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FRM Part II · FRM Exam Part II · Basel III: Finalising Post-crisis Reforms

A bank's average annual operational losses over the last ten years are 30 million euros. Its BIC is 100 million euros. The ILM formula is ILM = ln(exp(1) - 1 + (LC/BIC)^0.8), where LC (Loss Component) = 15 x average annual losses. Which is closest to the bank's ILM and resulting operational risk capital?

The Loss Component is 450 million euros, so LC/BIC is 4.5. Raising to 0.8 gives about 3.33, adding 1.718 gives about 5.05, and the natural log is about 1.62 to 1.69. Capital is therefore roughly 160 to 170 million euros, above the BIC, because losses are heavy.

  1. AILM about 1.0; capital about 100 million euros
  2. BILM about 1.69; capital about 169 million eurosCorrect
  3. CILM about 1.69; capital about 16.9 million euros
  4. DILM about 4.5; capital about 450 million euros

Explanation

LC = 15 x 30 = 450. LC/BIC = 4.5. 4.5^0.8 = exp(0.8 x ln 4.5) = exp(0.8 x 1.504) = exp(1.203) = 3.33. Add e - 1 = 1.718 gives 5.05. ln(5.05) = 1.62, so ILM is about 1.62 to 1.7, i.e. roughly 1.6-1.7, and capital = 100 x 1.62 = about 162-169 million euros. Option 4.5 uses the unadjusted ratio, and the 16.9 million option mis-scales.

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