You are the manager of a bond portfolio that has a face value of $10 million. The value of this portfolio is $9,448,456 today. The portfolio has a yield of 12.25% and a duration of 8.33 years. You plan to liquidate this portfolio in 6 months. Concerned about the changes in interest rates, you would like to lower the duration of your portfolio to 5 years. A T-Bond futures contract with the appropriate expiration is priced at 72 3/32 with a face value of $100,000, an implied yield of 12% and an implied duration of 8.43 years.

a. Indicate whether you should buy or sell futures to create the hedge that you want and determine the number of contracts you should use.

b. In six months, the portfolio has fallen in value to $8,952,597 and has a yield of 11.07%. The futures price is 68 16/32. Determine the profit from this transaction.

c. Using the duration, calculate the change in the value of the hedged position.