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FRM Part II · FRM Exam Part II · Risk Reporting

A bank reports operational loss events to its risk committee each month. Over 12 months the counts were 4, 6, 5, 3, 7, 5, 4, 6, 5, 5, 4, 6. The reporting team proposes an amber threshold at the mean monthly count plus one sample standard deviation. Month 13 has 8 events. Which statement is correct? (Sum of squared deviations is 16.)

The mean monthly count is 5 and the sample standard deviation is sqrt(16/11), about 1.21, giving an amber threshold near 6.21. Month 13 with 8 events exceeds it, so the amber threshold is breached and should be escalated in the report.

  1. AThe mean is 5, the sample standard deviation is about 1.21, threshold about 6.21, so month 13 breaches amberCorrect
  2. BThe mean is 5, the sample standard deviation is about 1.21, threshold about 6.21, so month 13 does not breach
  3. CThe mean is 5, the standard deviation is 1.33, threshold 6.33, so month 13 does not breach
  4. DThe mean is 5.5, threshold about 6.7, so month 13 breaches

Explanation

Sum of counts is 60, so mean is 5. Given sum of squared deviations 16, sample variance is 16/11 = 1.4545 and standard deviation about 1.206. Threshold is about 6.21. Eight exceeds it, so amber is breached. Option 2 reaches the wrong conclusion, and 1.33 would be an incorrect standard deviation (it is sqrt(16/9)).

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