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CHAPTER 5 QUESTIONS AND PROBLEMS 5.2. The term structure is upward sloping. Put the following in order of magnitude: a. The five-year zero rate b. The yield on a five-year coupon-bearing bond c. The forward rate corresponding to the period between 5 and 5.25 years in the future What is the answer to this question when the term structure is downward sloping? 5.3. The six-month and one-year zero rates are both 10% per annum. For a bond that lasts 18 months and pays a coupon of 8% per annum (with a coupon payment having just been made), the yield is 10.4% per annum. What is the bond's price? What is the 18-month zero rate? All rates are quoted with semiannual compounding. 5.4. It is January 9, 2003. The price of a Treasury bond with a 12% coupon that matures on October 12, 2009, is quoted as 102-07. What is the cash price? 5.5. The price of a 90-day Treasury bill is quoted as 10.00. What continuously compounded return (on an actual/365 basis) does an investor earn on the Treasury bill for the 90-day period? 5.6. What assumptions does a duration-based hedging scheme make about the way in which the term structure of interest rates moves? 5.7. It is January 30. You are managing a bond portfolio worth $6 million. The duration of the portfolio in six months will be 8.2 years. The September Treasury bond futures price is currently 108-15, and the cheapest-to-deliver bond will have a duration of 7.6 years in September. How should you hedge against changes in interest rates over the next six months? 5.8. Suppose that 6-month, 12-month, 18-month, 24-month, and 30-month zero rates are 4%, 4.2%, 4.4%, 4.6%, and 4.8% per annum with continuous compounding respectively. Estimate the cash price of a bond with a face value of 100 that will mature in 30 months pays a coupon of 4% per annum semiannually. 5.9. A three-year bond provides a coupon of 8% semiannually and has a cash price of 104. What is the bond yield? 5.10. Suppose that the 6-month, 12-month, 18-month, and 24-month zero rates are 5%, 6%, 6.5%, and 7%, respectively. What is the two-year par yield? 5.11. The cash prices of six-month and one-year Treasury bills are 94.0 and 89.0. A 1.5-year bond that will pay coupons of $4 every six months currently sells for $94.84. A two-year bond that will pay coupons of $5 every six months currently sells for $97.12. Calculate the 6-month, 1- year, 1.5-year, and 2-year zero rates.
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5.14. A 10-year, 8% coupon bond currently sells for $90. A 10-year, 4% coupon bond currently sells for $80. What is the 10-year zero rate? (Hint: Consider taking a long position in two of the 4% coupon bonds and a short position in one of the 8% coupon bonds.) 5.15. Explain carefully why liquidity preference theory is consistent with the observation that the term structure tends to be upward sloping more often than it is downward sloping. 5.16. It is May 5, 2003. The quoted price of a government bond with a 12% coupon that matures on July 27, 2011, is 110-17. What is the cash price?
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