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FRM Part II · FRM Exam Part II · Risk Measurement and Assessment

A bank fits a lognormal severity distribution to internal losses collected only above a reporting threshold of USD 50,000, but treats the data as if complete from zero. Relative to correctly accounting for the threshold, which outcome is most likely?

Ignoring the collection threshold biases the severity fit because the sample is truncated, and the observed event count understates total loss frequency from zero. The proper approach fits a conditional distribution that accounts for the threshold.

  1. AFrequency of losses above the threshold is overstated and severity is understated
  2. BSeverity parameters are biased because the fitted distribution reflects a truncated sample, and the frequency of all losses is understatedCorrect
  3. CThe model is unaffected because lognormal distributions are scale invariant
  4. DCapital is overstated only for the body, never the tail

Explanation

Data collected only above a threshold are left-truncated. Fitting without adjustment biases severity parameters (typically the mean is shifted upward, location misestimated) and the count of events covers only losses above the threshold, so total frequency from zero is understated. Correct treatment fits a conditional distribution.

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