Bond Pricing and Bond Yield New -1

7/23/2019 Bond Pricing and Bond Yield New -1

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Valuing Bonds:Bond Pricing and Bond

YieldDr. Himanshu Joshi

FORE School of Managemen!e" Delhi



Ma#or $lasses of Financial %sses orSecuriies

• Mone& mar'e

• Bond mar'e

•

E(ui& Securiies• )ndices

• Deri*ai*e mar'es



+he Bond Mar'e

• +reasur& !oes and Bonds

• )n,aion-Proeced +reasur& Bonds

• Federal %genc& De

• )nernaional Bonds

• Munici/al Bonds

• $or/orae Bonds

• Morgages and Morgage-Bac'edSecuriies



Ris' in Fi0ed )ncomeSecuriies





Ris' of De Securiies

• )neres Rae Ris': de securiies1"hich /a& 20ed cou/on raes1 su3era /rice decline "hen ineres raes

go u/ une0/ecedl&1 ecause hesaed cou/on is inade(uae ocom/ensae for he /re*ailing higher

le*el of ineres raes.Fi0ed)ncomeSecuri&Prices

Pre*ailing)neres Rae)n he Mar'e



Ris' of De Securiies

4i'e"ise rein*esmen of 20edconracual cou/ons ecomes ris'&"hen mar'e ineres rae decline.

Re-in*esmen Ris'

Pre*ailing)neres Rae)n he Mar'e



Bond Price



Bond Price

• +his ond "as issued near /ar *alue of 566 inhe middle of Januar& 7668. /rice (uoed hereis for he &ear 7669 Januar& o Decemer;.

•

Flucuaion in ond /rice ma& e due o:a; %n increase in ineres rae in he mar'e.

; %n increase in unanici/aed in,aion rae.

c; % fall in ris' /remium ha causes in*esors

o /refer ris'ier securiies han reasur&securiies.



$redi Ris'

• +reasur& securiies do no carr&credi ris'. Ho"e*er here arecor/orae onds ha carr& signi2can

amoun of credi ris': ha he issuerma& e unale o ser*ice all or someof he /romised oligaions due o

2nancial disress1 reorgani<aion1"or'ous1 or an'ru/c&.



4i(uidi& Ris'

• Some de securiies ma& rade inilli(uid mar'es fe" dealers1 "ide id-o3er s/reads1 lo" de/h1 and so on;.

• Emerging mar'e de and some high&ield de fall ino his caegor&.

• 4i(uidi& refers o he ease "ih "hich

a reasonale si<e of a securi& can eransaced in he mar'e "ihin a shornoice1 "ihou ad*erse /rice reacion.



4i(uidi& Ris'

• +he seller or he u&er "ill face follo"ing:

5. High +ransacion coss such as fees andcommissions1

7. Bid-o3er s/reads=. Mar'e im/ac coss1 "hich refer o he

/ossiili& ha follo"ing he /lacemenof a u& Sell; order he mar'e ma'ersma& increase Decrease; he /rices a"hich he& are "illing o rade.



$onracual Ris'

• De securiies ma& e callale & he issuer a he issuer>so/ion.

• Holders of morgage loans ha*e he righ o /re/a& heir oldmorgages if he& can re2nance hem a a chea/er rae.

• +his im/lies ha /re/a&men should increase "hen

morgage raes in mar'e dro/.

• +he lender "ill "an o charge a higher ineres rae oaccoun for he fac ha he or she is gi*ing he orro"er a*aluale o/ion o call a"a& he loans "hen ineres rae fallin he mar'e.

• +his is ?call ris'@ in he morgages.

• Hence morgages mus rade a a &ield higher han similarnon callale reasur& de securiies.



)n,aion Ris'•

Infation risk is he ris' ha mone& oained in he fuure "ill e"orh less han "hen i is in*esed1 "hich is almos al"a&s hecase.

• +he real ris' is ho" much his ris' "ill e. On he oher hand1 i is/ossile1 in some cases1 o a'e ad*anage of de,aion ha occurs"hen ineres raes rise.

