Assume an investor bought T-Bills worth $10,000 in an
auction for which he paid 97.563% of par, or $9756.30.
Substituting the values we get the discount rate of:
= (10000 – 9756.30)/10000 * 360/91 = 9.64%
The prices for T-Bill futures contracts are quoted both as a
discount from par and as a percentage of par value. For example,
the settlement price of 95.65 for the June contract represents a
discount rate of 100 – 95.65 = 4.35% of par, or 95.65% of 100.
But generally, T-Bill futures contracts are quoted in terms of
the IMM index, which is defined as
IMM Index = 100 – D, therefore if the IMM index is 94, then the
implied discount yield is 6%.
The minimum price change allowed per futures contract is one
basis point (.01%), which works out to be ($ 10,00,000 X .0001 X
3/12) = $ 25.
The Eurodollar futures prices on the IMM division of CME are
quoted as 100 – LIBOR, where LIBOR is an annualized three-month
rate. For example, the settlement price of 96.67 on a September
03 contract corresponds to an annualized LIBOR rate of 3.33%.
Unlike T-Bills, the yield on Eurodollar futures is quoted in
terms of add-on or simple interest rate. It is determined by:
Add-on- Yield =
|
Discount
|
X |
360
|
| |
Price |
|
Days to
Maturity |
Substituting,
.0333 = (Discount/$ 10,00,000 – Discount) X 360/91
Discount = $ 8347.24
If a T-Bill of $ 1 million is sold at a discount of $
8347.24, the discount yield would be:
= ($8347.24/$ 10,00,000) X 360/91 = 3.30%
Therefore, it can be inferred that for a give discount, the
discount yield will be less than the add-on yield.
Adapted from Strong A. Robert, Derivatives An Introduction, Hull C. John, Options, Futures and Other Derivatives, Financial Risk Management, IUP, www.cba.uiuc.edu
EXHIBIT IV NO ARBITRAGE FUTURES PRICE
EXHIBIT V CHARACTERISTICS OF T-NOTE AND T-BONDS
EXHIBIT VI CHEAPEST TO DELIVER BOND
ADDITIONAL READINGS & REFERENCES
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