# 005 - 5 Interest Rate Futures Introduction Answers to...

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27 Answers to Questions and Problems 1. A 90-day T-bill has a discount yield of 8.75 percent. What is the price of a \$1,000,000 face value bill? Applying the equation for the value of a T-bill, the price of a \$1,000,000 face value T-bill is \$1,000,000 2 DY(\$1,000,000)(DTM)/360, where DY is the discount yield and DTM 5 days until maturity. Therefore, if DY 5 0.0875 the bill price is: 2. The IMM Index stands as 88.70. What is the discount yield? If you buy a T-bill futures at that index value and the index becomes 88.90, what is your gain or loss? The discount yield 5 100.00 2 IMM Index 5 100.00 2 88.70 5 11.30 percent. If the IMM Index moves to 88.90, it has gained 20 basis points, and each point is worth \$25. Because the price has risen and the yield has fallen, the long position has a profit of \$25(20) 5 \$500. 3. What is the difference between position day and first position day? First position day is the first day on which a trader can initiate the delivery sequence on CBOT futures con- tracts. With the three day delivery sequence characteristics of T-bond futures, for example, first position day is the second to last business day of the month preceding the contract’s expiration month. For example, May 30 is the first position day for the JUN contract, assuming that May 30–June 1 are all business days. Position day is functionally the same, but it is not the first day on which a trader can initiate the sequence. For example, assuming June 10–12 are all business days, the position day could be June 10, with actual delivery occurring on June 12. 4. A \$100,000 face value T-bond has an annual coupon rate of 9.5 percent and paid its last coupon 48 days ago. What is the accrued interest on the bond? Accrued Interest 5 \$100,000 (0.095/2)(48/182.5) 5 \$1,249.32. Note that we assume that the half-year has 182.5 days. There are specific rules for determining the number of days in a half-year. 5. What conditions are necessary for the conversion factors on the CBOT T-bond contract to create favorable conditions for delivering one bond instead of another? Bill Price 5 \$1,000,000 2 0.0875 (\$1,000,000) (90) 360 5 \$978,125 5 Interest Rate Futures: Introduction

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There is one market condition under which the conversion factor method creates no bias: the yield curve is flat and all rates are 6 percent. Under any other circumstance, the conversion factor method will give incen- tives to deliver some bonds in preference to others. 6. The JUN T-bill futures IMM Index value is 92.80, while the SEP has a value of 93.00. What is the implied percentage cost-of-carry to cover the period from June to September? For the JUN contract the implied invoice amount is: Bill Price 5 \$1,000,000 2 0.0720(\$1,000,000)(90)/360 5 \$982,000 Paying this amount in June will yield \$1,000,000 in September when the delivered T-bill matures. Therefore, the implied interest rate is:
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005 - 5 Interest Rate Futures Introduction Answers to...

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