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FRM Part II · FRM Exam Part II · Risk Measurement and Assessment

A bank's LDA model produces a simulated annual aggregate loss distribution from 100,000 trials. The sorted results show that the 99,900th smallest loss is USD 180 million, the 99,000th smallest is USD 95 million, and the mean is USD 20 million. Expected loss of USD 20 million is covered by provisions and pricing. What is the unexpected-loss capital at the 99.9% confidence level?

Unexpected-loss capital is USD 160 million. The 99.9% quantile of the simulated distribution is USD 180 million, and subtracting the USD 20 million expected loss already covered by provisions and pricing leaves USD 160 million.

  1. AUSD 75 million
  2. BUSD 160 millionCorrect
  3. CUSD 180 million
  4. DUSD 95 million

Explanation

The 99.9% quantile is the 99,900th of 100,000 sorted results: USD 180 million. Capital for unexpected loss = 180 - 20 = USD 160 million. USD 180 million ignores the expected loss offset. USD 95 million is the 99% quantile. USD 75 million is 95 - 20, using the wrong quantile.

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