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Chapter 6 Problems

# Chapter 6 Problems - CHAPTER 6 Interest Rate Futures...

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CHAPTER 6 Interest Rate Futures Practice Questions Problem 6.1. A U.S. Treasury bond pays a 7% coupon on January 7 and July 7. How much interest accrues per \$100 of principal to the bond holder between July 7, 2011 and August 9, 2011? How would your answer be different if it were a corporate bond? There are 33 calendar days between July 7, 2011 and August 9, 2011. There are 184 calendar days between July 7, 2011 and January 7, 2011. The interest earned per \$100 of principal is therefore 3 5 33 184 0 6277 \$ . For a corporate bond we assume 32 days between July 7 and August 9, 2011 and 180 days between July 7, 2011 and January 7, 2011. The interest earned is 3 5 32 180 0 6222 \$ . Problem 6.2. It is January 9, 2013. The price of a Treasury bond with a 12% coupon that matures on October 12, 2020, is quoted as 102-07. What is the cash price? There are 89 days between October 12, 2012, and January 9, 2013. There are 182 days between October 12, 2012, and April 12, 2013. The cash price of the bond is obtained by adding the accrued interest to the quoted price. The quoted price is 7 32 102 or 102.21875. The cash price is therefore 89 102 21875 6 \$105 15 182 Problem 6.3. How is the conversion factor of a bond calculated by the CME Group? How is it used? The conversion factor for a bond is equal to the quoted price the bond would have per dollar of principal on the first day of the delivery month on the assumption that the interest rate for all maturities equals 6% per annum (with semiannual compounding). The bond maturity and the times to the coupon payment dates are rounded down to the nearest three months for the purposes of the calculation. The conversion factor defines how much an investor with a short bond futures contract receives when bonds are delivered. If the conversion factor is 1.2345 the amount investor receives is calculated by multiplying 1.2345 by the most recent futures price and adding accrued interest. Problem 6.4. A Eurodollar futures price changes from 96.76 to 96.82. What is the gain or loss to an investor who is long two contracts? The Eurodollar futures price has increased by 6 basis points. The investor makes a gain per contract of 25 6 \$150 or \$300 in total.

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Problem 6.5. What is the purpose of the convexity adjustment made to Eurodollar futures rates? Why is the convexity adjustment necessary? Suppose that a Eurodollar futures quote is 95.00. This gives a futures rate of 5% for the three- month period covered by the contract. The convexity adjustment is the amount by which futures rate has to be reduced to give an estimate of the forward rate for the period. The convexity adjustment is necessary because a) the futures contract is settled daily and b) the futures contract expires at the beginning of the three months. Both of these lead to the futures rate being greater than the forward rate. Problem 6.6. The 350-day LIBOR rate is 3% with continuous compounding and the forward rate calculated from a Eurodollar futures contract that matures in 350 days is 3.2% with continuous compounding. Estimate the 440-day zero rate.
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