fixed income trading strategies 4

7/25/2019 Fixed Income Trading Strategies 4

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Bond Trading Strategies


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2014 BSE Institute Limited

Objective: Session IV- V

At the end of the session, you will be able to -

!nderstand the relationshi" between bond "rice and yield#

!nderstand the $ethods to calculate %yield to $aturity

!nderstand the signi'cance of various ty"es of yields fro$ trading"ers"ective#

!nderstand how the yield curve can be derived#

!nderstand the conce"t of (uration, )odi'ed (uration in bond tradingstrategies#


3/28


Bond *ricing: Interest +ate +is s

Inverse relationshi" between bond "rices and yields#

*rices of a long ter$ bond are $ore sensitive to interest rate changesthan "rices of a short ter$ bond#

*rice of low-cou"on bond are $ore sensitive to interest rate change than"rices of high cou"on bonds#

Interest rate ris is inversely related to the bond&s cou"on rate i#e# "ricesof high cou"on bonds are less sensitive to changes in interest rate than"rices of low cou"on bonds#

An increase in a bond&s T) results in a s$aller "rice change than adecrease in T) of e.ual $agnitude#

The sensitivity of bond "rices to changes in yields increases at adecreasing rate as $aturity increases#

/in : Interest +ate 0 Bond Valuation


4/28


Bond *ricing: T) /inearInter"olation

1o$"licated way of $easuring T) but useful as it "rovides with a range ofan e2"ected yield#

It can also assist us in showing what a s$all deviation, for e2a$"le 34#56to 34#76 can do to the bond "rice

8or$ula:/+ )ar et +ate: /)+9+ )ar et +ate: 9)+/ower Bond *rice /B*; due to 9)+9igher Bond *rice 9B*; due to /)+

T) < /)+ = 9)+ - /)+;

9B* > )ar et *rice;

9B* > /B*;


5/28


Bond *ricing: T) /inearInter"olation

?2a$"le:

Bond 8ace Value:@3 #)ar et *rice:@3 #Bond *rice C 3 6 discount rate: @ DEE#7F#Bond *rice C 35 6 discount rate: @3 5 #3G#

1ou"on +ate:376#1ou"on *ay$ent: @37 # Ter$s to )aturity: years

T)H < 356 = 3 6 - 356;

T) H < 34# G6

/in : T) /inear Inter"olation

3 5 #3G > 3 ;

3 5 #3G > DEE#7F;


6/28


Bond *ricing: 1urrent ields

1urrent ields relates the annual cou"on interest to the $ar et "rice#

Annual Interest*rice of the Bond

The relationshi" between yield to $aturity T); and cou"on rate is asfollows:

Bond at a discount, T) current yield cou"on yield#

Bond at a "re$iu$, cou"on yield current yield T)#

Bond sells at "ar, T) < current yield < cou"on yield#

1urrent ields <


7/28


Bond *ricing: Jeighted ield

Jeighted ield is calculated when an investor is holding a series of bond inhisKher "ortfolio#

Ste"s to calculate:

3; As is the case with all invest$ent assets, the 'rst ste" in calculatingbond "ortfolio is to calculate the $ar et value of "ortfolio#

4; 1alculate individual 1urrent ield of the bond#

5; 1alculate the Jeighted ield by ta ing the "roduct of each individualbond $ar et value and its corres"onding yield#


8/28


Bond *ricing: Jeighted ieldPurchaseDate 7/11/2001

No. ofBonds

MarketValue

Weighted

urrent !ieldou"on #ate Maturit$ !%M

11.&'( '/&/2002 7.)7( *+00 *&)+)&.00 +1*+1.2'

11.1*( ,/1/2002 7.)'( **&0 *7'+0&.'0 +2&&,.01

1).'2( */)0/2002 7.27( *720 &0)+&0.00 +)',0.+,

12.&,( */10/2002 &.*1( *''0 &1&'12.00 +0127.0,

11.00( */2)/200) 7.&)( &0+0 &)'&&,.&0 +'7)*.,+

-u)0007'+.+

0 21&,&).'2

Portfolio

!ield 7.2)(


9/28


Bond *ricing: +ealised ields

+ealised ield > actual yield to the investor in a bond over a given"eriod#

It re"resents the horiMon returns to the investor fro$ all the 5co$"onents of bond return > cou"ons, returns fro$ reinvest$ent of thecou"on and ca"ital gainKloss fro$ selling the bond at the end of theholding "eriod#

