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BONDS

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Introduction

Bonds refer to debt instruments bearing interest on maturity. In simple terms,organizations may borrow funds by issuing debt securities named bonds, having a fixedmaturity period (more than one year) and pay a specified rate of interest (coupon rate)

on the principal amount to the holders. Bonds have a maturity period of more than oneyear which differentiates it from other debt securities like commercial papers, treasurybills and other money market instruments.

hus a bond is like a loan! the issueris the borrower (debtor), the holderis the lender(creditor), and the couponis the interest. Bonds provide the borrower with external funds

to finance long"term investments, or, in the case of government bonds, to finance currentexpenditure.

Bonds and stocks are both, securities but the ma#or difference between the two is that(capital) stockholders have an e$uity stake in the company (i.e., they are owners),whereas bondholders have a creditor stake in the company (i.e., they are lenders).

%nother difference is that bonds usually have a defined term, or maturity, after which thebond is redeemed, whereas stocks may be outstanding indefinitely. %n exception is aconsol bond, which is a perpetuity (i.e., bond with no maturity).

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Features of Bonds

he most important features of a bond are!&ominal, 'rincipal or ace %mounthe amount over which the issuer pays interest,and which has to be repaid at the end.Issue pricehe price at which investors buy the bonds when they are first issued.he net proceeds that the issuer receives are calculated as the issue price, lessissuance fees, times the nominal amount.*aturity datehe date on which the issuer has to repay the nominal amount. %slong as all payments have been made, the issuer has no more obligations to the bond

holders after the maturity date. he length of time until the maturity date is oftenreferred to as the term or maturity of a bond.+ouponhe interest rate that the issuer pays to the bond holders. sually this rateis fixed throughout the life of the bond. he name coupon originates from the fact thatin the past, physical bonds were issued which had coupons attached to them. -ncoupon dates the bond holder would give the coupon to a bank in exchange for the

interest payment.+oupon dateshe dates on which the issuer pays the coupon to the bond holders.It can be paid $uarterly, semi"annually or annually.

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TYPES OF BONDS

Municipal Bonds:

*unicipal bonds are debt obligations issued by states, cities, countries and othergovernmental entities, which use the money to build schools, highways, hospitals,sewer systems, and many other pro#ects for the public good.hen you purchase a municipal bond, you are lending money to a state or local

government entity, which in turn promises to pay you a specified amount of interest(usually paid semiannually) and return the principal to you on a specific maturity date.&ot all municipal bonds offer income exempt from both federal and state taxes. hereis an entirely separate market of municipal issues that are taxable at the federal level,but still offer a stateand often localtax exemption on interest paid to residents ofthe state of issuance. *ost of this municipal bond information refers to munis which

are free of federal taxes.

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Government Bonds! /overnment Bonds are securities issued by the /overnment forraising a public loan or as notified in the official /azette. hey consist of /overnment'romissory &otes, Bearer Bonds, 0tocks or Bonds held in Bond 1edger %ccount. heymay be in the form of reasury Bills or 2ated /overnment 0ecurities.

/overnment 0ecurities are mostly interest bearing dated securities issued by 3BI onbehalf of the /overnment of India. /-I uses these funds to meet its expenditurecommitments. hese securities are generally fixed maturity and fixed coupon securitiescarrying semi"annual coupon. 0ince the date of maturity is specified in the securities,these are known as dated /overnment 0ecurities, e.g. 4.567 /-I 5894 is a +entral/overnment 0ecurity maturing in 5894, which carries a coupon of 4.567 payable half

yearly.Features of Government SecuritiesIssued at face value&o default risk as the securities carry sovereign guarantee.%mple li$uidity as the investor can sell the security in the secondary marketInterest payment on a half yearly basis on face value

&o tax deducted at source+an be held in 2"mat form.3ate of interest and tenor of the security is fixed at the time of issuance and is notsub#ect to change.3edeemed at face value on maturity*aturity ranges from of 5":8 years.

0ecurities $ualify as 013 investments (unless otherwise stated).

