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.