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FRM Part II · FRM Exam Part II · Risk Mitigation

A bank assesses a process with inherent annual expected loss of USD 8.0 million. Two independent controls each reduce the loss frequency by the stated effectiveness: control A is 60% effective and control B is 50% effective. Assuming the effects multiply, and a third assessment shows control B actually operates effectively only 80% of the time (so its effective reduction is 50% x 0.8), what is the residual expected loss?

Residual expected loss is USD 1.92 million. Control B's effective reduction is 50% x 0.8 = 40%, so residual equals 8.0 x 0.4 x 0.6. Ignoring the operating-effectiveness adjustment would understate the residual loss.

  1. AUSD 1.28 million
  2. BUSD 1.92 millionCorrect
  3. CUSD 0.80 million
  4. DUSD 2.40 million

Explanation

Control B's effective reduction is 0.5 x 0.8 = 40%. Residual = 8.0 x (1 - 0.6) x (1 - 0.4) = 8.0 x 0.4 x 0.6 = 1.92 million. Using the stated 50% gives 1.6 million, and the 1.28 million option wrongly applies 0.8 as a further multiplier on the pass-through (8 x 0.4 x 0.5 x 0.8 = 1.28 is not the correct adjustment).

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