1
Bond Price  Yield Relationship
800
1000
1100
1200
1300
$1400
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Discount Rate
Bond Value
6 3/8
The PriceYield relationship for an option
free bond is a
convex
; nonliner
relationship
Bond prices and market interest rates
(yields) move in opposite directions..
Bond Price  Yield Relationship (2)
Consider a 5% coupon 30 year bond selling at par.
What will be the impact of a 1% change in yield in
either direction (
∆
y
= ±1%) on the price of this bond?
head2right
@
y
= 6%
barb4right
P
B
= $86.16
barb4right
%
∆
= –13.84%
head2right
@
y
= 4%
barb4right
P
B
= $117.38
barb4right
%
∆
= +17.38%
checkbld
This implies that the priceyield relationship is a
nonlinear, nonsymmetrical relationship, and the
priceyield graph will be convex to the origin.
Bond Price  Yield Relationship (3)
Consider a 5% coupon;
3year
bond selling at par.
Now a change in yield of 1% in either direction
(
∆
y
= ±1%)
has a smaller impact:
head2right
@
y
= 6%,
barb4right
P
B
= $97.33
barb4right
%
∆
= –2.71%
head2right
@
y
= 4%,
barb4right
P
B
= $102.80
barb4right
%
∆
= +2.80%
checkbld
The shorter is the Term to Maturity; the lower is
the bond price volatility.
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2
Bond Price  Yield Relationship (4)
Consider a
1% coupon
; 30year bond, selling for
$38.18 to yield 5%.
head2right
@
y
= 6%,
barb4right
P
B
= $30.81
barb4right
%
∆
= –19.31%
head2right
@
y
= 4%,
barb4right
P
B
= $47.86
barb4right
%
∆
= +25.34%
checkbld
The lower the coupon rate, the higher is the
bond price volatility.
Factors affecting Bond Price Volatility
•
Bond price volatility (i.e. the degree of its price
sensitivity to a changes in interest rates) depends
three factors:
–
Coupon rate:
the lower the coupon rate, the higher
is the bond price volatility.
–
Term To Maturity:
the longer is the Term to
Maturity; the higher is the bond price volatility.
–
The Yield to Maturity:
the higher is the Yield to
Maturity; the lower is the bond price volatility.
Duration – A Measure of Bond Price Volatility
square4
Duration
is a measure of the sensitivity of the
price of a bond to changes in interest rate.
square4
It encompasses all theses three factors  Maturity,
Coupon Rate, and Initial required Yield 
that
affect bond price volatility.
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 Spring '10
 nasseh
 Interest, Interest Rate, Bond duration, duration, Zerocoupon bond, Bond Price Convexity

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