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8/19/2019 11-Bond Portfolios I
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Managing Bond PortfoliosPassive Strategies (with a review of termstructures)
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Passive strategy Control risk Balance risk and return
Active strategy
Trade on interest rate predictions Trade on market inefficiencies
Managing Fixed ncome Securities!
Basic Strategies
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#evie$ of Term Structure of
nterest #ates%vervie$ of term structures
&arious rates used in practice Bond yields
Spot rates S'ort rates For$ard rates
(ield curve
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Yield Curves
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+'at does t'e record say,
(ield curves are mostly up$ard-sloping
nverted yield curves generally point to declininginterest rates
Steeply rising yield curves are generally interpreted
as signaling impending rate increases
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/sing Spot #ates to price
Coupon Bonds A coupon 0ond can 0e vie$ed as a series of ero
coupon 0onds
To find t'e value eac' payment is discounted at t'eero coupon rate
%nce t'e 0ond value is found one can solve for t'eyield
Similar maturity and default risk 0onds may sell atdifferent yields to maturity
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Sample Bonds
Bonds CFs and current yield curve Assuming annual compounding
A B
Maturity ) years ) years
Coupon #ate .4 54
Par &alue 1666 1666Cas' flo$ in 1-" .6 56
Cas' flo$ in ) 16.6 1656
Period Spot #ate
1 76*
2 76*3*
" 76."
) 76.3
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Calculation of Price /sing Spot
#ates 8Bond A and B9
Period Spot#ate
Cas'Flo$
P& of
Cas'Flo$
1 76* .6 *371)
2 76*3* .6 *"7.*
" 76." .6 ):7:*
) 76.3 16.6 513756
Total :357*)
Period Spot#ate
Cas'Flo$
P& ofCas'Flo$
1 76* 56 3.71:
2 76*3* 56 317*)
" 76." 56 ..7.6
) 76.3 1656 5""72"
Total 16)37*.
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Solving for t'e (TM
Bond A
Bond Price ; :357*)
(TM ; .7."4
Bond B
Price ; 16)37*.
(TM ; .7.14
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Bond-ndex Funds
Cas' flo$ matc'ing and dedication
mmuniation of interest rate risk Target date immuniation
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=esign a 0ond portfolio so t'at its performance $ill matc' t'at of some 0ond index Performance is measured t'roug' its total return over some
investment 'orion
Motivation! lo$ advisory fee and t'e overall poor performance of active 0ond managers
+'en constructing t'e portfolio Flexi0ility level! fre?uency of transaction T'e difficulty,
mpossi0le to fully replicate t'e index
Bond-ndex Funds ndexation! 'o$ does it $ork,
Passive ManagementBond ndexing
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@ia0ility Funding Strategies
Classification of lia0ilities
Type lia0ilities! 0ot' amount and timing are kno$n
7g7 Cs
! amount is kno$n timing is unkno$n
g7 @ife insurance policy ! timing is kno$n 0ut amount is unkno$n
?uity linked C
&! 0ot' timing and amount are unkno$n
nsurance policies
American options
=ifferent types of lia0ilities needs different investment strategies
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Cas' Flo$ Matc'ing
Also called dedicating a portfolio a 0ond is selected $it' a maturity t'at matc'es t'e last lia0ility stream! t'e amount of
coupon principal e?ual to t'e last lia0ility stream7 T'e reminding elements of t'elia0ility stream are t'en reduced 0y t'e coupon payment on t'is 0ond and t'en
anot'er 0ond is c'osen for t'e ne$ reduced amount of t'e next-to-last lia0ility7 oing 0ack in time t'is cas' flo$ matc'ing process is continued until all lia0ilities 'ave 0een matc'ed7
=ifference from immuniation! no duration re?uirement no re0alance re?uired no risk t'at lia0ilities $onDt 0e satisfied
=isadvantage,
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Cas' flo$ matc'ing and dedication
example
Consider t'e pro0lem of funding a stream of pension lia0ilities consisting
of E166 million at t'e end of eac' for t'e next t'ree years7
Assume t'at t'e follo$ing securities are availa0le for investment 8annual
coupon9
Securities P6 CF1 CF2 CF"
1 1667666 16 116 6
2 :*7666 5 5 165
" 16*7666 12 12 112
) :)7"":. 166 6 6
* 5*73"": 6 166 6
. 3*71"1* 6 6 166
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Target =ate mmuniation
Consider t'e follo$ing case! a life insurance company sells a C t'atguarantees an interest of .72*4 every . mont's for *7* years7 Supposet'e payment made 0y t'e policy 'older is E552672.27 An amount of
'as 0een guaranteed after *7* years7
Suppose t'at t'e portfolio manager 0uys E 552672.2 par value of a 0ondselling at par $it' a 127*4 yield and matures in *7* years $'at $ill 'appen, s t'e cas' flo$ 'edged,
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+'at affects total returns,
A 0ondDs total return is impacted 0y ts interest income and interest-on-interest ts price fluctuations
T'ese t$o forces $ork in t'e opposite direction s t'ere some point $'ere t'ey exactly offset eac' ot'er,
(es $'en t'e 0ond 'as 0een 'eld for t'e lengt' of t'e 0ondDs
duration Target date immuniation!
