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.