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Answer: It is suitable for modeling the tail of the operational loss distribution, but not for modeling the body of the distribution.
## Explanation **D is correct.** The power law describes the behavior of extreme events in the tail of a distribution, not the entire distribution. The mathematical formulation is: $$\Pr(v > x) \approx Kx^{-\alpha}$$ where: - $\Pr$ denotes probability - $v$ is the value of a random variable - $x$ is a high value of $v$ - $K$ and $\alpha$ are parameters This approximation is only valid for high values of $x$ (the tail region), which makes the power law suitable for modeling extreme operational losses but not routine losses in the body of the distribution. **Why other options are incorrect:** - **A is incorrect:** Operational losses do not follow a normal distribution, and the power law does not imply normality. In fact, operational losses typically exhibit fat tails, which is why the power law is useful for modeling them. - **B is incorrect:** The power law has been shown to be applicable to a wide range of distributions, including natural disasters (e.g., earthquake magnitudes). There is no evidence that it works better for fraud losses than for natural disaster losses. - **C is incorrect:** Routine operational losses that occur frequently are in the body of the distribution, not the tail. The power law is specifically designed for modeling extreme, low-frequency events in the tail region.
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An operational risk manager is presenting to a group of risk analysts about different techniques to model operational risk. An analyst asks the manager about the appropriate use of the power law in estimating operational losses. Which of the following would be a correct statement for the manager to make about the use of the power law?
A
It implies that operational losses tend to follow a normal distribution.
B
It is more effective in modeling some types of operational risk, such as losses from fraud, than others, such as losses from natural disasters.
C
It is generally used to estimate routine operational losses which occur at a relatively high frequency.
D
It is suitable for modeling the tail of the operational loss distribution, but not for modeling the body of the distribution.