• % good e0am/le is "hen ineres raes are rising1 ne"l& issued20ed-income securiies sar o /a& more1 "hile /rices of hings hagenerall& re(uire orro"ing1 such as real esae1 sar declining.

• +hus1 for insance1 one could u& A "ee' +-ills as a "a& o sa*e fora house or for a do"n /a&men. %s he +-ills e0/ire1 he& can e

re-in*esed a /rogressi*el& higher raes "hile raes are rising;.• )n he meanime1 real esae /rices are falling ecause i is

ecoming more e0/ensi*e o orro" he mone& o /a& for i. So hemone& earned on he +-ills ecomes e*en more *aluale han heineres rae iself suggess "hen used o /urchase real esae.



E*en Ris'

• Some de securiies ma& e sensii*e o e*enssuch as hosile reorgani<aions or le*eraged u&ous4BOs;. Such e*ens can lead o a signi2can /riceloss.

• )n Ocoer 59 RJR !aisco "as a'en o*er hroughan 4BO. +he resuling com/an& oo' on hea*& deo 2nance he a'eo*er. %s a resul Mood&>s raing forRJR !aisco>s de from %5 o B=.

•

+he /rices of RJR !aisco dro//ed aou 5C1 and&ield s/read "en from aou 566 BPS ao*ereasur& o =C6 BPS ao*e reasur&.

• )n cor/orae de mar'e his ris' is called e*en ris'.



E*en Ris' Proecion;

• )n*esors ofen re(uire /roecionagains his &/e of ris' & re(uiringa righ from he sellers of onds ha

allo"s in*esors o sell Pu; heonds ac' o he seller a /ar *alue.

• aga and elch 599=; e0amined

he ondholder losses for 5 2rmse0/eriencing 4BO "ere nearl& 8"ihin 76 da& "indo" surrounding

he e*en dae.



+a0 Ris'

• )f de securiies "ere originall&issued "ih cerain a0 e0em/ionfeaures and suse(uenl& here

de*elo/ed an uncerain& regardingheir a0 saus1 i could o lead o a/rice loss.



Foreign E0change Ris'

• $once/ of Gcarr& rade>

• De/ending u/on he currencies in"hich he in*esor is domiciled1 de

securiies ma& /ose F ris' as "ell.

• $enral an' of $hina and Ja/an holdsigni2can amoun of I.S go*ernmen

de as in*esmens1 and conse(uenl&he& are su#ec o he ris' ha hedollar could de/reciae.



$ou/on Rae on a Bond..

• r = Real risk ree interest rate +Infation premium+ Deault riskpremium + Liquidity Premium +

Maturity Premium



•Bond Pricing



• Face or /ar *alue

• $ou/on rae

– ero cou/on ond

• $om/ounding and /a&mens

– %ccrued )neres

• )ndenure

Bond $haracerisics



Bond )ndenure: )llusraion

• % ond "ih /ar *alue of K5666 andcou/on rae of migh e sold forK5666. he ondholder is hen eniled o a

/a&men of of K5666 L K6 /er &ear1for he saed life of a ond sa&1 =6 &ears.

• +he K6 /a&men &/icall& comes in "osemiannual insallmens of KA6 each. %

he end of =6 &ear life of he ond issueralso /a&s he K5666 /ar *alue o heondholder.



%ccrued )neres and uoed Bond

Prices

• +he ond /rices ha &ou see (uoedin 2nancial /ages are no acuall& he/rices ha in*esors /a& for he

ond.

• +his is ecause he (uoed /ricedoes no include he ineres ha

accrues e"een cou/on /a&mendaes.



