A manager has a $50 million portfolio that consists of 50% stock and 50% bonds (i.e., $25 million each) - The beta of the stock position is 0.8. - The modified duration of the bond position is 6.8 The manager wishes to achieve an effective mix of 60% stock (i.e., $30 million) and 40% bonds. Since the move is only temporary, and rather than having to decide which bonds to sell and which stocks to buy to achieve the desired mix, the manager will use futures contracts. - The price of the stock index futures contract is $300,000 (including the multiplier), and its beta is 1.1. - The price and modified duration of the bond futures contracts are $102,000 and 8.1 respectively.
a. How many stock index futures do you need to use? Should you short or long the stock index futures?
b. How many bond futures do you need to use? Should you short or long the bond index futures?