Explanation:
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
For a barbell made from only the 2-year and 15-year bonds, let and be the portfolio weights, with:
and the portfolio duration equal to the 7-year bond’s duration:
Solving gives:
So the correct pair is C: 55.54% and B: 44.46%. forum.sseiqforum
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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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