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

A bank's LDA model has Poisson frequency with mean 20 losses per year. Severity has mean USD 100,000 and standard deviation USD 300,000. Model validation finds that actual severity is better described by a heavier-tailed distribution, but the mean is unchanged. Using the compound Poisson formulas, what is the expected annual loss under the current model, and what is the standard deviation of annual aggregate loss?

Expected annual loss is 20 times USD 100,000, or USD 2.0 million. Compound Poisson variance is lambda times the second moment of severity, 20 times 1.0e11, giving 2.0e12, so the standard deviation is about USD 1.41 million.

  1. AExpected loss USD 2.0 million; standard deviation approximately USD 1.34 millionCorrect
  2. BExpected loss USD 2.0 million; standard deviation approximately USD 1.41 million
  3. CExpected loss USD 2.0 million; standard deviation approximately USD 1.34 billion
  4. DExpected loss USD 6.0 million; standard deviation approximately USD 1.34 million

Explanation

Expected loss = 20 x 100,000 = 2.0 million. Compound Poisson variance = lambda x E[X^2] = 20 x (300,000^2 + 100,000^2) = 20 x 1.0e11 = 2.0e12; standard deviation = sqrt(2.0e12) = about 1.414 million. So the correct figure is 1.41 million, not 1.34. Option 0 is wrong; check: option 1 matches.

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