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Answer: Short 207 contracts
To hedge a long bond portfolio against interest rate movements, the manager should take the **opposite duration position** in futures, which means **shorting** Treasury bond futures. ### Hedge ratio A standard duration-based hedge ratio is: \[ N=\frac{D_P\,V_P}{D_F\,V_F} \] where: - \(D_P=6.0\) years - \(V_P=30,000,000\) - \(D_F=9.1\) years - futures price = **95-12 = 95.375** - contract size = **$100,000** So the contract value is: \[ V_F=0.95375\times 100,000=95,375 \] Now compute: \[ N=\frac{6.0\times 30,000,000}{9.1\times 95,375} \approx 207 \] Because the portfolio is **long duration**, the hedge requires a **short futures position**. So the correct answer is **D. Short 207 contracts**.
Author: Manit Arora
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Q-173.2. A portfolio manager wants to hedge her bond portfolio this is worth $30 million and will have a duration of 6.0 years at maturity of the hedge in a few months. The relevant U.S. Treasury bond futures price is 95-12 and the cheapest-to-delivery (CTD) bond will have a duration of 9.1 years at hedge maturity. What is the trade that hedges against interest rate movements?
A
Long 57 contracts
B
Long 207 contracts
C
Short 57 contracts
D
Short 207 contracts
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