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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