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.