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

To construct a barbell portfolio with the same cost and same duration as the bullet, the portfolio manager must first calculate the cost of the bullet position, which is USD 63,865,800. The manager then needs to find the appropriate weights for the 2-Year and 15-Year Treasuries such that the weighted-average duration of these two bonds matches the duration of the 7-Year Treasury position. The cost of the bullet position is calculated as follows: \[ \text{Cost of bullet} = \left(\frac{106.443}{100}\right) \times \text{USD 60,000,000} = \text{USD 63,865,800} \] Let \( V_2 \) and \( V_{15} \) be the costs of the 2-Year and 15-Year Treasuries, respectively. The equation to match the duration is: \[ 6.272 = \left(\frac{V_2}{63,865,800}\right) \times 1.938 + \left(\frac{V_{15}}{63,865,800}\right) \times 11.687 \] From the cost equation: \[ V_2 = 63,865,800 - V_{15} \] Substituting \( V_2 \) in the duration equation: \[ 6.272 = \left[\left(63,865,800 - V_{15}\right)/63,865,800\right] \times 1.938 + \left(\frac{V_{15}}{63,865,800}\right) \times 11.687 \] Solving for \( V_{15} \) gives: \[ 400,566,297.6 = 123,771,920.4 - 1.938V_{15} + 11.687V_{15} \] \[ 276,794,377.2 = 9.749V_{15} \] \[ V_{15} = \text{USD 28,392,078.90} \] And \( V_2 \) is: \[ V_2 = 63,865,800 - V_{15} = 63,865,800 - 28,392,078.90 = \text{USD 35,473,721.10} \] The weights of the 2-Year and 15-Year Treasuries are then: \[ \text{Weight of 2-Year Treasury} = \frac{35,473,721.10}{63,865,800} = 55.54\% \] \[ \text{Weight of 15-Year Treasury} = \frac{28,392,078.90}{63,865,800} = 44.46\% \] Thus, the correct combination that describes the weights of the two bonds for the barbell portfolio is 55.54% for the 2-Year Treasury and 44.46% for the 15-Year Treasury, which corresponds to option C.

Author: LeetQuiz Editorial Team