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PRACTICE PROBLEMS
CHAPTER 8:
YIELD CURVE AND TERM STRUCTURE ANALYSIS
NOTE:
for this problem set assume all interest rates are
compounded semi-annually
.
Exercise 8.1:
Assume the following spot rate (zero coupon) curve for this problem.
Years
0.5
1.0
1.5
2.0
2.5
Rate
7.50
7.75
8.00
8.00
8.00
(a)
If all bonds are priced consistently with this curve, what would be the price of a two-
year semi-annual, 14% coupon security?
(b)
Find the par bond yield curve.
(c)
Use linear interpolation to find the spot rates with maturities 10 months and 14 months.
(d)
Find the forward rate curve,
f
0
(
i
,
i
+
2
1
), for
i
= 0.5, 1, 1.5, 2.
Using the spot rates in part
(c), find the forward rate
f
0
(1, 14/12).
Exercise 8.2:
The data in the next table reflects the conditions on October 8, 1985.
Coupon
Maturity
Price
YTM
9%
9/15/1987
100
3
32
8.96%
10
5
8
%
8/15/2015
100
10
5
8
%
You expect the yield curve will flatten, but you have no clue as to whether the over-all
interest rates will rise or fall.
Using the two securities suggest a “spread trade” that is
consistent with your expectations.
Exercise 8.3:
Assume the following spot rate (zero coupon) curve for this problem.
Years
0.5
1.0
1.5
2.0
2.5
Rate
11.00
10.50
10.00
9.50
9.00
Two-year bonds that are strippable and paying a coupon of 10.375% are selling at a yield of
10%.
Is it worthwhile to strip them and sell the stripped pieces?
Or is it better to sell
them as a unit?
(Assume that you own them and that the strips may be sold at spot
yields.)
Exercise 8.4:
Given the following data, find the zero coupon curve by using the bootstrap
method.
(Coupons are paid semi-annually.)
Coupon
Maturity
(
years
)
Price
(
decimal
)
7%
0.5
101.00
4%
1.0
98.82
8%
1.5
103.68
Exercise 8.5:
You’re given the following data. (Coupons are paid semi-annually.)
Coupon
Maturity
(
years
)
Price
(
decimal
)
6%
1.0
99.72
8%
1.0
101.63
5%
1.5
98.03
If
A
=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
5
.
102
5
.
2
5
.
2
0
104
4
0
103
3
and (from EXCEL)
A
−
1
=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢

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