The face value of the hedging swap, $F_h$, 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 values:

$$F_h = -10,000 \cdot \frac{1,200}{1,500} \cdot 0.75 = -6,000.$$

Things to Remember:

• Exact computation helps match hedge values with targeted risk figures correctly.
• Negative face values ensure alignment with hedging direction.
• Precise derivations are critical for achieving proper interest rate risk offsets.