bond risk - duration and convexity
TRANSCRIPT
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Bond Risk
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Risks of Fixed Income
SecuritiesOSystematic Risks
O Interest Rate Risk
O Reinvestment RiskO Purchasing Power Risk
O Exchange Rate Risk
OUnsystematic Risks
O Defaut !"redit# RiskO "a Risk
O $i%uidity Risk
&
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'ond Risk ( Rating )genciesO Standard ( Poor*s
O +oody*s
,
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Standard "redit Rating
System
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Investment Grade:
% .igh /radeAAA - AA Aaa - Aa
% +edium /rade A - BBB A - Baa
Non-Investment Grade:
%
S0ecuative BB - B Ba - B
% Defaut CCC - D Caa - C
Bonds Standard & Poors Moodys
Overall Range AAA - D Aaa - C
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'ond Pricing Formua
!"ou0on onds#
2
1. Semiannual Interest payment = Pmt = 58.75
2. Number of payments to call= n = 5 x 2 = 10
3. Face Value = Future Value = FV = $1000
4. Present Value = Current Price = PV = 1217.50
(must be input as a negative number)
5. Yield to Call = CPT I%= 6.58%
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Bond Price and Interest RatesInterest Rate on! Price
".4"# $121%.&'(p &' basis
points) ".*"# $11"'.32 +,$3%.1"-
(p %& basispoints) *.23# $112.2 +,$&&.24-
/o0n &' basis
points) %.*"# $12&.4' +$3".*'-
/o0n %& basispoints) %.%3# $12%.4 +$&".*-
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Bond Price and Interest Rates
Price
Interest Rate
Note the asymmetry in the relation.
Bond prices are more sensitie to
drops in interest rates.
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Bond A is more interest rate sensitie:better or bot! increases and decreases
in rates. For decreases"increases # in
rates it!ains"%oses# more "%ess#.
Bond A: &i'!er (on)exit*
Bond B: +o,er (on)exit*
Bond B is less interest rate sensitie: or
decreases "increases# in rates it 'ains
"%oses# %ess "more#.
(on)exit*
(on)exit*is a more acc-rate meas-re o interest rate sensiti)it*
t!an -ration. Bond A is more con)ex and se%% at a !i'!er /rice.
ie%d to mat-rit*
Bon
d
Price
ie%d to mat-rit*
Fig. 2
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Interest Rate Ris o bonds
Price RiskInerse relation "et#een"ond price and interestrates.
Reinestment Risk$irect relation "et#eencopon renestment incomeand interest rates.
(an be eliminatedb* !o%din' t!ebond to mat-rit*.
$ecreases ininterest rates&aora"le and )ise
)ersa.
(an be eliminatedb* !o%din' eroco-/on bonds.
Increases ininterest rates&aora"le and )ise
)ersa.
3!ese are aected
o//osite%* b*
c!an'es in interest
rates. (an t!e* be
oset4 Yes
3o e%iminate interest rate
ris hold a 'ero copon
"ond to matrity.
3o e%iminate interest rate
ris o&&set price and
reinestment risk.RA3I6
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-ration is te point in time in a bon!s life
#here the price risk and reinestment risko&&set each otherso tat te bon! is
immunizedaainst interest rate ris5.
(o) to immni'e a "ond a!ainst interest
rate risk) hold it to its dration.
For a ero co-/on bond d-ration ise-a% to mat-rit*.
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Duration (
Immuni8ationO Duration9 a conce0t deveo0ed y
Fred +acauay in 16,5 that 0rovides
a time:weighted measure of asecurity*s cash ;ows in terms of0ayack
O Immunization9 the conce0t ofminimi8ing the im0act of changes ininterest rates on the vaue ofinvestments
11
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Duration
1&
-rationis a6erae maturity of a coupon bon!.
/uration is a risk*mana!ement strate!yin fi7e!
income in6estment.
Imm-niation strate'* re-ires t!at
ex/ected *ie%d on t!e bond = rea%ied *ie%d
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Rules of Duration)
1. /uration of a 8ero,coupon +no interest payment-
bon! is e9ual to maturity:
2. /uration is ier 0en coupon rate is lo0er.
