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# FRM 2009 Full II q20 - Uniform vs. Normal Operational Losses

#### fullofquestions

##### New Member
Consider the following potential operational risks. Due to a rogue trader, we estimate that over a 1
year period there is a 10% chance we could lose anywhere between € 0 and € 100MM (equal
probability for all points within that range and 0 probability of any losses outside that range). Due to
model risk, we estimate that over a 1 year period there is a 20% chance that we will lose € 25MM
normally distributed with a standard deviation of € 5MM. Which of the following statements is true?

a. The expected loss from a rogue trader is less than the expected loss from model risk.
b. The expected loss from a rogue trader is greater than the expected loss from model risk.
c. The maximum unexpected loss from a rogue trader at the 95% confidence level is less than the
maximum unexpected loss at the 95% confidence level from model risk.
d. The maximum unexpected loss at the 95% level from a rogue trader is greater than the maximum
unexpected loss at the 95% level from model risk.

20. CORRECT: D. This question tests understanding of expected vs. unexpected loss. The rogue
trader has an expected loss (severity multiplied by probability) of €5MM while the model risk has an
expected loss of €5MM. Therefore both A and B are incorrect. We therefore must examine unexpected
losses. The rogue trader has a much wider distribution (Uniform) and a lower probability of
occurrence than the model risk (normal distribution). Therefore the rogue trader has a greater risk of
unexpected losses.
Unexpected loss for rogue trader at 95% confidence level: 50MM - 5MM = 45MM

The loss from model risk at the 95th percentile corresponds to the 75th percentile for the normal
distribution with mean 25 and standard deviation 5, so unexpected loss for model risk at 95%
confidence level: < (25MM + 1.645*5MM) - 5MM < 30MM. Reference: Dowd, Chapter 16.

Question 1: EL of rougue trader = avg(0,100) *.1 = 5M Got it. How do you arrive at EL of model? EAD*PD*LGD does not work.

Question 2: How do you calculate the WCL of rogue trader(50M)? Does formula [ 1 - alpha = integral(from wcl to infinity) f(x)dx] come into play?

The answer is totally intuitive, however, finding EL of model and WCL of rogue are unclear. Much appreciated for a bit of intuition.