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FRM Part I · FRM Exam Part I · Operational Risk

A bank's Business Indicator Component is USD 2,000 million and its loss component (15 x average annual operational losses over ten years) is USD 1,500 million. Under the revised Basel standardised approach, the internal loss multiplier is ILM = ln(exp(1) - 1 + (LC/BIC)^0.8). Which statement is correct about the bank's capital requirement?

The ILM is below 1, so capital is less than the BIC. With LC/BIC of 0.75, the ratio raised to 0.8 is about 0.794, and ln(1.718 + 0.794) is about 0.921. Capital is therefore roughly USD 1,842 million, below the BIC of 2,000 million, because losses are lower than the BIC benchmark.

  1. AILM is below 1, so capital is less than the BICCorrect
  2. BILM equals 1, so capital equals the BIC
  3. CILM is above 1, so capital exceeds the BIC
  4. DILM cannot be computed because LC is below BIC

Explanation

LC/BIC = 0.75. 0.75^0.8 = exp(0.8 x ln0.75) = exp(0.8 x -0.28768) = exp(-0.23015) = 0.7943. exp(1) - 1 = 1.71828. Sum = 2.5126; ln = 0.9212. ILM < 1, so capital = about 0.921 x 2,000 = 1,842 million, below BIC. ILM equals 1 only when LC = BIC, and exceeds 1 when LC > BIC.

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