CFA三級知識點必備：Fixed-income-打印版

Fixed-Income

Portfolio

Management

CFAй???畝?

???BobHong



1-29

1.Decompose

expected

returns

2-29

Decomposeexpectedreturns

?Examiningthesecomponentsleadstoabetterunderstandingofthedriving

forcesbehindexpectedreturns.

?Expectedreturns[E(R)]canbedecomposed

E(R)|yieldincome

z

+rolldownreturn

+E(changeinpricebasedoninvestor'sviewyieldsandyieldspreads)

-E(creditlosses)

+E(currencygainsorlosses)

9Onlyapproximately;

9Betterunderstandtheirowninvestmentpositions;

9Appliedtoanannualperiod;

9Notreflecttaxes.

3-29

Yieldincome

?Yieldincomeistheincomethataninvestorreceivesfromcoupon

paymentsrelativetothebond’spriceaswellasinterestonreinvestment

income.

annualcouponpayment

z

Yieldincome=

currentbondprice

9Annualcouponpayment=coupon+reinvestmentincome

9Whenreinvestmentincome=0,yieldincome=currentyield

4-29

Rolldownreturn

?Rolldownreturn:returnresultsfromthebond“rollingdown”theyield

curveasthetimetomaturitydecrease,assumingzerointerestratevolatility.

zEqualsthebond’spercentagepricechangeassuminganunchanged

yieldcurveoverthestrategyhorizon.

BondpriceendBondpricebeginning

zRolldownreturn=

Bondpricebeginning

?Rollyield=yieldincome+rolldownreturn

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Expectedchangeinpricebasedonyields

?Theexpectedchangeinpricebasedoninvestor’sviewsofyieldsandyield

spreadsreflectsaninvestor’sexpectationofchangesinyieldsandyield

spreadsovertheinvestmenthorizon.

zE('pricebasedoninvestor'sviewofyieldsandyieldspreads)

1

2

=-modifieddurationu'yield

uconvexityu('yield)

2

zExpectedchange=0ifexpectedyieldcurvesandyieldspreadstoremain

unchanged

zConvexityestimatestheeffectofthenon-linearityoftheyieldcurve

zEmbeddedoption:effectiveduration,effectiveconvexity

zFloatingratenoteshavemodifieddurationnearzero

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Expectedcreditloss¤cygain/loss

?Expectedcreditlossrepresenttheexpectedpercentageofparvaluelostto

defaultforabond.

zExpectedcreditlosses

=Probability(default)uexpectedlossseverity(lossgivendefault)

?Currencygainorloss

zAnyexpectedfluctuationsinthecurrencyexchangerateorexpected

currencygainsorlossesovertheinvestmenthorizon.

zCanbelockedinovertheinvestmenthorizonusingcurrencyforwards.

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Estimationoftheinputs

?Easiestcomponent:yieldincome.

?Relativelystraightforward:rolldownreturn.

?Mostuncertain

zInvestor’sviewsofchangesinyieldsandyieldspreads;

zExpectedcreditloss;

zExpectedcurrencymovements.

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Example

?AnnmanagesaBritishpound-denominatedcorporatebondportfolio.

HerdepartmentheadinNewYorkhasaskedAnntomakea

presentationonthenextyear’stotalexpectedreturnofherportfolio

inUSdollarsandthecomponentsofthisreturn.Thefollowingshows

informationontheportfolioandAnn’sexpectationsforthenextyear.

?Calculatethetotalexpectedreturnofthebondportfolio,assumingno

reinvestmentincome.

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Example

Notionalprincipalofportfolio(inmillion)

?100

?2.75

Annual

1year

Averagebondcouponpayment(per?100)

Couponfrequency

Investmenthorizon

Currentaveragebondprice

?97.11

Expectedaveragebondpriceinoneyear(assumingan

unchangedyieldcurve)

?97.27

Averagebondconvexity

0.18

3.70

Averagebondmodifiedduration

Expectedaverageyieldandyieldspreadchange

Expectedcreditlosses

0.26%

0.10%

0.50%

Expectedcurrencylosses(?depreciationversusUS$)

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Example

?CorrectAnswer:

zYieldincomeoveraoneyearhorizon=2.75/97.11=2.83%.

zRolldownreturn=(97.27-97.11)/97.11=0.16%.

zRollyield=yieldincome+rolldownreturn=2.83%+0.16%=2.99%.

zTheexpectedchangeinpricebasedonAnn’sviewsofyieldsand

yieldspreads=(-3.70*0.0026)+[1/2*0.18*(0.0026)2]=-0.96%.

zExpectedcreditlosses=-0.1%.

zExpectedcurrencylosses(?depreciationversusUS$)=-0.5%.

zTotalexpectedreturn=2.83%+0.16%+?-0.96%?+?-1%?+

?-0.5%?=1.43%.

