A Note On Interest Rate Futures
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ARBITRAGE WITH T-BILL FUTURES Contd..
Futures Contract(1.0291) = (1.01574) (1 + R120,
210)
R120, 210 = 0.01315 (R120, 210 stands for the forward interest rate from day
120 to day 210)
Futures Price = 100/1.01315 = 98.70
Futures discount yield = (100 – 98.70)/100 X 360/90 = 0.052 or 5.20%
IMM Index = 100 – 5.20 = 94.80
Since the IMM Index is the same as that in the table, no arbitrage
opportunity exists.
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Opportunities for arbitrage exist when the futures
price deviates from the theoretical price. Suppose instead of selling
for 94.80, T-Bill futures sell for 95.02, the appropriate strategy would
be to borrow for 120 days, buy 210 day T-Bills and sell futures due in
120-days. An arbitrageur can borrow at a 120-day repo rate of 4.85%. The
IMM index of 95.02 translates into a price of $9,87,875.
Discount yield = 100 – 95.02 = 4.98%
Futures price = 10,00,000 (1 – Discount yield X 90/360)
= $9,87,875
The following transactions would yield an arbitrage profit, |
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TODAY
Buy 210-day T-Bill ($9,71,708)
Borrow $9,71,708 @ 4.85% for 120 days ($9,71,708)
Sell one futures contract @ 95.02 - -
Net cash requirement $0
120 Days Later
Deliver T-Bill on futures contract; collect $9,87,875
Repay Repo Loan ($9,71,708)
Pay Repo Interest
0.0485 X 9,71,708 X 120/360 ($15709.28)
Net cash receipt $457.72
To avoid any opportunities for arbitrage, given the repo rate of 4.85%, the
futures price should be 94.97. At this price, the inflow from short sale of the
futures would be very close to the cost of borrowing for buying 210-day T-Bill
(See Exhibit IV).
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
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