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PRACTICE PROBLEMS
CHAPTER 17:
TREASURY FUTURES CONTRACTS
Exercise 17.1:
Consider a Tbond futures contract.
The face value is $100,000, the
initial margin is $3,000 and the maintenance margin is $2,500.
The daily futures
prices are 101.5, 101.84, 101.66, 102.03, 101.91.
What’s the total gain or loss for
the long position?
The short position?
Which position requires a margin call?
What’s the final margin account balance for each position?
Exercise 17.2:
Consider a tenyear Tnote futures contract.
The face value is
$100,000, the initial margin is $1,500 and the maintenance margin is $1,000.
The
daily futures prices are 99.34, 99.88, 100.25, 100.31, 100.66.
What’s the total
gain or loss for the long position?
The short position?
Which position requires a
margin call?
What’s the final margin account balance for each position?
Exercise 17.3:
The quoted discount rates of two U.S. Tbills and their maturities are
shown below.
(a) Find the forward rate (using annual compounding) that can be locked in for the
purposes of
borrowing
between July 23, 1998 and December 17, 1998.
(b) Find the rate that can locked in for the purposes of
lending
.
(c) Find the
spread
between the borrowing rate and the lending rate.
We’ll still assume that
Price
= 1
−
dn
/360.
Discount Rates:
Settlement
Maturity
T
i
Bid
Ask
(
Offer
)
5/18/98
7/23/98
66 days
5.04%
5.02%
12/17/98
213 days
4.92%
4.90%
(d) Now, the yield curve in this example is downward sloping, and so the forward rate
should be less than the
T
2
= 213day rate (intuitively, the forward rate has to be
low in order to “pull down” the longterm rate).
However, the forward rates seem
to be higher than the
T
2
discount rates.
What’s going on here?
Exercise 17.4:
The quoted discount rates of two U.S.
Tbills and their maturities are
shown below.
(a) Find the forward rate (using annual compounding) that can be locked in for the
purposes of borrowing between August 17, 1998 and November 15, 1998.
(b) Find the corresponding lending rates.
Discount Rates:
Settlement
Maturity
T
i
Bid
Offer
6/18/98
8/17/98
60 days
6.55
6.53
11/15/98
150 days
6.70
6.68
(c) Repeat this question for the following data, i.e., find the borrowing and lending
rates that can be locked in between July 18, 1998 and October 16, 1998:
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Discount Rates:
Settlement
Maturity
T
i
Bid
Offer
6/18/98
7/18/98
30 days
7.20
7.18
10/16/98
120 days
7.18
7.16
Exercise 17.5:
Suppose our Tbond futures price is 99.337 and we are short traders.
(a) For delivery, we have three Tbonds to choose from,
Coupon
Quoted price
Conversion factor
12.000%
139.333
1.3781
11.250%
138.625
1.3599
7.250%
95.000
0.9159
Which is the cheapest to deliver bond?
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