A $ 200 million bond portfolio currently has a modified duration of 6.53. The portfolio manager

wishes to increase the modified duration of the bond portfolio to 9.50 by using a futures

contract priced at $ 95,650. The futures contract has an implied modified duration of 12.65. The

portfolio manager has estimated that the yield on the bond portfolio is about 12% more volatile

than the implied yield on the futures contact.

A) Indicate whether the portfolio manager should enter a short or long futures position.

B) Calculate the number of contracts needed to change the duration of the bond portfolio.

C) Assume that on the horizon date, the yield on the bond portfolio has increased by 30

basis points and the portfolio value has decreased by $3,929,754. The implied yield on

futures has increased by 30 basis points, and the futures contract is priced at $ 92,616.

Calculate the overall gain on the position (bond plus futures). Determine the ex post

duration with and without the futures transaction.