The correct answer is B: USD -52,500

The impact of a small change in yield on a bond's (or portfolio's) value is calculated using Modified Duration:

Approximate % change in bond price ≈ - Modified Duration × ΔYield

Approximate change in value ≈ - Modified Duration × ΔYield × Bond Value

Here, ΔYield = +10 basis points = +0.10% = +0.001 (in decimal form).

We calculate the value change for each bond individually, then sum them up for the total portfolio impact.

Step-by-step calculation:

Bond 1:
Value = $4,000,000
Modified Duration = 7.5
Change = -7.5 × 0.001 × 4,000,000 = -30,000

Bond 2:
Value = $2,000,000
Modified Duration = 1.6
Change = -1.6 × 0.001 × 2,000,000 = -3,200

Bond 3:
Value = $3,000,000
Modified Duration = 6.0
Change = -6.0 × 0.001 × 3,000,000 = -18,000

Bond 4:
Value = $1,000,000
Modified Duration = 1.3
Change = -1.3 × 0.001 × 1,000,000 = -1,300

Total portfolio impact:

-30,000 + (-3,200) + (-18,000) + (-1,300) = -52,500

Thus, a 10 bp increase in yield causes an approximate loss of USD 52,500 on the portfolio.

Alternative (faster) method using Portfolio Modified Duration:

1. Calculate total portfolio value = 4M + 2M + 3M + 1M = $10,000,000
2. Calculate portfolio modified duration (value-weighted average):
   = (4M×7.5 + 2M×1.6 + 3M×6.0 + 1M×1.3) / 10M
   = (30M + 3.2M + 18M + 1.3M) / 10M = 52.5M / 10M = 5.25
3. Portfolio change ≈ -5.25 × 0.001 × 10,000,000 = -52,500

Both methods give the same result.

Why the other options are wrong:

• A (-41,000): Likely a calculation error (e.g., forgetting one or more bonds or using wrong weights).
• C (-410,000): Common mistake — forgetting to convert 10 bp to 0.001 (using 0.01 instead).
• D (-525,000): Mistake of treating duration as Macaulay or using Δy = 0.10 (10%) instead of 0.001.

Key FRM tip: Always convert basis points to decimal form (10 bp = 0.001). The negative sign indicates an inverse relationship between yield and price.