Bond Terminology Coupon rate Realized Yield

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BondTerminology

Couponrate:istheannualcouponamountexpressedasapercentageoftheface- value.

Thecurrentyieldistheannualcoupondividedbythecurrentmarketpriceofthe bond.

Yieldtomaturity(YTM)istheratethatmakesthepriceofthebondjustequalto thepresentvalueofitsfuturecashflows.YTMisIRRofabond

RealizedYield:Therealizedyieldisanex-postmeasureofthebond'sreturns.The realizedyieldistheaverageannualrateofreturnthatwasactuallyearnedonthe investment.

BondIndenture:Thebondindentureisathreepartycontractbetweenthebond issuer,thebondholders,andthetrustee

BondCreditRatings

Creditratingisanassessmentofthecreditqualityofthebondissuebasedonthe issuer'sfinancialcondition.

Theprimaryquestioninbondratinganalysisiswhetherthefirmcanserviceits debtinatimelymanneroverthelifeofagivenissue.

Whiledecidinguponthecreditratingofaparticularissuefactorsrelatedtothe firmaswellastheissueareconsidered.

Splitratingisobtainedwhenthereisdisagreementamongdifferentbondrating agenciesoncreditqualityofaparticularissue.

FloatingRateBonds/Notes

AFloatingRateNote(FRN)isabondwithacouponthatisadjustedperiodically toabenchmarkinterestrate.

Alsoknownasfloaters,variableratenotes,adjustableratenotes.

Afloatercapsetsalimittotheamountofincreaseincouponrate.Thepriceof cappedfloaterwillbelessthanpriceofaregularfloater.

InverseFloaterisabondwhosecouponpaymentfallswithincreasein referencerate.

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BondValueinmonetaryterms:

BondValue=PresentValueofthecoupons+PresentValueoftheFaceValue

P

=

2n t=1

I /2 (1+ r /2)t

+

(1 +

M r /2)2n

Forazerocouponbond,pricewillbeequaltopresentvalueofmaturitycashflow

astherearenointermediarycashflowsonthebond.

P

=

M (1+ r)n

Priceyieldcurve:

Therelationshipbetweenthemarketyieldonthebondanditspriceisreferredtoas thepriceyieldcurve.

Theprice?yieldcurvebringsoutthreeimportantpoints:

1. Whenthediscountrateisbelowthecouponrate,bondispricedatpremium toitsparvalue.

2. Whenthediscountrateishigherthanthecouponrate,bondispricedata discounttoitsparvalue.

3. Theprice-yieldrelationshipisnotastraightlinebutconvex.

Differentmeasuresofbondyields:

NominalYield:isthecouponrateofaparticularbond.

CurrentYield:calculatescurrentincomefromabondasapercentageoftheprice. Itisanequivalentofdividendyieldforstocks

CY

=

I P

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RealizedYield:Measurestheestimatedrateofreturnforabondlikelytobesold priortomaturity.

P =

hp I t =1 (1 + r )t

+

(1

Php + r )hp

YieldToMaturity

Yieldtomaturity(YTM)istheratethatmakesthepriceofthebondjustequaltothe

presentvalueofitsfuturecashflows.YTMisIRRofabond.

P

=

2T t=1

I /2 (1+ r /2)2t

+

PT (1+ r /2)2T

Generally,marketpricesareobservedinthebondmarket.Thusifabondispriced higherthanitspar,itcanbeconcludedthatthecurrentrateofinterestislessthan thestatedcouponrateandisalsotrueviceaversa.

YTMofaZeroCouponBond:

TheYTMofazerocouponbondisthatdiscountratewhichwhenusedtodiscount thecashflowtobeobtainedattheendofmaturityperiodwillequatethevaluetoits currentmarketprice.

P

=

M (1+ r)n

YieldCurve

YieldCurve(termstructureofinterestrates):isastaticfunctionthatrelatesthe termtomaturitytoyieldtomaturityofaparticularqualitybond.

Typesofyieldcurves:

RisingYieldCurve:isformedwhentheyieldsonshort-termissuesarelowandrise consistentlywithlongermaturitiesandflattenoutattheextremes.

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Decliningyieldcurve:isformedwhentheyieldsonshort-termissuesarehighand yieldsonsubsequentlylongermaturitiesdeclineconsistently.

Flatyieldcurve:isformedwhenshorttermyieldsareapproximatelyequaltolong termyields.

Humpedyieldcurveisformedwhenyieldsonintermediatetermissuesareabove thoseonshort-termissuesandtheratesonlongtermissuesdeclinetolevelsbelow thosefortheshorttermandthenlevelout.

SpotRate

Spotrateisthediscountrateforacashflowataspecificmaturity.

Theoreticalspotratecurvecanbederivedfromtheobservableyieldcurveby processofbootstrapping.

ForwardRate

Forwardraterepresentsmarket'sexpectationoffutureshort-terminterest rates.

Calculationofforwardratesisbasedonthepremisethatinvestorwillbe indifferentbetween1)investinginoneyearriskfreesecurityand2)investingin sixmonthsriskfreesecurityandreinvestingtheamountreceivedinanothersix monthsriskfreesecurity,iftheyproducethesamereturnforone-year investmenthorizon.

Theyieldonsixmonthsriskfreeinstrumentthatwillberequiredsixmonths fromnowtomakeinvestorindifferentiscalledsix-monthforwardrate.

BondPriceVolatility

Thereexistsaninverserelationshipbetweenpriceofthebondandinterest rates.

BondPriceVolatilityismeasuredasapercentagechangeinthepriceofthe bond.

BondPriceVolatility=(EndingPriceoftheBond/BeginningPriceoftheBond)?1

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CharacteristicsofBondPriceBehavior

Bondpricesmoveinverselytointerestrates.

