A $200 million bond portfolio currently has a modified duration of 6.53. In anticipation of a decline in interest rates, the portfolio manager seeks to increase the modified duration of the portfolio to 9.5 by using a Treasury bond futures contract priced at 95,650. The futures contract has an implied modified duration of 12.65 the portfolio manager has estimated the yield beta of her portfolio to be 1 relative to the implied yield on the futures contract. Required:
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.