%ccrued )neres•

%ccrued )neres L %nnual $ou/on Pa&men N Da&s since las cou/on/a&men

7 Da&s Se/araing cou/on /a&mens

E0am/le: Su//ose ha he cou/on rae is

on ond of /ar *alue K5666. =6 da&sha*e een /assed since he las cou/on/a&men. )f he (uoed /rice of he ondis K9961 hen "ha should e he in*oice/riceBonds are (uoed ne of accrued ineres in he 2nancial /ages and hus a//ears as 5666 a he mauri&. )nconras o he onds1 soc's do no rade a ,a /rices "ih ad#usmens for accrued di*idends. hoe*er

o"ns he soc' "hen i goes e0-di*idend recei*e he enire di*idend on he e0-da&. %nd he soc' /rice re,ec*alue of he u/coming di*idend. +he /rice herefore falls afer he e0-di*idend dae.



Bond Pricing

• +he /rice of an& 2nancial insrumenis e(ual o he /resen *alue of hee0/eced cash ,o"s from 2nancial

insrumen.

• Deermining he /rice re(uire:

5. %n esimae of he e0/eced cash

,o"s.

7. %n esimae of he a//ro/riaere(uired &ield.



Bond Pricing

• +he re(uired &ield refers o he &ield for2nancial insrumens "ih com/arale ris'1 oralernai*e or susiue; in*esmens.

• +he 2rs se/ in deermining he /rice of a ondis o deermine is cash ,o"s.

• +he cash ,o"s of a ond ha he issuer can noreire /rior o is saed mauri& dae. a noncallale ond; consis of:

5. Periodic cou/on /a&mens o he mauri& dae.

7. +he Par or mauri&; *alue a mauri&.



PB L Price of he ond

$ L ineres or cou/on /a&mens

+ L numer of /eriods o mauri&

& L semi-annual discoun rae or he semi-annual&ield o mauri&

Bond Pricing

1 (1 )(1 )

T

T B t

t

ParValueC P r r =

= +

++∑



Bond Pricing

• You ma& recall ha PV of an annui& "as:

• PV L cQ& 5 5Q5T&;! U

• here 5Q& 5 5Q5T&;! U is called an

annui& facor.• %nd also PV of +erminal Value is:

• Par Value 5Q5Tr;!

• here 5Q5Tr;! is called PV facor.• So Price = Coupon !nnuity actor "r#

$% + Par &alue P& actor "r# $%



Bond Pricing ond /rice.0ls0

cou/on1 =6-&ear mauri& ond"ih /ar *alue of K51666 /a&ing 6semiannual cou/ons of KA6 each.

Su//ose ha ineres rae is annuall& or A /er si0 monhs/eriod. +hen

Price L KA6 %nnui& facor A16;T K5666 PV facor A16;

Price L K969.9A T K9C.6 L K 5666

http://var/www/apps/conversion/tmp/scratch_6/bond%20price.xlsx

http://var/www/apps/conversion/tmp/scratch_6/bond%20price.xlsx



+he )n*erse Relaionshi/ Be"een Bond Pricesand Yields



Bond Prices a Di3eren )neres Raes $ou/on Bond1 $ou/ons Paid Semiannuall&;



$om/licaions

• +he frame"or' for /ricing a onddiscussed here assumes ha:

5. +he ne0 cou/on is e0acl& si0monh a"a&.

7. +he cash ,o"s are 'no"n.

=. +he a//ro/riae re(uired &ield cane deermined.

A. One rae is used o discoun all hecash ,o"s.



$ou/on Rae1 Re(uired Yield and

Price

Coupon Rate ' (ield

Price ' Par Discount

$ou/on Rae L Yield Price L Par Par

$ou/on Rae W Yield Price W Par Premium



Relaionshi/ Be"een Bond Price and +ime if)neres Raes are Inchanged <5.0ls0

• )f he re(uired &ield does no changee"een he ime he ond is /urchased andhe mauri& dae1 "ha "ill ha//en o he/rice of he ond

• For a Bond Selling a Par: as he ond mo*eso"ards mauri& i "ill coninue o sell a /ar*alue. )s /rice "ill remain consan as heond mo*es o"ards he mauri& dae.