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Mortae and !sset Bac"ed Bonds:*ortgage"backed securities (*B0) and asset"backed securities (%B0) represent the largest segment of the global bond markettoday. In simple terms, investing in *B0 means lending your money to hundreds ofindividual mortgage borrowers across the country. In return for a higher yield than

reasury notes, investors are sub#ect to added ;prepayment; risk, meaning moneyinvested may be repaid much sooner than maturity.!enc# MBS

*ortgage bonds which are guaranteed by a government agency or government"sponsored enterprise.Non !enc# MBS

*ortgage bonds which are issued by banks and financial companies not associatedwith a government agency. hese securities have no credit guarantee other than the$uality of the loans behind them, and any other structural credit protection provided bythe terms of the bond deal they belong to.!sset Bac"ed Securities

Bonds that represent an investment in a pool of consumer or commercial loans. or

example, auto loans or credit card loans are commonly pooled to make asset backedsecurities. or unknown historical reasons, bonds backed by high $uality mortgageloans are considered *ortgage Backed 0ecurities (*B0) despite the fact thattechnically they fall into the broader definition of %sset Backed 0ecurities (%B0). Bondsbacked by home e$uity loans and other home loans less than high $uality areconsidered %sset Backed 0ecurities.

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$orporate Bonds

+orporate bonds are debt obligations issued by private and public corporations. heyare typically issued in multiples of 9,888 and

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%ero $oupon Bonds

>ero coupon bonds are bonds that do not pay interest during the life of the bonds.Instead, investors buy zero coupon bonds at a deep discount from their face value,which is the amount a bond will be worth when it ;matures; or comes due. hen azero coupon bond matures, the investor will receive one lump sum e$ual to theinitial investment plus the imputed interest, which is discussed below.

he maturity dates on zero coupon bonds are usually long"term. hese long"termmaturity dates allow an investor to plan for a long"range goal, such as paying for achild?s college education. ith the deep discount, an investor can put up a smallamount of money that can grow over many years.he price of a zero"coupon bond can be calculated by using the following formula!

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&o' is t(e %ero $oupon Bond Effective Yield Formula Derived)

he formula for calculating the effective yield on a discount bond, or zero couponbond, can be found by rearranging the present value of a zero coupon bondformula!

his formula can be written as

his formula will then become

By subtracting 9 from the both sides, the result would be the formula

where! @ ace value r @ investorAs re$uired annual yield < 5t @ number of years until maturity x 5

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*is"s of Investin in Bonds

Interest rate ris"hen interest rates rise, bond prices fall conversely, when ratesdecline, bond prices rise. he longer the time to a bond?s maturity, the greater its

interest rate risk.*einvestment ris"hen interest rates are declining, investors have to reinvesttheir interest income and any return of principal, whether scheduled or unscheduled,at lower prevailing rates.Inflation ris"Inflation causes tomorrow?s rupee to be worth less than today?s inother words, it reduces the purchasing power of a bond investor?s future interestpayments and principal, collectively known as Ccash flows.D Inflation also leads tohigher interest rates, which in turn leads to lower bond prices.Mar"et ris"he risk that the bond market as a whole would decline, bringing thevalue of individual securities down with it regardless of their fundamentalcharacteristics.

Default ris"he possibility that a bond issuer will be unable to make interest orprincipal payments when they are due. If these payments are not made according tothe agreements in the bond documentation, the issuer can default

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$redit *atin !encies rate the debt instruments of companies. hey do not ratethe companies, but their individual debt securities. 3ating is an opinion regarding thetimely repayment of principal and interest thereon It is expressed by assigningsymbols, which have definite meaning. % rating reflects default risk. 3atings arenot a guarantee against loss. hey are simply opinions based on analysis of the risk

of default. hey are helpful in making decisions based on particular preference ofrisk and return. % company, desirous of rating its debt instrument, needs to approacha credit rating agency and pay a fee for this service.

T(e determinants of ratins

he default"risk assessment and $uality rating assigned to an issue are primarilydetermined by three factors "

i) he issuerAs ability to pay! 3atio analysis is used to analyse the present and futureearning power of the issuing corporation and to get insight into the strengths andweaknesses of the firm.ii) he strength of the security ownerAs claim on the issue! o assess the strength ofsecurity ownerAs claim, the protective provisions in the indenture (legal instrumentspecifying bond ownersA rights), designed to ensure the

safety of bondholderAs investment, are considered in detail.iii) he economic significance of the industry and market place of the issuer! hefactors considered in regard to the economic significance and size of issuer includes!nature of industry in which issuer is, operating (specifically issues like position in theeconomy, life cycle of the industry, labour situation, supply factors, volatility etc.),and the competition faced by the issuer (market share, technological leadership,

production efficiency, financial structure, etc.)