+ealised yield to the investor is the rate which e.uates cash Now fro$ all 5sources to the initial cash Now#

/in : +ealised ields


10/28


1allable Bonds

Bonds that allow the issuer to alter the tenor of a bond, by redee$ing it"rior to the original $aturity date, are called callable bonds#

The inclusion of this feature in the bond&s structure "rovides the issuerthe right to fully or "artially retire the bond, and is therefore in thenature of call o"tion on the bond#

The call o"tion "rovides the issuer the o"tion to redee$ a bond, ifinterest rates decline, and re-issue the bonds at a lower rate#

The call o"tion, therefore, can e ectively alter the ter$ of a bond, andcarries an added set of ris s to the investor, in the for$ of call ris , and

re-invest$ent ris #


11/28


Bond *ricing: 1all *rovisions

)ost bonds have call buy; "rovisions >

Allows issuers to re"ay the investor&s "rinci"al early than s"eci'ed date#

It is co$$only P1alledQ when the $ar et interest rate dro"s#

It is also P1alledQ when the issuer sees a surge in its credit .uality#

If the bond is P1alledQ, then the call date is usually one of the two datesthat se$iannual interest is due i#e# ne2t "ay$ent date#

+eason for calling > when $ar et rate dro"s, new bonds can be issuedat a lower interest rate#


12/28


Bond *ricing: ield to 1all

T) is calculated on the assu$"tion that the bond will be called only on $aturity# Ifthe bond is callable before $aturity, how would we $easure the average rate ofreturn for the bonds subject to the call "rovision R

/in : ield to 1all

8ro$ a trading "ers"ective,

Bond $ar et analyst believe that T1 is $ore relevant than T)#

Bond is $ore susce"tible to the "revailing $ar et senti$ents#

T1 is calculated the sa$e way as T) but the TT) will change to the a$ount ofti$e left for the bond to e2"ire or $ature and the call "rice re"laces the "ar value#

Bonds are callable by the issuer if the "revailing $ar et rate is below the Bond&scalculated T)#


13/28


Bond *ricing: Investor *rotection

1all "rotection is the a$ount of ti$e before a newly issued bond iscallable#

1all "rovisions, which $ust e2"licitly state the callable o"tions by theissuer, $ust be fully considered and understood by investors#

Bonds with li$ited or no call "rovisions have higher e2"ected returns toco$"ensate for the ris that the bond $ight be called for rede$"tion#

+e"urchase of the bond by the issuer is done at a slightly higher "ricethan the "revailing $ar et "rice i#e# "re$iu$s are o ered#


14/28


9oriMon Analysis

A $ethod of $easuring the discounted cash Now fro$ an invest$ent,using ti$e "eriods or series that di er fro$ the invest$ent&scontractual $aturity#

The horiMon date $ight be the end of a business cycle or so$e otherdate deter$ined in the "ers"ective of the investor&s overall "ortfoliore.uire$ent#

9oriMon analysis calculation include reinvest$ent assu$"tions, "er$itco$"arison with alternative invest$ents that is $ore realistic in ter$sof individual "ortfolio re.uire$ents than traditional T) calculations#

/in : 9oriMon Analysis


15/28


9olding *eriod +eturns

It is generally "erceived that high yield bonds "rovide higher rate ofreturns which is false#

In "rinci"le, all bonds $ust o er identical rates of return over any holding"eriod#

If Bond A do$inates Bond B, the "ossibility of $ar et forces forcing the"rice of the bond A to dro" or for lower returns Bond B to a""reciate invalue is signi'cant#In other words, we will see a convergence of PreturnsQ of all bonds#

In fact des"ite their di erent T)&s, each bond will "rovide a rate of returnover the co$ing years e.ual to this years short ter$ rate#

/in : 9olding *eriod


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In "rinci"le, des"ite di erent T)&s, each bond will "rovide a rate ofreturn over the co$ing year e.ual to this year&s short ter$ rate#

?2a$"le:

ero 1ou"on Bond 8ace Value: @3Bond *rice: @D4 #D5

TT): 3 year

1a"ital ain: @G7# G 3 -D4 #D5;

