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FRM Part I · FRM Exam Part I · Operational Risk

A bank models annual operational losses in one business line with Poisson frequency of mean 12 events per year and independent severity with mean USD 250,000 and standard deviation USD 500,000. What are the mean and variance of the aggregate annual loss (variance in USD squared)?

The aggregate mean is USD 3.0 million and the variance is 3.75 × 10^12. For a compound Poisson, variance equals λ times the second moment of severity, 12 × (500,000² + 250,000²), not λ times the severity variance alone.

  1. AMean USD 3.0 million; variance 3.0 × 10^12Correct
  2. BMean USD 3.0 million; variance 9.0 × 10^12
  3. CMean USD 3.0 million; variance 0.75 × 10^12
  4. DMean USD 3.0 million; variance 3.75 × 10^12

Explanation

Mean = 12 × 250,000 = 3.0 million. For compound Poisson, variance = λ × E[X²] = 12 × (500,000² + 250,000²) = 12 × (2.5×10^11 + 6.25×10^10) = 12 × 3.125×10^11 = 3.75×10^12. So the correct value is 3.75×10^12, which is the last option, not the first.

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