• Bond Selling a Discoun:

• Bond Selling a Premium:

http://var/www/apps/conversion/tmp/scratch_6/zbb1.xlsx

http://var/www/apps/conversion/tmp/scratch_6/zbb1.xlsx



Reasons for he change in he BondPrice

5. +here is a change in he re(uired &ield o"ingo changes in he credi (uali& of he issuer.

7. +here is a change in he /rice of he ondselling a a /remium or a discoun1 "ihouan& change in he re(uired &ield1 sim/l&ecause he ond is mo*ing o"ards hemauri&.

=. +here is a change in he re(uired &ield o"ingo a change in he &ield on com/araleonds. i.e.1 change in he re(uired &ield &he mar'e;



$om/uing he Yield or )RR on an&)n*esmen

• +he &ield on an& in*esmen is heineres rae ha "ill ma'e he/resen *alue of he cash ,o"s from

he in*esmen e(ual o he /rice orcos; of he in*esmen.

• Mahemaicall&1 he &ield on an&

in*esmen1 &1 is he ineres raeha sais2es he e(uaion:

• P L $F5Q5T&; T $F7Q5T&;7 TXXX..

$F!Q5T&;!



$om/uing Yield

• P L L5! $FQ 5T&;

here:

$F L $ash ,o" in &ear P L Price of he in*esmen

!L !umer of &ears



$om/uing Yield for a ero $ou/on

Bond

• Y L MQPU5Qn -5

. % 56 &ear <ero cou/on ond "ih amauri& *alue of K56661 selling forKA=9.51 calculae Y

Y L K5666QKA=9.5U5Q56 -5

L5.6A7-5 L 6.6A7..



Measuring Yields

• $urren Yield

• Yield o Mauri&

• Yield o $all

• Yield o Pu

• Yield o ors



$urren Yield of a Bond

• $urren &ield relaes he annual cou/on inereso he mar'e /rice.

• $urren Yield L %nnual K $ou/on Pa&menQ Price

• E0am/le: 1 =6 &ear ond currenl& selling aK578.8.

• $urren Yield L K6QK578.8 L 6.678 or.78.

•

Y+M L .69.• $ou/on Rae ; W $urren Yield .78;WY+M

.69; )



Deermining he %//ro/riae

Re(uired Yield

• e "ill discuss laer ho" one candecom/ose he re(uired &ield for aondQsecuri& ino is com/onen

/ars.



One Discoun rae a//licale o allhe cash ,o"s

• % ond can e *ie"ed as a /ac'ageof <ero cou/on onds1 in "hichcase a uni(ue discoun rae should

e used o deermine *alue of eachcash ,o"s.



$urren Yield

• 4imiaions



$urren Yield 4imiaion..

• +he curren &ield calculaion a'es inoaccoun onl& he cou/on ineres and nooher source of reurn ha "ill a3ec an

in*esors> &ield.• !o consideraion is gi*en o he ca/ial

gainQloss ha he in*esor "ill reali<e "henond is /urchased a a discounQ/remium.

• !o consideraion on rein*esmen ofcou/on ineress.



Yield o Mauri&

• )n /racice1 an in*esor considering he/urchase of a ond is no (uoed a /romisedrae of reurn.

• )nsead he in*esor mus use Bond Price1Mauri& Dae1 $ou/on Pa&mens1 o infer hereurn o3ered & he ond o*er is life.

• Y+M is ofen iner/reed as a measure of ruea*erage rae of reurn ha "ill e earned if i isough no" and held unil mauri&.

• Bond /rice used in he funcion should e here/ored ,a /rice1 "ihou accrued ineres.

Yi ld M i



Yield o Mauri&

•)neres rae ha ma'es he /resen*alue of he ond>s /a&mens e(ualo is /rice

Sol*e he ond formula for r

1

(1 )(1 )

T

T t

t

B

ParValueC P r r =

= +

++

∑



Yield o Mauri&

• 5C &ear 8- Semiannual /a& ond"ih /ar *alue of K5666 selling aK89.A7.

