Bond Pricing and Bond Yield New

7/24/2019 Bond Pricing and Bond Yield New

1/61

Valuing Bonds:Bond Pricing and Bond

YieldDr. Himanshu Joshi

FORE School of Managemen!e" Delhi


2/61

Ma#or $lasses of Financial %sses orSecuriies

Mone& mar'e

Bond mar'e

E(ui& Securiies )ndices

Deri*ai*e mar'es


3/61

+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


4/61

Ris' in Fi0ed )ncomeSecuriies


5/61


6/61

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


7/61

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


8/61

Bond Price


9/61

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.


10/61

$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


11/61

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


12/61

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.


13/61

$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.


14/61

)n,aion Ris'

Infation riskis 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.


15/61

E*en Ris'

Some de securiies ma& e sensii*e o e*enssuch as hosile reorgani


16/61

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.


17/61

+a0 Ris'

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

de*elo/ed an uncerain& regardingheir a0 saus1i could o lead o a/rice loss.


18/61

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.


19/61

$ou/on Rae on a Bond..

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

Maturity Premium


20/61

Bond Pricing


21/61

Face or /ar *alue

$ou/on rae

ero cou/on ond

$om/ounding and /a&mens

%ccrued )neres

)ndenure

Bond $haracerisics


22/61

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.


23/61

%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.


24/61

%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.


25/61

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.


26/61

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&.


27/61

PBL 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

TB t

t

ParValueCPrr=

= +

++


28/61

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# $%


29/61

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_3/bond%20price.xlsxhttp://var/www/apps/conversion/tmp/scratch_3/bond%20price.xlsx


30/61

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


31/61

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


32/61

$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.


33/61

$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


34/61

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


35/61

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;


36/61

$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&;7TXXX..

$F!Q5T&;!


37/61

$om/uing Yield

P L L5! $FQ 5T&;

here:

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

!L !umer of &ears


38/61

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

Bond

Y L MQPU5Qn-5

. % 56 &ear


39/61

Measuring Yields

$urren Yield

Yield o Mauri&

Yield o $all

Yield o Pu

Yield o ors


40/61

$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; )


41/61

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.


42/61

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

% ond can e *ie"ed as a /ac'ageof


43/61

$urren Yield

4imiaions


44/61

$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


45/61

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


46/61

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

Tt

t

B

ParValueCPrr=

= +

++


47/61

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".


48/61

$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


49/61

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

Bond *elling at Relations,ip

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

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

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

B d P i d Yi ld


50/61

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


51/61

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


52/61

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.


53/61

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

E0am/le 5A A Yield o $all


54/61

E0am/le 5A.A Yield o $all


55/61

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


56/61

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


57/61

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.

Yi ld S d M f Fl i


58/61

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


59/61

/ gRaes Securiies: Discoun Margin

Mehod

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


60/61

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
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Bond Pricing and Bond Yield New