19. On August 1, a portfolio manager has a bond portfolio worth $10 million. The duration of the portfolio is 7.1 years. The December T-bond futures price is currently 91-12, and the cheapest to deliver bond has a duration of 8.8 years. Yields are 9.5% on the futures and 9.5% on the bond portfolio. How should the portfolio manager immunize the portfolio against changes in interest rates over the next two months?

1. Long 14 T-bond futures contracts.
2. Long 49 T-bond futures contracts.
3. Short 9 T-bond futures contracts.
4. Short 49 T-bond futures contracts.
5. Short 88 T-bond futures contracts.

20. In question 19, afterthe portfolio was immunized against interest rate changes, the duration of the total portfolio including the T-bondfutures is: a. 0 b. 6 months c. 7.1 years d. 8.8 years e. None of the above