Statistics Risk Assessment & Management 3 ā Questions and Answers
Question 1: A factory's equipment fails on average once every 500 operating hours. Using the Poisson model, what is the probability of exactly zero failures in 500 hours?
- eā»Ā¹ ā 0.368 (Correct answer)
- eā»ā°Ā·āµ ā 0.607
- 1 ā eā»Ā¹ ā 0.632
- 0.50
Correct answer: eā»Ā¹ ā 0.368
With Ī» = 1 failure per 500-hour interval, P(X=0) = e^(ā1) ā 0.368 by the Poisson PMF.
Question 2: Tail dependence in copula models refers to:
- The correlation between assets during normal market conditions
- The tendency of joint extreme losses to occur together (Correct answer)
- The marginal distribution of each asset independently
- The linear regression slope between two risk factors
Correct answer: The tendency of joint extreme losses to occur together
Tail dependence captures whether extreme negative events in multiple variables co-occur more than a Gaussian copula would predict.
Question 3: Which risk response strategy involves shifting the financial consequences of a risk to a third party?
- Avoidance
- Mitigation
- Transfer (Correct answer)
- Acceptance
Correct answer: Transfer
Risk transfer, such as purchasing insurance or using derivatives, moves the financial burden of potential losses to another party.
Question 4: The coefficient of variation (CV) is used in risk analysis to:
- Measure absolute risk regardless of scale
- Compare relative risk across variables with different means (Correct answer)
- Calculate the probability of ruin
- Estimate the maximum loss at a confidence level
Correct answer: Compare relative risk across variables with different means
CV = standard deviation / mean, allowing apples-to-apples risk comparison across projects or assets with different expected values.
Question 5: In credit risk modeling, Probability of Default (PD) combined with Loss Given Default (LGD) and Exposure at Default (EAD) yields:
- Expected Loss (EL) (Correct answer)
- Unexpected Loss (UL)
- Economic Capital
- Sharpe Ratio
Correct answer: Expected Loss (EL)
Expected Loss = PD Ć LGD Ć EAD, the standard formula for the average anticipated credit loss over a period.
Question 6: A risk analyst finds that the loss distribution has a kurtosis of 6. Compared to a normal distribution (kurtosis = 3), this indicates:
- Fewer extreme events than normal
- Heavier tails and higher chance of extreme losses (Correct answer)
- A symmetric distribution with no skew
- Lower variance than a normal distribution
Correct answer: Heavier tails and higher chance of extreme losses
Excess kurtosis (kurtosis > 3) indicates leptokurtic (fat-tailed) distributions where extreme events are more probable than Gaussian models predict.
Question 7: Which of the following best describes a stress test in risk management?
- A routine VaR calculation at the 99% confidence level
- Simulation of extreme but plausible adverse scenarios to assess resilience (Correct answer)
- Regression of historical losses on macroeconomic variables
- Optimization of a portfolio to minimize expected loss
Correct answer: Simulation of extreme but plausible adverse scenarios to assess resilience
Stress testing evaluates how a firm or portfolio performs under severe hypothetical or historical crisis scenarios beyond normal VaR assumptions.
Statistics Risk Assessment & Management 3
A factory's equipment fails on average once every 500 operating hours.
Using the Poisson model, what is the probability of exactly zero failures in 500 hours?