Chapter 30 Exercises

Work these the way a catastrophe-management desk works: never ask "is this risk good?" in isolation; ask "what does it do to our worst case in this zone, and can the company survive that?" Items marked with a dagger (†) have worked solutions in Appendix: Answers to Selected Exercises. Section references like (§30.3) point you back to the chapter. All dollar figures here are illustrative teaching numbers, not real losses.

A. Recall and definitions

  1. † Explain in one or two sentences why catastrophe "breaks the law of large numbers." Name the specific assumption that fails. (§30.1)
  2. Name the three modules of a catastrophe model and state, in a phrase, what each one answers. (§30.2)
  3. † Define the average annual loss (AAL) and the probable maximum loss (PML). For each, say whether it belongs in the price or on the balance sheet. (§30.3)
  4. What is an exceedance-probability (EP) curve, and which two key numbers are read from the same curve? (§30.3)
  5. Translate each into the other: a 0.4% annual exceedance probability is what return period? A "1-in-50-year" loss is what annual probability? (§30.4)
  6. Define accumulation management and explain what a peril zone (CRESTA zone) is. (§30.5)
  7. † Define the protection gap in one sentence. (§30.7)
  8. What does it mean to say a catastrophe model is "backward-looking," and in which direction does that tend to bias its output for a peril that climate change is intensifying? (§30.6)

B. The EP curve, AAL, and PML

  1. Using the illustrative EP curve in §30.3, state (a) the approximate 1-in-100-year loss, (b) the approximate 1-in-250-year loss, and (c) which of those a rating agency is more likely to use as a capital standard, and why. (§30.3, §30.4)
  2. † An insurer's catastrophe modeler reports an AAL of \$6M and a 1-in-100-year PML of \$240M for the coastal book. The chief underwriter says, "Fine — we collect more than \$6M of cat load in premium, so we're covered." Explain what the chief underwriter is confusing, and what the \$240M figure is actually for. (§30.3)
  3. Explain why "probable maximum loss" is a misleading name on two counts (it is neither the maximum nor "probable" in the everyday sense). What three things must always be specified when someone quotes a PML? (§30.3)
  4. † A broker says your quoted cat load looks high because "there hasn't been a bad storm here in years." Using the AAL and the shape of the catastrophe loss distribution (§30.1), explain why recent calm years are not evidence the load is too high. (§30.1, §30.3, §30.6)

C. Return periods (kill the misconception)

  1. † A homeowner whose street flooded last year says she is now safe because "that was the hundred-year flood." Explain precisely why she is wrong, and give her the correct way to think about next year's risk. (§30.4)
  2. Compute the chance of at least one 1-in-100-year event over a 30-year mortgage, showing the formula $1-(0.99)^{30}$, and explain in one sentence why the answer (~26%) matters for how a lender thinks about coastal collateral. (§30.4)
  3. Two 1-in-100-year floods strike the same town within a decade. A journalist writes that "the models are clearly broken." Is that a fair conclusion? Explain. (§30.4)
  4. † Why might a regulator and a rating agency disagree about what return period to use — the regulator pushing for a lower cat load and the agency for capital against a longer return period? Whose concern is affordability and whose is solvency? (§30.4, §30.7, and Ch. 4)

D. Accumulation management — underwrite the zone

  1. † Underwrite this submission. Your Port Hadley zone has a \$250M PML limit and currently sits at a \$210M modeled zone PML (per §30.5's table). A new \$25M coastal warehouse account is submitted; the model says it would add about \$22M to the zone PML at the 1-in-100 level. The account is well-constructed and adequately priced on its own AAL. State your decision and your reasoning, and give two ways you might write it anyway if you wanted to. (§30.5)
  2. Explain why an account's marginal contribution to a zone PML can be larger than its own standalone modeled loss. What property of catastrophe losses inside a zone causes this? (§30.5, §30.1)
  3. † Find the red flag. A submission for a \$30M coastal hotel arrives with the "year built" and "roof type" fields blank and the location given only as a ZIP code. Identify the two distinct data problems and explain how each would tend to make the model understate the account's catastrophe contribution. (§30.2)
  4. Your company writes property in four zones: three coastal Gulf/Atlantic zones and one large inland zone. Growth has been easy in the inland zone and hard on the coast. Explain, in accumulation terms, why inland growth is "good" growth for the catastrophe profile and why piling more onto the coast is not — even if the coastal accounts are individually profitable. (§30.5, and Ch. 29)

