Solutions for Select End-of-Chapter Questions and Problems: Chapter Twenty-Two

Solutions for Select End-of-Chapter Questions and Problems: Chapter Twenty-Two

4. An FI holds a 15-year, $10 million par value bond that is priced at 104 with a yield to maturity of 7 percent. The bond has a duration of eight years, and the FI plans to sell it after two months. The FI’s market analyst predicts that interest rates will be 8 percent at the time of the desired sale. Because most other analysts are predicting no change in rates, two-month forward contracts for 15-year bonds are available at 104. The FI would like to hedge against the expected change in interest rates with an appropriate position in a forward contract. What will this position be? Show that if rates rise 1 percent as forecast, the hedge will protect the FI from loss.

The expected change in the spot position is –8 x $10,400,000 x (0.01/1.07) = -$777,570. This would mean a price change from 104 to 96.2243 per $100 face value of bonds. By entering into a two-month forward contract to sell $10,000,000 of 15-year bonds at 104, the FI will have hedged its spot position. If rates rise by 1 percent, and the bond value falls by $777,570, the FI can close out its forward position by receiving 104 for bonds that are now worth 96.2243 per $100 face value. The profit on the forward position will offset the loss in the spot market.

The actual transaction to close the forward contract may involve buying the bonds in the market at 96.2243 and selling the bonds to the counterparty at 104 under the terms of the forward contract. Note that if a futures contract were used, closing the hedge position would involve buying a futures contract through the exchange with the same maturity date and dollar amount as the initial opening hedge contract.

6. Suppose an FI purchases a Treasury bond futures contract at 95.

a. What is the FI’s obligation at the time the futures contract is purchased?

The FI is obligated to take delivery of a $100,000 face value 20-year Treasury bond at a...