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2.Immunization-

multiple

liabilities

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Managingmultipleliabilities

?Approachestomanagemultipleliabilities

zCashflowmatching

9Entailsbuildingadedicatedportfolioofzero-couponorfixed-

incomebondstoensurethattherearesufficientcashinflowstopay

thescheduledcashoutflows.

zDurationmatching

9Extendstheideasoftheprevioussectiontoaportfolioofdebt

liabilities.

zContingentimmunization

9Allowsforactivebondportfoliomanagementuntilaminimum

thresholdisreachedandthatthresholdisidentifiedbytheinterest

rateimmunizationstrategy.

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Cashflowmatching

?Itisaclassicstrategytoeliminatetheinterestrateriskthroughbuildinga

dedicatedassetportfolioofhigh-qualityfixed-incomebonds,sothat

matchestheamountandtimingofthescheduledcashoutflows.

zEachcashflowareplacedinaheld-to-maturityportfolio

?Whycompanydonotbuybackandretireitsliabilities?

zThebuybackstrategywouldbedifficultandcostly;

zMostcorporatebondsareratherilliquid

zThecorporatehasmotivationtoimprovethecompany’screditratingby

cashflowmatching.

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Cashflowmatching

?Accountingdefeasance

zAwayofextinguishingadebtobligationbysettingasidesufficienthigh

qualitysecurities,suchasUSTreasurynotes,torepaytheliability.

?Aconcernforcashflowmatchingstrategyisthecash-in-advance

constraint

zCash-in-advanceconstraintmeanssecuritiesarenotsoldtomeet

obligations;

zForcompany,sufficientfundsmustbeavailableonorbeforeeach

liabilitypaymentdatetomeettheobligation;

zTheremightbelargecashholdingsbetweenpaymentdates,socash

reinvestmentriskwouldbefaced,astheshort-terminvestmentsreturns

arerelativelylow.

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Durationmatching

?Durationmatchingformultipleliabilities

zThemoneydurationoftheimmunizingportfoliomatchesthemoney

durationofthedebtliabilities;

zMarketvaluesandcashflowyieldsoftheassetsandliabilitiesarenot

necessarilyequal.

zMatchmoneydurationisuseful.

?Basispointvalue(BPV)isusedtomeasuremoneyduration,means1bps

changeincashflowyield,themarketvaluechange.

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Durationmatching

?Immunizationofmultipleliabilitiesisessentiallyaninterestraterisk

hedgingstrategy

zChangesinthemarketvalueoftheassetportfoliocloselymatch

changesinthedebtliabilitieswhetherinterestratechanges.

zAlthoughmoneydurationforassetsandliabilitiesarethesame,the

differenceinstructureofassetandliabilityshowsadifferencein

dispersionandconvexity.

?Rebalancingisneeded

zIntheory,assetmanagerneedstomakearebalancewhenneeded,so

thatthemoneydurationoftheassetcanmatchthemoneydurationof

theliability;

zInreality,themanagerlikelywaitsuntilthemismatchislargeenough

tojustifythetransactionscostsinsellingsomebondsandbuyingothers.

zMethodtorebalance

9Sellorbuythebonds;

9Useinterestratederivatives.

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Contingentimmunization

?Contingentimmunization

zThepresenceofasignificantsurplusallowstheassetmanagerto

considerahybridpassive-activestrategy;

zTheideabehindcontingentimmunizationisthatassetmanagerscan

pursueactiveinvestmentstrategies.

9Whenactivelymanagedassetsperformedpoorly,themandate

revertstothepurelypassivestrategyofbuildingaduration

matchingportfolio,andthenmanagingittoremainonduration

target.

