Answer: USD -525,000

## Explanation To calculate the portfolio price change for a 10 bp increase in yield: **Formula**: ΔPortfolio Value = -Portfolio Modified Duration × Portfolio Value × Δy **Step 1: Calculate portfolio value-weighted modified duration** - Total portfolio value = 4,000,000 + 2,000,000 + 3,000,000 + 1,000,000 = **10,000,000** - Weighted duration = (4,000,000/10,000,000 × 7.5) + (2,000,000/10,000,000 × 1.6) + (3,000,000/10,000,000 × 6.0) + (1,000,000/10,000,000 × 1.3) - = (0.4 × 7.5) + (0.2 × 1.6) + (0.3 × 6.0) + (0.1 × 1.3) - = 3.0 + 0.32 + 1.8 + 0.13 = **5.25 years** **Step 2: Calculate price change** - Δy = 10 bp = 0.0010 - ΔPortfolio Value = -5.25 × 10,000,000 × 0.0010 - = -52,500,000 × 0.0010 = **-52,500** **Alternative calculation (bond by bond):** - Bond 1: -7.5 × 4,000,000 × 0.0010 = -30,000 - Bond 2: -1.6 × 2,000,000 × 0.0010 = -3,200 - Bond 3: -6.0 × 3,000,000 × 0.0010 = -18,000 - Bond 4: -1.3 × 1,000,000 × 0.0010 = -1,300 - **Total**: -30,000 - 3,200 - 18,000 - 1,300 = **-52,500** **Therefore, the portfolio value decreases by USD -52,500.**

Author: LeetQuiz Editorial Team