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

In a scenario workshop, experts estimate that a payment-fraud event occurs once every 20 years on average. If it occurs, the severity is estimated at USD 40 million with 60% probability and USD 100 million with 40% probability. Assuming at most one event per year and no other losses, what are the expected annual loss and the probability of at least one such event in a year (to the nearest percent)?

Expected annual loss is USD 3.2 million and the annual probability is 5%. The event happens once in 20 years, so frequency is 5%. Expected severity is 0.6 times 40 plus 0.4 times 100, or 64 million, and 5% of 64 million is 3.2 million.

  1. AExpected annual loss USD 3.2 million; probability 5%Correct
  2. BExpected annual loss USD 64 million; probability 5%
  3. CExpected annual loss USD 3.2 million; probability 20%
  4. DExpected annual loss USD 1.6 million; probability 5%

Explanation

Annual frequency is 1/20 = 5%. Expected severity = 0.6x40 + 0.4x100 = 24 + 40 = 64 million. Expected annual loss = 0.05 x 64 = 3.2 million. Using the severity alone gives 64 million, and treating 20 as the probability is a frequency error. Using 0.025 gives 1.6 million, which is a halving error.

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