You are the manager of a bond portfolio of $10 million face value of bonds worth $9,448,456. The portfolio has a yield of 12.25 percent and a duration of 8.33.

You plan to liquidate the portfolio in six months and are concerned about an increase in interest rates that would produce a loss on the portfolio. You would like to lower its duration 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 percent, and an implied duration of 8.43 years.

a. Should you buy or sell futures? How many contracts should you use?

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