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FRM Part II · FRM Exam Part II · Risk Identification

A bank combines scenario output with loss data. Experts estimate for a fraud scenario: a 10% chance per year of a loss event, with severity of either USD 10 million (probability 70%) or USD 50 million (probability 30%) given an event. Assuming at most one event per year, what is the annual expected loss, and what is the probability that a single year's loss exceeds USD 20 million?

Expected annual loss is USD 2.2 million and the probability of exceeding USD 20 million in a year is 3%. Mean severity is USD 22 million, multiplied by a 10% event probability. Exceeding USD 20 million needs both an event and the USD 50 million outcome: 0.10 times 0.30.

  1. AExpected loss USD 2.2 million; probability 3%Correct
  2. BExpected loss USD 2.2 million; probability 30%
  3. CExpected loss USD 3.0 million; probability 3%
  4. DExpected loss USD 1.0 million; probability 10%

Explanation

Mean severity given event = 0.7x10 + 0.3x50 = 7 + 15 = USD 22 million. Expected annual loss = 0.10 x 22 = USD 2.2 million. A loss above USD 20 million requires an event and the USD 50 million severity: 0.10 x 0.30 = 3%. The 30% option forgets to condition on the event occurring.

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