FRM Part I · FRM Exam Part I · Operational Risk
A bank fits a lognormal severity to internal loss data for a cell. The fitted ln(loss) has mean 10 and standard deviation 1.5 (losses in USD). Which expression gives the expected loss per event?
The mean of a lognormal severity is exp of mu plus sigma squared over two, here exp(10 + 1.5 squared / 2), about USD 68,000. Using exp(10) gives only the median, which understates the average loss because the distribution is right-skewed.
- Aexp(10 + 1.5^2/2)Correct
- Bexp(10)
- Cexp(10 + 1.5)
- Dexp(10 + 1.5^2)
Explanation
For a lognormal variable, E[X] = exp(mu + sigma^2/2). With mu=10 and sigma=1.5, the exponent is 10 + 1.125 = 11.125. exp(10) is the median, not the mean, so it understates the expected loss for a skewed distribution.
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