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

A bank's LDA model uses a Poisson frequency with mean 20 events per year and a severity distribution with mean USD 0.5 million. Because of limited data, the modeler is considering two severity fits. Under the first, the severity tail is thin; under the second, a heavy-tailed fit has the same mean. For the same frequency, which statement is correct about the expected annual loss and the 99.9% capital estimate?

Expected annual loss equals frequency times mean severity, 20 x USD 0.5 million = USD 10 million under both fits. The heavy-tailed fit, however, produces a materially higher 99.9% quantile, illustrating how tail assumptions drive capital and create model risk.

  1. AExpected annual loss is USD 10 million under both fits, but the 99.9% estimate will be materially higher under the heavy-tailed fitCorrect
  2. BExpected annual loss is USD 20 million under both fits, and the 99.9% estimate is identical
  3. CExpected annual loss is USD 10 million under the thin fit and higher under the heavy-tailed fit
  4. DExpected annual loss is USD 10 million under both fits, and the 99.9% estimate is lower under the heavy-tailed fit

Explanation

Expected annual loss = frequency x mean severity = 20 x 0.5 = USD 10 million for both fits since means are equal. The extreme quantile depends on tail thickness, so the heavy-tailed fit gives a much larger 99.9% value. This shows capital sensitivity to the model choice (model risk) even when expected loss is unchanged.

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