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FRM Part II · FRM Exam Part II · Risk Mitigation

A bank assesses a key control that addresses a risk with inherent annual expected loss of USD 20 million. Testing shows the control is effective in 80% of cases, and a second independent control, effective in 50% of cases, operates in sequence on whatever the first fails to stop. Assuming independence, what is the expected residual annual loss?

Expected residual loss is USD 2.0 million. The first control lets through 20% of the USD 20 million loss and the second lets through 50% of that, so 20 x 0.2 x 0.5 equals 2.0, a combined effectiveness of 90%.

  1. AUSD 2.0 millionCorrect
  2. BUSD 4.0 million
  3. CUSD 10.0 million
  4. DUSD 6.0 million

Explanation

The first control leaves 20% of the loss, and the second leaves 50% of that. Residual = 20 x 0.20 x 0.50 = USD 2.0 million. Check: combined effectiveness is 1 - 0.1 = 90%, so 10% of 20 = 2. USD 4.0 million ignores the second control; USD 10 million applies only the 50% control; USD 6 million adds failure rates incorrectly.

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