You are the manager of a bond portfolio of $20 million face value of bonds worth $19,548,476. The portfolio has a yield of 10.20% and a duration of 7.43. You plan to liquidate the portfolio in 6 months and are concerned about an increase in interest rates that would produce a loss on the portfolio. You would like to lower duration to 4 years. A T-bond futures contract with the appropriate expiration is priced at 71.975 with a face value of $100,000, an implied yield of 10% and an implied duration of 7.53.
In 6 months, the portfolio value has fallen to $18,752,517 and the futures price is 67.85.
a. What is the profit or loss on the bond portfolio (must state if gain or loss and the amount)?
b. What is the profit or loss on the futures contracts (must state if gain or loss and the amount)?
c. What is the net gain or loss on the combined bond portfolio and the futures contracts (must state if gain or loss and the amount)?