Answer: $169,412

## Explanation To calculate the face value of the offsetting TIPS position needed for the regression hedge, we use the following formula: \[ \text{Face Value of Hedge} = \text{Face Value of Position} \times \frac{\text{DV01}_{\text{Position}}}{\text{DV01}_{\text{Hedge}}} \times \beta \] Where: - Face Value of Position = $100,000 - DV01 of T-bond (position) = 0.072 - DV01 of TIPS (hedge) = 0.051 - β (hedge adjustment factor) = 1.2 \[ \text{Face Value of TIPS} = 100,000 \times \frac{0.072}{0.051} \times 1.2 \] First, calculate the DV01 ratio: \[ \frac{0.072}{0.051} = 1.4117647 \] Then multiply by the face value: \[ 100,000 \times 1.4117647 = 141,176.47 \] Finally, multiply by the beta coefficient: \[ 141,176.47 \times 1.2 = 169,411.76 \approx \$169,412 \] Therefore, the face value of the offsetting TIPS position needed is **$169,412**, which corresponds to option B. This regression hedge accounts for the historical relationship between the two instruments through the beta coefficient, providing a more accurate hedge than a simple DV01-based hedge.

Author: LeetQuiz .