Andrew Jacobson Financial

Suppose That A Bond Portfolio With A Duration Of 12 Years Is Hedged Using A Futures

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4.15. It is July 30, 1992. The cheapest-to-deliver bond in a September 1992 Treasury bond futures contract is a 13 percent coupon bond, and delivery is expected to be made on September 30, 1992. Coupon payments on the bond are made on February 4 and August 4 each year. The term structure is flat and the rate of interest with semiannual compounding is 12% per annum The conversion factor for the bond is 1.5. The current quoted bond price is $110. Calculate the quoted futures price for the contract.

4.16. An investor is looking for arbitrage opportunities in the Treasury bond futures market. What complications are created by the fact that the party with a short position can choose to deliver any bond with a maturity of over 15 years?

4.17. Suppose that the Treasury bill futures price for a contract maturing in 33 days is quoted as 90.04 and the discount rate for a 123-day Treasury bill is 10.03. What is the implied repo rate? How can it be used?

4.18. Suppose that the 9-month interest rate is 8% per annum and the 6-month interest rate is 7.5% per annum (both with continuous compounding). Estimate the futures price of 90-day Treasury bills with a face value of $1 million for delivery in 6 months. How would the price be quoted?

4.19. Assume that a bank can borrow or lend money at the same interest rate in Euromarkets. The 90-day rate is 10% per annum and the 180-day rate is 10.2% per annum both expressed with continuous compounding. The Eurodollar futures price for a contract maturing in 90 days is quoted as 89.5. What arbitrage opportunities are open to the bank?

4.20. A Canadian company wishes to create a Canadian T-bill futures contract from a U.S. Treasury bill futures contract and forward contracts on foreign exchange. Using an example, explain how this can be done. For the purposes of this problem, assume that a futures contract is the same as a forward contract.

4.21. A 5-year bond with a yield of 11% (continuously compounded) pays an 8% coupon at the end of each year.

(b) What is the bond's duration?

(c) Use the duration to calculate the effect on the bond's price of a 0.2% decrease in its yield.

(d) Recalculate the bond's price on the basis of a 10.8% per annum yield and verify that the result is in agreement with your answer to (c).

4.22. Portfolio A consists of a 1-year discount bond with a face value of $2,000 and a 10-year discount bond with a face value of $6,000. Portfolio B consists of a 5.95 year discount bond with a face value of $5,000. The current yield on all bonds is 10% per annum

(a) Show that both portfolios have the same duration.

(b) Show that the percentage changes in the values of the two portfolios for a 10-basis-point increase in yields is the same.

(c) What are the percentage changes in the values of the two portfolios for a 5% per annum increase in yields?

(d) Which portfolio has the higher convexity?

4.23. Suppose that a bond portfolio with a duration of 12 years is hedged using a futures contract where the underlying asset has a duration of 4 years. What is likely to be the impact on the hedge of the fact that the 12-year rate is less volatile than the 4-year rate?

4.24. Suppose that it is February 20 and a treasurer realizes that on July 17, the company will have to issue $5 million of commercial paper with a maturity of 180 days. If the paper were issued today, it would realize $4,520,000. (In other words, the company would receive $4,520,000 for its paper and have to redeem it at $5,000,000 in 180 days time.) The September Eurodollar futures price is quoted as 92.00. How should the treasurer hedge the company's exposure?

4.25. On August 1, a portfolio manager has a bond portfolio worth $10 million. The duration of the portfolio is 7.1 years. The December Treasury bond futures price is currently 91-12 and the cheapest-to-deliver bond has a duration of 8.8 years. How should the portfolio manager immunize the portfolio against changes in interest rates over the next 2 months?

4.26. How can the portfolio manager change the duration of the portfolio to 3.0 years in Problem 4.25?

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