You are the manager of a bond portfolio of $10 million face value of bonds worth $9,448,546. The portfolio has 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 convert your portfolio to synthetic cash. A T-bond futures contract with the appropriate expiration is priced at 72 3/32 with a face value of $100,000, and an implied duration of 8.43 years. Use a yield beta of 1.0. Hints: (i) target duration is zero, (ii) the bond portfolio is worth $9,448,546: that’s the B in equation 6.4, (iii) the futures price (the “f” in equation 6.4) is 72 3/32 percent of $100,000 = $72,094.

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

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