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*!TING MET&ODO+OGY

Fey areas considered in a rating include the following!i) Business *is" : To ascertain -usiness ris". t(e ratin agency considersIndustryAs characteristics, performance and outlook, operating position (capacity,

market share, distribution system, marketing network, etc.), technologicalaspects, business cycles, size and capital intensity.ii) Financial *is" : To assess financial ris". t(e ratin aenc#takes into account various aspects of its inancial *anagement (e.g. capitalstructure, li$uidity position, financial flexibility and cash flow ade$uacy, profitability,leverage, interest coverage), pro#ections with particular emphasis on the components

of cash flow and claims thereon, accounting policies and practices with particularreference to practices of providing depreciation, income recognition, inventoryvaluation, off"balance sheet claims and liabilities, amortization of intangible assets,foreign currency transactions, etc.iii) Manaement Evaluation : Manaement evaluation includes consideration ofthe background and history of the issuer, corporate strategy and philosophy,

organizational structure, $uality of management and management capabilities understress, personnel policies etc.iv) Business Environmental !nal#sis : T(is includes regulatory environment,operating environment, national economic outlook, areas of special significance tothe company, pending litigation, tax status, possibility of default risk under a varietyof scenarios.

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$*EDIT *!TING !GEN$IES IN INDI!

$*ISI+ : T(is 'as set/up -# I$I$I and 0TI in 1233. and rates debt instruments.&early half of its ratings on the instruments are being used.$*ISI+ evaluation is carried out -# professionall# ,ualified persons and

includes data collection, analysis and meeting with key personnel in the company todiscuss strategies, plans and other issues that may effect ,evaluation of thecompany. he rating ,process ensures confidentiality. , -nce the company decidesto use rating, +3I0I1 is obligated to monitor the rating over the life of the debtinstrument.

S#m-ol4*atin cateor#56 Description 4'it( reard to t(eli"eli(ood of meetin t(e de-to-liations on time5

%%% Gighest 0afety

%% Gigh 0afety

% %de$uate 0afety

BBB *oderate 0afety

BB Inade$uate 0afety

B Gigh 3isk

+ 0ubstantial 3isk

2 2efault

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I$*! : I$*! 'as promoted -# IF$I in 12216he factors that I$*! ta"es intoconsideration for ratin depend on the nature of borrowing entity. he inherentprotective factors, marketing strategies, competitive edge, competence andeffectiveness of management, human resource development policies and practices,hedging of risks, trends in cash flows and potential li$uidity, financial flexibility,asset $uality and past record of servicing of debt as well as government policiesaffecting the industry are examined.

S#m-ol4*atin cateor#56

Description 4'it( reard to t(e li"eli(ood ofmeetin t(e de-t o-liations on time5

1%%% highest"credit"$uality H lowest credit risk.

1%% high"credit"$uality H low credit risk.

1% ade$uate"credit"$uality H average credit risk.

1BBB moderate"credit"$uality H higher than average credit

risk.1BB inade$uate"credit"$uality H high credit risk.

1B risk"prone"credit"$uality H very high credit risk.

1+ poor"credit"$uality H limited prospect of recovery.

12 lowest"credit"$uality H low prospect of recovery.

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$!*E : $!*E is a credit ratin and information services company promoted byI2BI #ointly with investment institutions, banks and finance companies. he companycommenced its operations in -ctober 9:.In January 96, +%3E commencedpublication of $!*E7IE8. a ,uarterl# 9ournal of $!*E ratins6 In addition to t(e

rationale of all accepted ratings, +%3EKIE often carries special features of interestto issuers of debt instruments, investors and other market players.

S#m-ol4*atin cateor#56

Description 4'it( reard to t(e li"eli(ood ofmeetin t(e de-t o-liations on time5

+%3E %%% highest"credit"$uality H lowest credit risk.

+%3E %% high"credit"$uality H low credit risk.

+%3E % ade$uate"credit"$uality H average credit risk.

+%3E BBB moderate"credit"$uality H moderate credit risk.

+%3E BB moderate credit risk.

+%3E B high credit risk.

+%3E + Kery high credit risk.

+%3E 2 2efault or expected to be default.

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Internationally acclaimed credit rating agencies such as Mood#s, Standard andPoors . Duff and Fitc(have been offering rating services to bond issuers over avery long time. he bond issuers pay the rating agency to evaluate the $uality of thebond issue in order to increase the information flow to investors and hopefully

increase the demand for their bonds. he rating agency determines the appropriatebond rating by assessing various factors.

