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FRM Part I · FRM Exam Part I · Enterprise Risk Management and Future Trends

A firm's board sets a risk appetite of a maximum 1-year 99% economic capital usage of USD 400 million. The business lines have been allocated limits of USD 150 million (trading), USD 180 million (lending) and USD 120 million (asset management), and the standalone usage equals the limits. Diversification across the lines is such that the aggregate capital is 85% of the sum of standalone amounts. Which conclusion is correct?

Standalone limits total USD 450 million. Applying the 85% diversification factor gives aggregate capital of USD 382.5 million. This is below the USD 400 million appetite, leaving USD 17.5 million of headroom, so there is no breach. Ignoring diversification would wrongly suggest a USD 50 million breach.

  1. AAggregate capital is USD 382.5 million, which is within appetite, with USD 17.5 million of headroomCorrect
  2. BAggregate capital is USD 450 million, which breaches appetite by USD 50 million
  3. CAggregate capital is USD 382.5 million, which breaches appetite because the sum of limits exceeds USD 400 million
  4. DAggregate capital is USD 450 million, which is within appetite after diversification

Explanation

Sum of limits = 150 + 180 + 120 = 450. Aggregate with diversification = 0.85 x 450 = 382.5. This is below the 400 appetite, leaving 17.5 headroom. The sum of limits exceeding appetite is not a breach because appetite is measured on the diversified aggregate. Option 2 ignores diversification.

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