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.

1) What if your target duration were 5?

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.

c) Repeat but with a yield beta of 0.9978.