10. A bond portfolio has market value $50 million and effective duration 4.25. The portfolio manager would like to duration match a particular bond market index whose duration is 3.75. The dollar duration of the 10-year Treasury note futures contract is $4,500.

(a) What position would the portfolio manager have to take in the futures contract to duration match the portfolio?

(b) The futures contract price is 107.60. What is the market value of the hedge position that the portfolio manager must take?