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Answer: 55.54%
The correct weights are **55.54% in the 2-year Treasury** and **44.46% in the 15-year Treasury**. So the correct combination is **C and B** respectively. [forum.sseiqforum](https://forum.sseiqforum.com/question/vrm-barbel-and-bullet-portfolio/) ## How to get it For a barbell made from only the 2-year and 15-year bonds, let \(w_2\) and \(w_{15}\) be the portfolio weights, with: \[ w_2 + w_{15} = 1 \] and the portfolio duration equal to the 7-year bond’s duration: \[ 1.938w_2 + 11.687w_{15} = 6.272 \] Solving gives: \[ w_{15} = \frac{6.272 - 1.938}{11.687 - 1.938} \approx 0.4446 \] \[ w_2 = 1 - 0.4446 \approx 0.5554 \] ## Final answer - **2-year Treasury: 55.54%** - **15-year Treasury: 44.46%** So the correct pair is **C: 55.54%** and **B: 44.46%**. [forum.sseiqforum](https://forum.sseiqforum.com/question/vrm-barbel-and-bullet-portfolio/)
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A fixed-income portfolio manager currently holds a bullet 7-year US Treasury position with USD 60 million face value. The manager would like to create a cost matching barbell portfolio by purchasing a combination of a 2-year Treasury and a 15-year Treasury that would have the same duration as the 7-year US Treasury position. The data for the three US Treasuries are listed below:
| Maturity | Price | Duration |
|---|---|---|
| 2 Years | 100.972 | 1.938 |
| 7 Years | 106.443 | 6.272 |
| 15 Years | 122.175 | 11.687 |
Which of the following combinations correctly describes the weights of the two bonds that the manager will use to construct the barbell portfolio?
A
14.22%
B
44.46%
C
55.54%
D
85.78%
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