Problem Set 2 Answers
The following is a list of prices for zero coupon bonds with different maturities and par value of $1,000.
Use this information for solving problems 1-3.
Maturity (Years)
Price
Spot
rate
Forward
rate
1
$952.38
5%
5%
2
$873.44
7%
9.04%
3
$827.85
6.5%
5.51%
4
$792.09
6%
4.51%
1.What is, according to the expectations theory, the expected forward rate in the
fourth
year?
4
4
4
4
3
3
3
(1
y )
(1
0.06)
f
0.0451
(1
y )
(1
0.065)
+
+
=
=
=
+
+
2.What is the price of a 4-year maturity bond with a 10% coupon rate paid annually?
(Par value =
$1,000)
2
3
4
100
100
100
1100
P
1136.67
1
0.05
(1
0.07)
(1
0.065)
(1
0.06)
=
+
+
+
=
+
+
+
+
3.You have purchased a 3-year maturity bond with a 10% coupon rate paid annually.
The bond has a
par value of $1,000. What would the price of the bond be one year from now if the implied
forward rates stay the same?
100
1100
P
1047.83
(1
0.0904)
(1
0.0904)(1
0.0551)
=
+
=
+
+
+
Given the following pattern of forward rates, solve problem 4:
Year
Forward Rate
1
4%
2
6%
3
7%
4. If one year from now the term structure of interest rates changes so that it looks exactly the same as it
does today, what would be your holding period return if you purchased a 3-year 10% annual
coupon bond today and held it for 2 years?
buy
100
100
1100
P
1119.41
(1
0.04)
(1
0.04)(1
0.06)
(1
0.04)(1
0.06)(1
0.07)
=
+
+
=
+
+
+
+
+
+

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