CRA Quantitative Risk Analysis 2 — Questions and Answers
Question 1: In a Monte Carlo simulation for project risk, what does the 80th percentile of the cost distribution represent?
- The average expected cost outcome
- The cost value below which 80% of simulated outcomes fall (Correct answer)
- The maximum possible cost in the simulation
- The cost associated with 80% probability of project failure
Correct answer: The cost value below which 80% of simulated outcomes fall
The 80th percentile means 80% of simulated outcomes produced a cost at or below that value, making it a confidence threshold.
Question 2: Which correlation measure is most appropriate when assessing the relationship between two non-normally distributed risk variables?
- Pearson correlation coefficient
- Spearman rank correlation (Correct answer)
- Covariance matrix
- Linear regression slope
Correct answer: Spearman rank correlation
Spearman rank correlation is non-parametric and does not assume normality, making it suitable for non-normal distributions.
Question 3: A risk has a 5% annual probability of occurrence and a loss of $2 million. What is the annual expected loss (AEL)?
- $40,000
- $100,000 (Correct answer)
- $200,000
- $400,000
Correct answer: $100,000
AEL = probability × impact = 0.05 × $2,000,000 = $100,000.
Question 4: In quantitative risk analysis, what is the primary purpose of a tornado diagram?
- To model correlated risk variables simultaneously
- To rank input variables by their sensitivity impact on the output (Correct answer)
- To display the full probability distribution of outcomes
- To calculate Value at Risk across multiple scenarios
Correct answer: To rank input variables by their sensitivity impact on the output
A tornado diagram ranks variables from most to least influential on the output metric, identifying which risks drive the most uncertainty.
Question 5: Which of the following best describes 'epistemic uncertainty' in quantitative risk analysis?
- Uncertainty from inherent randomness in a process
- Uncertainty arising from lack of knowledge or data (Correct answer)
- Uncertainty caused by model parameter rounding
- Uncertainty from correlated risk events occurring simultaneously
Correct answer: Uncertainty arising from lack of knowledge or data
Epistemic uncertainty stems from incomplete knowledge and can theoretically be reduced by gathering more information.
Question 6: A lognormal distribution is commonly used to model financial losses because it:
- Allows negative values, reflecting potential gains
- Is symmetric around the mean, simplifying calculations
- Ensures values are positive and captures right-skewed loss distributions (Correct answer)
- Has a fixed variance regardless of the mean
Correct answer: Ensures values are positive and captures right-skewed loss distributions
Lognormal distributions are bounded at zero and positively skewed, making them well-suited for loss severities that cannot be negative.
Question 7: In Extreme Value Theory (EVT), the Generalized Pareto Distribution (GPD) is used to model:
- The central tendency of loss data
- Losses that exceed a high threshold (tail events) (Correct answer)
- The correlation structure between risk factors
- The frequency of routine operational losses
Correct answer: Losses that exceed a high threshold (tail events)
GPD models the distribution of excess losses beyond a given threshold, making it ideal for tail risk quantification.
CRA Quantitative Risk Analysis 2
In a Monte Carlo simulation for project risk, what does the 80th percentile of the cost distribution represent?