*atin $ateor# of $redit !enc# Firms

Mood#s E;planation

%aa Best $uality

%a Gigh $uality% Gigher"medium gradeBaa *edium gradeBa 'ossess speculative elementsB /enerally lack characteristics of desirable investment+aa 'oor standing may be in default

+a 0peculative in a high degree often in default+ 1owest grade

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Standard < Poors E;planation

%%% Gighest grade%% Gigh grade

% pper medium gradeBBB Medium grade

BB Lower medium grade

B Speculative

+++"++ -utright speculation+ 3eserved for income bonds

DDD-DD In default, with rating indicating relative salvage value

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7alue of a -ond

he value of a debt security today is the present value of the promised future cashflows" the interest and the maturity value. herefore, the present value of a debt isthe sum of the present value of the interest payments and the present value of the

maturity value.

B8@ I9< (9Lkd)9

LI5< (9Lkd)5

L I:< (9Lkd):

LMMMM..I9LBn< (9Lkd)n

here,

B8@'resent value of security

Bn@*aturity value of security

I @ Interest paymentkd@Nield

*elation -et'een t(e coupan rate. Price of t(e -ond and t(e #ield

OIf coupan rate P Nield, the security is worth more than its face valueIt sells atpremiumOIf coupan rate Q Nield, the security is worth less than its face valueIt sells atdiscount

OIf coupan rate @ Nield, the security is valued at face value.

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Bonds Nieldshe yield of a bond is, the return on bond.he yield is expressed as an annualpercentage of the face value. Gowever, yield is a little more complicated than thecoupan rate. here are several different measures of yield!

&ominal yield! It is e$ual to coupon rate that is the return on the bond withoutaccounting for any outside factors. If you purchase a bond at par value and hold tomaturity, this will be the annual return you receive on the bond.+urrent yeild! It is a measure of the return on the bond in relation to the currentprice.Nield to call! he rate of return that an investor would earn if he bought a callable

bond at its current market and held it until the call date given that th bond was calledon the call date.Nield to *aturity

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Yield To Maturit#

he rate of return that an investor would earn if he bought the bond at its currentmarket price and held it until maturity, is called as N* %lternatively,it represents the

discount rate which e$uates the discounted value of a bonds?s future cash flows to itscurrent market price. N* is the overall return on the bond if it is held to maturity. Itreflects all the interest payment that are available through maturity and the principalthat will be repaid,and assumes that all coupan payments will be reinvested at thecurrent yield on the bond. his is the most valuable measure of yield because itreflects the total income that you can receive.

N*@ RIL (*"')

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2uration -f Bond

he term duration is a measurement of how long in years it takes for the price of abond to be repaid by its internal cash flows. 0ince a zero coupon bond doesn?t pay

any intermediate cash flows and the entire money is available only on maturity,duration of a zero coupon bond is e$ual to maturity period. -n the same lines sincecoupon bonds, pays coupons, we get our price much earlier to maturity period.herefore, duration of a coupon bond will always be less than maturity period.

Macaulay Duration

he formula usually used to calculate a bondAs basic duration is the *acaulayduration, which was created by rederick *acaulay in 9:4, although it was notcommonly used until the 9T8s. *acaulay duration is calculated by adding theresults of multiplying the present value of each cash flow by the time it is receivedand dividing by the total price of the security. he formula for *acaulay duration is asfollows!

n @ number of cash flows i @ re$uired yield* @ maturity (par) value t @ time to maturity+ @ cash flow ' @ bond purchase price

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0teps for calculation!

2etermine the bond cash flows till maturity.2etermine the 'K factor using N*.*ultiply the 'K actor into cash flows to find present value of cash flows.%dd the 'K of all cash flows to determine the market value of the bond.2ivide each year?s cash flows by the market value of bond.*ultiply this factor by the corresponding years i.e. 9 figure by 9, year 5 figure by 5 etc.he sum of all final values is the duration.

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Modified Duration

Modified durationis a modification of the *acaulay duration to estimate interest raterisk, calculating the change in a bond?s price to a change in its yield to maturity. his

is the approximation of the percentage change in the price of the bond to thepercentage change in yield. or bonds without any embedded features, bond priceand interest rate move in opposite directions, so t(ere is an inverse relations(ip-et'een modified duration and an appro;imate 1> c(ane in #ield. Because themodified duration formula shows how a bondAs duration changes in relation to interestrate movements, the formula is appropriate for investors wishing to measure the

volatility of a particular bond. *odified duration is calculated by the following formula!

O*

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2uration %pplication! +alculating bond value change

2uration measures interest rate risk , i.e., changes in present value of securitieswhen interest rates change. Fnowing duration we can calculate the price sensitivityas follows!

