A fixed income money manager has a bond portfolio with a 70 percent allocation to longterm bonds and a 30 percent allocation to short-term bonds. The portfolio is currently valued at $75 million. The manager wishes to reduce the long- term bonds allocation to 55 percent and increase the short-term bonds allocation to 45 percent for a period of three months. The modified duration of the long-term bonds is 7.5 and of the short-term bonds is 4.5.

A bond futures contract that expires in three months is priced at $95,750 and has a modified duration of 6.25. Assume that the modified duration of cash equivalents is 0.25. Also assume that interest rates that drive long-term and short- term bond prices have a yield beta of 1 with respect to interest rates that drive the bond futures market.

A. Show how the manager can achieve his goals by using bond futures. Indicate the number of contracts and whether the manager should go long or short.

B. After 2 months (not three, but two), the short-term bonds are down 5.63 percent and long-term bonds are down 9.38 percent. The bond futures price is $88,270.

B1. What is the value of a re-balanced portfolio?

B2. What would have been the value of the portfolio without rebalancing?