bonds overview pricing yield

7/24/2019 Bonds Overview Pricing Yield

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Overview of Fixed Income

Markets


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Features of Debt Securities

Bond and Bond Indenture

Bond Covenants Negative Covenants: restrictions on

asset sale, additional borrowing,negative pledge of collateral

Armative Covenants: maintaincertain ratios and protability


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Types of Bonds

According to Coupon ratestructure:

Straigt Bond

!ero Coupon bonds

Step "p notes

Deferred Coupon Bonds

F#oating rate securities$ Floating rate bonds, inverse oater, ination indexed

bonds

Floor and cap in oater


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Types of Bonds

According to redemption andretirement:

%on&'morti(ing securities$ Bu##et Bonds

'morti(ing securities) *repaymentOptions$ risk wi#e investing in MBS

Ca## provisions

%on refundab#e bonds) +edemption vs,+efunding,


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Options -mbedded in Bonds

Options with investor:

Conversion Option

Put provision

Floors

Options with issuer

Call provision

Prepayment Option

Accelerated Sinking Fund

Caps


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+isks 'ssociated wit Investingin Bonds

Interest rate risk

.ie#d Curve +isk

Ca## +isk *repayment +isk

+einvestment +isk


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+isks 'ssociated witInvesting in Bonds

Credit risk /Credit spread risk 0downgrade risk1

2i3uidity +isk

+isk in F#oating rate Bonds

Reset risk: if reset period increases

Cap risk: if coupon cannot go beyond a value

Formula/spread risk: if spread above referencereects te credit risk! ten re"uired return #illbe e"ual to coupon and $ond % par else di&er'


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-xcange +ate risk

%or a &' investor Which of the followingstatements concerning the e(change rate

risk of investing in foreign onds is mostaccurate? f the foreign currenc#:

A)appreciates* the ond+s coupon increases!

")depreciates* ond investors lose* all else

e,ual! C)depreciates* the ond+s coupon pa#ments

will turn into more &!'! dollars!


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In4ation risk

Sovereign +isk

5o#ati#ity +isk/for bonds wit options1


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'uction of Bond Securities

"niform *rice 'uction /book bui#ding1

Discriminatory *rice 'uction


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Bond Market Index

Bencmark for measuringperformance especia##y if a portfo#iois being managed on performance

fee basis,

Bencmark for bond index funds

Determining risk and return of abond portfo#io,


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Bui#ding and Maintaining aBond Index

"niverse of Bonds is broader and morediverse tan stocks) di6erent issuers7maturity7 type,

"niverse of bonds canges constant#y)severa# bond issues by variouscorporations7 canging caracteristics7

specia# features etc, 5o#ati#ity of bonds

*rob#ems in bond pricing due to #i3uidity,


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Bond 5a#uation

' bond as coupon interest of 89: andF5; +s, 8999, If time to maturity is 89years7 wat is te price of te bond

given a yie#d of at if te interest payment is semi

annua#=

Ca#cu#ate te va#ue of a 89 yr (erocoupon bond wit F5; 8999 and yie#dof


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Bond 5a#uation

Discount7 *remium and par va#uebonds

5a#ue wit time

' 89: bond as .TM ;y=


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Bond .ie#d

>at is yie#d=

Current ield

>at is te current yie#d of a @9 yearbond wit par va#ue of +s 8999coupon rate of A: paid semiannua##ytrading +s,


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Bond .ie#d

ield to .aturit#

/otal return ; Coupon Interest +ecovery of *rincipa# a#ong wit capita#gain or #oss +einvestment Income

' bond as E yr maturity7 F5; +s,89997 Issue price ;


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.ie#d to maturity

Consider a @9 year G8999 par va#ue bondwit A: coupon rate /semi annua#payments1 wit a fu## price of G


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.TM vs, +ea#i(ed .ie#d

>at if reinvestment rate canges to at is te rea#i(ed yie#dnow=

'n investor as a bond of maturity E9years7 paying annua# coupon of ,:purcased +s,


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Bond prices and .ie#ds

+einvestment risk

0ractice #ourself:

Consider a bond wit


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Bond prices and .ie#ds

"ond price vs ields

' bond as face va#ue +s, 8999coupon of A: paid semi annua##y,>at is its price if te .TM of tebond is

i1 E: ii1 A: iii1 8@:

