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