Make portfolio duration close to your 'olding period
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xample! mmuniing t'e
Palmer CorporationDs E1666 @ia0ility
iven information Palmer Corporation 'as a E1666 lia0ility due in .73: years
f Palmer purc'ased a default-free 0ond $it' a :4 couponrate par of E1666 and maturity of 16 years for E1666 8'as
a duration of .73: years9 to repay t'e lia0ility due in .73:
years
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xample! mmuniing t'e
Palmer CorporationDs E1666 @ia0ility
T'e total return from t'is 0ond 'eld under different reinvestment assumptions
Holding Period (years)
Return Sources Rate 1 3 5 6.79 9 1
Cou!on inco"e 5# $9 $%7 $&5 $611 $'1 $9
Ca!ital gain $%'7 $%3& $175 $1 $39 $
nterest on cou!on $1.13 $17 $5& $15 $191 $%&1
otal Return $37' $5%1 $679 $'16 $1& $11&1
otal yield 37.# 15.# 11.# 9.# '.5# '.%#
Cou!on inco"e 7# $9 $%7 $&5 $611 $'1 $9
Ca!ital gain $13% $19 $'3 $56 $19 $
nterest on cou!on $% $%5 $7' $1&9 $%79 $355
otal Return $9% $3% $55& $'16 $1197 $1395
As time passes
t'e interest on
coupon
component 'as
a greater
impact on totalreturn7
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xample! mmuniing t'e
Palmer CorporationDs E1666 @ia0ility
Holding Period (years)
Return Sources Rate 1 3 5 6.79 9 1
Cou!on inco"e 9# $9 $%7 $&5 $611 $'1 $9
Ca!ital gain $ $ $ $ $ $
nterest on cou!on $% $3% $13 $%5 $3'7 $&95
otal Return $9% $3% $55& $'16 $1197 $1395
otal yield 9.# 9.# 9.# 9.# 9.# 9.#
Cou!on inco"e 11# $9 $%7 $&5 $611 $'1 $9
Ca!ital gain *$11% *$95 *$75 *$56 *$1' $
nterest on cou!on $% $& $1%9 $%61 $5% $6&7
otal Return $% $%15 $5& $'16 $1%9& $15&7
otal yield %.# 6.7# '.5# 9.# 9.7# 9.'# >ote t'at t'e total yield is :4regardless of t'e reinvestment rate7
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>et +ort' mmuniation
P& of asset must e?ual t'e P& of lia0ilities
=uration of t'e assets must matc' t'e duration of lia0ilities
+'y matc' duration, T'e assets must 'ave a dominance patter over t'e lia0ilities
for prescri0ed yield c'anges 8e7g7 'ig'er convexity9
Immunization provides a hedge for the portfolio’s value,
but not its cash flo!!!
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xample
T'ree strips $it' maturity T;1 2 and " and (TM of .4 54 164 respectively7
@ia0ility 166 million at t'e end of eac' year $'en market yields are at 164!=uration ;17:)2
/se strip " to immunie t'e lia0ility7 +e make t'e $eig'ted average of durations
for t'e 'edged portfolio 8assetlia0ility9 to 0e ero7 T'e price of stripe " is T'en8 is t'e num0er of stripe " to 0uy9
;6
$'ere
%r
To get ;-271)
+'at $ill 'appen at end of year 1 and 2,
Note: we can also use strip 1 and 3 together to form a portfolio that matures PV andduration of the liability
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>otes on duration of 0ond
portfolios For assets $it' e?ual yields t'e duration of a 0ond portfolio
is e?ual to t'e $eig'ted average of t'e durations of t'e
0onds in t'e portfolio Portfolio needs to 0e re0alanced $'en interest rate c'anges
mmuniation risk non-parallel s'ift in t'e yield curve
credit risk and call risk T'e immuniation tec'ni?ue can 0e generalied to satisfy
multi-period lia0ilities
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>otes on duration of 0ond
portfolios T'e portfolio duration 'o$ever does not c'ange linearly $it' time7 T'e
portfolio needs t'erefore to 0e re0alanced periodically to maintaintarget date immuniation xample!
$it' E1:)53 in lia0ility in 3 years $it' current market interest rate at 34! P& ;E16666
mmunie t'e lia0ility $it' " year ero and perpetuity paying annual coupon!duration ; 811649G164 ; 11 year
Assume portfolio 'as $4 in ero 81-$94 in perpetuity! $;*64
>ext year interest rate does not c'ange P& of o0ligation ; E11666 Portfolio gro$s to E11666 too! ero gro$s from E*666 to E**666 and perpetuity paid
E*66 and still $ort' E*666 =uration! 2 years and 11 years! $ ; *G:! needs 8*G:9H11666 ; .111711 in ero
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