CHAPTER 15
1.
A bond futures contract with one deliverable bond has a maturity date in 2 years from now
have, par value of $100, and annual coupon of $8. If the futures delivery date is in 1 year,
determine the futures price if
(a) R0,1 = R0,2 = 8 percent.
(b) R0,1 = 5 percent, R0,2 = 10 percent.
F=
C + Par
1 + f 0,2
a. F =
108
= 100
1.08
b. (1 + R0,2 )2 = (1 + R0,1)(1 + f 0,2)
(1.10) 2  (1.05)(1  f 0, 2 )
f 0, 2  0.1524  15.24%
F=
2.
108
= 93.72
1.1524
Consider a bond futures contract with one deliverable bond having a maturity date in 3
years choose from, par value of $100, and annual coupon of $8. If the futures delivery date
is in 1 year, determine the futures price if
(a) R0,1 = R0,2 = R0,3 = 8 percent.
(b) R0,1 = 5 percent, R0,2 = 7 percent, R0,3 = 9 percent.
a. F =
8
108
+
= 100
1.08 (1.08)(1.0 8)
b. (1.07)2 = (1.05)(1 + f0,2)
f0,2 = 9.04%
(1.09)3 = (1.07)2(1 + f0,3)
f0,3 = 13.11%
F=
8
108
+
= 94.90
1.09038 (1.09038)(1.13113)
3.
A bond futures contract has one deliverable bond with a maturity date in 3 years from now
have, par value of $100, and annual coupon of $8. If the futures delivery date is in 2 years,
determine the futures price if
(a) R0,1 = R0,2 = R0,3 = R0,4 = 8 percent.
(b) R0,1 = 5 percent, R0,2 = 7 percent, R0,3 = 9 percent.
4.
a. F =
108
= 100
1.08
b. F =
108
= 95.48
1.13113
Suppose a bond futures contract has one deliverable bond with a maturity date in 30 years
from now, par value of $100, price of $95, and annual coupon of $8. If the futures delivery
date is in 1 year, determine the futures price if R0,1 = 4 percent.
F = P0,30 (1 + R0,1 )  C 1
 95(1.04)  8  90.80
5.
Assume that the price quotation of the CBT Treasury bond futures contract changes from
96–14 to 97–09. What are the gains and losses to the short and long as a result of markingto-market for 1 contract with $100,000 par value?
96–14: 96,000 + 14/32(1,000) = 96,437.50
97–09: 97,000 + 09/32(1,000) = 97281.25
97,281.25 – 96,437.50 = 843.75
6.
An individual owns a 21-year maturity bond with an annual coupon of 10 percent, a face
value of $100,000, and a price of $95,000. To protect against rising interest rates, this
individual shorts one CBT Treasury bond futures contract with a delivery date 2 years
hence and a futures price of 92–16. In the course of the next year, interest rates change. The
bond price drops to $88,000 and the futures price drops to 86–16.
(a) Overlooking bond coupon and marking-to-market, compute the gains or losses on the
bond position, the futures position, and the net position.
(b) Suppose we knew the relationship between the futures and spot prices. For every dollar
change in the futures, the spot price changed $1.10. Determine the optimal hedge ratio.
a. -P0
-95,000
+P1
+88,000
+F0
+92,500
-F1
-86,500
= -1,000
1
slope
b. Hedge ratio =
Slope =
1.00
= 0.9091
1.1
Hedge ratio=
7.
1
= 1.1
0.9091
A bond dealer owns a 21-year maturity bond with an annual coupon of 5 percent, a face
value of $100,000, and a price of $95,000. To hedge against rising interest rates, the dealer
shorts one CBT Treasury bond futures contract with a delivery date 2 years hence and a
futures price of 92–16. In the course of the next year, interest rates drop. The futures price
goes to 97–16. At what interest rate on the bond would the hedge just break even?
-P0
-95,000
+P1
+P1
+F0
+92,500
-F1
-97,500 = 0
P1 = 100,000
5,000
= 0.05 = 5%
100,000
8.
A bond futures contract has one deliverable bond that has a maturity date in 2 years from
now, par value of $100, and annual coupon of $7.25. If the futures delivery date is in one
year, determine the spot price of two-period strips per $100 of par if the futures price is
$101.98 and if one-period strips have a price of $91.50 per $100 of par value.
0
|
91.50
0.9150
1
|
101.98
0.950862
100
|
S2 = 100(0.9150)(0.950862) = $87.00.
2
|
107.25
|
divide by 107.25
divide by 100
9.
A bond futures contract has one deliverable bond that has a maturity date in 3 years from
now, par value of $100, and annual coupon of $6.75. If the futures delivery date is in one
year, determine the futures price if the prices of 1-, 2-, 3-period strips per $100 par are
$94.00, 86.00, $79.00.
0
|
1
|
F
2
|
6.75
3
|
106.75
F = [(6.75)(0.86) + (106.75)(0.79)]/(0.94) = $95.89
If you compute the forward interest rates, you can find the answer as follows:
F = 6.75/(1 + f0,2) + 106.75/[(1 + f0,2)(1 + f0,3)]
10.
Assume that the price quotation of the CBT Treasury bond futures contract changes from
98–17 to 99–12. What is the loss to the short as a result of marking-to-market for 3
contracts with $100,000 par value?
99–12:
98–17:
99,375
-98,531.25
$843.75
This is also (27/32)($1,000) = $843.75
The total loss to the short should be $843.75 X 3 = $2531.25
11.
A bond dealer owns a 16-year maturity bond with an annual coupon of 6.00 percent, a face
value of $100,000, and a price of $100,000. To hedge against rising interest rates, the dealer
shorts one CBT Treasury bond futures contract with a delivery date 2 years hence and a
futures price of 102–16. In the course of the next year, interest rates rise 2%. The futures
price goes to 87. What is the net loss on the hedge?
0
|
-100,000
+102,500
P1:
1
2
|
|
+82,881.04 = P1
= -17,118.96
-87,000
= +15,500.00
Net = -1,618.96
N = 15; I/YR = 8%; PMT = 6,000; FV = 100,000.