E120
Homework 5
Due 29/02/2012
1. For the following bond, calculate the bond’s duration:
8% coupon rate
pays annual coupons,
$1000 face value,
9% yield to maturity,
seven years to maturity.
Use this information to estimate the percentage change in bond price given a

0
.
25%
change in the YTM.
2. For the following bond, calculate the bond’s duration:
7
.
50% coupon rate,
pays semiannual coupons,
$1000 face value,
9% yield to maturity,
three years to maturity.
Use this information to estimate the percentage change in bond price given a +0
.
5%
change in the YTM.
3. Suppose you have two bonds with the same yields to maturity. Bond
A
has duration
D
A
and price
P
A
.
Bond
B
has duration
D
B
and price
P
B
.
Show that a portfolio
consisting of these two bonds (one share of bond
A
, and one share of bond
B
) has
duration:
D
P
=
P
A
P
A
+
P
B
D
A
+
P
B
P
A
+
P
B
D
B
.
4. Consider a twoyear spot rate of 5% and a fiveyear spot rate of 6%.
What is the
(equilibrium) implied forward rate for a loan starting in two years and maturing three
years later?
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 Spring '08
 ILAN

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