A Note On Interest Rate Futures
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ARBITRAGE WITH T-BILL FUTUREST-Bill future
prices are worked out after considering the implication of cost of carry.
The cost of carry is the net cost of carrying the commodity forward at a
future date. Thus, the futures price can be depicted as:
F1 = S0 (1 + Cc0,1)
Where, F1 = Futures price at time 1
Cc0,1 = Cost of carry from time 0 to 1
S0 = Spot commodity price
Carrying cost helps investors establish the relationship between the futures
price and the spot price. In interest rate futures, the quotes for both the
spot price as well futures price of the T-Bill are given. These values can
be used to determine the cost of carry and the resultant, also known as the
implied repo rate[2]. In the absence of any arbitrage, this rate would be
prevalent between two dates.
Example:
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Assume a mutual fund owns T-Bills that have a face
value[3]of $5 million and a current market value of $49,43,727. Faced by
the demand for money by the fund participants, the fund enters into a
repurchase agreement with a financial institution. The institution
provides the advance equal to the current market value with a promise
from the fund to repurchase the bills at $49,45,460 after four days. The repo rate works out to be
$ 49,45,460 - 49,43,727 X 365 = 3.20%
$ 49,43,727 4
There is an opportunity for arbitrage if the T-Bill itself yields more
than the institution's repo rate (3.20%). The fund can make arbitrage
benefit by borrowing from the institution at this rate and investing
more in T-Bills. |
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Example:
Assume the following quotes are available in a T-Bill futures market:
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INSTRUMENT
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MATURITY |
PRICING INFO |
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T-Bill futures market
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120 days
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IMM Index = 94.80
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T-Bill
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120 days
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Discount yield = 4.65 %
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T-Bill
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210 days
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Discount yield = 4.85 %
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Buying the futures contract is equivalent to buying the 120-day bill followed by
a 90-day T-Bill when the 120-day T-Bill matures. This is because on the date of
expiration of the futures contract, the longer maturity T-Bill will have 90 days
to maturity and hence will be deliverable against the futures. Therefore, buying
the futures contract today is equivalent to buying the 210-day T-Bill. The
person long on the futures will receive a 90-day T-Bill in 120-days. With the
data for 120 and 210-day T-Bill provided, the price of the futures contract can
be worked out to find whether any opportunity for arbitrage exists.
D = (100 –P)/100 X 360/t
P120 = 100 – 100 X .0465 X (120/360) = 98.45
Unannualized yield for 120 days = (100 – 98.45)/98.45 = 0.01574
Annualized yield = 0.01574 X 360/120 = 0.04722 or 4.72%
P210 = 100 – 100 X .0485 X (210/360) = 97.1708
Unannualized yield for 210 days = (100 – 97.1708)/97.1708 = 0.0291
Annualized yield = 0.0291 X 360/210 = 0.04988 or 4.99%.
SPREADING WITH INTEREST RATE FUTURES
TABLE II TRANSACTIONS INVOLVING BUYING THE TED SPREAD
TREASURY BONDS FUTURES
PRICING OF T-BOND FUTURES CONTRACTS
QUOTED FUTURES PRICE
TABLE III STEPS TO CALCULATE QUOTED FUTURES PRICE
CONCLUSION
EXHIBIT I LIST OF ACTIVELY TRADED SHORT TERM INTEREST RATE FUTURES
EXHIBIT II LIST OF ACTIVELY TRADED LONG TERM INTEREST RATE FUTURES
EXHIBIT III T-BILL FUTURES AND EURODOLLAR FUTURES
EXHIBIT IV NO ARBITRAGE FUTURES PRICE
EXHIBIT V CHARACTERISTICS OF T-NOTE AND T-BONDS
EXHIBIT VI CHEAPEST TO DELIVER BOND
ADDITIONAL READINGS & REFERENCES
[2] Repo is short for repurchase
agreement. In this type of contract,
one party sells a security and also promises to buy it back at a
predetermined price on some future date.
[3] The stated principal amount of an instrument.
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