Actuary Certification Risk Assessment 3 — Questions and Answers
Question 1: In mortality risk assessment, what is the 'select period' in a select-and-ultimate mortality table?
- The period during which recently underwritten lives exhibit lower mortality than the general population (Correct answer)
- The age at which mortality rates peak
- The time frame used to select pricing assumptions
- The duration of the policy contract
Correct answer: The period during which recently underwritten lives exhibit lower mortality than the general population
The select period reflects the underwriting effect — newly insured individuals have been health-screened, so their mortality is lower than that of the general population for a set number of years.
Question 2: What is 'systematic risk' in the context of an insurance enterprise risk management framework?
- Risk that can be diversified away with a larger portfolio
- Risk arising from errors in the company's internal systems
- Market-wide risk that affects all insurers simultaneously and cannot be diversified (Correct answer)
- The risk of individual large claims
Correct answer: Market-wide risk that affects all insurers simultaneously and cannot be diversified
Systematic risk (also called non-diversifiable risk) stems from macroeconomic or market-wide factors like catastrophes, pandemics, or interest rate shocks that affect all insurers.
Question 3: Which of the following best describes 'basis risk' in a catastrophe hedging strategy using industry loss warranties (ILWs)?
- The risk that the reinsurer defaults on its obligation
- The mismatch between actual company losses and the industry loss trigger (Correct answer)
- The uncertainty in pricing the derivative contract
- The credit spread on catastrophe bonds
Correct answer: The mismatch between actual company losses and the industry loss trigger
Basis risk in ILWs arises because the industry-wide trigger may be activated (or not) in ways that do not perfectly correlate with the specific insurer's actual losses.
Question 4: The 'ruin probability' in classical collective risk theory is defined as the probability that:
- Annual claims exceed annual premium income
- The surplus process becomes negative at some point in time (Correct answer)
- The combined ratio exceeds 100% in any single year
- Reserve levels fall below regulatory minimums
Correct answer: The surplus process becomes negative at some point in time
Ruin probability (ψ) measures the chance that an insurer's surplus U(t) drops below zero at any time t, given initial surplus u and net premium rate c.
Question 5: What does the 'coefficient of variation' (CV) measure in loss distribution analysis?
- The absolute magnitude of expected losses
- The ratio of the standard deviation to the mean, measuring relative variability (Correct answer)
- The probability of exceeding the VaR threshold
- The correlation between two lines of business
Correct answer: The ratio of the standard deviation to the mean, measuring relative variability
CV = σ/μ expresses variability as a percentage of the mean, allowing comparison of dispersion across distributions with different scales.
Question 6: In an actuarial loss development framework, the 'tail factor' applied beyond the last development period accounts for:
- Investment returns on held reserves
- Losses that have occurred but will not be fully reported until after the observed development period (Correct answer)
- Anticipated future inflation adjustments
- Reinsurance recoveries on settled claims
Correct answer: Losses that have occurred but will not be fully reported until after the observed development period
The tail factor captures development beyond the available data — IBNR claims and late-emerging losses that extend past the oldest maturity in the triangle.
Question 7: A portfolio manager measures the 99% one-day VaR as $2 million. Under Basel III, the minimum capital charge for market risk uses a multiplier applied to the:
- 99% one-day VaR only
- 60-day average of the 99% ten-day VaR scaled by √10 (Correct answer)
- Expected shortfall at 97.5% confidence
- Stressed VaR over a 250-day historical window
Correct answer: 60-day average of the 99% ten-day VaR scaled by √10
Basel III internal models approach requires the 60-day average of the 99% ten-day VaR (scaled by √10 from daily VaR) multiplied by a factor of at least 3.
Actuary Certification Risk Assessment 3
In mortality risk assessment, what is the 'select period' in a select-and-ultimate mortality table?