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FRM Part I · FRM Exam Part I · Operational Risk

An analyst models annual operational loss events for one cell as Poisson with mean 4 events per year. Each loss has an expected severity of USD 250,000. Assuming frequency and severity are independent, what is the expected annual aggregate loss, and what is the probability of zero loss events in a year (to three decimals)?

Expected aggregate loss is the expected number of events times the expected severity, 4 times USD 250,000, or USD 1,000,000. The probability of no events in a Poisson model with mean 4 is e to the minus 4, about 0.018.

  1. AUSD 1,000,000 and 0.018Correct
  2. BUSD 1,000,000 and 0.982
  3. CUSD 250,000 and 0.018
  4. DUSD 62,500 and 0.073

Explanation

Expected aggregate loss = E[N] x E[X] = 4 x 250,000 = 1,000,000. P(N=0) = e^-4 = 0.0183. The second option takes the complement (at least one event), and the third uses only the severity.

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