Foragivenchangeininterestrates,longermaturitybondsexperiencealarger pricechange.

Bondpricevolatilityincreasesatadiminishingrateastermtomaturity increases.

Bondpricemovementsresultingfromequalabsoluteincreaseanddecreasein yieldisnotsymmetrical.

Highercouponbondsshowsmallerpercentagepricefluctuationsforagiven changeinyield.

Duration:MeasureofBondPriceVolatility

Durationisameasureofthesensitivityofthebond'spricetointerestrate movements.

Bondswithhigherdurationhavehigherpricevolatilityandthusareriskierthan bondswithlowerduration.

MacaulayDuration

MacaulayDurationisthetotalweightedaveragetimeforrecoveryofthepayments andprincipalinrelationtothecurrentmarketpriceofthebond.Itmeasuresbond pricevolatilityintermsoftimeperiod.

n Ct * t

D =

t=1 (1 + i)t n Ct

t=1 (1+ i)t

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CharacteristicsofMacaulayDuration

1. MacaulayDurationforazerocouponbondwillbeequaltoitstermto maturity.

2. Thedurationmeasureforacouponbondwillalwaysbelessthanitstermto maturity.

3. Thereisaninverserelationbetweencouponandduration. 4. Thereispositiverelationbetweentermtomaturityandduration.However,

durationincreasesatadecreasingratewithincreasedmaturity. 5. Thereisaninverserelationshipbetweenyieldtomaturityandduration.

ModifiedDuration:

Modifieddurationisanadjustedmeasurethatcanbeusedasanapproximatefor interestratesensitivityofanoptionfreebond.

DurationMod

=

DurationMac (1+ i)

Pricechangeduetoduration:

P P

*100

=

-DMod

*

i

ApplicationofDuration:Bondtradingstrategies

Longerdurationimplieslargerpricevariationforagivenchangeinyield.

Portfoliomanagercandecidethebondsthatshouldbecomprisedinhisportfolio

basedonhisexpectationsofdirectionofchangeofmarketyield.

Ifheexpectsinterestratestomoveuphewantstoprotecthisportfoliofrom deteriorationinpricesandthuswouldliquidatelongerdurationbondsand investinshorterdurationbonds.

Convexity

Modifieddurationassumesthatthereexistslinearrelationshipbetweenprice andyieldforabond.

Convexityisameasureofthecurvatureofthepriceyieldrelationship.

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Convexityisadesiredfeaturebecausepresenceofconvexityimpliesthatprice willincreasemoreincaseinterestratesfallandwilldecreaselessincase interestratesrise.

Convexity

=

1 (1+ i)2

n t=1

CFt (1+ i)

*

(t 2

+

t)

Thepriceyieldrelationshipforahighcoupon,short-termmaturitybondwillbe

almoststraightline.

Bondwithlowcouponandlonger-termmaturitywillexhibithighlyconvex

price-yieldrelationship.

ConvertibleBonds

Aconvertiblebondisahybridinstrumentwithfeaturesofbothbondandequity.

Aconvertiblebondisexchangeableforafixednumberofsharesoftheissuing company'sstockatthebondholder'sdiscretion.

ConversionPricecanbecalculatedbyfollowingformula:

ConversionPrice=Bond'sparvalue/Conversionratio

ConversionRatio=Facevalueofbond/ConversionPrice

ConversionValue=ConversionRatio*Marketpricepershareatthetimeof

conversion

Premiumoverconversionvalue=Conversionvalue?Marketpriceofa

Convertiblesecurity

Theconversionpriceisusuallyadjustedforanystocksplitsorstockdividendsto

protectinvestorsinconvertiblebondsfromdilution.(Antidilutionclause)

Advantagesofconvertiblebonds:Issuingcompany

Riskyfirms,whichmayfinditdifficulttoraisemoneyviaconventionalbonds exceptbyofferingaveryhighcouponratemayissueconvertiblebondsand lowerthecostofdebt.

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Asvalueofconvertiblebondisequaltosumofvaluesofanordinarybondand valueofconversionoption,thevalueofordinarybondwilldecreasewith increasedriskinessoffirm'scashflowsandthevalueofoptionwillbehigher.

Thus,itisbeneficialforafirmwithriskycashflowstoissueconvertiblebonds.

Aconvertiblebondcanbeviewedasadeferredequitysalebyacompanyata premiumovercurrentprevailingmarketprice.

Therestrictionsintheformofbondindentureimposedbyinvestorsin convertiblesmaybelessstringentascomparedtotheonesimposedbyinvestors inordinarybonds.

Advantagestobuyers:

Convertiblesofferbondholdersachancetoparticipateinthestockprice appreciation.

Convertiblesofferawaytolimittheriskassociatedwithequity,whichmay resultinbigswingsineitherdirection.

Warrants

Warrantsaresecuritiesthatgivetheholderstherighttobuysharesofcommon stockdirectlyfromacompanyatafixedpriceforagivenperiod.

Eachwarrantspecifiesthenumberofsharestheholdercanbuy,theexercise priceandtheexpirationdate.

Warrantisarightavailabletotheholder,notanobligation.

ForcedConvertibles:CallableBonds

Thecallfeaturegivestheissuerofthebondtherighttobuybackthebondata particularprice.

Theoptiontocallisavailabletotheissuerthuscallablefeatureisadisadvantage totheinvestor.

Thedisadvantagestotheinvestorbecauseofcallfeatureistwofold:

Asthebondiscallableataparticularprice,investorcannotenjoythe appreciationinbondvaluethatmightbeavailableduetodeclininginterest rates.

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