3. /uration usually rises 0it te bon!s maturity.
4. /uration of a coupon bon! is ier 0en its
;
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. /uration of a portfolio of bon!s is e9ual to te
0eite! a6erae of te !uration of in!i6i!ual
bon!s.
&. coupon bon! can be consi!ere! to be a series
of >ero,coupon bon!s 0ere te maturity of eac>ero is e9ual to te time 0en te cas flo0 occurs:
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7. Price c!an'e in a bond :
(!an'e inPrice
is d-ration in *ears* is ie%d to mat-rit*
(!an'e in ie%d tomat-rit* *
PP
=
*"1 9 *#
". The chan!e in price o& a "ond in response to achan!e in interest rates is proportional to itsmodi&ied dration+ lon!er the modi&ied dration)
lar!er the price chan!e.
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;odiied -ration"1 9 *#
= .> *ears or >*ear and > mont!s.
At t!is /oint t!e rea%ied *ie%d on t!e
bond ,i%% be e-a% to t!e /romised *ie%d
or sma%% c!an'es in interest rates.
*., "ond is immni'ed a!ainst interest rate
risk i& the holdin! period -inestors decision/
is e0al to its dration.
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Duration
15
?xam/%es:
a. Price c!an'e in t!e 5@*ear bond or a 50 basis
increase in *ie%d to mat-rit* rom .5 to 7.0
* = 0.5 = 0.005
* = 0.5C P = 10D1.17C
= =.1D#"10D1.17#".005#
= @ $21.D "%oss#
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b. Cane in price for a 1' year'ero copon "ondfor a
1'' basis points !ecrease in interest rate or ytm += "#-.
* = 100 basis /oints = 1
= @ 0.01
= =D.2
PP = *D.2#"0.0E2#
= $>D
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&7
10. -ration o a /orto%io o bonds:
/= ,i< i#
,!ere ,i
and i
are t!e /orto%io ,ei'!ts in maret
)a%-e and t!e -ration o t!e it! bond.
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Duration
&1
In)estment trate'*)
When interest ratesare expected to decline, bond
prices increase. !itch to long duration (long
maturit" and lo! coupon rate)bonds. #nd,!hen
interest rates are expected to go up, s!itch to short
duration bonds.
Duration is longer for long maturit"and lo!
coupon bonds, and vice versa.
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Uses for DurationO Providing a measure of a ond*s
voatiity
O Estimating the change in the price ofa bond based on changes in interestrates
O Immuni8ing a ond or ond 0ortfoioagainst interest rate risk
&&
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&,
$ration: s!o,s
c!an'e in bond
/rice a'ainst
interest rate
c!an'es. Note
the linear
relationship.
Cone1ity:Note the
cratre. !o,s t!at
bonds 'ain more in
res/onse to interest
rate decreases and%ose %ess in res/onse
to increases in rates.
$ration s. Cone1ity
Bon
d
Price
ie%d to mat-rit*
Fig. $
Act-a% bond
/rices be!a)et!is ,a*
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(!an'e inPrice
is d-ration in *ears
* is ie%d to mat-rit*
(!an'e in ie%d tomat-rit* *
PP
=
*"1 9 *#
Bond Price c!an'e -sin' -rationG
Bond Price c!an'e -sin' (on)exit*G
PP
=
* 9"1 9 *#
Additiona% term d-e to (on)exit*
12
x Cone1ityx *#2H
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&2
Con6e7ity
12
x Cone1ityx *#2H
*#2is a%,a*s
/ositi)e re'ard%ess o
si'n o
*
* /ositi)eC Bond /rice
dro/s.
(on)exit* term red-ces
/rice dro/ t!ro-'!
*#2and t!e eect is bi''er
or !i'!er (on)exit*.
* ne'ati)eC Bond /rice
increases.
(on)exit* term increases
/rice 'ain t!ro-'!
*#2and t!e eect is bi''er
or !i'!er (on)exit*.
A%,a*s c!oose !i'! (on)exit* Bonds
Cone1ityterm is a%,a*s
/ositi)e and hi!her &or
hi!her Cone1ity
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&3
Cre!it Ris5 Price Ris5 Rein6estment Ris5