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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#
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2014 BSE Institute Limited
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 $aturity increases#
/in : Interest +ate 0 Bond Valuation
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2014 BSE Institute Limited
Bond *ricing: T) /inearInter"olation
1o$"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*;
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2014 BSE Institute Limited
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;
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2014 BSE Institute Limited
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$, cou"on yield current yield T)#
Bond sells at "ar, T) < current yield < cou"on yield#
1urrent ields <
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2014 BSE Institute Limited
Bond *ricing: Jeighted ield
Jeighted ield is calculated when an investor is holding a series of bond inhisKher "ortfolio#
Ste"s to calculate:
3; As is the case with all invest$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 $ar et value and its corres"onding yield#
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2014 BSE Institute Limited
Bond *ricing: Jeighted ieldPurchaseDate 7/11/2001
No. ofBonds
MarketValue
Weighted
urrent !ieldou"on #ate Maturit$ !%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)(
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2014 BSE Institute Limited
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
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2014 BSE Institute Limited
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 #
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2014 BSE Institute Limited
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 $ar et rate dro"s, new bonds can be issuedat a lower interest rate#
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2014 BSE Institute Limited
Bond *ricing: ield to 1all
T) is calculated on the assu$"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 $ar et rate is below the Bond&scalculated T)#
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2014 BSE Institute Limited
Bond *ricing: Investor *rotection
1all "rotection is the a$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#
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2014 BSE Institute Limited
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
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2014 BSE Institute Limited
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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2014 BSE Institute Limited
9olding *eriod +eturns
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$"le:
ero 1ou"on Bond 8ace Value: @3Bond *rice: @D4 #D5
TT): 3 year
1a"ital ain: @G7# G 3 -D4 #D5;
+ate of +eturn: @G7# G K @D4 #D5 < F6
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9olding *eriod +eturns
ero 1ou"on 8ace Value: @3Bond *rice: @F73#G
TT): 4 years ear 4 Interest +ate: 3 6 ear 4 Bond *rice: 3 K 3#3 ; < @D D# D#9olding *eriod +eturns:
D D# D > F73#G ; K F73#G < F6
Si$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
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2014 BSE Institute Limited
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 $aturity increases#
Interest rate ris is inversely related to the bond&s cou"on rate i#e# "rices ofhigh cou"on bonds are less sensitive to changes in interest rate than "ricesof low cou"on bonds#
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2014 BSE Institute Limited
Bonds: ield 1urve
*lotting of T) against the Ter$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
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2014 BSE Institute Limited
Bonds: ield 1urve
7/25/2019 Fixed Income Trading Strategies 4
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2014 BSE Institute Limited
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
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2014 BSE Institute Limited
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#
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2014 BSE Institute Limited
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
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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#