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

A bank's LDA model for one risk category has an expected annual loss of USD 20 million and a 99.9% annual aggregate loss quantile of USD 260 million. A validator finds that the severity model was fitted with a lognormal distribution, but a goodness-of-fit test on the largest losses shows a heavier tail than the fitted distribution. The bank re-estimates using a generalized Pareto tail and the 99.9% quantile rises to USD 380 million, with the expected loss unchanged. What are the unexpected loss (quantile less expected loss) under each model and the percentage increase in unexpected loss?

Unexpected loss equals the 99.9% quantile minus expected loss, giving USD 240 million originally and USD 360 million under the heavier-tailed model. That is a 50% increase, (360 − 240)/240, illustrating how severity distribution choice drives capital.

  1. AOriginal 240; revised 360; increase 50%Correct
  2. BOriginal 260; revised 380; increase 46%
  3. COriginal 240; revised 360; increase 46%
  4. DOriginal 280; revised 400; increase 43%

Explanation

Unexpected loss = quantile minus expected loss: 260 - 20 = 240 and 380 - 20 = 360. The increase is (360 - 240)/240 = 50%. Using the quantile alone gives 46%, which wrongly treats the total quantile as the capital figure and ignores the expected loss deduction. This shows model risk from distribution choice in the tail.

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