FRM Part II · FRM Exam Part II · Risk Measurement and Assessment
An operational risk manager notices that a bank's loss database only records events with a gross loss above USD 100,000, but the severity model is fitted as if all losses were observed. If the fitted distribution is a lognormal, what is the likely effect on the estimated severity parameters when the truncation is ignored?
Ignoring the collection threshold biases the fitted mean severity upward, because small losses are absent, and understates loss frequency, because many events go unrecorded. A correct approach fits a truncated (conditional) distribution and adjusts frequency for losses below the threshold.
- AThe mean of the fitted severity is biased upward and the frequency of losses is biased downward relative to the true full populationCorrect
- BThe mean severity is biased downward and the frequency is biased upward
- CBoth severity and frequency are unbiased because truncation affects only the tail
- DSeverity volatility is overstated while the mean is unaffected
Explanation
Ignoring the threshold means only large losses are fitted, so the severity location is pushed up. Because small losses are missing, the count of observed events understates the true number of losses, so frequency is biased downward. Correctly, the likelihood should be conditional on exceeding the threshold.
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