Question

Question 9. Price Sensitivity Hedge Mr. Toriop manages a bond portfolio valued at $27,492,045. The bonds in this portfolio have a face value of $25 million. The portfolio has a yield of 8.35 percent and a duration of 7.67. Mr. Toriop is worried that interest rates will rise within the next year. He would like to lower the duration of your bond portfolio to 5 years. He finds a one-year bond futures contract and thinks that it would be an appropriate hedge for your portfolio. This futures contract is priced at 109 17/32, has an implied yield of 8 percent, and has an implied duration of 7.9 years. The futures contract size is $100,000. a. Should Mr. Toriop buy or sell futures? (1 mark) b. How many contracts should Mr. Toriop use? c. Suppose that the portfolio’s value falls to $26,557,089, and the futures price turns out to be 103 8/32 in one year’s time. What is the net profit from the hedged position? d. If Mr. Toriop were to liquidate the entire bond portfolio in one year’s time given the information in part (c), what would be the total proceeds received? (1 mark)

Answer 1

a). Futures price fall if interest rates rise so in order to hedge an interest rate rise, futures contracts have to be shorted. Mr.Toriop should sell futures.

b). Number of contracts to be shorted = (Bond portfolio value*desired duration of portfolio)/(Value of one futures contract*duration of futures contract)

Value of one futures contract = 109 17/32 = 109%*1,000 + (17*1,000/32) = 109,531.25

Number of contracts = (27,492,025*5)/(109,531.25*7.9) = 158.86 or rounding it off to 159 contracts need to be shorted.

c). Loss from bond portfolio after one year = current bond portfolio value - previous portfolio value

= 26,557,089 - 27,492,045 = -934,956

Futures contract price now = 103 8/32 = 103%*100,000 + (8*1,000/32) = 103,250

Gain from futures contract = (price one year before - price now)*number of contracts = (109,531.25 - 103,250)*159 = 998,718.75

Net profit = gain from futures contract - loss from portfolio

= 998,718.75 - 934,956 = 63,762.75

d). Portfolio value after one year is 26,557,089 so if the entire portfolio is liquidated this would be the total proceeds received.