Answer: Weight of 2-Year Treasury = 55.54%; Weight of 15-Year Treasury = 44.46%

## Explanation To construct a barbell portfolio with the same cost and duration as the bullet portfolio: **Given:** - Cost of bullet = USD 63,865,800 - Duration of bullet = 6.272 - Duration of 2-Year Treasury = 1.938 - Duration of 15-Year Treasury = 11.687 **Equations:** 1. **Cost constraint:** V₂ + V₁₅ = 63,865,800 2. **Duration constraint:** (V₂/63,865,800) × 1.938 + (V₁₅/63,865,800) × 11.687 = 6.272 **Solving:** From equation (1): V₂ = 63,865,800 - V₁₅ Substitute into equation (2): 6.272 = [(63,865,800 - V₁₅)/63,865,800] × 1.938 + (V₁₅/63,865,800) × 11.687 Multiply both sides by 63,865,800: 400,566,297.6 = 123,771,920.4 - 1.938V₁₅ + 11.687V₁₅ 400,566,297.6 = 123,771,920.4 + 9.749V₁₅ 276,794,377.2 = 9.749V₁₅ V₁₅ = 28,392,078.90 V₂ = 63,865,800 - 28,392,078.90 = 35,473,721.10 **Weights:** - Weight of 2-Year Treasury = 35,473,721.10 / 63,865,800 = 55.54% - Weight of 15-Year Treasury = 28,392,078.90 / 63,865,800 = 44.46% **Why other options are incorrect:** - **A**: Incorrectly calculates weights as duration ratios: 1.938/(1.938+11.687) = 14.22% - **B**: Switches the correct weights - **D**: Switches the incorrect weights from A

Author: LeetQuiz Editorial Team