E. Pricing and the model

  1. † Price this risk (the cat load). A coastal account's modeled AAL for hurricane is \$48,000 on a \$20M building. Expenses and profit load on the property line run roughly 35% of premium. Working only with the catastrophe portion, what minimum cat-load premium must the rate carry so that the cat pure premium is covered after the load? Show the build-up and state clearly that the figures are illustrative. (§30.3, and Ch. 11)
  2. The same account's AAL is fully loaded into the price, but the account still gets declined in a catastrophe review. Explain how both facts can be true at once. (§30.3, §30.5)
  3. Explain how the financial module means that the terms you set in Chapter 12 (a 5% named-storm deductible, a sublimit) actually change the account's modeled loss and therefore its zone consumption — not just its price. (§30.2, and Ch. 12)

F. Climate, the moving baseline, and limits

  1. † Explain why a catastrophe model calibrated on the last fifty years tends to understate today's hurricane risk, and state the disciplined underwriting response (three concrete actions). (§30.6)
  2. Walk the chain: a climate-conditioned model raises the indicated coastal rate → a prior-approval regulator suppresses it for affordability → trace the consequences for the private market, the FAIR Plan / residual market, and the protection gap. (§30.6, §30.7)
  3. The chapter says insurability is "a property of the risk plus the available machinery, not of the risk alone." Give two pieces of machinery (from anywhere in the book) that can narrow a catastrophe protection gap, and explain how each helps. (§30.7, and Ch. 26, 27, 34)

G. Memo, ethics, and judgment

  1. † Write the memo. Draft a short (150–250 word) referral memo to your CUO recommending whether to write a desirable \$40M coastal manufacturing account that would push the Port Hadley zone from \$210M to an estimated \$238M against a \$250M limit. State the cat finding, the trade-off, and your recommended conditions. (§30.5, and Ch. 38)
  2. Ethics dilemma. Your company is profitably managing its zone PML by non-renewing the most wind-exposed homes in a coastal county; doing so widens that county's protection gap and pushes families onto the state FAIR Plan. Is the company doing something wrong? Argue both sides honestly, then state the most defensible posture for an underwriter. (§30.7, theme 6)
  3. † A colleague treats a single vendor model's 1-in-100 PML as "the number" and refuses to load for model uncertainty or the climate trend, calling that "second-guessing the science." Explain why deferring to the model on the central estimate while reserving judgment on its uncertainty is not anti-science — it is the correct use of a model. (§30.2, §30.6)
  4. Model vs. judgment. In Chapter 32 the underwriter overrides a predictive model's score on Harbor Steel (a 7 down to a 6). Yet this chapter warns you almost never to override a cat model's accumulation number downward. Reconcile these: what is different about the two kinds of model, and what makes overriding one defensible and the other reckless? (§30.2, §30.5; preview Ch. 32)

H. The Underwriting File

  1. † Underwriting-File extension. Add the catastrophe-contribution line to the Harbor Steel file. In your own words, state (a) what running Harbor Steel through the cat model settled (the AAL and the zone PML findings), (b) what it explicitly did not settle, and (c) the one caveat the file should carry to the next renewal. Use only facts from this chapter and earlier; do not pre-empt the capstone bind. (§30, The Underwriting File)
  2. Harbor Steel's 5% named-windstorm deductible and its cession to the cat XOL treaty both reduce the account's modeled net loss in the zone. Explain how each one does so, and why that is what let the account "fit within the Port Hadley zone aggregate with limited headroom." (§30.2, §30.5; Ch. 12, 27)
  3. The file flagged "limited headroom" in the Port Hadley zone. Name two specific things that, by the next renewal, could turn that limited headroom into no headroom — and what the underwriter should do about each in advance. (§30.5, §30.6, The Underwriting File)