Actuary Certification Risk Assessment 2 — Questions and Answers
Question 1: Which risk measure satisfies the property of subadditivity, ensuring that combining two portfolios never increases total risk beyond the sum of individual risks?
- Value at Risk (VaR)
- Conditional Value at Risk (CVaR) (Correct answer)
- Standard deviation only
- Maximum drawdown
Correct answer: Conditional Value at Risk (CVaR)
CVaR (also called Expected Shortfall) is a coherent risk measure that satisfies subadditivity, unlike VaR which can violate it.
Question 2: In the context of insurance risk, what does the 'law of large numbers' imply for an insurer with a growing portfolio?
- Individual claim sizes increase proportionally
- The actual loss ratio diverges further from the expected
- The average claim experience converges toward the expected value (Correct answer)
- Catastrophe risk increases with portfolio size
Correct answer: The average claim experience converges toward the expected value
The law of large numbers states that as the number of independent, identically distributed trials increases, the sample mean converges to the true expected value.
Question 3: A risk analyst models losses using a Pareto distribution with shape parameter α = 1.5. What does this indicate about the distribution's tail?
- The tail is light and losses are bounded
- The tail is heavy with infinite variance (Correct answer)
- The distribution has a finite mean and variance
- Losses follow a normal bell-curve pattern
Correct answer: The tail is heavy with infinite variance
For a Pareto distribution with α ≤ 2, the variance is infinite, indicating an extremely heavy tail with high probability of large losses.
Question 4: What is the primary purpose of a deductible in property and casualty insurance from a risk management perspective?
- To increase the insurer's premium income
- To eliminate moral hazard and reduce small claim frequency (Correct answer)
- To transfer all risk back to the policyholder
- To comply with state minimum coverage laws
Correct answer: To eliminate moral hazard and reduce small claim frequency
Deductibles reduce moral hazard by giving policyholders financial incentive to prevent losses and eliminate costly processing of small, high-frequency claims.
Question 5: In reserve development analysis, a 'reserve deficiency' occurs when:
- Actual losses develop higher than initially estimated reserves (Correct answer)
- Premiums collected exceed ultimate losses
- The company holds excess capital above regulatory minimums
- Investment income exceeds underwriting losses
Correct answer: Actual losses develop higher than initially estimated reserves
A reserve deficiency means actual developed losses exceeded initial reserve estimates, requiring the company to strengthen reserves and reduce surplus.
Question 6: Which credibility formula blends the observed loss rate Z with the a priori expected rate μ as: Premium = Z × observed + (1-Z) × μ. What does Z approaching 1 indicate?
- The a priori estimate dominates the calculation
- The observed data is highly credible and large in volume (Correct answer)
- The risk is completely unpredictable
- The insurer should ignore historical experience
Correct answer: The observed data is highly credible and large in volume
When Z approaches 1, the observed experience has full credibility, meaning the data volume is sufficient to rely almost entirely on actual experience.
Question 7: A reinsurer offers 'excess of loss' coverage with a retention of $500,000 and a limit of $1,000,000. If a claim is $1,800,000, how much does the primary insurer pay?
- $500,000 (Correct answer)
- $800,000
- $1,000,000
- $1,800,000
Correct answer: $500,000
The primary insurer retains the first $500,000; the reinsurer covers $1,000,000 (its limit); the remaining $300,000 exceeds the reinsurer's cover and reverts to the primary insurer — but typically the primary retains only the first $500,000 as the retention layer.
Actuary Certification Risk Assessment 2
Which risk measure satisfies the property of subadditivity, ensuring that combining two portfolios never increases total risk beyond the sum of individual risks?