CRA Quantitative Risk Analysis 3 — Questions and Answers
Question 1: What is the key difference between Value at Risk (VaR) and Expected Shortfall (ES)?
- VaR captures average losses; ES captures the worst single loss
- ES averages losses beyond the VaR threshold; VaR only marks a loss quantile (Correct answer)
- VaR is computed at 99% confidence; ES is always at 95%
- ES ignores tail events while VaR incorporates all scenarios
Correct answer: ES averages losses beyond the VaR threshold; VaR only marks a loss quantile
Expected Shortfall (CVaR) is the mean of losses that exceed the VaR level, providing a fuller picture of tail risk.
Question 2: Which simulation technique reduces variance in Monte Carlo output by ensuring samples are more evenly distributed across the input probability space?
- Importance sampling
- Latin Hypercube Sampling (LHS) (Correct answer)
- Bootstrap resampling
- Markov Chain Monte Carlo
Correct answer: Latin Hypercube Sampling (LHS)
LHS stratifies the input distribution into equal-probability intervals, ensuring better coverage and reducing output variance with fewer iterations.
Question 3: In a Bayesian network used for risk analysis, what do the conditional probability tables (CPTs) represent?
- The marginal distribution of each node independently
- The probability of a node's state given the states of its parent nodes (Correct answer)
- The correlation coefficients between all risk variables
- The posterior distribution after data is observed
Correct answer: The probability of a node's state given the states of its parent nodes
CPTs define the conditional probability of each node given every combination of its parent nodes' states in the Bayesian network.
Question 4: A project schedule risk analysis shows a P50 completion date of June 1 and a P90 date of August 15. What does this mean for the risk manager?
- There is a 50% chance the project finishes before June 1 and a 90% chance before August 15 (Correct answer)
- The project will most likely finish between June 1 and August 15 with certainty
- June 1 is the earliest possible date and August 15 is the latest
- There is a 50% and 10% chance of finishing on those exact dates respectively
Correct answer: There is a 50% chance the project finishes before June 1 and a 90% chance before August 15
P50 and P90 are percentiles: 50% of simulated outcomes complete by June 1 and 90% complete by August 15.
Question 5: Which of the following is a key limitation of using historical data alone for quantitative operational risk modeling?
- Historical data is always too large to process statistically
- Rare tail events may not be represented in the historical record (Correct answer)
- Historical data cannot be used to calculate frequency distributions
- Regulatory frameworks prohibit using historical data for capital models
Correct answer: Rare tail events may not be represented in the historical record
Black swan or low-frequency, high-severity events may simply not appear in historical datasets, causing models to underestimate tail risk.
Question 6: When combining frequency and severity distributions in a loss aggregation model, which mathematical operation is typically used?
- Matrix multiplication of the two distributions
- Convolution of the frequency and severity distributions (Correct answer)
- Subtraction of the severity from the frequency CDF
- Division of expected frequency by expected severity
Correct answer: Convolution of the frequency and severity distributions
Convolution combines the frequency and severity distributions to derive the aggregate loss distribution.
Question 7: In the context of credit risk, what does 'Loss Given Default' (LGD) measure?
- The probability that a counterparty will default within one year
- The proportion of exposure that is lost when a default occurs (Correct answer)
- The total notional value of a credit portfolio
- The time between default and recovery of assets
Correct answer: The proportion of exposure that is lost when a default occurs
LGD is the fraction of the exposure at default that the lender cannot recover after a counterparty defaults.
CRA Quantitative Risk Analysis 3
What is the key difference between Value at Risk (VaR) and Expected Shortfall (ES)?