincorrectregardingfactorslinkedtolong-termratevolatility

No,sheisincorrectregardingfactorslinkedtoshort-termratevolatility

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Case:RowanMadison

Answer:A

Madison’sresponseiscorrect;researchindicatesthatshort-termrate

volatilityismostlylinkedtouncertaintyregardingmonetarypolicy,whereas

long-termratevolatilityismostlylinkedtouncertaintyregardingthereal

economyandinflation.

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Case:RowanMadison

BasedonExhibit1,theresultsofAnalysis1shouldshowtheyieldonthe20-

yearbonddecreasingby:

A.0.3015%.

B.0.6030%.

C.0.8946%.

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Case:RowanMadison

Answer:B

BecausethefactorsinExhibit1havebeenstandardizedtohaveunit

standarddeviations,atwostandarddeviationincreaseinthesteepness

factorwillleadtotheyieldonthe20-yearbonddecreasingby0.6030%,

calculatedasfollows:

Changein20-yearbondyield=–0.3015%×2=–0.6030%.

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Case:RowanMadison

BasedonExhibit1,theresultsofAnalysis2shouldshowtheyieldonthefive-

yearbond:

A.decreasingby0.8315%.

B.decreasingby0.0389%.

C.increasingby0.0389%.

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Case:RowanMadison

Answer:C

BecausethefactorsinExhibit1havebeenstandardizedtohaveunit

standarddeviations,aonestandarddeviationdecreaseinboththelevel

factorandthecurvaturefactorwillleadtotheyieldonthefive-yearbond

increasingby0.0389%,calculatedasfollows:

Changeinfive-yearbondyield=0.4352%–0.3963%=0.0389%.

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Case:LizTyo

LizTyoisafundmanagerforanactivelymanagedglobalfixed-incomefundthat

buysbondsissuedinCountriesA，B，andC.Sheandherassistantare

preparingthequarterlymarketsupdate.Tyobeginsthemeetingbydistributing

thedailyratessheet,whichincludesthecurrentgovernmentspotratesfor

CountriesA,B,andCasshowninExhibit1.

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Case:LizTyo

Exhibit1Today’sGovernmentSpotRates

Maturity

Oneyear

CountryA

0.40%

0.70

CountryB

-0.22%

-0.20

CountryC

14.00%

12.40

Twoyears

Threeyears

Fouryears

Fiveyears

1.00

-0.12

11.80

1.30

-0.02

11.00

1.50

0.13

10.70

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Case:LizTyo

Tyoasksherassistanthowthesespotrateswereobtained.Theassistantreplies,

“Spotratesaredeterminedthroughtheprocessofbootstrapping.Itentails

backwardsubstitutionusingparyieldstosolveforzero-couponratesoneby

one,inorderfromlatesttoearliestmaturities.”

Tyothenprovidesareviewofthefund'sperformanceduringthelastyearand

comments,“Thechoiceofanappropriatebenchmarkdependsonthecountry's

characteristics.Forexample,althoughCountriesAandBhavebothanactive

governmentbondmarketandaswapmarket,CountryC'sprivatesectorismuch

biggerthanitspublicsector,anditsgovernmentbondmarketlacksliquidity.”

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Case:LizTyo

Tyofurtherpointsout,“Thefund'sresultsweremixed;returnsdidnotbenefit

fromtakingonadditionalrisk.Weareespeciallymonitoringtheriskinessofthe

corporatebondholdings.Forexample,ourlargestholdingsconsistofthree

four-yearcorporatebonds(Bonds1,2,and3)withidenticalmaturities,coupon

rates,andothercontractterms.ThesebondshaveZ-spreadsof0.55%,1.52%,

and1.76%,respectively:”

Tyocontinues,“Wealsolookatriskintermsoftheswapspread.Weconsidered

historicalthree-yearswapspreadsforCountryB,whichreflectthatmarket's

creditandliquidityrisks,atthreedifferentpointsintime.”Tyoprovidesthe

informationinExhibit2.

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Case:LizTyo

Exhibit2SelectedHistoricalThree-YearRatesforCountryB

Period

GovernmentBondYield(%)Fixed-for-FloatingLiborSwap

(%)

1

6

1

Monthago

Monthago

2Monthago

-0.10

-0.08

-0.07

0.16

0.01

0.71

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Case:LizTyo

Tyothensuggeststhatthefirmwasabletoaddreturnbyridingtheyieldcurve.

Thefundplanstocontinuetousethisstrategybutonlyinmarketswithan

attractiveyieldcurveforthisstrategy.

Shemovesontopresenthermarketviewsontherespectiveyieldcurvesfora

five-yearinvestmenthorizon.

CountryA:“Thegovernmentyieldcurvehaschangedlittleintermsofits

levelandshapeduringthelastfewyears,and1expectthistrendto

continue.Weassumethatfuturespotratesreflectthecurrentforward

curveforallmaturities.”

CountrγB:“Becauseofrecenteconomi