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 weights for each bond
$1.2M / $9.1M = 0.1319$3.4M / $9.1M = 0.3736$2.9M / $9.1M = 0.3187$1.6M / $9.1M = 0.1758Step 3: Calculate weighted durations
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 = 7.477 ≈ 7.5
Therefore, the portfolio duration is closest to 7.5.
Key Concept: Portfolio duration is calculated as the market-value weighted average of the individual bond durations, not as a simple arithmetic average.
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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.