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Answers to Questions and Problems
1. A 90-day T-bill has a discount yield of 8.75 percent. What is the price of a $1,000,000 face value bill?
Applying the equation for the value of a T-bill, the price of a $1,000,000 face value T-bill is $1,000,000
2
DY($1,000,000)(DTM)/360, where DY is the discount yield and DTM
5
days until maturity. Therefore, if
DY
5
0.0875 the bill price is:
2. The IMM Index stands as 88.70. What is the discount yield? If you buy a T-bill futures at that index value
and the index becomes 88.90, what is your gain or loss?
The discount yield
5
100.00
2
IMM Index
5
100.00
2
88.70
5
11.30 percent. If the IMM Index moves
to 88.90, it has gained 20 basis points, and each point is worth $25. Because the price has risen and the yield
has fallen, the long position has a profit of $25(20)
5
$500.
3. What is the difference between position day and first position day?
First position day is the first day on which a trader can initiate the delivery sequence on CBOT futures con-
tracts. With the three day delivery sequence characteristics of T-bond futures, for example, first position day
is the second to last business day of the month preceding the contract’s expiration month. For example,
May 30 is the first position day for the JUN contract, assuming that May 30–June 1 are all business days.
Position day is functionally the same, but it is not the first day on which a trader can initiate the sequence.
For example, assuming June 10–12 are all business days, the position day could be June 10, with actual
delivery occurring on June 12.
4. A $100,000 face value T-bond has an annual coupon rate of 9.5 percent and paid its last coupon 48 days ago.
What is the accrued interest on the bond?
Accrued Interest
5
$100,000 (0.095/2)(48/182.5)
5
$1,249.32.
Note that we assume that the half-year has 182.5 days. There are specific rules for determining the number
of days in a half-year.
5. What conditions are necessary for the conversion factors on the CBOT T-bond contract to create favorable
conditions for delivering one bond instead of another?
Bill Price
5
$1,000,000
2
0.0875 ($1,000,000)
(90)
360
5
$978,125
5
Interest Rate
Futures:
Introduction