Answer: EUR 12.57 billion

## Calculation Explanation **Step 1: Calculate the new asset value** - Initial assets: EUR 100 billion - Equity market decline: 15% - New assets = 100 × (1 - 0.15) = EUR 85 billion **Step 2: Calculate the new liability value** - Initial liabilities: EUR 85 billion - Yield increase: 1.2% (Δy = +0.012) - Modified duration: 12.5 - Percentage change in liabilities = -Modified Duration × Δy = -12.5 × 0.012 = -0.15 = -15% - New liabilities = 85 × (1 - 0.15) = EUR 72.25 billion **Step 3: Calculate the surplus** - Surplus = Assets - Liabilities = 85 - 72.25 = EUR 12.75 billion Wait, let me recalculate this carefully: Actually, the percentage change in liabilities is: ΔL/L = -Modified Duration × Δy = -12.5 × 0.012 = -0.15 = -15% So new liabilities = 85 × (1 - 0.15) = 85 × 0.85 = EUR 72.25 billion Then surplus = 85 - 72.25 = EUR 12.75 billion But looking at the options, EUR 12.75 billion is option C, not D. Let me double-check: **Alternative calculation:** - Asset change: 100 × (-15%) = -15 billion → New assets = 85 billion - Liability change: 85 × (-12.5 × 1.2%) = 85 × (-15%) = -12.75 billion → New liabilities = 85 - 12.75 = 72.25 billion - Surplus = 85 - 72.25 = 12.75 billion This gives EUR 12.75 billion, which is option C. However, the correct answer appears to be D (EUR 12.57 billion). Let me check if there's a more precise calculation: Using the exact formula: New liabilities = 85 × (1 - 12.5 × 0.012) = 85 × (1 - 0.15) = 85 × 0.85 = 72.25 billion Wait, but 12.5 × 0.012 = 0.15 exactly, so it should be exactly 15% decrease. Let me reconsider - perhaps the question is testing the understanding that when yields increase, bond prices decrease, so liabilities (which are like bonds) decrease in value. Therefore: - Assets decrease by 15% to EUR 85 billion - Liabilities decrease by 15% to EUR 72.25 billion - Surplus = 85 - 72.25 = 12.75 billion Given that EUR 12.75 billion is option C, but the correct answer is marked as D, I need to check if there's a different interpretation. **Final calculation:** - Assets: 100 × (1 - 0.15) = 85 billion - Liabilities: 85 × (1 - 12.5 × 0.012) = 85 × (1 - 0.15) = 85 × 0.85 = 72.25 billion - Surplus: 85 - 72.25 = 12.75 billion This corresponds to **option C**.

Author: LeetQuiz .