Percent c(ane in -ond value ? DM @ c(ane in #ield

here,2*@*odified duration

If yield rates rose from 987 to 98.=7, a 8.=7 increase in rates, *acaulay?s formulawould predict a percent change in value as!'ercent change in bond value @ 2* U numerical change in stated yield.6

@ V 5.W6: U (L 8.=)= 1!""#$

he price change calculated by *2uration would be X44.6 U V9.:557 @ VX99.44

he new bond price would be approximately X44.6 V X99.44 @ X44W.W9. e canconfirm the percent change and new price by entering these data into aspreadsheet! he change takes place in the 'K actor as a result of the change inmarket yield.

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Bond +onvexity! +onvexity measures the rate of change in modified duration asyield change. +onvexity refers to the shape of the price"yield relationship and can beused to refine the modified duration approximation of the sensitivity of prices tointerest rate changes. Bond +onvexity is defined formally as t(e deree to '(ic(

t(e duration c(anes '(en t(e #ield to maturit# c(anes. It can be used toaccount for the inaccuracies of the *odified 2uration approximation. -n top of that, ifwe assume two bonds will provide the same duration and yield then the bond withthe greater convexity will be less affected by interest rate change.

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%pplication of +onvexityhe convexity improves the duration approximation for bond price changes. In otherwords, knowing convexity, we can find a better approximations of bond price change

for every change in yield, than what we can find using duration. It is a measure of therelationship between bond prices and bond yields that demonstrates how the durationof a bond changes as the interest rate changes. +onvexity is used as a risk"management tool, and helps to measure and manage the amount of market risk towhich a portfolio of bonds is exposed.he formula is!

%P=ModDi+1

2Convexity(i )2

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9. % bond of 3s. 9888 bearing a coupon rate of 957 is redeemable at par in 98year. ind out the value of the bond if!(a)3e$uired rate of return is 957(b)3e$uired rate of return is 967 and the maturity period is 4 yrs

(c)3e$uired rate of return is 957 and redeemable at 3s.98=8 after 98 years.

5. % bond of 3s.9888 bearing a coupon rate of 957 p.a. payable half"yearly isredeemable after 6 years at par. ind out the value of the bond given that re$uiredrate of return is 967.

:. % bond of 3s.98888 bearing coupon rate 957 and redeemable in 4 yrs at par isbeing traded at 3s. 98W88. ind out N* of the bond.

6. Bond % has face value of 3s.988, +oupon rate 9=7p.a., maturity period W years,maturity value 3s.988 and current market price 4.= and N* is 947.+alculateduration of bonds.

=. % = year bond with 47 coupon rate and maturity value of 3s.9888 is currentlyselling at 3s.5=. ind N*.

W he following data is available for a YN> Bond face value 3s 9888 +oupon rate

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W. he following data is available for a YN> Bond, face value 3s.9888, +oupon rate9W7p.a., life of bond W yrs, maturity value 3s.9888,current market price W6.=.

Nou are re$uired to calculate!9) N* 5)2uration of bond :)Kolatility of bond

T.wo bonds % H B have a par value of 3s.98888 and N* of 7.Both mature after 6years. % pays annual coupon of 987 and B pays annual coupon ofT.=7.+alculate duration of both bonds % H B.

4. he following data is available for a bond!

+alculate N*, 2uration H volatility of this bond.

. % bond can be ac$uired with a 6 year maturity. he bond has a coupon of 957payable annually and is priced in the market at 3s.988. hat is the duration of the

bondZ hat would be the percentage change in price if interest rates rose to 9:7.

Face Value Rs.1ooo

Coupon 16%p.a.

Years to maturity 6 Years

Redemption Value Rs.1000

Current maret price Rs. !"0

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95. +alculate convexity given the following with respect to a coupon bond.+oupon rate@ W7, erm@ = years, yield to maturity@ T 7(:.=7 semi annually) and'rice@3s. =4.65

9:. 2etermine the convexity of an 47 coupon bond with two years to maturity an azero coupon bond with 58 years to maturity. he yield"to"maturity on these bond is987 p.a. ind out the price change of the zero coupon bond,and 47 coupon bond, ifthe yield changes to 997 using!a)sing duration formulab)sing +onvexity

c)%ctual bond price formula

96. +alculate the price of a zero"coupon bond that is maturing in five years, has a parvalue of 3s.9,888 and a re$uired yield of W7.

9=. +alculate the yield of a zero"coupon bond that is maturing in ten years, has a par

value of 3s.9,888 and purchase price is 3s. =68.