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

The correct answer to the question is option C, which indicates that the weights of the 2-Year and 15-Year Treasuries in the barbell portfolio should be 55.54% and 44.46%, respectively. The explanation for this answer is based on the requirement to create a barbell portfolio with the same cost and duration as the existing 7-year US Treasury position. First, the cost of the 7-year Treasury position is calculated by taking the price of the bond (106.443) and multiplying it by the face value (USD 60 million), which equals USD 63,865,800. Next, the equation to match the cost of the barbell portfolio is set up as follows: \[ V_2 + V_{15} = USD 63,865,800 \] where \( V_2 \) is the cost of the 2-Year Treasury and \( V_{15} \) is the cost of the 15-Year Treasury. To match the duration of the 7-year Treasury, the weighted-average duration of the 2-year and 15-year Treasuries is calculated using the following equation: \[ 6.272 = \left(\frac{V_2}{63,865,800}\right) \times 1.938 + \left(\frac{V_{15}}{63,865,800}\right) \times 11.687 \] Substituting \( V_2 \) from the first equation into the second equation, we get: \[ 6.272 = \left(\frac{63,865,800 - V_{15}}{63,865,800}\right) \times 1.938 + \left(\frac{V_{15}}{63,865,800}\right) \times 11.687 \] Solving this equation for \( V_{15} \), we find: \[ V_{15} = USD 28,392,078.90 \] Using the first equation again, we can find \( V_2 \) as: \[ V_2 = 63,865,800 - V_{15} = 63,865,800 - 28,392,078.90 = USD 35,473,721.10 \] Finally, the weights of the 2-Year and 15-Year Treasuries are calculated as: \[ \text{Weight of 2-Year Treasury} = \frac{V_2}{V_2 + V_{15}} \times 100 = \frac{35,473,721.10}{63,865,800} \times 100 \approx 55.54\% \] \[ \text{Weight of 15-Year Treasury} = \frac{V_{15}}{V_2 + V_{15}} \times 100 = \frac{28,392,078.90}{63,865,800} \times 100 \approx 44.46\% \] Thus, the correct combination that matches the cost and duration of the 7-year US Treasury position is the one with weights of 55.54% for the 2-Year Treasury and 44.46% for the 15-Year Treasury, which corresponds to option C.

Author: LeetQuiz Editorial Team