The correct answer is A.

The face value of the offsetting position, $F_h$, is calculated using the formula:

$$F_h = -F_p \cdot \frac{\text{DV01}_p}{\text{DV01}_h} \cdot \hat{\beta}$$

Where:

• $F_p$: The face value of the bond to be hedged.
• $\text{DV01}_p$: The DV01 of the bond to be hedged.
• $\text{DV01}_h$: The DV01 of the hedging swap.
• $\hat{\beta}$: The regression hedge adjustment factor.

Substituting the given values, we find:

$$F_h = -100 \cdot \frac{0.300}{0.250} \cdot 0.800 = -96 \text{ million}.$$

Things to Remember:

• Negative values indicate the opposite position direction needed.
• Mathematically neutralizing P&L ensures strategic stability against yield movements.