A Note On Interest Rate Futures
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PRICING OF T-BOND FUTURES CONTRACTSFor T-bond
futures, it is up to the seller to decide which bond to deliver. Therefore
he/she identifies the cheapest to deliver bond (Refer Exhibit VI). This is
done by computing the cost of delivery for each deliverable bond as follows:
Cost = (Quoted Price + Accrued Interest) – (Quoted Futures Price X
Conversion Factor + Accrued Interest).
Quotes for Treasury Bonds
The prices of Treasury bonds are quoted in terms of dollars and 32nds of a
dollar. Therefore, a quote of 94-22 means that the price of a bond with a
face value is $100,000 is $94,687.5 (since the quote is in terms of a bond
with a face value of $100). However, the price paid by the purchaser is not
the quoted price[7] but the cash price[8] . The relationship between the two is:
Cash Price = Quoted Price + Accrued Interest since last Coupon Date.
Example:
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Assume that on April 8, 2003, a fund manager is
holding US Treasury bonds maturing on July 8, 2020, carrying a coupon
rate of 12%. The bond is quoting at 93-08 (or $93.25). The interest is
paid semi-annually on January 8 and July 8 every year. As per the day
count convention, the interest on the government bond accrues on an
actual basis. The last coupon payment date in this case was January 8,
2003.
Therefore, the accrued interest between January 8 and April 8, 2003 is,
= (90/181) X $6 = $2.98
Where the number of days between Jan 8 and April 8 is 90
Number of days between Jan 8 and July 8 is 181
And $6 is the coupon payment on January 8 and July 8 |
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Therefore, the cash price per $100 face value for a July 8,
2003 bond is
= $93.25 + $2.98 = $96.23
QUOTED FUTURES PRICE
A futures contract on a security that provides the holder with a known income is
known as a Treasury bond futures contract. The assumption underlying the
contract is that both the cheapest to deliver bond and the delivery date are
known. Then the relationship of the futures price to the spot price is
determined by the following formula:
F0 = (S0 – I)ert
Where,
F0 = Cash Future Price
S0 = Cash bond price
I = Present value of coupons during the life of the futures contract
r = Risk free interest rate
t = The time difference between the maturity of the futures contract and the
current time.
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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
[7] Quoted price is sometimes
referred to as the clean price.
[8] Cash price is sometimes referred to as the dirty price.
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