'ns$ i189


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.ie#d to ca##

'n


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.ie#d to >orst

It is te worst yie#d outcome of a## tegiven possib#e ca## provisions of tebond

For -g$ ' @9 yr7 89: semiannua# paybond as a fu## price of 88@ and can beca##ed at 89@ in Hve years and at par in

seven years, Ca#cu#ate te .TM7 .TC 7.ie#d to Hrst *ar ca##,

>at is yie#d to worst=


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C#ean *rice vs, Dirty *rice

Dirty *rice ; C#ean *rice 'ccruedInterest

Ca#cu#ation of 'ccrued Interest$

Coupon(No of days since lastco!pon"no of days between twoco!pons payment dates#

Day Count Conventions$ E9LEA97'ctua#LEA97 'ctua#LEA7 'ctua#L'ctua#


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Measuring Interest rate risk

Cange in price due to cange inyie#d

Measured by D"+'TIO%

Measures interest rate senstivity


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Duration

Concept 8

Weighted time to maturit#1.acula#2s 3uration)

Ca#cu#ate te duration of a bond witface va#ue 8999 coupon rate


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Duration

'dding a Ca## option vs, duration

'dding a *ut option vs, duration

So $ig%er (&ower# co!pon means &ower

(%ig%er# d!ration

&onger (s%orter# mat!rity means

%ig%er (&ower# d!ration $ig%er (lower# mar'et yield means

&ower (%ig%er# d!ration


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Duration

Concept 4

S#ope of *rice .ie#d Curve) Hrst derivativeof price yie#d curve w,r,t yie#d /macu#ay

and modiHed duration Duration ; cange in priceLcange in

yie#d

's s#ope of price yie#d curve of bond isnegative +JS is negative

Cange in price ; & D cange in yie#d

Measures interest rate risk


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Duration

Concept 5

Sows te percentage cange inprice for one percent cange in yie#d,Measures interest rate senstivity

Say duration is A,


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Duration Nuestions

' bond as a duration of , If yie#dincreases from : to


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*5B*

It is te cange in va#ue /rupeeterms1 of a bondLportfo#io wen yie#dcanges by 8 basis point or 9,98:

It can be ca#cu#ated direct#y byHnding price at new yie#d or viaduration

06"0 7 duration ( 8!8889 ( ondvalue


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Convexity

'n increase in price of a bond wit 8:decrease in yie#d is more tan adecrease in price of te bond wit 8:

increase in yie#d, .ie#d ; 89:7 time ; E yrs7 F5 ; 8999

coupon ; : paid annua##y, >at is te

price if .TM ; : and if .TM ; 88: >at do you observe in terms of

percentage cange in price=


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Convexity

+eason$ Convexity

More convex a bond) better it is

Measures cange in Duration) secondderivative of price w,r,t yie#d dividedby bond price

2P

2

y

= 1

(1+y)2

CFt

(1+ y)t(t2 + t)

t=1

N

Convexity = 1

P

2P

2y


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Convexity

Conve(it# makes .acula#2s and.odied duration less relialemeasure of risk!

-6ective Duration is suitab#e for bonds

Due to presence of convexity as ittakes average price cange

In case of embedded options in a bond


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Convexity

Ca##ab#e bonds ave negativeconvexity, So price fa## is more tanprice rise7 ence average price

cange captured by e6ectiveduration is usefu#,


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-6ective Duration

Te formu#a for ca#cu#ating tee6ective duration of a bond is$

-6ective duration ; /bond pricewen yie#ds fa## &bond price wenyie#ds rise1 L @ /initia# price1 /cange in yie#d in decima# form1


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-6ective Duration

0ractice ;uestion

Suppose a ca##ab#e bond as a ca##price of G899 is se##ing today forGat is te e6ectiveduration of te bond=


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Duration and Convexitye6ect

Conve(it# makes duration aloneinsu


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Duration does not a#one measure teentire price cange e6ect

percentage cange in price ;duration e6ect convexity e6ect

P&duration x / Qy1 Pconvexity / Qy1@R x 899

If Qy is in decima# convert eac effectback to percentage,

i d C i


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'ame ,uestion as earlier

' bond as

bonds overview pricing yield

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