FRM Part I · FRM Exam Part I · Operational Risk
A bank estimates annual operational loss frequency as Poisson with mean 4 events. Each loss has mean severity USD 2 million. A new control program is expected to cut frequency by 25% and severity by 10%. Assuming independence of frequency and severity, by how much does the expected annual loss fall?
Expected annual loss falls by USD 2.6 million. It goes from 4 times 2, or 8 million, to 3 times 1.8, or 5.4 million, because frequency and severity reductions multiply rather than add.
- AUSD 2.0 million
- BUSD 2.6 millionCorrect
- CUSD 2.8 million
- DUSD 3.2 million
Explanation
Before: 4 x 2 = 8 million. After: 3 x 1.8 = 5.4 million. Reduction = 2.6 million. Adding the percentage cuts (35% of 8 = 2.8) is wrong because the effects compound multiplicatively: 1 - 0.75 x 0.9 = 32.5%.
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