11-bond portfolios i

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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comm 324 --- W. SuoSlide .Slide .

/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



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



Bond-ndex Funds

Cas' flo$ matc'ing and dedication

mmuniation of interest rate risk Target date immuniation



=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



@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,



+'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



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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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





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



>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!!!



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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comm 324 --- W. SuoSlide 2"Slide 2"

>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

11-bond portfolios i

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