Explanation:
The duration of a portfolio of bonds is the weighted average (using market value weights) of the durations of the bonds in the portfolio. First, let's find the weights.
| Bond | Price as Percentage of Par | Face Value $ | Market Value $ |
|---|---|---|---|
| 1 | 95.5000 | 2,000,000 | 1,910,000 |
| 2 | 88.6275 | 3,000,000 | 2,658,825 |
| 3 | 114.8750 | 5,000,000 | 5,743,750 |
| Total | 10,312,575 |
The weights based on market values are:
Weight of bond 1 = 1,910,000 / 10,312,575 = 0.1852
Weight of bond 2 = 2,658,825 / 10,312,575 = 0.2578
Weight of bond 3 = 5,743,750 / 10,312,575 = 0.5570
| Bond | Weights | Duration | Weighted Duration |
|---|---|---|---|
| 1 | 0.1852 | 6.95 | 1.2871 |
| 2 | 0.2578 | 9.77 | 2.5187 |
| 3 | 0.5570 | 14.81 | 8.2492 |
| Total | 12.0550 |
(Book 4, Module 58.2, LO 58.g)
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Question 11
Assume an investor holds a portfolio of bonds as follows:
$2,000,000 par value of 10-year bonds with a duration of 6.95 priced at 95.5000.$3,000,000 par value of 15-year bonds with a duration of 9.77 priced at 88.6275.$5,000,000 par value of 30-year bonds with a duration of 14.81 priced at 114.8750.The duration of this portfolio is closest to:
A
10.64.
B
12.06.
C
13.28.
D
13.57.
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