+ate of +eturn: @G7# G K @D4 #D5 < F6


17/28



ero 1ou"on 8ace Value: @3Bond *rice: @F73#G

TT): 4 years ear 4 Interest +ate: 3 6 ear 4 Bond *rice: 3 K 3#3 ; < @D D# D#9olding *eriod +eturns:

D D# D > F73#G ; K F73#G < F6

Si$ilarly, a 5 year Mero cou"on bond bought at @G F#55 being soldafter 3 years with 4 nd year li ely interest rate of 3 6 and 5 rd year

rate of 336#*rice for the 5 year bond after one year is3 K 3#3 ; 3#33; < @F3D#+ate of +eturn: F3D > G F#55;K G F#55; < F6


18/28


Ter$ Structure of Interest

Inverse relationshi" between bond "rices and yields#

*rices of a long ter$ bond are $ore sensitive to interest rate changes than"rices of a short ter$ bond#

*rice of low-cou"on bond are $ore sensitive to interest rate change than"rices of high cou"on bonds#

An increase in a bond&s T) results in a s$aller "rice change than adecrease in T) of e.ual $agnitude#

The sensitivity of bond "rices to changes in yields increases at a decreasing

rate as $aturity increases#

Interest rate ris is inversely related to the bond&s cou"on rate i#e# "rices ofhigh cou"on bonds are less sensitive to changes in interest rate than "ricesof low cou"on bonds#


19/28


Bonds: ield 1urve

*lotting of T) against the Ter$s to )aturityU

ield curve shows the ter$ structure of interest rates by "lotting the yield-to-$aturity of all bonds of the sa$e .uality with the $aturities rangingfro$ the shortest to the longest available#

If the short ter$ yield rates are lower, it is called a "ositive yield curve#

If the short ter$ yield rates are higher, it is called a negative yieldcurve#

If the di erence between the$ is not signi'cant, then we will have a Natyield curve#

/in : ield 1urve


20/28


Bonds: ield 1urve


21/28


Bond (uration

(evelo"ed by a 'nancial econo$ist, 8rederic +# )acaulay, duration is anPesti$ate of the econo$ic life of a bond as $easured by the weightedaverage ti$e to recei"t of interest and "rinci"al "ay$entsQ#

In si$"lest of words, it indicates the ti$e re.uired to recover the costincurred i#e# the ti$e it ta es for the cou"ons and "rinci"al to cover thebond "rice incurred#

)ore technically, we attach weight to each of this "ay$ents and the weighta""lied to each "ay$ent ti$e should be "ro"ortional to the total valueof the bond accounted for by that "ay$ent#

/in : (uration ?2"lained


22/28


Bond (uration

In si$"le words, it $easures bond "rice volatility by $easuring the Plengthor lifeQ of a bond#

Signi'cance:

Bond&s duration, $easured in years, shows the bondholders howsensitive the bond&s "rice is to changes in the "revailing interest rate#

Shorter the duration, the less sensitive is a bond&s "rice to Nuctuationsin $ar et interest rate#

In other words, greater the duration of a bond, greater is the "ercentagevolatility#

+ecall, *rices of a long ter$ bond are $ore sensitive to interest ratechanges than "rices of a short ter$ bond#


23/28


Bond )odi'ed (uration

)odi'ed duration is the "ercentage change in the bond "rice for each"ercentage > "oint change in T)# It is also the degree of variance inthe bond "rice for each "ercentage "oint change in the T)#

*ercentage change in the bond "rice is just the "roduct of $odi'edduration and the "ercentage change in the bond&s T)#

)odi'ed (uration < )acaulay (uration K 3= T)Kn;;

/in : )odi'ed (uration


24/28


1onve2ity

)odi'ed duration $easures the sensitivity of bond "rices to changes in T)#

1onve2ities $easures the sensitivity of $odi'ed duration to changes ininterest rates#

In other words,)odi'ed duration $easures the s"eed at which bond "rices changes to

changes in T)#

1onve2ities $easures the rate of acceleration i#e# degree of acceleration atwhich bond "rices changes to changes in T)#

* H 3 =y; 4

3 T

t=1

18 t

3 =y ; t

t 4 = t;)1onve2ities A8ocused A""roach#

fixed income trading strategies 4

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