Chapter 30 Quiz

Twenty questions: fifteen multiple choice and five short answer. Answers are in the collapsed block at the bottom — try the whole set before opening it. All figures are illustrative.

Multiple choice

  1. Catastrophe risk is fundamentally different from ordinary fire risk because it violates which assumption behind the law of large numbers? - A. That losses are measurable - B. That losses are independent - C. That the premium is economically feasible - D. That the insurer is solvent

  2. The three modules of a catastrophe model are: - A. Frequency, severity, and credibility - B. Underwriting, pricing, and claims - C. Hazard, vulnerability, and financial - D. Distribution, retention, and cession

  3. Which module of a cat model translates a hazard intensity (e.g., a wind speed) into a percentage of property value lost? - A. The hazard module - B. The vulnerability module - C. The financial module - D. The reinsurance module

  4. The AAL (average annual loss) is best described as: - A. The worst loss the portfolio could ever suffer - B. The catastrophe pure premium — the long-run expected annual cat loss, loaded into the rate - C. The amount of reinsurance the company must buy - D. The loss at the 1-in-250-year return period

  5. The PML (probable maximum loss) is most directly used to size: - A. The agent's commission - B. The expense ratio - C. Reinsurance and the capital held against the tail - D. The coinsurance penalty

  6. "1-in-100-year loss" correctly means: - A. A loss that happens exactly once every hundred years - B. A loss with a 1% probability of being exceeded in any given year - C. A loss that cannot occur twice in the same century - D. The maximum loss in a hundred-year period

  7. Over a 30-year mortgage, the approximate probability of at least one 1-in-100-year event is: - A. About 1% - B. About 26% - C. About 50% - D. Exactly 30%

  8. An exceedance-probability curve plots, for each loss level, the: - A. Expense ratio at that loss level - B. Annual probability that the loss will exceed that level - C. Number of policies in force - D. Reinsurer's ceding commission

  9. A peril zone (CRESTA zone) is used in accumulation management because: - A. It groups exposures a single catastrophe event would strike together (correlated) - B. It is required by the Fair Credit Reporting Act - C. It sets the agent's territory for commission purposes - D. It defines the policy's coinsurance percentage

  10. An account is judged in a catastrophe review primarily on its:

    • A. Standalone modeled loss in isolation
    • B. Loss ratio over the past year
    • C. Marginal contribution to the zone PML
    • D. Number of prior claims

  11. A backward-looking catastrophe model in a warming climate tends to:

    • A. Overstate the risk for intensifying perils
    • B. Understate the risk for intensifying perils
    • C. Have no systematic bias
    • D. Become more accurate every year automatically

  12. The protection gap is:

    • A. The deductible on a catastrophe policy
    • B. The share of economic catastrophe losses not covered by insurance
    • C. The gap between the AAL and the PML
    • D. The reinsurer's retention

  13. Why is a coastal property book's average year dangerous to rely on for pricing and capital?

    • A. Because the average is always wrong
    • B. Because most years are near zero and the average hides a thin, enormous tail
    • C. Because regulators forbid using averages
    • D. Because the average equals the PML

  14. A submission arrives with "year built" and "roof type" blank and only a ZIP-code location. The most likely effect on the cat model output is that it:

    • A. Overstates the account's catastrophe contribution
    • B. Understates the account's catastrophe contribution (optimistic defaults, imprecise location)
    • C. Has no effect, since the model ignores those fields
    • D. Automatically declines the account

  15. Which structure most directly reduces an account's modeled net catastrophe loss (and thus its zone consumption)?

    • A. Lowering the agent's commission
    • B. A higher percentage named-windstorm deductible and/or ceding the slice to reinsurance
    • C. Increasing the policy limit
    • D. Removing the coinsurance clause

Short answer

  1. In two or three sentences, explain why an underwriter must keep the AAL and the PML in "different mental boxes," and give the decision each one drives.

  2. A homeowner says, "Last year was the hundred-year flood, so I'm safe for the rest of my life." Correct his reasoning in two or three sentences.

  3. Explain why an account's marginal contribution to a zone PML can exceed its own standalone modeled loss.

  4. Name one reason a regulator might suppress a model-indicated coastal cat load, and trace one consequence of that suppression for the private market or the protection gap.

  5. The cat model is one place where the machine often beats human judgment, yet the chapter still says "reserve judgment." Reserve judgment for what, specifically?

Answer key (try the quiz first) **Multiple choice** 1. **B** — Catastrophe destroys *independence*; the losses become correlated by a common cause. (§30.1) 2. **C** — Hazard, vulnerability, and financial. (§30.2) 3. **B** — The vulnerability module (damage functions / fragility curves), which is COPE turned into math. (§30.2) 4. **B** — The AAL is the catastrophe pure premium, loaded into the rate. (§30.3) 5. **C** — The PML sizes reinsurance and the capital held against the tail. (§30.3) 6. **B** — A 1% annual exceedance probability, every year, with no memory. (§30.4) 7. **B** — $1-(0.99)^{30}\approx 26\%$. (§30.4) 8. **B** — The annual probability of exceeding each loss level. (§30.3) 9. **A** — A zone groups exposures a single event would strike together, so they are treated as correlated. (§30.5) 10. **C** — Marginal contribution to the zone PML, not standalone quality. (§30.5) 11. **B** — It tends to understate risk for perils climate is intensifying (a known-sign error). (§30.6) 12. **B** — The uninsured share of economic catastrophe loss. (§30.7) 13. **B** — Most years are near zero; the average conceals the heavy right tail. (§30.1) 14. **B** — Optimistic construction defaults and an imprecise location both tend to understate the cat contribution. (§30.2) 15. **B** — A higher named-storm deductible and/or ceding the marginal slice reduces modeled *net* loss. (§30.2, §30.5) **Short answer** 16. The AAL is the *expected* cat loss and belongs in the **price** (charge for the average storm); the PML is a *tail* loss and belongs on the **balance sheet** (size reinsurance and capital to survive the bad case). Confusing them means either underpricing the average (slow death) or under-capitalizing the tail (sudden death); defending an account's adequate price (AAL) when the objection was the zone PML is arguing past the point. (§30.3) 17. A "1-in-100-year" flood is a 1% chance *every* year, not a once-a-century schedule; the dice have no memory, so last year's flood does not reduce next year's probability at all. Over his remaining decades the cumulative chance is substantial (e.g., ~26% over 30 years). He should treat next year as carrying the same ~1% risk as any year and insure/mitigate accordingly. (§30.4) 18. Inside a peril zone, losses are correlated — a single event strikes the new account *and* everything already in the zone at the same time. So the new account's loss stacks on top of the existing zone loss in the same event; its marginal effect on the zone's worst-case (PML) reflects that stacking, which can exceed what the account would lose on its own. (§30.5, §30.1) 19. A regulator (often prior-approval) may suppress the load to keep coverage *affordable* for coastal residents. Consequence: at a suppressed price the insurer cannot earn its cost of capital on the exposure, so the private market withdraws; risk migrates to the residual market/FAIR Plan (often itself underpriced), and the protection gap widens. (§30.4, §30.7) 20. Reserve judgment for the *uncertainty around the model's number*: which vendor model and calibration, how much to load for model error, and what manual adjustment to make for what the model is known to miss (newer construction, the non-stationary climate trend). Defer to the model on the central tail estimate; judge its error bars and blind spots. (§30.2, §30.6)