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Answer: 55.54%
The question is about constructing a cost matching barbell portfolio with the same duration as a 7-year US Treasury position. The portfolio manager is looking to combine a 2-year and a 15-year Treasury to achieve this goal. The correct answer is C, which represents the weights of the two bonds in the barbell portfolio. To understand why, let's break down the process: 1. **Cost Matching**: The cost of the 7-year Treasury is calculated by taking its price (106.443) and multiplying it by the face value (USD 60 million), resulting in USD 63,865,800. 2. **Duration Matching**: The duration of the 7-year Treasury is 6.272. The goal is to match this duration with a combination of the 2-year and 15-year Treasuries. The duration of the 2-year Treasury is 1.938, and the duration of the 15-year Treasury is 11.687. 3. **Setting Up the Equations**: To match the cost, the sum of the costs of the 2-year and 15-year Treasuries (V2 and V15, respectively) must equal the cost of the 7-year Treasury: \[ V2 + V15 = 63,865,800 \] 4. **Matching Duration**: The weighted-average duration of the two bonds must equal the duration of the 7-year Treasury: \[ 6.272 = \left(\frac{V2}{63,865,800} \times 1.938\right) + \left(\frac{V15}{63,865,800} \times 11.687\right) \] 5. **Solving the Equations**: By substituting V2 from the first equation into the second, we get a single equation in terms of V15. Solving this equation gives us the value for V15, which is the cost of the 15-year Treasury. Subtracting this from the total cost gives us the cost of the 2-year Treasury (V2). 6. **Calculating Weights**: The weights of the 2-year and 15-year Treasuries are then calculated by dividing their respective costs by the total cost of the portfolio. The solution process leads to the weights of 55.54% for the 2-year Treasury and 44.46% for the 15-year Treasury, which corresponds to option C. This combination ensures that the cost and duration of the barbell portfolio match those of the original 7-year Treasury position.
Author: LeetQuiz Editorial Team
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Given the following data on price and duration for each bond in a fixed-income portfolio, determine the appropriate proportions of a 2-year Treasury and a 15-year Treasury that a portfolio manager should acquire. The goal is to create a barbell portfolio with a combined duration equivalent to their existing 7-year US Treasury position. How should the portfolio manager allocate investments between the 2-year Treasury and the 15-year Treasury to achieve this duration match?
A
14.22%
B
44.46%
C
55.54%
D
85.78%
