A $500 million bond portfolio currently has a modified duration of 12.5. The portfolio manager intends to decrease the modified duration of the portfolio to 8 by using a Treasury bond futures contract priced at 105,250. The futures contract has an implied modified duration of 9.25. The portfolio manager has estimated the yield beta of her portfolio to be 1 relative to the implied yield on the futures contract.

How many contracts will be needed to change the duration of the portfolio as intended?

Without regard to your answer to (1), assume that the number of contracts needed is 2,496. Also assume, that the implied yield on the portfolio decreased by 0.50%, the portfolio increased in value by 31,343,750, and the futures contract increased in value to 109,742. What is the profit or loss on the futures contract?

What is the return on the portfolio including the futures position?

Based on the performance of the recent performance of the portfolio, what is the duration of the portfolio? Specifically, calculate the duration of the portfolio excluding the futures position.

Did the futures position modify the duration of the portfolio? What is the duration of the portfolio including the futures position?

Answer rating: 100% (QA)

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