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Answer: Short 138 contracts
The portfolio currently has a duration of 6.0 years, but the manager only wants to reduce it to 2.0 years. That means the hedge must offset only **4.0 years** of duration, not all 6.0 years. ### Step 1: Use the same hedge ratio as in the previous question From Q-173.2, a full hedge to zero duration requires about **207 short contracts**. ### Step 2: Scale the hedge to the desired duration reduction Only 4 of the 6 duration years need to be hedged: \[ N=207\times \frac{4}{6}\approx 138 \] Since this is still a hedge against interest rate risk, the position is **short** futures. So the correct answer is **D. Short 138 contracts**.
Author: Manit Arora
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Q-173.3. The same portfolio manager above—i.e., owning a portfolio with duration of 6.0 years’ worth $30 million and hedging with Treasury bond futures contracts priced at 95-12 and CTD bond with duration of 9.1 years—wants to reduce the portfolio duration to 2.0 years instead of reducing the duration to zero. What is the trade that reduces the portfolio from 6.0 years to a hedged position with duration of 2.0 years?
A
Long 94 contracts
B
Long 138 contracts
C
Short 94 contracts
D
Short 138 contracts
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