A Note On Interest Rate Futures
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TREASURY BONDS FUTURES Contd..Therefore, the
prices at which the underlying bonds trade varies. Because of the variation
in prices, futures contracts specify a conversion factor[6] (announced by the
exchange prior to commencement of trading in a particular contract for all
bonds eligible for delivery) to make the delivery of one among many possible
bonds consequential. The conversion factors are used to standardize all
deliverable bonds to bonds yielding 6%.
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To work out the conversion factor, the maturity period
and times to coupon payment dates of a bond are approximated to the
nearest three months. If after rounding, the bond lasts for an exact
number of half-years, the first coupon is assumed to be paid in 6
months. If after rounding, the bond does not last for an exact number of
half-years (i.e. there is an extra 3 months), the coupon is assumed to
be paid after 3 months and accrued interest is subtracted. The examples
given below illustrate the calculation of the conversion factor |
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Example:
Consider an 8.5% coupon bond with 20 years and two months to maturity. The coupon payments are made semi-annually. Assume that the first coupon payment is to be made after six months. The discount rate is 6% per annum with semi-annual compounding. The value of a $100 face value bond is then,
The conversion factor is the value divided by its face value = 128.89/100 = 1.2889
Example:
Consider a 9% coupon bond with 15 years and four months to maturity. In this case, the period of the bond to maturity is assumed to be 15 years and three months. Discounting all the cash flows back to a point in time three months from today gives:
The next logical step is to calculate the interest rate for a 3-month period is (Ö1.03 – 1) X 100 = 1.4889% and discount back the value of 133.39 to the present date i.e. 133.9/1.014889 = 131.94. Accrued interest = 2.25. Therefore, the conversion factor is (131.94 - 2.25)/100 = 1.2969. The conversion factor computed is used to determine the amount received by the party with the short position, when he/she delivers the bond. It is computed for each $100 face value of the bond deliverable, using the following formula:
Cash Received = Quoted Futures Price X Conversion Factor + Accrued Interest since Last Coupon Date
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
[6] The conversion factor is the
factor used to adjust the invoice
price so that a higher amount is paid for the delivery of a bond with
a higher coupon.
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