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3.Strategies

forstableyield

curve

19-29

Yieldcurvestrategies

?Assumeyieldcurveisupwardsloping

Activestrategies

(1)Buyandhold

(2)Rolldown/ridetheyield

curve

Stableyieldcurve

(3)Sellconvexity

(4)Carrytrade

(1)Parallelshift

Levelchange

(2)Flattening

(3)Steepening

(4)Lesscurvature

Morecurvature

(5)Decreaseratevolatility

Increaseratevolatility

Slopechange

Curvaturechange

Ratevolatilitychange

20-29

Yieldcurvemovement

2.1Strategiesforstableyieldcurve

?(1)Buyandhold

zSelectandholdbondstoearnhigherYTM;

zBenefitfrom:couponcollectionandreinvestment,indicatingbyhigher

YTM;

zAlthoughholdwithoutactivetrading,itisstillanactivemanagement,

sincethebond’scharacteristicsdivergefromthebenchmark.

?(2)Riding(rolldown)theyieldcurve

zWhenpriceisupwardsloping,buylongtermbondsandsellshort

termbonds;

zBenefitfrom:highergainduringpriceappreciationandlowerloss

duringpricedepreciation;

zParticularlyusefulwhen:yieldcurvearestableandrelativelysteep,since

thepricewillappreciatemoreasthetimepasses.

zIftheforecastendingyieldonaparticularbondislower(higher)than

theforwardrate,thenitcanbeexpectedtoearnareturngreater

than(lessthan)theone-periodrate.

21-29

Strategiesforstableyieldcurve

?(3)Sellconvexity

zBuybondswithlowerconvexity,orsay,sellbondswithhigher

convexity.

9E.g.BuycallablebondsorMBS(negativeconvexity).

zBenefitfrom:differenceinconvexitybetweenbondswithsame

duration.

?(4)Carrytrade

zAcarrytradeinvolvesbuyingasecurityandfinancingitatarate

thatislowerthantheyieldonthatsecurity;

zBenefitfrom:thespreadbetweentworates;

zThecarrytradecanbeinherentlyrisky,becausetheportfolioholds

(typically)longer-termsecuritiesfinancedwithshort-termsecurities.

22-29

Carrytrade

?Intra-marketcarrytrades(tradeonlyinonemarket)

zThereareatleastthreebasicwaystoimplementacarrytradetoexploit

astable,upward-slopingyieldcurve:

9Buyabondandfinanceitintherepomarket.

9Receivedfixedandpayfloatingonaninterestrateswap.

9Takealongpositioninabond(ornote)futurescontract.

23-29

4.Expected

excessreturn

24-29

Expectedexcessreturn

?Holding-periodexcessreturn

zXR≈(s×t)–(Δs×SD)

zWhereXRistheholding-periodexcessreturn,sisthespreadatthe

beginningoftheholdingperiod,tistheholdingperiodexpressedin

fractionsofayear,Δsisthechangeinthecreditspreadduringthe

holdingperiod,andSD=spreadduration.

?Expectedexcessreturn

zEXR≈(s×t)–(Δs×SD)–(t×p×L)

zWherepistheannualizedexpectedprobabilityofdefault,Listhe

expectedlossseverity.

zNotethattheterm(p×L)istheexpectedannualcreditloss.

25-29

Example

?Acorporatebondhasaspreaddurationoffiveyearsandacredit

spreadof2.75%.

1.Whatistheapproximateexcessreturnifthebondisheldforsix

monthsandthecreditspreadnarrowsto2.25%?Assumethe

spreaddurationremainsatfiveyearsandthatthebonddoesnot

experiencedefaultlosses.

2.Whatistheinstantaneous(holdingperiodofzero)excessreturnif

thespreadrisesto3.25%?

3.Assumethebondhasa1%annualizedexpectedprobabilityof

defaultandexpectedlossseverityof60%intheeventofdefault.

Whatistheexpectedexcessreturnifthebondisheldforsix

monthsandthecreditspreadisexpectedtofallto2.25%?

26-29

Example

?CorrectAnswer:

zSolutionto1:

UsingEquation1,theexcessreturnonthebondisapproximately

3.875%=(2.75%×0.5)–[