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FRM Part II · FRM Exam Part II · Integrated Risk Management

A bank's board sets a firmwide economic capital risk appetite of USD 500 million for operational risk. Standalone capital for three units is USD 250 million, USD 200 million and USD 150 million, totaling USD 600 million. The risk team estimates a diversification benefit equal to 20% of the sum of standalone capital. Management allocates the diversified total to units proportionally to standalone capital. What is the diversified capital allocated to the unit with USD 200 million standalone, and does the total fit within appetite?

The diversified total is 600 × 0.8 = USD 480 million, which fits within the USD 500 million appetite. Allocating proportionally scales each standalone figure by 0.8, so the unit with USD 200 million standalone receives USD 160 million.

  1. AUSD 160 million; total USD 480 million fits within appetiteCorrect
  2. BUSD 200 million; total USD 600 million exceeds appetite
  3. CUSD 160 million; total USD 600 million exceeds appetite
  4. DUSD 166.7 million; total USD 500 million fits exactly

Explanation

Diversified total = 600 × (1 − 0.20) = USD 480 million, below the USD 500 million appetite. Proportional allocation scales each unit by 0.8, so 200 × 0.8 = USD 160 million. Using undiversified figures would wrongly exceed appetite; scaling to 500 would ignore the actual estimate.

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