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Answer: 7.5.
## Explanation To calculate the portfolio duration, we need to compute the weighted average duration of all bonds in the portfolio, where the weights are based on the market values of each bond. **Step 1: Calculate total portfolio value** Total portfolio value = $1.2M + $3.4M + $2.9M + $1.6M = $9.1 million **Step 2: Calculate weight of each bond** - Bond A weight = $1.2M / $9.1M = 0.1319 - Bond B weight = $3.4M / $9.1M = 0.3736 - Bond C weight = $2.9M / $9.1M = 0.3187 - Bond D weight = $1.6M / $9.1M = 0.1758 **Step 3: Calculate weighted duration for each bond** - Bond A weighted duration = 0.1319 × 3.2 = 0.4221 - Bond B weighted duration = 0.3736 × 7.6 = 2.8394 - Bond C weighted duration = 0.3187 × 12.4 = 3.9519 - Bond D weighted duration = 0.1758 × 1.5 = 0.2637 **Step 4: Sum weighted durations** Portfolio duration = 0.4221 + 2.8394 + 3.9519 + 0.2637 = 7.4771 ≈ 7.5 **Verification with direct calculation:** Portfolio duration = (1.2×3.2 + 3.4×7.6 + 2.9×12.4 + 1.6×1.5) / 9.1 = (3.84 + 25.84 + 35.96 + 2.4) / 9.1 = 68.04 / 9.1 = 7.4769 ≈ 7.5 Therefore, the portfolio duration is closest to **7.5**, which corresponds to option C.
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A portfolio consists of four bonds with the following characteristics:
| Bond | Market Value | Duration |
|---|---|---|
| A | $1.2 million | 3.2 |
| B | $3.4 million | 7.6 |
| C | $2.9 million | 12.4 |
| D | $1.6 million | 1.5 |
The duration of the portfolio is closest to:
A
5.4.
B
6.2.
C
7.5.