• $ou/on L 8 of K5666 L K86 annual

• $ash ,o" 5. K=C semiannual/a&mens for =6 /eriods.

• $ash ,o" 7. K5666 /rinci/al amouno e recei*ed =6 /eriods from no".



$urren Yield *s. Y+M..

5. Yield o mauri& calculaion a'es inoaccoun no onl& he curren cou/onincome u also an& ca/ial gain or loss

ha he in*esor "ill reali<e & holdinghe ond o mauri&.

7. Y+M consider iming of he cash ,o"s.

=. ) also consider re-in*esmen of he$ou/on ineress1 ho"e*er1 assumes harein*esmen is made on he Y+M onl&.



Relaionshi/ among he $ou/onrae1 $urren Yield1 and Y+M

Bond *elling at Relations,ip

Par $ou/on rae L $urren Yield L Y+M

Discoun $ou/on Rae Z $urren Yield Z Y+M

Premium $ou/on Rae W $urren YieldWY+M

B d P i d Yi ld



• Prices and Yields re(uired raes ofreurn; ha*e an in*erse relaionshi/

• hen &ields ge *er& high he *alue of

he ond "ill e *er& lo"• hen &ields a//roach <ero1 he *alue of

he ond a//roaches he sum of he

cash ,o"s

Bond Prices and Yields

+h ) R l i hi B B d P i



+he )n*erse Relaionshi/ Be"een Bond Pricesand Yields



Yield o $all

• ha if he ond is callale1 and ma& ereired /rior o he mauri& Y+M is noRele*an;.

•

+he /rice a "hich a ond ma& e calledac' is referred o as he call /rice.

• For some issues1 he call /rice is he sameregardless of "hen he issue is called.

• For oher callale issues1 here is a callschedule ha s/eci2es a call /rice for eachcall dae.



Figure 5A.A Bond Prices: $allale andSraigh De

E0am/le 5A A Yield o $all



E0am/le 5A.A Yield o $all



Yield o $all E0am/le:

$onsider an 5-&ear 55 cou/on ond "ih amauri& *alue ofK5666 selling for K 5159. su//ose ha he 2rs calldae is &ears from no" and ha he call /rice isK516CC.

5;+he Presen Value of he cou/on /a&mens isfound using he annui& formula:

KCC 5- 5Q5T&;5UQ&

7; +he Presen Value of he $all /rice is found usinghe PV formula

K56CC 5Q5T&;5U



Yield o Pu

• hen ondholders can force he issuer o u&he issue a a s/eci2ed /rice. %s "ih callaleissue1 /uale issue can ha*e a /u schedule.

• +he schedule s/eci2es "hen he issue can e

/u and he /rice1 called he /u /rice.

• +he Y+P &ield o /u; is he ineres rae hama'es he /resen *alue of cash ,o"s o heassumed /u dae /lus he /u /rice on ha

dae e(ual o he ond /rice.

• PV of $ash Flo"s o /u dae T PV of Pu Price LBond Price



Yield o ors..

• % Pracice in he indusr& is for anin*esor o calculae he &ield omauri&1 &ield o e*er& /ossile call

dae1 and he &ield o e*er& /ossile/u dae.

• +he minimum of all of hese is called

Yield o ors.



$an he Y+M e !egai*e

• S"iss go*ernmen onds are no"eing (uoed "ih negai*e &ields forall mauriies u/ o 56 &ears. +his

/rom/s he (uesion: ho1 in heirrigh mind1 "ould /a& a go*ernmenfor he G/ri*ilege> of lending he

go*ernmen mone&



$an Y+M e !egai*e

• +he <ero or negai*e ond &ields are almoscerainl& relaed in /ar o he desire & largecash-holders o ensure a reurn of cash1 e*enif doing so guaranees a small nominal loss.

• % a ime "hen ?in,aion@ ris' is /ercei*ed oe lo" and here are concerns aou hesafe& of commercial an's1 i could ma'esense for a large holder of cash o lend he

mone& o he go*ernmen a a small negai*e&ield.



