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 weights for each bond** - Weight of Bond A = $1.2M / $9.1M = 0.1319 - Weight of Bond B = $3.4M / $9.1M = 0.3736 - Weight of Bond C = $2.9M / $9.1M = 0.3187 - Weight of Bond D = $1.6M / $9.1M = 0.1758 **Step 3: Calculate weighted durations** - Bond A weighted duration = 3.2 × 0.1319 = 0.4221 - Bond B weighted duration = 7.6 × 0.3736 = 2.8394 - Bond C weighted duration = 12.4 × 0.3187 = 3.9519 - Bond D weighted duration = 1.5 × 0.1758 = 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 = 7.477 ≈ 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.

Author: LeetQuiz .