A portfolio is worth $12,000,000.

The futures price of a Treasury bond futures contract is 105 and each contract is for the delivery of bonds with a face value of $100,000.

On the delivery date the duration of the bond that is expected to be cheapest to deliver is 5 years.

On the hedge termination date the duration of the portfolio will be 3 years.

How should the portfolio manager hedge the bond portfolio against changes in interest rates?

a. Buy 69 futures contracts

b. Sell 686 futures contracts

c. Buy 686 futures contracts

d. Sell 69 futures contracts