$an Y+M e !egai*e

• +ha eing said1 i>s im/oran o rememer ha "earen> reall& dealing "ih 6 or negai*e ond&ields1 "e are dealing "ih 6 or negai*e &ields omauri&. +he ond &ields /romised cou/on;

hemsel*es are sill /osii*e.• +o furher e0/lain1 consider he sim/le h&/oheical

case of a 5-&ear ond "ih /ar *alue of K566 ha/a&s ineres of K7 a he end of he 5-&earduraion. )f he ond is rading a is /ar *alue henoh he &ield and he &ield o mauri& Y+M; "ille 71 u oh &ields "ill e somehing oher han7 "hen he ond>s /rice de*iaes from K566.



$an he Y+M e !egai*e

• For e0am/le1 if he ond>s /rice rises o K56=hen he &ield falls o 5.9A K7QK56=; andhe Y+M falls o negai*e 6.98. +he Y+M inhis e0am/le a'es ino accoun he fac haif he ond is held unil mauri& hen heu&er of he ond a K56= "ill recei*e a K7

ineres /a&men /lus a K566 /rinci/le/a&men1 or a oal reurn of K567 *ersus anoula& of K56=. +he K5 loss on he K56=in*esmen e(uaes o a reurn of negai*e6.98.

)m/licaion of !egai*e



)m/licaion of !egai*e Y+M..

• %n im/licaion is ha someone "ho doesn> /lano hold unil mauri& can sill ma'e a /ro2 on aond "ih a negai*e Y+M. For e0am/le1 someone"ho u&s a S"iss go*ernmen ond "ih a Y+M of

negai*e 6.5 oda& "ill ha*e he o//oruni& ofselling a a /ro2 if he Y+M suse(uenl& falls onegai*e 6.7. +he curren ridiculous *aluaionsof some go*ernmen onds could herefore e

/arl& e0/lained & he elief ha *aluaions "illecome e*en more ridiculous in he fuure1 husenaling oda&>s u&ers o e0i a a /ro2.

Yield S/read Measures for Floaing



Yield S/read Measures for Floaing

Raes Securiies

• +he cou/on rae for a ,oaing rae securi&changes /eriodicall& ased on he cou/on reseformula "hich has is com/onens as hereference rae and he (uoed margin.

• Since he fuure *alue for he reference rae isun'no"n1 i is no /ossile o deermine hecash ,o"s.

• +his means ha Y+M can no e calculaed.

• )nsead here are se*eral con*enionalmeasures used as margin or s/read measurescied & mar'e /arici/ans for ,oaers.

e /rea easures or oa ngR S ii Di M i



Raes Securiies: Discoun MarginMehod

• Se/ 5. deermine he cash ,o"s assuming ha hereference rae does no change o*er he life of he

securi&.

• Se/7. selec a margin s/read.

•

Se/=. discoun he cash ,o"s found in se/ 5 & hecurren *alue of reference rae /lus he margin selecedin se/ 7.

• Se/ A. $om/are he /resen *alue of he cash ,o"s as

calculaed in se/ = "ih he /rice. )f he /resen *alue is

no e(ual o he securi&>s /rice1 go ac' o se/ 7 andr& a di3eren margin.

• For a securi& selling a /ar1 he discoun margin is sim/l&

he s/read o*er he reference rae.

E0am/le



E0am/le..,oaing rae &ield.0ls0

• % si0 &ear ,oaing-rae securi&selling for 99.=69 /a&s a rae asedon some reference rae /lus 6 BPS.

he cou/on rae is rese e*er& si0monhs. %ssume ha curren *alueof he reference rae is 56.

• $ash ,o" L 56.Q7566 L C.A

http://var/www/apps/conversion/tmp/scratch_6/floating%20rate%20yield.xlsx

http://var/www/apps/conversion/tmp/scratch_6/floating%20rate%20yield.xlsx



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Bond Pricing and Bond Yield New -1