Answer: USD -52,500

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.

Author: LeetQuiz .